Transcript for:
Key Concepts in SAT Prep and Grammar

I went from an 1180 on the PSAT to a 1590 on the SAT and over the past 3 years I've released hundreds of videos to help students Ace the SAT this video is a completely free digital SAT prep course designed to help you improve as much as possible in only about 18 hours of prep if you only have 8 hours or less to prep for the digital sat then I recommend you check out my free 7-hour digital SAT prep course which you can find right here the first 7 and 1/2 hours of this course are actually the same as the free 7-hour course but the rest of this course adds on additional training and practice for those with more time to prepare as a result I highly recommend this course to anyone with the time to complete it before their sat while there are time stamps for each section I highly recommend that you watch the entire course in the order it is presented I also want to note that while reading and writing is a combined section on the digital sat there are still questions that primarily test your reading abilities and questions that primarily test your writing abilities therefore at certain points in the course you will notice that I will speak exclusively about either reading or writing questions put a lot of time effort and planning into this course and I would greatly appreciate it if you would subscribe and like the video with that being said please enjoy the course and let's get started with a guide on what you need to know for the writing questions on the digital sat so we have subject verb agreement as a basic rule the subject and the verb of a sentence must agree in number singular or plural here's an example the dog barks loudly the subject dog is singular and the verb barks is singular here's a second example the dogs bark loudly the subject dogs is plural and the verb bark is plural now at this point you may be wondering how do I know if a verb is singular or plural one trick that can help you is to use what I call the he they test so as an example we would say he barks so as you can see he is singular and Barks then would be singular if we were to say um he bark obviously that would not work because he is singular and bark is plural now we would say they bark okay so as you can see by using he and they you can kind of figure out if a verb is singular or plural with that being said let's take a look at question number 19 to how we can apply this so we have when writing the other black girl 2021 novelist zakiah deila Harris Drew on her own experiences working at a publishing office the award-winning book is Harris's first novel but her writing blank honored before okay in this case we have her subject or our subject which is writing okay so writing is our subject writing is singular okay so since writing is singular we need to have a singular verb that matches that so option A were well we would say they were we would not say he were okay we would say he was and we would say they were so were is plural so we can get rid of a since it's plural I'll mark that with a p then we have have been well we would say they have been and we would say he has been so as you can see have been would have to also be plural so we can mark that with a p and then we have has been okay we would say he has been so as you can see that would be singular we would say they have been okay so we can mark C as a singular verb if we look at option D we have are we would say they are and we would say he is okay so d would be plural as well okay so we can go and get rid of that we see our only answer Choice here that is singular is option C and we have to match the number of our verb to the number of our subject writing is singular so our answer here has to be C all right let's keep moving we've got indefinite pronouns okay indefinite pronouns such as everyone someone and no one take singular verbs here's an example everyone has their own opinion the indefinite pronoun here is everyone and it's singular the verb has is also going to have to be singular example number two no one knows the answer the indefinite pronoun no one is singular and the verb knows is singular okay now let's talk about compound subjects when two subjects are joined by and they usually will take a plural verb example of this would be JN and Sarah are going to the party subjects JN and Sarah are plural so so the verb are must also be plural we would not say John and Sarah is going to the party because is is singular we would have to use R which is plural let's take a look at a second example apples and oranges are fruits subjects apples and oranges are plural so the verb R must be used and keep in mind R is plural is is singular now let's talk about collective nouns collective nouns represent a group of individuals can take either a singular or plural verb depending on the context however most commonly collective nouns take a singular verb and I really want you to pay close attention to the fact that most commonly collective nouns do take a singular verb now collective nouns utilize a singular verb when they act when the entity acts as a whole in a plural verb when the individual members of The Entity act independently so let's look at an example of this the team is practicing for the game the team collectively is practicing so the verb is is singular now in example two the team are in disagreement on the course of action in this case the people on the team disagree with each other so they are acting independently so the verb is plural okay if we scroll up we can see that collective nouns will utilize a singular verb when the entity acts as a whole as in example one the team as a whole is practicing for the game but in example two it's the individual members of The Entity that are acting independently in order to be in disagreement okay so we would state that the team are in disagreement on the course of faction now once again I want to stress that most commonly as an example three you will see that collective nouns will have a singular verb so here's another one Congress is discussing the bill the collective noun Congress is singular since they are collectively discussing the bill so the verb is must also be uh singular we would say congress is discussing the bill not Congress are discussing the bill all right now let's talk about intervening phrases these are words or phrases that come between the subject and the verb do not affect the agreement okay so an example would be the cat along with its kittens sits by the window the subject here is cat it is not kittens okay and cat is singular so the verb sits must also be used okay and sits is singular okay we would say he sits we would say they sit okay so once again you can use that he they test as well if you're not sure if a verb is singular or plural all right let's take a look at example two the boys as well as their friends are playing soccer subject is boys which is plural and the verb are is also going to be used since our subject is plural we need to also have that plural verb all right let's take look at a example question here so we got number 26 the classic children's board game Shoots and Ladders is a version of an ancient nepes game Pera SOA in both games players encounter good or bad spaces while traveling along a path landing on one of the good spaces then we have a verb a player to skip ahead and arrive closer to the end goal let's identify the number of our subject so we have landing on one of the good spaces well on one of the good spaces is a prepositional phrase okay we would ignore the prepositional phrase when identifying our subject so our subject here is landing okay Landing is going to be singular so I'm going to mark that with an S for singular now let's identify a through D which ones are plural and which ones are singular so we have allows well we would say he allows and we would say they allow okay so allows is singular since we would use it with he but not they if we take a look at B we have are allowing we would state that they are allowing and he is allowing okay so are right there we have plural next we have have allowed we would State they have allowed we would State he has allowed so once again C would be plural as well if you look at option D we would State he allows and we would state that they allow okay so that would be plural there okay we would say landing on one of the good spaces allows a player to skip ahead and arrive closer to the end goal so as you can see only option here that's singular for our verb is option A and once again we need to maintain that singularity in both our subject and our verb they need to match okay so our answer there would have be a all right now let's talk about pronoun usage okay we have pronoun antecedent agreement a pronoun must agree in number and gender with its antecedent an example of this would be Sarah lost her keys the feminine pronoun her agrees with the female antecedent Sarah let's look at example number two the boys finished their homework the plural pronoun their agrees with the plural antecedent boys okay so pronoun usage there should be fairly simple let's take a look at a question to practice we have question 19 public awareness campaigns about the need to reduce single-use Plastics can be successful says researcher Kim Borg of monach University in Australia when these campaigns give C consumers a choice for example Japan achieved a 40% reduction in plastic bag use after cashiers were instructed to ask customers whether blank wanted a bag well let's identify our subject okay our subject here would be customers we know customers is plural okay so we scroll down here so we've got customers which is plural if we look at our options we've got four different pronouns okay one is singular you is singular and it is singular they is plural we have to maintain um we have to match our number okay so we can get rid of options B C and D since they would not match in number with our subject okay our subject is plural that or I'm sorry our noun is plural okay the noun that we're referring to with our pronoun that noun is plural since our noun is PL plural our pronoun will also need to be plural so our answer there would have to be answer Choice a all right let's talk about ambiguous pronouns pronouns should have clear antecedence to avoid confusion here is an incorrect example and as we go through these examples try to pay attention to where I'm giving an incorrect example versus where I am giving a correct example because otherwise you may end up getting confused I will try to make it as clear as I can as I go through this so here would be an incorrect example Sarah and Lisa went shopping and she bought a dress the pronoun she is ambiguous it's not clear whether it refers to Sarah or Lisa okay so make sure that it's clear who you are referring back to if you are going to use a pronoun now here is a correct example Tom saw joh and congratulated him okay this one is admittedly not the greatest example but it still works and here's why when we say that Tom saw John okay Tom is still our subject okay he saw John okay John is the object of the verb saw okay so Tom saw John and congratulated him okay this is clear that Tom saw John and Tom is the one congratulating John okay the pronoun him is referring to the antecedent John okay let's look at another example and this one's a bit more clear I gave Mary the book that she wanted okay the pronoun she refers the antecedent Mary all right let's go ahead and move on to pronoun case pronouns have different forms depending on their function in the sentence subjective objective and possessive so here's an example I went to the store the subjective pronoun I acts as the subject of the sentence so got example two she gave him the gift the objective pronoun him acts as the object of the verb gave now let's talk about pronoun reference pronouns should refer clearly and unambiguously to their intended antecedence here's an example the man who won the race was happy the pronoun who refers to the man who won the race here's another example the dog that barked is mine the pronoun that refers to the dog that barked now let's talk about modifier or placement and comparison Mis modifiers modifiers should be placed near the words they modify to avoid ambiguity or confusion now here's an incorrect example followed by the correct example I saw a draft with binoculars the modifier with binoculars should be placed near I okay in this example it should be obvious that there's a mistake because you wouldn't have a draft that is using binoculars it's the individual I the subject who is actually the one using the binoculars so we need to move with binoculars in front of I okay so here's how we would correct that with binoculars I saw a draft let's take a look at example number two okay so once again we'll start with the incorrect example Jon caught the ball running quickly the modifier running quickly should be placed near Jon it's not the ball that is running quickly because a ball cannot run it is Jon who is running quickly okay so we need running quickly to refer uh to be placed next to John so here's how we would correct that we'd State running quickly as an introductory modifier John caught the ball okay running quickly is being applied to John now let's talk about dangling modifiers modifiers should clearly modify the intended subject or noun here's an incorrect example after finishing the project the snack was devoured by John well the snack is not what has finished the project okay a snack cannot finish a project okay JN is the one who finishes the project so the modifier after finishing the project should modify whoever finished the project which is John not snack so here's how we could correct that after finishing the project J ate a snack in this case we clearly have J being uh what comes after this introductory modifier of after finishing the project all right let's go over another example riding the bike the tree came into view and once again this is an incorrect example the modifier riding the bike should modify whoever was riding the bike not the tree since a tree obviously cannot ride a bike so here's how we could correct that riding the bike John noticed the tree came into view so as we can see we have our modifier modifying um who is actually riding the bike all right let's take a look at this with a question all right so in 1453 English King Henry V 6 became unfit to rule after falling Gravely ill as a result Parliament appointed Richard third Duke of York who had a strong claim to the English Throne to rule as Lord protector upon recovering 2 years later okay so here we have an introductory modifier upon recovering 2 years later well we know the person who fell ill is King Henry okay so we need to have King Henry after this so if you look at our options we have Henry as what's being modified the reign of Henry it can't be the reign of Henry because Henry is the one who fell ill so Henry is the one who will recover two years later we have Henry's Reign okay it's not his Reign that is being modified and it's not it was Henry who resumed his Reign okay it's not it we need to modify Henry okay Henry needs to be what is immediately after that comma okay so our answer there would have to be a now this is a pretty common type of question on the digital sat so make sure you understand how to work with these introductory modifiers all right let's talk about comparative and superlative adjectives adjectives should be used correctly when comparing two or more items so here's an example this book is taller than that one we're comparing the height of two books now really what I'm trying to teach right here is pretty simple right if we're comparing two things we would state that one is taller than the other now let's take a look at example two if we're stating that we're comparing you know one to many doing a one to many comparison it's not a one to one comparison so in this case an example two we have she is the smartest student in the class we're comparing the intelligence of students in the class so this is a one to many comparison we're comparing the one which is she to all of the students in the class so we would State she is the smartest student in the class all right parallel comparisons comparisons should be parallel in structure here's an example she likes to run swim and Hike Okay so this one isn't really a comparison this one's just a list of activities so we want to maintain parallelism we would not say she likes to run swimming and hiked right we would want to maintain parallelisms to this so she likes to run swim and Hike example two the company is efficient reliable and customer oriented this is a parallel list of qualities of the company now let's talk about double comparisons avoid using two comparative forms in the same sentence so this kind of goes back to the school example so an incorrect example would be she is more talented than any other student in the school okay now a much better way to say this would be she is the most talented student in the school as you can see it cuts down on the wordiness and also since we're doing a on to many comparison okay we would want to state that she is the most talented student in the school not that she is more talented than any other student in the school okay because that just adds on wordiness we want to be as concise as we can so our answer there would have to be she is the most talented student in the school all right now let's talk about parallel ISM parallel structure in list items in a list should be presented in parallel a form we've kind of talked about this already but I want to go a little bit further with it so we have as an example he likes to read write and listen to music okay so parallel list of activities read write and listen the chef prepared a delicious appetizer main course in dessert this is a parallel list of dishes now let's talk about parallel structure in comparison so this is where we get into that comparisons that we didn't really touch on as much earlier when making comparisons the elements being compared should have parallel structures here's an example the company is as successful as it is innovative we're comparing success and Innovation which are two um two qualities that can describe uh the company all right example two she is not only a talented singer but also a skilled dancer okay we're comparing talent in singing and dancing now you want to pay attention to that structure you want to maintain parallel structure so let's talk about parallel structure and clauses Clauses should maintain par structure to enhance Clarity and coherence example once again we have parallel list of activities she likes to swim to run and to play tennis so now we have to swim to run and to play okay now I know I'm stressing parallelism a lot that's because it's pretty important on the digital SAT writing section I will um I will say that compared to the paper sat it seems like parallelism has been um showing up a little bit less often on the digital SAT practice test than it did on the paper sat um but that's just something that I've noticed um anyway let's talk about example number two he wants to travel to explore and to experience new cultures we have a parallel list of desires all right now let's talk about verb tenses proper use of verb tenses verb tenses indicate the time at which an action takes place it is important to use the appropriate verb tense to convey the correct time frame all right so let's talk about the future simple tense I will go to the party tomorrow this is future simple tense indicates a future action let's talk about example number two they have already finished their homework this is present perfect tense it indicates an action completed in the past with a present result now let's talk about sequencing events verb tenses help to indicate the chronological order of events choose the appropriate verb tense to accurately represent the sequence of actions here's an example she finished her meal and then paid the bill this is past simple tense it indicates actions completed in the past another example he had left before I arrived this is past perfect tense it indicates an action completed before another past action okay so the first past action that's completed is he had left okay and then the next past action would be before I arrived okay so I arrived now let's talk about consistency in verb tenses maintaining consistency in verb tenses throughout a sentence or paragraph helps to ensure Clarity and coherence and this is something that is commonly tested on the SAT writing section so you do really want to pay attention to this part right here so let's talk about an example she walks to work every day and always arrives on time this is present simple tense it indicates a habitual action the way you might see this tested on the digital SAT writing section would be that arrives would be an answer option and it would be left blank on the digital writing section so you would have she walks to work every day and always blank on time and you would have to recognize that you have walks as your verb tense in the sentence and you have to match the verb tense then of your answer Choice which would be arrives here so that's one of the ways that you could see this tested let's give another example the team played well but they lost the game this is past simple tense and indicates a past event so once again the way you would likely see this tested is lost or played might be left out as a blank and then you'd have to recognize your verb that is left so in this case let's say that loss was left out as a blank you would recognize you have played which is the past simple tense and then you would need to select your answer choice that represents the past uh simple tense as well all right let's talk about more complex verb tenses so we have future perfect the future perfect tense is used to express an action that will be completed before a specific point in the future an example would be by this time next year I will have graduated from college future perfect tense is indicating an action completed in the future before another future event all right let's talk about the conditional tense the conditional tense is used to express actions that are dependent on a condition or hypothetical situations an example is if it rained we would have stayed indoors so once again this is conditional tense expresses a hypothetical situation okay in this case the hypothetical situation is if it rained past perfect tense the past perfect tense is used to express an action completed before another past action or a specific point in the past an example is she had already finished the book before the movie was released once again this is past perfect tense indicates an action completed before another past event let's talk about the conditional perfect okay conditional perfect tense is used to express hypothetical actions that would have been completed under certain conditions an example is if they had studied harder so that is the hypothetical um action they would have passed the exam so conditional perfect tense expresses a hypothetical situation in the past so the condition here is if they had studied harder then what would have happened is they would have passed the exam so once again the condition if they had studied harder what would have happened is they would have passed the exam so there's the conditional perfect now we have the present perfect continuous present perfect continuous tense is used to express ongoing actions that started in the past and continue into the present an example is they have been playing tennis all morning so once again this is present perfect continuous continuous tense indicates an ongoing action starting in the past and continuing into the present okay so they began okay this action start started in the past they began playing tennis in the past and it's continuing into the present they have been playing tennis all morning past perfect continuous the past perfect continuous tense is used to express ongoing actions that started and continued in the past before another past event an example is he had been working at the company for five years before he was promoted okay so once again we are expressing ongoing actions that started and continued in the past before another past event okay so he had started working at the company before this past event okay so he started and continued working at the company four or five years before he was promoted which is the past event all right by understanding the nuances of different verb tenses you can accurately convey the time frame sequence and continuity of events in your writing all right let's talk about sentence structure so let's start with runon sentences and runon sentences are very commonly tested on the digital SAT writing section so you do need to pay close attention here you want to avoid runon sentences by properly separating independent clauses and we'll talk about how to do that later on okay so let's take a look at a couple examples first so we have I walked to the store comma and I bought some groceries I walked to the store is an independent clause I bought some groceries is another independent clause we can connect two independent clauses with a comma and one of the Fanboys which are for and nor but or yet and so all right let's talk about uh or next example she studied hard for the test but she still failed okay so she studied hard for the test it's an independent clause and then we have a comma and one of the Fanboys in this case but and then we have she still failed which is also an independent clause okay let's go ahead and move on to commas spes okay do not use a comma to join two independent clauses without a coordinating conjunction or appropriate punctuation here's an incorrect example I studied all night I passed the exam here we have a comma splice because we are trying to connect two independent clauses with only comma and without one of the Fanboys okay so that's an incorrect here's how we can correct that we would State I studied all night comma and I pass the exam now a second incorrect example would be he ran fast he lost the race he ran fast as an independent clause he lost the race as an independent clause here's how we could correct this he ran fast comma but he lost the race so let me quickly touch on how you can kind of know when to use which coordinating conjunctions and if you hear coordinating conjunctions just think the Fanboys okay the Fanboys are the most common examples of coordinating conjunctions okay so how would we know to use but here instead of something like so or yet well he ran fast if he ran fast we would expect him to win the race but he lost the race so this is a contrast what would be expected so we could use but in this case let's take a look at fragments so you want to ensure that sentences have a subject and a verb and are not incomplete once again you want your sentences to be complete so let's look at an incorrect example after finishing the race okay this would be a sentence fragment it is not a complete idea it is not a complete sentence if we look at the correct version of that it would be after finishing the race I felt tired I felt tired is an independent clause okay after finishing the race is referring to I okay so that's a complete sense let's look at incorrect example number two running towards the Finish Line okay we don't know who is running towards the Finish Line this isn't a complete thought if we look at how we' correct that we would have running towards the Finish Line I felt exhilarated okay in this case we are referring to I we are modifying I all right looking at D dependent clauses dependent clauses can't stand alone as complete sentences and must be attached to an independent clause okay let me zoom in okay so dependent clauses can't stand alone as complete sentences must be attached to an independent clause an example of this although it was raining hard or although it was raining they went for a walk okay although it was raining is a dependent clause okay it cannot stand alone as a complete sentence all right example number two when the bell rings class ends when the bell rings is the dependent clause there okay it cannot stand on its own as a sentence now let's talk about independent clauses independent clauses can stand alone as complete sentences an example would be I went to the store that is a complete thought it's complete idea has a subject and a finite verb if we look at example number two the Sun was shining brightly okay that is also a complete sentence now let's talk about sentence logic and Clarity eliminating redundancy this is something that was very very commonly tested on the paper writing section uh now that the SAT has moved digital I haven't been seeing it tested quite as much but it is still something that's important to know okay you have eliminating redundancy remove unnecessary repetition in sentences to improve Clarity and conciseness so here is an incorrect example and there's a few of these that I'll go over so starting with I saw him with my own eyes with my own eyes is redundant if I say I saw him the only way I can do that is with my own eyes so You' correct that by just stating I saw him okay now here's two other examples that I think are a little bit more similar to what you could see on the SAT writing section so one option would be I ran home to Megan Megan is my sister eliminate the redundancy of saying Megan back to back okay so here's how we could do that we would State I ran home to Megan comma my sister okay my sister is describing who Megan is and by doing this we're able to repeat stating Megan back to back so we can get rid of that we can also eliminate having to use is by just using that comma here's another incorrect example the teacher explained the concept briefly in a short manner okay briefly and in a short manner mean the same thing so we would only want to use one of those and the most concise way to do that would be to get rid of in a short Manner and just say briefly so as you can see in the correcting example we could State the teacher explained the concept briefly let's talk about Clarity of pronoun reference you want to ensure that pronouns have clear and unambiguous antecedence so we've kind of already touched on this let's just go over it again okay an incorrect example would be after Sarah told Rachel the bad news she was very upset it's unclear if she refers to Sarah or Rachel the corrected example would be after Sarah told Rachel the bad news Rachel was very upset okay here's two more correct examples John gave the book to Mary and she read it the pronoun it refers to the book the pronoun she will refer back to Mary all right another example would be the dog followed its owner wagging its tail happily obviously the dog would be what's referring to by its logical comparison you want to make logical and meaning comparisons in sentences and what this is really talking about is you want to make sure you're comparing like to like so as an example apples are healthier than Donuts we're comparing food to food an example two the flight was longer than the duration of the sunset okay in this case it's presumed that we're talking about the flight's duration we're comparing that to the duration of the sunset okay if we look at option C or example C Sweden's obesity rate is less than that of the United States and example three is one that I think is really important to highlight okay when we say Sweden's obesity rate is less than that of the United States the key part I want you to pay attention to here is that we included that of if we were to say Sweden's obesity rate is less than the United States that's not as good as if we State Sweden's obesity rate is less than that of the United States because by adding that of okay we know that we're referring to the obesity rate of the United States which is more clear than if we just say Sweden's obesity rate is less than the United States all right let's talk about appropriate word choice you want to use words that accurately convey the intended meaning in a sentence an example is the book he purchased was truly captivating the word captivating accurately describes the engaging nature of the book now on the digital sat you'll more commonly see word choice questions like this show up actually towards the um on the on the digital SAT practice test it's been towards the beginning of the sections and it's also in my opinion um categorized more so in actually the reading section because it's more so about the word in context but I did still want to touch on it here because you do still need to understand words in context in order to be able to answer questions on the writing section now some of you guys may be wondering at this point you know what's the difference sort of between reading and wri writing on the digital sat since they're all sort of combined into the same section and it's really just about the classification of the different questions so some questions can be classified more as reading questions even though it's within the reading and writing section which is now combined section and some questions can be more confined um to testing your writing abilities so when I'm talking about writing questions I'm talking about questions that are specifically designed to test your writing ability when I talk about reading questions I'm talking about reading questions that are specifically designed to test your reading comprehension your understanding of words and context and things like that um so even though they are combined into the same sections they do there are still questions that are more so testing writing and some that are more so testing reading but anyways here's example number two it was an incredibly grueling Marathon the word grueling conveys the extreme difficulty and exhaustion associated with the marathon next we have idioms indiction prepositions so let's talk about the appropriate use of idioms you want to use idiomatic expressions correctly to convey the intended meaning an example would be she passed away it's an idiomatic expression for she died they got along well that's an idiomatic expression for they had a good relationship I'll talk about correct preposition choice and this is what um you might see more commonly on the digital SAT writing section so using the correct preposition in phrases and expressions an example would be she is afraid of spiders okay the preposition here would be afraid of so you could have options that are um afraid in um afraid with but obviously you would state that she is afraid of spider so when we're talking about preposition choice this is the way that um it could show up so example two is I am interested in playing the piano okay so in this case we are looking at in okay interested in playing the piano okay so the proposition there would be in um and then let's talk about uh proper use of prepositional phrases so something that is just generally very useful to recognize on the digital SAT writing section is prepositional phrases I've already kind of talked about how you need to get get rid of them when you're determining your subject um which is helpful for matching the number of the subject to the number of your verb uh using prepositional phrases accurately to provide additional information about the subject or object of a sentence an example this would be the cat is sitting on the chair so on the chair is the prepositional phrase she walked through the forest through the forest would be the prepositional phrase there now I can talk about punctuation apostrophes you want to use apostrophes to indicate possession or contraction an example would be John's car is old we have an apostrophe for possession since the car belongs to John next we have it's raining outside this is an apostrophe used for contraction because it's in this case is it is we would say it is raining outside example three the children's toys were scattered all over the room this is an apostrophe being used for plural possession children is already plural so we would add on the apostrophe s to indicate that it's possessive of the toys example four these are the cats bows okay cats with an S is the plural version of cat then we need to add an apostrophe onto the end of that to indicate that it is the cats bows okay there is a possessive relationship there if you look at example number five we're going to the park this is an apostrophe for contraction the contraction would be we are to were if you look at example six they're my best friends this is an apostrophe for contraction they being the contraction of they are now let's talk about semicolons and periods this is something that's obviously very important to understand uh so we have use semicolons to separate independent clauses or or or to separate items in a series that already contain commas okay and you are going to see kind of both of these uses on the digital SAT writing section you want to use periods at the end of a complete sense so an example would be I went to the store with a semicolon I bought some milk and bread okay so we have two independent clauses that we're connecting with a semicolon so semicolon separates independent clauses example number two my best friends are John who is a lawyer Mary who is a nurse and Tom who is a teacher in this case we have a semicolon separating items in a series that already contain commas so as you can see we state name comma and then occupation who is a lawyer Mary comma who is a nurse Tom comma who is a teacher so in this case within the list itself we have commas so we' actually use semicolons to separate each item in that list example three I haven't been feeling well I think I might have the flu so we would use a semicolon to separate these two independent clauses look at example four the museum exhibit includes paintings from go the Dutch artist Monae the French impressionist and climp the Australian symbolist okay in this case semicolon separates items in a series that already contain commas okay so if we scroll up example four is similar to example two example number five she couldn't make it to the party she was caught up with work so in this case we're splitting up two independent clauses with a period if you look at example six the weather was perfect for a walk it was mildly Sunny with a cool breeze we're using a period to separate two independent clauses there as well all right let's give an example here with question number 23 John Henson director of language revitalization program of the Chickasaw Nation in Oklahoma help produce the world's first indigenous language instructional app Chickasaw blank and then we have Chickasaw TV in 2010 and a Rosetta Stone language course in 2015 so what you'll see here is we have this list and we are using a comma before we State the date okay so we have comma before we State the date so if we scroll down to our answer choices we need to look for one that has a comma before we State the date so we can get rid of A and B since they use semicolons here and here then if we look at the differences between C and D we see that the differences are right here whether or not we use a semicolon or comma after the year now if we scroll up we see that after the year we are using a semicolon okay we're using a semicolon to split up this list of items where comma is used with each item okay so after 2019 we need to have that semicolon okay so our answer there would have to be C all right let's talk about common you want to use commas to separate items in a series after introductory phrases to set off non-essential Clauses or phrases and to separate coordinate adjectives an example is I bought apples oranges and bananas at the store a comma separates the items in a series example two however comma they still manage to win the game a comma after an introductory phrase is what we're using there all right colons you want to use colons to introduce a list to separate Clauses when the second Clause explains or amplifies the first or to introduce a quote or example so here's an example the ingredients for the recipe are flour sugar eggs and milk in this case we have a colon introducing a list example two he had one thought in mind to succeed in this case we have a colon separating Clauses example number three we have her dream was simple yet profound to travel the world and discover herself in the process in this case the colon introduces a clause that elaborates and explains the dream mentioned in the preceding clause in example three and example one are really the two best examples of what you could see for the use of a colon on the digital SAT writing section in particular example three okay but both of them are really the way that you would kind of see this show up on the on the digital SAT writing section so uh example three is one that I want to talk a little bit more about so let's just go and discuss it her dream was simple yet profound to travel the world and discover herself in the process if your second Clause is illustrating explaining or describing what came before it that's a very common case where you're going to want to use a colon okay so I want to I want to really focus in on that that when your second Clause explains or amplifies the first that's a situation where you're going to want to use a colon all right let's talk about dashes so you'll use dashes to set off parenthetical elements or to emphasize certain words or phrases example would be the car dash a bright red sports car-h caught everyone's attention Okay in this case a bright red sports car is non- essential you could State the car caught everyone's attention and it doesn't change the meaning of the sentence if we look at example two she was determined Against All Odds to finish the race okay in this case we are emphasizing Against All Odds all right if we take a look at adjectives and adverbs we want to know proper use of adjectives so you use adjectives to describe or modify nouns an example would be she wore a beautiful dress to the party in this case the adjective beautiful is describing the noun dress another example would be the tall building can be seen from miles away the adjective tall is describing the noun building let's talk about proper use of adverbs so you'll use adverbs to modify verbs adjectives or other adverbs an example would be he ran quickly to catch the bus the adverb quickly is modifying the verb ran another example would be she spoke softly to avoid waking the baby the adverb softly is modifying the verb spoke let's talk about word pairs so we need to know commonly confused words so use appropriate words and avoid common mistakes in word usage so let's talk about a few examples and then I have a list that I'll kind of run through of some commonly confused words so we have example one their dog is friendly this is the correct possessive pronoun okay so it's t h i r when you want a possessive pronoun now in contrast if we look at example number two we have they apostrophe re e going to the party okay they're going to the party this is a contraction of they are so you need to understand the difference between t h e i and t e y apostrophe re e this is a contraction for they are let's look at example one again we have accept the invitation to agree to something okay so the version of accept with an a at the start if we look at example two we have except for him except with an E here everyone attended the meaning now except ex CT is excluding someone let's look at our next example your advice is helpful well in this case we have the noun advice if you look at example number two I advise with an S not a c you to listen to his instruction okay this is a verb all right so now we have a list of word pairs that you should know which I'll quickly go over we have accept versus except which I discussed above effect which is to influence versus effect which is a result compliment which is something that completes versus complement which is praise for example I give a compliment to someone when I say I like their shoes next we have elicit which is to draw out versus illicit which is forbidden by law its which is a possessive form of it versus it apostrophe s it's which is a contraction of it is we have principal which is main versus the principle or versus principle which is a fundamental belief or rule so example would be life principles right fundamental beliefs about life stationary not moving stationary writing materials then used in comparisons then at a time or at that time their T he i r possessive form of they uh there t h e re e is in that place and there th h e y apostrophe re e which is a contraction of they are two is a preposition two which is also or excessively and then two which is the number your which is a possessive form of you and your with an apostrophe r e which is a contraction of you are let's talk about who which and whom we have the proper use of who versus whom you use who to refer to the subject of a sentence and whom to refer to the object of a verb or preposition so an example is who is the man who fixed my car well the subject of the verb fixed example two to whom should I address the letter the object of the preposition to all right so let's talk about the he him trick this is really what I want to use to highlight the who versus whom because it makes things a bit simpler it can help you determine whether to use who or whom in a sentence so let's use example number one okay so if the answer to this question could be he then we'll use who if the answer to the question could be him then we'll use whom okay so who is the man who fixed my car well we could State he is the man who fixed my car okay so we would State who instead of whom okay so ask a question who fixed my car the answer is he fixed my car so we would use who example number two to whom should I address the letter well we can ask the question should I address the letter to him we wouldn't State should I address the letter to to he we would say should I address the letter to him so because of that we would want to use whom there okay so that's the that is the the he him test that you can use okay so once again that's the the he him test all right using the he him trick makes it easier to decide whether to use who or whom based on the role the word plays in the sentence proper use of which you use which to introduce nonrestrictive Clauses and that to introduce restrictive Clauses so when you think non-restrictive versus restrictive another way to think about that is essential versus non-essential so if we take a look at example one the car which is red belongs to John if we were to remove which is red we would have the car belongs to John that doesn't substantially change the meaning of the sentence okay so that's fine if you look at option two or example two the car that is red belongs to John well this is restricted because we are restricting the car to the one that is red okay we're not just stating the car belongs John we are stating the card that is red so presumably this is in a series of multiple cars of different colors and we are stating it is the one that is red so this is restrictive to just the car that is red okay so that's the difference between non-restrictive and restrictive all right let's talk about distinguishing between these two understand the difference between Clauses that are necessary for understanding the sentence and those that provide additional information example one the book that she borrowed is on the Shelf okay that she borrowed is restrictive it's restricting which book it is it is the book that she borrowed you look at example two her car which is blue is parked outside this is non-restrictive we are just adding in more information but we're not restricting which car it is if we were to State her car that is blue as parked outside then we would be restricting car but we're not in this case we're just providing additional information so it's non-essential all right let's talk about transitions using transition words and phrases effectively use transitional words and phrases to create coherence and a smooth flow between ideas and paragraphs example one first we went to the store then we went to the park okay so first would be a transition here and then we have then so we're indicating a sequential progression example two however some people disagree with this Viewpoint in this case we are providing a contrast with however we want to coherently connect ideas and paragraphs ensure that ideas and paragraphs are logically connected to maintain coherence in writing example number one the first reason for this decision is financial okay so we're stating the first reason and then we have additionally it aligns with our long-term goals so we are providing a second reason therefore we would use additionally because we're adding on look at example exle two in conclusion there are several factors consider when making this decision so in conclusion would be our transition there we want to maintain a smooth flow logical progression and writing okay and I'll go over a bunch of transitions I want you to know uh in a bit here but for now let's keep talking organize ideas and sentences to ensure a logical progression smooth flow of information so to begin with we analyze the data next we identifi the trends finally we drew conclusions so in this case since we would start with to begin with and we have next an example Le question that you could see is you would have to answer what transition should be here you would notice that we are going in a sequence so you would want to use finally if we are at the last part of that sequence okay we drew conclusions example two moreover it is important to consider the potential consequences before taking action so in that case that' be something that we are adding on to all right so here's some common SAT writing transitions along with example sentences so first off let's start by talking about introductory so examples would be to begin with first and foremost in the first place initially so an example would be initially we conducted a thorough analysis of the data next let's talk about addition and continuation this is very common additionally furthermore moreover in addition two also moreover so an example would be furthermore the results of the study support our hypothesis let's talk about contrast another very common one we have however on the other hand conversely nevertheless nonetheless yet instead and in contrast okay in contrast is a very common one same with however so in this case for our example we have however some people may hold a different viewpoint on this issue so a different Viewpoint than what was discussed previously so that would indicate to us that we would be looking for a contrast there next let's talk about cause and effect so we would state in our previous sentence that we had some sort of cause and then in the sentence that we were transitioning to we have our effect so as a result stating as a result of what came before consequently as a consequence of what came before therefore thus for this reason hence so consequently so as a consequence of what came before thus what came after consequently the company experienced a significant growth so before this we would probably expect to have something like the company changed um its leadership to focus on growth or something like that and then as a result of them changing the leadership the company experienced significant growth all right sequence and time uh this one's also fairly common so you would use this if you are going in sort of a progression so we have next then sub quently or in other words what came after or you know the next thing uh afterward meanwhile simultaneously simultaneously be at the same time finally eventually ultimately an example would be afterward we proceeded to analyze the gathered data all right now let's talk about how you would transition if you are giving an example so you would use for instance to illustrate specifically a case in point as an example to demonstrate an example of this would be four instance so you you will often see for instance or for example those are probably the two most common versions of this so for instance many successful companies started as small startups okay so before this we could have some sort of claim that um successful companies don't just arise from spin-offs of large corporations and then we say for instance many successful companies started as small startups obviously small startups is different from a spin-off from a major corporation okay so we'd be providing an example to that claim all right question number or number seven comparing and contrasting so we've already kind of talked about contrasting in this case we'll talk about comparing there are some in here that are kind of repeats from contrasting but um this is kind of two very similar things so I did categorize them together so we have similarly okay so something similar to what came before likewise pretty much the same similar layer if something's like what came before it in the same way very similar to the first two on the contrary so this would be contrast however which is a contrast conversely which is a contrast in contrast which is obviously a contrast and then on the other hand which is also a contrast okay in this case likewise we are doing something that's similar okay so likewise the second study also found users preferred option A to option b so presumably the sentence that came before it would be something stating that we had study a or the first study found users preferred option A to option b okay and then we're stating likewise the second study also found users preferred option A to option b all right summary and conclusion so in conclusion to sum up overall in summary okay so an example would be in conclusion the findings strongly support our hypothesis so you would use the if you are coming to a conclusion or you are stating a summary of what came before all right emphasis okay some examples of emphasis would be indeed okay indeed is probably the most common example of emphasis you have notably specifically in fact and particularly an example would be indeed the data supports the hypothesis that was initially proposed finally we have a comparison of options some examples would be whereas okay so we State something that came before it and then we have another option we would State whereas option for an example would be we would say option one is a mediocre option whereas option two is a superior option next we have in contrast to so once again that can also be used as a comparison of two different things on the other hand once again that can also be used as a comparison and as a as a contrast alternatively okay You' provide some sort of alternative something that came before it and then conversely which once again can be used as a contrast as well okay an example would be alternatively we can consider a different approach to solve this problem remember transitions are not just words or phrases to be inserted randomly in your writing okay they need to actually serve a purpose okay they serve a signpost to guide your Reader through your ideas helping to create a logical and coherent flow all right lastly let's talk about subjunctives subjunctives are used to express hypothetical or unreal situations wishes recommendations and emotions here's a more detailed explanation of when and how to use subjunctives all right number one use of were and hypothetical statements in hypothetical or contrary to fact situations use were instead of was after the pronouns I he she and it okay example one if I were a bird I would fly freely in the sky we wouldn't state if I was a bird we would state if I were a bird I would fly freely in the sky okay keep in mind this is a hypothetical obviously I am not a bird if you look at example two she speaks as if she were the queen okay once again this is hypothetical as if okay she's not actually the queen so we State she speaks as if she were the queen okay keep in mind that this is different from what You' expect respect when you're just straight up matching the number of your verb to the number of your subject because obviously if we were just doing that we would State she was but we have to take account for the fact that this is a subjunctive we are in a hypothetical okay as if she were the queen she's not actually the queen this is hypothetical so we have to keep in mind that we need to use were instead of was after the pronouns I he she and it all right number two use use of the base form of the verb after certain verbs after certain verbs of recommendation request suggestion or necessity use the base form of the verb infinitive without to to express the subjunctive mood an example would be it is important that he arrive on time once again this is a this is a difference from when you are just strictly matching the number of your subject to the number of your verb if we would State he arrives and we would State they arrive but because we are in the subjunctive we would state it is important that he arrive on time so once again you need to pay close attention to if you're in the subjunctive or if you are not example number two the teacher insisted that we study for the exam okay now let's talk about the use of past subjunctive form for wishes or desires so when expressing wishes or desires about unreal or unlikely situations in the past or in the present or past use the subjunctive form of the verb I wish I were taller it would be an example of that example two she wish she wishes she had studied harder for the test all right number four use of War to for unlikely or hypothetical future events to indicate unlikely or hypothetical future events used the phrase War to followed by the base form of the verb now if you are someone who grew up in the US um and who you know spoke English you know throughout their childhood this should come pretty naturally okay an example would be if it were to rain tomorrow we would have we would have to cancel the picnic okay so once again we are in that hypothetical okay and in this case we're in the hypothetical future event okay if it were to rain tomorrow future we would have to cancel the picnic suppose I were to win the lottery what would you do once again this would be a hypothetical future event okay if I were suppose I were to win the lottery that's future and hypothetical we say I were to okay it's important to use subjunctives carefully and appropriately in formal writing subjunctives are often used in more formal or literary text and can add depth and Nuance to your writing by understanding when and how to use subjunctives you can effectively convey hypothetical situations wishes recommendations and emotions in your writing all right this SAT writing guide covers the various aspects of grammar sentence structure word use punctuation and coherence in writing it's important to study and understand these rules in order to improve writing skills and achieve a higher score on the SAT writing section and I will add on to that that it's important to practice and get practice and Reps under your belt seeing these questions and applying what was covered here now let's talk about how to approach different types of SAT writing questions by knowing which approach you want to use for certain questions you'll be able to be more efficient and comfortable when taking the test here's how I recommend that you approach questions on the digital SAT writing section that ask you to complete the text so it conforms to the conventions of Standard English what I want you to do is take a look at your answer choices first and identify what you ultimately need to discover or identify as you do your initial read through in order to answer the question so in this case when we glance at our answer choices we see that they are all pronouns they one you and it are all pronouns so now what I'm going to do is as I do by read through I'm going to be looking for what the noun is that I'd be replacing with this pronoun so let's go ahead and read through we have public awareness campaigns about the need to reduce single euse Plastics can be successful says researcher Kim Borg of monach University in Australia when these campaigns give consumers a choice for example Japan achieved a 40% reduction in plastic bag use after cashiers were instructed to ask customers whether and now we have a pronoun here blank wanted a bag Well we'd be asking the customers whether they want a bag okay and as you can see customers is plural and since customers is plural the pronoun that replaces it cannot be singular so our answer would have to be a since that is the only pronoun out of a c and d which is plural so as you can see by recognizing what we need to identify during our read through we're able to be more efficient on the writing section here's a second example of how I recommend approaching questions that ask you to complete the text so it conforms the conventions of Standard English so same approach you're going to start by looking at your answer choices identify what the difference is between all of them in this case we see its punctuation so now what we're going to be looking for as we go through the text and read it is do we have an independent clause before this punctuation do we have an independent clause after it what kind of phrase or Clause do we have after it what kind of phrase or Clause do we have before it so you have in ancient Greece an epicurian was a follower of epicurus a philosopher whose beliefs revolved around the pursuit of pleasure epicurus defined pleasure as the absence of pain in the body and of trouble in the soul okay so that's an independent clause next we have positing that all of life that all life's virtues derived from this absence that is not an independent clause okay that's a participle phrase now one thing you can note is that if you have something that or a phrase that ends in or if you have a word that ends in ing or Ed that starts off a phrase okay there's a decent chance you might be looking at a participle phrase so understand that so in this case we have this ing okay so that's indicative that you should be looking for a participle phrase and in this case we do have one now a par participle phrase is not an independent clause since it's not an independent clause we can get rid of D next between B and C we see that one uses a colon one uses a semicolon however when you're connecting a participial phrase to a main Clause you would either use a comma an M Dash or no punctuation if it's inte if it's already integrated okay so you would not be using a colon or a semicolon in this case we use a comma which is perfect okay so our answer would have to be a so once again key thing to recognize with a question like this which is just the question type of complete the text or conforms the conventions of Standard English Begin by taking a look at your answer choices identify the differences identify what you need to look for before you do your read through of the text and then as you do your read through of the text identify what it is that you were searching for in this case it's was there an independent clause um before this Punctuation is there an independent clause or what kind of phrase are we dealing with afterwards and then identify the correct punctuation for that because this question type is so common on the digital SAT writing section I want to give a third example of it so we have Which choice completes the text what conforms to the conventions of Standard English it'll Begin by taking a look at your answer choices again in this case we see the difference is whether we you're using they are it is their which is plural and possessive its which is singular and possessive okay so let's go and take a look we'll go through we'll identify what we're looking for in this case we're looking for what is the number of our subject and is it possessive Okay so we've got British scientists James Watson and Francis Crick won the Nobel Prize in part for their 1953 paper announcing the double helix structure of DNA but it is misleading to say that Watson and Crick discovered the double helix okay and then we have blanks findings we based on a famous x-ray image of DNA fibers photo 51 developed by x-ray crystallographer rosand Franklin and her graduate student Raymond Gosling well the subject is Watson and Crick okay so two people so we have a plural subject so we can get rid of B and we can get rid of D now keep in mind that it is their findings they do own the findings it is possessive so plural and possessive means our answer there would have to be C option A is they are which is not possessive okay option C is plural possessive so our answer would have to be C because this question type on the digital SAT writing section is so common I'm going to go ahead and give a few more examples so we have answer choices a through D is where we're going to start we're going to identify the differences between them okay you have a comma here and here but not here and here we have commas in options a b and d after chin but not in option C and then we have commas after claim so ultimately I'm looking for a couple things first thing I'm going to look for is if steina chin is non essential because that would get rid of options A and B or C and D depending on whether it is not essential or not okay and then the next difference I'll be looking for is if I need to have a comma after claims so it looks like if we look up claims is before this quote so whether or not that quote is integrated or not if it's integrated we will not need a comma if it is not integrated then we would need a comma so let's go ahead and take a look we've got in 1937 Chinese American Screen Actor anime Wong who had portrayed numerous villains and secondary characters but never a heroin finally got a starring role in Paramount Pictures daughter of Shanghai a film that critic steina chin claims expanded the range of possibilities for Asian images on screen all right we've got a film that critic steinach chin claims expanded the range okay if we were to remove steinach chin we would have a film that critic claims expanded the range Well we'd have to say a Critic if we're going to remove steinich and we couldn't just say critic claims we'd have to say a Critic claims okay so we can go ahead and get rid of A and B because we know that it is essential okay the meaning would change if we were to remove sinish in let's go and take a look at C and D we have critic stach chin claims and then we go straight into the quote versus a comma before claims and a comma after claims well we already know we don't need a comma before claims so just based on that we could get rid of D but I also want to just add an option e here and let's talk about what the case would be if we had um critic steina chin um claims and then a comma okay so let's just pretend that this would was an option as well well if we go up we've got a film that critic steinach chin claims expanded the range of possibilities for Asian images on screen as you can see that's already integrated into the text which means that since it's integrated into the text we do not need a comma there okay so e would also be incorrect if that were to be some answer Choice okay so our answer there would have to be answer Choice C okay so once again to kind of sum all of this up okay We Begin by looking at the differences in our answer Choice there we identify what we need to look for in the question as we do our read through once we identify those things we come down we eliminate wrong answer choices and get to the right one here's another example of how I recommend you approach questions that ask you to conform to conventions of Standard English so I'd start by taking look at my answer choices in this case we've got a version of claim in all of them so what I'll be looking for is my subject I want to know the number of my subject and I also want to know what tense I'm in so let's go ahead and go through number 23 in 1637 the price of tulip Skyrocket in Amsterdam with single bulbs of rare variety selling for up to the equivalent of $200,000 in today's US dollar some historians blank okay so we got historians as our subject that this tulipmania was the first historical instance of an asset bubble which occurs when investors Drive prices to high is not supported by actual demand all right so before this comma we need to have an independent clause okay so in order to have an independent clause we need to have a finite verb after historians okay so let's take a look at our options we got option option A some historians claiming that this tulip Mania was the first historical instance of an asset bubble okay now since we don't have an independent clause following this comma we cannot we cannot use claiming here okay because if we were to say some historians claiming that this tulip Mania was the first historical instance of an asset bubble that's just not an independent clause okay so we can get rid of option A we would have some historians claim that this tulip Mania was the first historical instance of an asset bubble that would make an independent clause and claim is a finite verb okay so we have an independent clause in B so B will be our answer there let's take a look at C and D as well we've got option C some historians having claimed that this tulip Mania was the first historical instance of an acid bubble this prevents essentially very close to the same problem as a we are using a nonfinite participle and this will not complete an independent clause so if we were to use having claimed we would not have an independent clause before the comma okay and if we're going to have a sentence we need to have an independent clause so we can get rid of option C if we had to take a look at option D okay we would have some historians to claim that this tulip Mania was the first historical instance of an asset bubble once again that would not make an independent clause okay to claim there is a nonfinite infinitive so we can get rid of because once again we would not have an independent clause the only option out of a c and d that would give us an independent clause prior to this comma right here okay is option b because it provides a finite verb here's another example we have Which choice completes the text so it conforms to conventions of Standard English I look at my options I've got food with a colon a comma no comma and well or nothing no punctuation after it okay so what I'll be looking for is do I have an independent clause before food and then what kind of phrase or Clause do I have after food so we have researchers studying Mago sensation have determined why some soild Dwelling ground worms in the Southern Hemisphere move in the opposite direction of Earth's magnetic field when searching for food that's an independent clause before food so I'm going to Mark I see at food after that we have in the northern hemisphere the magnetic fields Point down into the ground but in southern hemisphere it points up toward the surface and away from worms food sources okay that's also an independent clause so we have two independent clauses we cannot connect them with just well or with no punctuation or with just a comma so our answer there would have to be answer Choice a here's another example with question 25 Which choice completes text and forms Convention of Standard English start with the answer choices we got a bunch of pronouns so I'll be looking for the noun I'm replacing got scientists believe that unlike most other species of barnicle interal barnicles can dissolve the smell like secretions they used to attach blank to a turtle seashell enabling the Barnacles okay so ultimately I'm our subject here is the turtle Barnacles okay so that's the noun we need to replace Turtle Barnacles can dissolve the smutling secretions they Ed to attach so have to be them themselves to a sea turtle shell we know it's plural so obviously we would get rid of a and we would get rid of D okay we know it has to be themselves because we wouldn't state that Turtle Barnacles can dissolve the SMC secretions they use to attach them to a sea turtle shell okay it is themselves okay so our answer there half beb here's another example how I recommend approaching questions where you ask to conform to the conventions of Standard English in this case I'll look at my answer choices to start I've got a bunch of different forms of the verb allow so what I'm going to be looking to do is identify the number of my subject and also try to pay attention to tense as I read through this we have a classic children's board game Shoots and Ladders is a version of an ancient nepes game parapata soap in both games players encounter good or bad spaces while traveling along a path landing on one of the good spaces blank a player to skip ahead and arrive closer to the end goal right so I want to identify my subject I have this prepositional phrase of on one of the good spaces where on is the preposition that starts it off so in order to identify your subject make sure that you are getting rid of those prepositional phrases so our subject here is landing Landing is going to be singular look at my options I have option A allows I'll use the he they test here so I would State he allows but I would State they allow so I see option D would have to be incorrect since allow is plural but allows is singular if look at option b we have are allowing well are allowing we State they are allowing but he is allowing so we know that that's plural so can get rid of that as well if look at C we have have allowed we would State they have allowed but he has allowed so once again we see C would be plural as well so answer there would have to be option A since we need to maintain that Singularity that is in our subject to the singularity that must match with our verb so our answer there would have be a here's another example so if we take a look at our answer choices we've got equations and though anytime I have a transition word like though or however I'm going to be looking to see if it needs to be on the left side of whatever punctuation or the right side or in other words does it need to be contained with the first independent clause or the first clause or does it need to be with the second clause or phrase okay so that's one thing I'll be looking for the second thing is we have a colon here we have just commas here with no Fanboys and we have no Fanboys or commas or any punctuation in D and then option C we have a period so what I'm going to look for is if we have two independent clauses because that'll help me figure out punctuation as well so I'm looking where to place though and then if we've got two independent clauses in 1943 in the midst of World War II mathematics professor Grace Hopper was recruited by the US military to help the war effort by solving complex equations Hopper's subsequent career would involve more than just equations though as a pioneering computer programmer okay and as a pioneering computer programmer is an introductory modifier to hopper Hopper would help usher in the digital age that's an independent clause we also have an independent clause with Hopper's subsequent career would involve more than just equations so we have two independent clauses okay we can't connect them with a comma and no Fanboys or with no punctuation so we get rid of B and D so now the question is does though need to come or be attached basically to the first independent clause or the second well we have Hopper subsequent career would involve more than equations though okay that would need it be applied or connected to the first independent clause we wouldn't State though and then have the introductory modifier after that though as a Pioneer and computer programmer Hopper would help Usher in the digital age okay that would make sense we have to have that though connected to this first independent clause okay the other thing that you can note is that your second independent clause here of as a Pioneer and computer programmer copper would help Usher in the digital age is illustrating the idea that came before it or the preceding idea prior to this colon which is that her subsequent career would involve more than just equations which we are illustrating okay by her being a computer programmer okay the equations part was referring more to her being a mathematician so we are illustrating this idea anytime you are illustrating the idea that came before it okay you will often be using a colon okay so answer has to be answer Choice a here's another example so if I take look at my answer choices here I've got Henry resumed his reign the reign of Henry resumed Henry's Reign resumed and it was Henry who resumed his Reign so as you can see here basically what's getting switched around is what's at the beginning first you have Henry then you have the reign of Henry then you have Henry's Reign then you have it was Henry if you see that your subject is just being like turned and switched around in the beginning you're probably going to be looking at an introductory modifier so in this case if I take a look back up at where my blank is I have a pawn recovering two years later okay that's an introductory modifier so what comes after it needs to be who it is modifying who is recovering 2 years later okay so let's go ah and read through our text figure out who that is we have in 1453 English king Herer the vi became unfit to rule after falling Gravely ill as a result Parliament appointed Richard third Duke of York who had a strong claim to the English Throne to rule as protector P covering two years later what we know that King Henry is the one who fell ill so he would be the one recovering so what needs to come after this comma is King Henry so we have option A Henry which is the subject that this introductory modifier is modifying okay we have option b the reign of of Henry it's not the reign of Henry that is recovering 2 years later it's not Henry's Reign that is recovering 2 years later and it's not it that is recovering two years later it is Henry himself okay so we need to have the correct subject after the introductory modifier so our answer there has to be answer Choice a here's how I recommend that you approach transition questions on the digital SAT writing section if you take a look at question n it says Which choice completes the text with the most logical transition now in contrast to questions that ask you to conform to the conventions of Standard English I actually recommend that you don't look at your answer choices first when dealing with transition questions here's how instead I think you should approach it start by reading through the text although novels and poems are considered distinct literary forms many authors have created Hybrid Works that incorporate elements of both okay so here we have a claim that many authors have created Hybrid Works that incorporate elements of both both being the poems and the novels then we have Bernardine avisto the emperor's babe blank is a verse novel a book-length narrative complete with characters and a plot but conveyed in short crisp lines of poetry rather than Poe okay so this is an example of how novels and poems are not necessarily distinct but instead how many authors have created Hybrid Works that incorporate elements of poetry and a normal novel or in other words a normal narrative okay so as we can see we are providing an example of the claim that we are given above okay so I'd be looking for something like for example okay so D would be perfect there now the reason I recommend that you um you don't look at your answer choices first is because that could potentially sway you before you go through and you read the actual text so I recommend you try to come up with your own answer Choice first and then take a look at your options that way you're less likely to be swayed by wrong answer choices here's another example once again we have Which choice completes the text to most logical transition we'll start by reading through at 2 weeks old the time their critical socialization period begins wolves can smell but cannot yet see or hear domesticated domesticated dogs can see hear and smell by the end of two weeks okay so in this case we have a contrast we have at two weeks old wolves can smell but they cannot see or hear but domesticated dogs can see hear and smell by the of TW weeks so looks like we have a contrast we'll keep reading this relative lack of sensory input may help explain why wolves behave so differently around humans than dogs do from a very young age wolves are more wary and less exploratory so in this case we do have a contrast so I'd be looking for something like domesticated dogs by contrast can see hear and smell by the end of two weeks as we can see we have by contrast as an option so that works out perfectly okay so our answer would have to be c one thing I will make note of is that with digital SAT writing section and the SAT writing section before it went digital you tend to get um very similar transition choices and you tend to have similar transition themes across the different practice tests now what I mean by this is you will often see situations where you would use something like for example or something exemplifies what came before it or a contrast or something where you're stating something in other words or where you're giving you know something for instance which is kind of similar to for example um and some other ones that you might see are consequently subsequently consequently being if something is a consequence of what came before subsequently being if something came after what was talked about previously so getting practice with the transition questions is very very helpful because you often see similar transitions being used across the practice tests which is obviously going to be indicative that those transitions are ones that the College Board would want you to know for the actual digital sat here's another example so once again we have Which choice completes the text most logical transition I'll start by filling in the blank with what I expect to be there after I do my read through and then I'll go through my answer choices we have researchers Helena miljevic Brandt Lucia Santa Maria and Marco Tony report that well mathematicians may have traditionally worked alone evidence points to a shift in the opposite direction so one thing I'll point out here is anytime I have any sort of shift or any sort of um you know indication that we have some sort of change going on or even some sort of something that's staying the same I want to pay attention to that on a transition question in this case we have a shift in the opposite direction of working alone so presumably working together then we have mathematicians are choosing to collaborate with peers a trend illustrated by the rise in the number of mathematics Publications credited to multiple authors okay so in this case we are stating that they are choosing to work with peers that's pretty much an example of what came before so I would probably be looking for something along the lines of four example here okay if we look at our options we get option A similarly well it's not similar to what came before okay we're just kind of illustrating what we previously claimed if we look at option b for this reason it's not a consequence of what came before it so we can get rid of B okay what came before it did not cause mathematicians choosing to collaborate with their peers if we look at option C furthermore we're not adding on to what came before we're illustrating it okay if we look at option D we have increasingly okay increasingly mathematicians are choosing to collaborate with their peers a trend illustrated by the rise in the number of mathematics Publications credited to multiple authors so as you can see D would have to be our answer there now obviously that's not the same as what I came up with as for example but when we state that increasingly mathematicians are choosing to collaborate with their peers well is that a good transition from what came before which stated that we are moving in the opposite direction of working alone yes because the opposite of working alone would be an increase in collaboration okay so obviously that's a great transition there and it is illustrating what came before okay so our answer would have to be D here's how I recommend answering questions on the digital SAT writing section where you're presented with a students or someone's notes and then you have to answer questions following that first thing I recommend that you do is take a look at what your actual prompt is okay and the prompt will basically be the last part before Which choice most effectively uses relevant information from the notes to accomplish the goool so when I say prompt I'm referring to the section right here okay so the student wants to present the study and its findings from here once I know the prompt and identify what I want to look for as I do my read through in this case it's pretty broad it's just the study and its findings okay so I'll go back up let's do the read through okay petaurus were flying reptiles that existed millions of years ago in 2021 study act analyzed fragments of pterosaur jaw bones located in the Sahara Desert she was initially unsure if the bones belong to a juvenile or adult petaurus she used Advanced microscope techniques to determin that the bones had few growth lines and relative few growth lines relative to the bones of fully grown bosur she concluded that the bones belonged to juveniles okay so the findings is that the bones belong to juveniles okay the study is ultimately whether these um these jaw bones are from that of a juvenile or an adult okay so let's go ahead and look at our options we got option A in 2021 uh CT studied potur jaw bones and was initially unsure if the bones belonged to juveniles or adults that does not present the findings so we can get rid of option A when you're dealing with questions like this you need to be strict and make sure that you're answering all parts of the prompt this one does not include findings we get rid of a b the jaw bones located in the Sahara Desert where the focus of a 2021 study also does not talk about the findings option C in a 2021 study CT used Advanced microscope techniques to analyze the jaw bones of potur flying reptiles that existed millions of years ago once again we do not discuss the findings in option C so we got to get rid of it and then we take a look at option D in a 2021 study CT determined that potur jaw bones located in the Sahara Desert had a few growth lines relative to the bones of fully grown potur and thus belong to juveniles okay right there we do both a presenting of the study if we go up our prompt present the study and its findings we do both of those answer there has to be D here's another example of how I recommend that you approach questions where you're given a set of notes and asked to do something with it in this case we see that our prompt is the the student wants to compare the two women's contributions to the March on Washington and then we have the generic part of the question which is which Choice most effectively uses relevant information from the notes to accomplish this goal okay so we're going to focus in right here student wants to compare the two women's contributions to the March on Washington so since I'm looking for a comparison I'm going to look for things that are different and possibly things that are the same as well so we have African-American women played prominent roles in the Civil Rights Movement including at the famous 1963 March in Washington civil rights activist Anna hedgman one of the March's organizers was a political adviser who had worked for President Truman civil rights activist Daisy Bates was a well-known journalist and advocate for school desegregation so it looks like they have two different positions then we have hedgman worked behind the scenes to make sure a woman was included in the lineup of speakers at the March Bates was the sole woman to speak delivering a brief but memorable address to the cheering crowd qu so hedgman worked behind the scenes and Bates was a speaker looks like it's the main difference there the similarity would be that they both had important contributions to the march in Washington so you've got option A hedgman and Bates contributed to the march in different weights in different ways Bates for example delivered a brief but memorable address all right so are we comparing the two women's contributions well we say that they contributed in different ways and then we only state the way that Bates contributed I would prefer an option where we talk about the way that they each contributed um in their own distinct way so I'm going to leave this one as neutral for now let's take a look at B hedgman worked in politics and helped organize the Mars while B Bates was a journalist and school desegregation activist advocate well we never mentioned bates's role in the March on Washington there so I'm going to get rid of B option C States although hedgman worked behind the scenes to make sure a woman speaker was included Bates was the sole woman to speak at the March okay this is much better than option A okay option A States they both contributed to the march in different ways but then we only um discuss how Bates contributed K so we can get rid of a now Okay C is much better because it states how hedgman contributed okay she worked behind the scenes to make sure woman was included and then we also discuss how Bates contributed being the sole one to speak at the margin obviously these are both different so that's a great comparison okay we can take a look at d as well here we have many African-American women including baates and hedgman fought for civil rights but only one spoke in the March the focus here is not on comparing baits and hedgman so we can get rid of D keep in mind you're prompt prompt States the student wants to compare the two women's contributions specifically to the March on Washington so our answer there would have to be answer Choice C now let's talk about how to approach different types of sat reading questions by knowing which approach you want to use for certain questions you'll be able to be more efficient and comfortable when taking the SAT here's a tip on how to answer one of the most commonly asked questions on the digital sat reading section if you take a look at the prompt it states which always completes the textt with the most logical and precise word or phrase what I recommend doing when you see a question with that type of prompt is start by reading from the beginning and then once you get to this blank right here fill it in with what you think should go there now that might require that you continue reading on but ultimately what your goal should be is to fill in the blank with a word before you actually take a look at your answer choices this is important because it'll help you avoid being swayed by what the answer choices say so let's go and illustrate this with question one former astronaut Elena choa says that although she doesn't have a definite idea of when it might happen she blanked that humans will someday need to be able to live in other environments than those found on Earth this conjecture informs her interest in future research Miss missions to the Moon okay well if she has interest in future research missions to the Moon I would assume that she believes that someday humans would need to be able to live in other environments than those found on Earth okay so I would fill in right here with believes now at this point I would then take a look at my answer choices so I have answer Choice a as an option which is it demands well we can't say that she demands humans will someday need to be able to live in other environments because obviously she cannot demand that we have B speculates she speculates that humans will someday need to be able to live in other environments than those found on Earth and that would make sense because it informs her interest in future research missions to the Moon okay so that makes a ton of sense if we take a look at C doubts well she obviously doesn't doubt it because she's interested in future research missions to the moon and she cannot establish it to establish something would basically be to prove something she's unable to prove that humans will someday need to be able to live in other environments and those found on Earth qu or answer would have to be be speculates and as you can see by filling in this blank with a word before we actually take a look at our answer choices we're much less likely to be swayed by what they say because we already know what should fill in that blank based on the context of the question here's another example with question two beginning in the 1950s Navajo Nation legislator Annie Dodge wanka continuously worked to promote Public Health this blank effort involved traveling throughout the vast Navajo Homeland and writing a medical dictionary for speakers of Dyan bad the Navajo language all right I would say this consistent effort okay we say that she continuously worked to promote Public Health then we go on to talk about her effort which involved traveling throughout the Homeland writing medical dictionary so obviously this is a consistent effort so that's what I'd fill in there before taking a look at my answer choices now if we take a look at our options we have a and partial well there's not any sides to be taken here so you can't have a neutral stance on something that doesn't have two sides so that wouldn't make sense we have B offhand offhand would have a negative connotation so that wouldn't make sense here either if we take a look at C persistent okay persistent and consistent very very similar in meaning okay both in this context would basically mean that there is a consistent or um continued effort involv um by Annie okay so that would make a lot of sense we take like a d mandatory no one is forcing her to do that so that wouldn't make sense okay so our answer would be C here's how I recommend you approach digital sat reading questions that ask you to State the main purpose or the main idea of text so to illustrate this I'm going to use question number seven in 2007 computer scientist Louis vanan was working on converting printed books into a digital format he found that some words were distorted enough that digital scanners couldn't recognize them but most humans could easily read them based on that finding vanan invented a simple security test to keep automated Bots out of websites the first version of the recapture test asked users to type one known word and one of the many words scanners couldn't recognize correct answers proved the users were human and added data to the book digitizing project so for main purpose and Main Idea questions what I recommend you do is come up with your own answer before taking a look at the answer choices that way you're not easily swaye by an choices that are close to correct but have slight flaws in them that actually make them incorrect so let's go and start by coming up with our main purpose for this prompt okay so ultimately we start out by talking about how um vanan was using digital scanners and how it couldn't recognize some of the words then we talk about how he uses this to create the recapture test and then we talk about the application of the recapture test and how it's used to protect websites so ultimately it's really about the creation of the recapture test okay so let's take a look at our options now that we've just identified the main purpose as the creation of the recapture test so we have option A to discuss van On's invention of recapture okay that looks perfect we'll put a check by that let's take a look at BC and D we have B to explain how digital scanners work okay obviously that's not the main purpose okay we don't even really discuss necessarily that much about digital how digital scanners actually work we just mentioned them in the beginning and talk about how they can't actually recognize some of the words but that's really just to introduce how they came up with the recapture test so just to lead us to the creation of it we have C to call attention to Van On's Book digitizing Project the focus isn't on his book digitizing project okay that's just how he ended up discovering or creating recapture okay so we can get rid of C as well there if we take a look at D we have to indicate how popular recapture is okay once again that is not um ultimately the main purpose now do we State anywhere even that it is popular okay we say that if we go up he invented a simple security test to keep automated bots on a websites we don't even necessarily mention that it is popular now some of us may know this from just our general knowledge of what goes on on the internet but we have to acknowledge that the main purpose here is talking about the creation of recapture okay so our answer has to be a now you'll notice by coming up with our own answer for the main purpose first it helped us to be able to eliminate answer choices that were similar or were mentioned at somewhere in the text but weren't actually the main purpose but were just maybe a step to get us to the main purpose here's another example of how I recommend approaching questions that ask you about the main purpose or main idea on the digital sat reading section so I'm going to illustrate this with question 11 the following text is from Maggie poke Johnson's 1910 poem poet of our race in this poem the speaker is addressing Paul Lawrence Dunbar black author thou with stroke of Mighty pen Hast told of joy and mirth and read the hearts and souls of men as cradled from their birth the language of the flowers thou H has rested them all and I the Little Brook responded to thy call okay so we're going to start out by coming up with our own main purpose before actually taking a look at your choices that way we're not as SED by an choices that are close to correct but have slight flaws that actually make them incorrect so let's go and start by discussing what the main purpose of this is let's start with this first part okay so we have thou with stroke of Mighty pen has told of joy and mirth and read the hearts and souls of men as cradled from their birth okay so we're ultimately complimenting um Paul Lawrence dunbar's work as a poet stating that he's told of joy and mirth read the hearts and souls of men so essentially stating that um he's very in tune with obviously The Souls of men or in other words um the soul really representing you know the inner thoughts of people sort of who they are deep deep down in their soul we have as cradled from their birth so from um from their birth presumably until death and we take a look at the second part we have the language of the flowers thou Hast read the all and E the Little Brook responding to thy call okay so here we're talking more so about nature okay so presumably this is a poet who is talking both about uh humans and nature um clearly it sounds like they are very in tune with both of them K has read them all all the language of the flowers so very great at writing um both about humans and about nature okay so main purpose I would sayate is that Paul Lauren Dunbar is an incredible poet who's great at writing both about um humans maybe The Human Experience as well as nature so we have option A to praise a certain writer for being especially perceptive regarding people in nature okay as you can see that's very supported by the text okay that's also in line with the main purpose that we came up with before taking a look at the answer choices that looks really good we'll take a quick look at b c and d as well we have B to EST that a certain writer has read extensively about a variety of topics well that's not the main purpose okay and we're also not explicitly stating or there's no real support for that the certain writer has read extensively about a variety of topics okay this is pretty much all figurative language if we scroll up and take a look at the poem so there's really not any support for that being the main purpose um ultimately the main purpose is that um they are especially perspective regarding people in nature right we talk about how um they have told of joy and mirth read the hearts and souls of men and that's really the key part there hearts and souls of men okay so that's perceptive about people and then perceptive about nature that language of the flowers that has read them all okay so tons of support for a if we take a look at C to call attention to a certain writer is careful and elaborate elaborately detailed writing process we're not discussing the writing process okay if we take look at D we've got uh to recount fond memories of an afternoon spent in nature with a certain writer okay we never state that this is from an afternoon they spent together okay so D doesn't have any support our answer there would have to be a as you can see coming up with our own answer Choice first help us to avoid getting stuck between answers and it also helps us to get rid of answer choices that seem like they would be close to a correct answer but have slight flaws that we ultimately can then use to rule them out as incorrect here's some advice on how to answer this really common digital sat reading question the question states which Choice best describes the function of the underlined sentence as a whole when you come across a question like this the first thing I'd recommend doing is going ahead and reading through so let's go and start doing that with question 8 following text is from Edith Wharton's 1905 novel The House of Mirth Lily Bart and a companion are walking through a park Lily had no real intimacy with nature but she had a passion for the appropriate and could be keenly sensitive to a scene which was fitting which which was the fitting background of her own Sensations the landscape outspread below her seemed an enlargement of her present mood and she found something of herself in its calmness its breath its long reaches okay so immediately what I'm seeing is before we had a claim okay that she could be keenly sensitive to a scene which was the fitting background of her own Sensations okay now we are going ahead and showing or proving that claim okay we have the landscape outspread below her seemed enlargement of her present mood and she found something of herself in its calmness okay that's very directly supportive of that claim that we had in the previous sentence okay that she finds something of herself in its calmness or in other words that it's fitting um she's keenly sensitive to a scene which was the fitting background of her own Sensations okay so obviously that's supportive its breath it's long free reaches all right let's keep reading on on the nearest slopes the sugar mels wavered like Pires of light lower down was a massive massing of gray Orchards and here and there the lingering of an Oak Grove all right so this is pretty much from here down just a description of the setting for the most part so we have Which choice best describes the function of the underline sentence if in the text as a whole so from here I'd go down to my answer choices so have option A it creates a detailed image of the physical setting of the scene well it looks like actually the sentence after the underline one is what is really giving more of a detailed image of the physical setting of the scene okay so I would go ahead and I would get rid of a if we take a look back at the sentence that is underlined and I'll go ahead and remove some of this blue so you can see it a little bit better okay we state that the landscape outspread below her seemed an enlargement of her present mood and she found something of herself and its calmness it's breath it's long for reaches as you can see that's really not creating a detailed image of the physical setting okay so we could remove it based on that and one thing I do recommend you do on the SAT reading and writing section is you can cross out answer choices okay and you can cross them out based on what makes them false or what makes them incorrect okay so if we take a look at B now it establishes that a character is experiencing an internal conflict okay well ultimately it's not really establishing that the character is experiencing an internal conflict okay if we go back up to the underl sentence it says the landscape outspread below her seemed an enlargement of her present mood and she found something of herself and its calmness its breath its long fore reaches well here we have it found she found something of herself in its calmness okay so it doesn't sound like there's much internal conflict there okay it sounds like she would be calms we can get rid of B if we take a look at C we have it makes an assertion that the next sentence expands on okay well the next sentence is really just a description of the scene of the setting okay so ultimately we're not making an assertion okay and the next sense is what obviously not be expanding on that if we take a look at D now we have it illustrates an idea that is introduced in the previous sentence okay if we go back up in the previous sentence as I pointed out earlier it states that she could be keenly sensitive to a scene which was the fitting background of her own Sensations okay we then go on to state that she found something of herself in its calmness its breath its long for reaches okay and the landscape outspread below her seemed an enlargement of her present mood okay that's ultimately supportive of the claim that came before it okay so as we can see there our answer would have to be D okay so I think the key things that I want you to take away from this tip is basically if you have an underlined sentence like this okay be looking for the role that it plays as you read through here's something you need to watch out for on one of the most commonly asked questions on the digital sat reading section that question is Which choice best states the function of the underlined sentence in the overall structure of the text so I'm going to approach this just like I approached the previous question but then once we get to the answer choices I'm going to show you some common wrong answer choices to watch out for so we have a study by a team including Finance Professor Madu V suggests that exposure to Sunshine during the workday can lead to overly optimistic Behavior using data spanning from 1994 to 2010 for a set of us companies the team compared over 29,000 annual earnings forecasts to the actual earnings later reported by those companies all right so ultimately we see that we start out here with a suggestion or sort of a hypothesis that exposure to Sunshine during the workday can lead to overly optimistic Behavior then we talk about how we are gathering the data okay so right here we have data collection then we have the team found that the greater the exposure to Sunshine at work in the two weeks before managers spended an earnings forecast the more the com the manager forecast exceeded what the company actually earned that year so then we have summary okay so we start with hypothesis data collection summary all right so ultimately if we scroll down we got option A to summarize the result of the team's analysis well that would be the summary okay and this is one of the common wrong answer choices that I wanted to point out to you guys is that often times when you have a sentence underlined like this in the text one of the answer choices which is obviously going be a wrong answer choice is they will select either the sentence before or the sentence after or another sentence somewhere in the text okay and they will put that down as one of the wrong answer choices so you need to watch out for that in this case it's the summary which we see is the sentence that is after the sentence that's underlined okay so we can get rid of a because we know it's not the underlined sentence that's giving the summary it is the following sentence so always watch out for that if we take a look at B we have to present a specific example that illustrates the stud's findings so this is more so of a misinterpretation okay so I would identify this as a Mis interpretation wrong answer choice and the reason I identify it as that is because some people would look at this underlined text and they would think that it is a specific example illustrating the study's findings but it's not okay they're talking about how they are collecting this data okay this is not a specific example either because ultimately okay we're looking at 29,000 annual earnings forecast so obviously that is not specific okay also we have to recognize that this is data collection okay this is not providing of an example we are collecting the data okay so if we look at option b we can get rid of it okay we would classify that in my opinion as a misinterpretation because this is not a specific example if we take a look at C we have to explain part of the methodology used in the team study okay often times on the SAT if you see methodology you should probably be thinking how the experiment or the study is being um set up and how data is being collected okay so that's what you want to think about when you think about methodology and as you can see in this case that underlined sentence okay that's describing the methodology used okay they used data spanning from 1994 to 2010 for a set of us companies the team compared over 29,000 annual earnings forecasts to the actual earnings later reported by those companies okay that's an example of a methodology okay so C is perfect there we'll take look at d as well okay D states to call out a challenge the team faced in conducting its analysis the way I would classify answer Choice D is just as a random wrong answer Choice sometimes on the SAT reading section and this isn't specific to just this question type this is specific to just generally almost any type of question on the SAT reading and writing section you may just get some answer choices that are fairly random and this one is fairly random there really isn't any challenge that's discussed at all in the text anywhere okay so the fact that they would put that there is really just random okay so we can get rid of d as well there as you can see your answer there will be C what I really wanted to point out in this is the common wrong answer choices that you will see on questions that asks you to State the function of underlying sentences in the overall structure of text here's a tip for anyone who struggles with reading comprehension on the digital sat reading and writing section if we take a look at question 10 we'll start by reading the question which states according to the text what is true about mother we have the following text is adapted from Edith nesbit's 1906 novel The Railway children mother did not spend all her time in paying Dole visits to Dole ladies and sitting doly at home waiting for do Lazi us to pay visits to her she was almost always there ready to play with the children and read to them and help them to do their home lessons besides this she used to write stories for them while they were at school and read aloud to and read aloud read them aloud after tea and she always made up funny pieces is a poetry for their birthdays and for other great occasions okay so in this case on a reading comprehension question like this you really just have to go to your answer choices there's not much you can do before that okay so we'll go and go to answer Choice a we have she wishes that more ladies would visit her so the biggest tip that I would have for anyone who struggles with reading comprehension on the digital sat and the sat in general is you need to try to make it less about comprehension and more about evidence and textual support okay so if you take a look at option A she wishes that more ladies would visit her okay the biggest tool have if you are someone who struggles with reading comprehension is the ability to go back to the text okay so she wishes more ladies would visit her let's see if there's any textual evidence for that because if there's not we can get rid of it so we have mother did not spend all her time in paying dull visits to dull ladies and sitting D at home waiting for D ladies to pay visits to her she was almost always there ready to play with the children read to them and then we talk about the children for the rest of this okay ultimately is there any evidence that she wishes that more ladies would visit her no there is not so you can get rid of a okay and one piece of advice for the reading and writing section is when you get rid of an answer Choice try to get rid of um it based on the part of that's false so she wishes that more ladies would visit her okay there's no evidence that she wishes that okay you would have to make um you can't even make a reach for that there's not it's not even like it would be a large reach there's just no textual evidence of support us you have to get rid of a okay if you take a look at B now birthdays are her favorite special occasion and this is where being strict on the digital sat reading section is important okay you want to be strict this part right here birthdays are her favorite special occasion that's what makes be wrong okay and let's say you didn't remember um that she never stated this well you can go back to the text and you can look for special occasions so let's go and take a look for that or birthdays in particular okay so if we go back to the text we look for birthdays okay we see right here is the only mention of birthdays so we have she always made up funny pieces of poetry for the birthdays and for other great occasions okay great occasions does not mean it's her favorite okay so on the SAT reading section be strict when getting rid of an choices if it states that it's someone's favorite special occasion but it just states that uh it's a great occasion in the text you can't make that jump there's not textual evidence of support that their favorite okay now if we take a look at C we have she creates stories and poems for her children well let's see if we have evidence for that okay if you're not someone who's great with comprehension go back to the text so creates stories and poems for children well let's take a look there we have she was almost always there ready to play with the children read to them and help them do their home lessons besides this she used to write stories okay so we have that she creates stories for them and while they were at school and read them aloud after tea and she always made up funny pieces of poetry okay so she made up funny pieces of poetry made up means that she's writing them or creating them okay so she creates stories and homes for her children we see that that has textual support C would have to be our answer okay and then D reading to her children is her favorite activity well once again there's no mention of anything being her favorite activity let's say that you um forgot that you're not great at comprehension you just go back to the text look for where we talk about reading to her children then okay we have that up here she was almost always there ready to play with the children and read to them and help them do their home lessons Okay and then after that if we go down okay it doesn't really look like we're talking about um we talk about reading again here read to them a lot after tea but once again we don't say that it's her favorite okay so we can get rid of that by being strict on the favorite part okay so if you are someone who struggles with comp comprehension try to identify the subject in your answer Choice identify where that subject is in the text okay read that section of the text and then determine if there is textual evidence to support it if there is not any evidence to support it then it cannot be correct okay every answer choice on the SAT has to have evidence from the text to support it here's a tip for anyone who struggles with reading comprehension on the digital sat reading and writing section what I recommend doing is taking a look at your prompt before you end up reading through the passage and do this each time because then you know what to look for as you read through and it avoids you having to do a second read through which if you struggle with reading comprehension you probably would have to okay so based on the text how does Lord Chancellor respond to the crowd so we're ultimately going to be looking for L Lord Chancellor's response to the crowd as we do our initial read through so let's goad and start we have the following text is adapted from Louis Carrol's 1889 satirical novel of sylv and Bruno a crowd is gathered outside a room belonging to the warden an official who represents the Lord Chancellor or who reports to Lord Chancellor one man who is more more excited than the rest flung his hat High into the air and shouted as well as I could make out who Roar for the suben everybody roared but whether it was for the suben or not it did not clearly appear some were shouting bread and some taxes but no one seemed to know what it was they really wanted all this I saw from the open window of the warden's breakfast Saloon looking across the shoulder of the Lord Chancellor what can it all mean he kept repeating to himself I never heard such shouting before and at this time of the morning too and with such unanimity okay so we have his response contained right here okay he states that what can it all mean okay he kept repeating to himself he's never heard such shouting at this time in the morning so he does know what it means okay but then he ends with and with such unanimity or in other words such togetherness or closeness okay so everyone's together but Lord chancer can't make out what they all want all right so that's his response we've got option A he asks about the meaning of the crowd's shouting even though he claims to know what the crowd wants well he doesn't claim to know what the crowd wants okay so anytime you have an answer choice on the SAT reading or writing section that you can get rid of based on a piece of it that is incorrect cross out that piece that makes it Incorrect and move on you got B he indicates a desire to speak to the crowd okay it never has any sort of portion in the text that indicates he has a desire to speak to the crowd okay if you didn't remember that for example if you have bad reading comprehension you would go back to where the response is contained okay which we see is in this bracket of blue right here if you take a look there you see what can it all mean he kept repeating to himself I never heard such shouting before and at this time of the morning too and with such unanimity obviously right there there is no indication he wants to speak to the crowd so you could get rid of B and then C he expresses a sympathy for the crowd's demands okay well does it ever show that he's expressing Sympathy for the crowd's demands once again it does not okay so you would get rid of that okay if you weren't sure on that you would go back to that section and notice how I've narrowed this down to a section so if you are someone who struggles reading comprehension make sure that you try to narrow down where you need to look back to okay sometimes it'll be in a case like this where you're only looking at one portion of the text which is his response because you really don't need to focus on the other portions because you're not asked about them okay in other cases you may have to jump around a little bit more because it may not be confined to one section of the text okay and now we'll take a look at answer Choice D he describes the crowd being united that's supported he talks about um and with such unanimity would be the quotation that would support that even though the crowd clearly appears otherwise okay and then let's say that you weren't sure if the crowd clearly appears otherwise okay that's actually not contained within this small section it's not confined there okay that one to find support for you it actually have to go up okay so the crowd appears otherwise everybody roared but whether it was for the subord or not it did not clearly appear some were shouting bread others taxes no one seemed to know what they really wanted okay so that would show that the crowd appears otherwise even though he describes the crowd as being united okay so answer D has a ton of textual support there here's how I recommend that you approach questions on the digital sat reading and writing section that asks you to support or weaken any sort of claim or hypothesis I'm going to illustrate this with question 13 question 13's prompt states which finding if true would most directly support the student's claim in order to answer a question like this you will need to identify the hypothesis or claim in this case a claim so let's go and start by reading through question 13 and when you go through you want to identify that claim so we'll mark it with a c when we find it we have born in 1891 to a kicha speaking family in the Andes Mountains of Peru Martin chambi is today considered to be one of the most renowned figures of Latin American Photography in a paper for an art history class A student claims so this is very very clear we mark it with a c that chambi photographs have considerable ethnographic value in his work chami was able to capture diverse elements of Peruvian Society representing his subjects with both dignity and authenticity so now we'll go and take a look at our options we have option A shami took many commissioned photographs of wealthy peruvians but he also prod hundreds of images carefully documenting the people's sites and customs of indigenous communities of the Andes well that's ultimately supporting the fact that his photographs have considerable ethnographic value and his work he's capturing diverse elements okay so both the wealthy and the indigenous communities a perubian society representing a subjects of both dignity and authenticity okay we have he's documenting the peoples the sites the Customs okay so that would be supportive of the authenticity aspect okay as far as the dignity aspect the fact that he's taking you know hundreds of images carefully documenting um the indigenous communities of the Andes okay I'd say that because he's in particular documenting the indigenous communities as well as the wealthy peruvians but in this case I'm more so concerned with the indigenous communities the fact that he's documenting both of those okay is showing that he's showing them with dignity okay there's no sort of bashing or anything like that okay he's both um you know taking these portraits of wealthy as well as the poor with no sort of partiality to either so he's representing them with dignity authenticity um because of that has considerable ethnographic Val ethnographic value okay so that looks good we'll take a look at b c and d as well we have option b Chan's photographs demonstrate a high level of technical skill as seen his strategic use of Illumination to create dramatic light and Shadow contrast now that they may very well be true however the problem is we need to directly support the students's claim and the student's claim isn't that chambi is the most technically skilled photographer okay so we wouldn't want to focus on his technical skill we'd want to focus on the ethnographic value of the photographs he is taking okay the fact that he's capturing diverse elements provan Society not on the actual technical skill so this is an example of something that is fairly unrelated to the actual claim that is being made here we take look at C we have during his lifetime chambi was known and celebrated both within and outside his native Peru as his work was published in places like Argentina Spain and Mexico so this answer choice I would actually classify it as you would select this if you had a misinterpretation of part of the text because if we scroll up when we state that chami photographs have considerable ethnographic value we're not stating that um himself and him as a photographer is being valued in multiple aspects or parts of the world okay which is what anro C is trying to sort of that's kind of the claim C is insinuating with its support here okay saying that Cham is known and celebrated within and outside his native Peru as his work was published in places like Argentina Spain and Mexico so I'd classify this as a misinterpretation type of wrong answer choice if we take a look at D we have some of the peoples and places chami photographed had long been popular subjects for Peruvian photographers well once again we need to keep in mind the claim that we're trying to support okay we know that the claim is that his photographs have considerable ethnographic value in his work he's capturing diverse elements proving in society representing the subjects with both dignity and authenticity okay no part of D is ultimately supportive of that okay D is really just stating something it's just stating that some of the peoples and places Jim photographed have been long popular subjects for provan photographers that's not supportive of the claim okay and also one thing I also want to point out here is you need to directly support the claim the word directly there is important okay because you have to keep in mind your answer Choice must directly support it can't just be um you know some sort of tangent that is a reach to support it needs to directly support and the only answer choice that does that here is answer Choice a so the big takeaway I want you to have from this type of question is as you read through identify that claim or that hypothesis that you either need to support or weaken here are some common wrong answer Choice types to questions that ask you about findings that either support or weaken a researcher's hypothesis or someone's claim okay so I'm going to illustrate this with question number 16 so to start we're going to first identify what the research of hypothesis is as we do our read through R question 16 and then we'll get into the answer choices so we have in the mountains of Brazil BT and BM two plants in the velio family establish themselves on soiless nutrient poror patches of Quartzsite Rock plant ecologists Anna a and Patricio debitto Costa used microscopic an nails to determined that the roots of BT and BM which grow directly into the cord site have clusters of fine hairs near the root tip further analysis indicated that these hairs secrete both malic and citric acids the researchers hypothesize so now we have our hypothesis I'm going to mark this with an H that the plant depend on dissolving underlying rock with these acids as the process not only creates channels for continued growth but also releases phosphates that provide the vital nutrient phosphorus okay so now we have to find support for that hypothesis I'll try to leave that hypothesis within the frame so you can still see it we have option A other species in the velocci family are found in terrains with more soil but have root structures similar to BT and BM okay ultimately this is pretty unrelated to the actual hypothesis at hand here okay our hypothesis is that the uh plants depend on dissolving underlying rock with these acids um because that they then use this to release phosphates that provide the vital nutrient phosphorus well if you have the same family there are other um other species in the same family that have root structures that are similar but are found in terrains with more soil that's not really telling us any support or not weakening either the claim that the um these plants are ultimately using these acids to not only create channels for continued growth but also to release phosphates to provide the vitam nutrient phosphorus so this really doesn't weaken it doesn't support either um it's it's for the most part unrelated so we can get rid of a based on that so that would fit into sort of um the neutral or unrelated category for the most part if we take a look at B we have though BT and BM both secrete citric and malic acids each species produces these acids in different proportions okay this right here it's not supportive of our hypothesis it's not weakening our hypothesis it's just neutral and unrelated so fits in into pretty much the same bucket as answer Choice a would there okay if we take a look at option C now we have the roots of BT and BM carve new entry points into rocks even when cracks in the surface are readily available all right well if we go back up to our hypothesis okay we know that if these roots are or these cracks are already available readily available we would expect that if they didn't need the phosphorus they would just grow into the cracks okay because they wouldn't need to ultimately create these new cracks which is more costly and requires more energy from the actual plant itself to make these new cracks okay so this is actually supportive of that hypothesis right because if they were to just take the cracks that were already entered not create new ones then that would support the idea that or that would weaken the hypothesis and support the idea that they don't actually need the phosphorus but because they are actively carving new entry points into the Rocks even though the cracks are already available and they're not just growing into the cracks this supports the idea that they would need to do that in order to get the phosphorus okay so we know our answer there is going to have to be C we can take a look at d as well because uh let's see what wrong Choice bucket that falls into so I can teach that we have BT and BM Thrive even when transferred to the surfaces of rocks that do not contain phosphates well if they're thriving on rocks that don't contain phosphates that would weaken our hypothesis that BT and BM need to get phosphorus from these rocks by carving in these new entry points okay so if they're thriving without phosphorus then that would weaken that hypothesis okay so D would fall into the bucket of being the opposite of what we need so the opposite in this example would be something that weakens our hypothesis now now if our question was What would most directly weaken the hypothesis then D would be right and C would actually be the opposite okay so I wanted to point out those wrong answer Choice Types on questions that are asking you to support or weaken a hypothesis or a claim here's one of the biggest things you need to watch out for on the digital sat reading section when asked to logically complete text so the way I would approach question 17 is I'd start by taking a look at the prompt in this case we just got Which choice logically completes the text then I'll go back up and I'll start reading so we have herbivorous sarod dinosaurs could grow more than 100t long and weigh up to 80 tons and some researchers have attributed the evolution of sods to such massive size as to increased plant production resulting from high levels of atmospheric carbon dioxide during the mesic ERA this case we have researchers attributing something so I'll mark that with an A so any sort of hypothesis claim attribution along those lines or speculation I will Mark with a letter in this case a for attribution and I'll keep reading however there is no evidence of significant spikes in carbon dioxide levels coinciding with relevant periods and S OD Evolution such as when the first large sods appear when several sorod lineages underwent further Evolution toward gigantism or when sods reached their maximum known sizes suggesting that blank okay well as you can see we have a contrast here and then we go on to describe that there's no evidence for the attribution so I got no evidence I'm underline that I'll draw the arrow back to attributions so we know that there's no evidence for that all right suggesting that what we have option A fluctuations in atmospheric carbon dioxide affected different sorod lineages differently well once again we have no evidence for fluctuations in atmospheric carbon dioxide okay so no evidence for these fluctuations so I can get rid of a we can go move on to B we have the evolution of larger body sizes and sods did not depend on increased atmospheric carbon dioxide okay we know that in our attribution we thought that it did depend or at least coincide with this increase increased plant production resulting from high levels atmospheric carbon dioxide but we know there's no evidence of significant spikes in carbon dioxide levels okay so we would then that the evolution of larger body sizes did not depend on increased atmospheric carbon dioxide okay so there's evidence to support that so we can go ahead and Mark B is our answer I'm going to quickly go over C and D as well and we can discuss which box of wrong answer choice they fit into because there are common types of wrong answer choices on the digital sat reading section so here we have C atmospheric carbon dioxide was higher when the largest known sods lived than when it was than it was when the first Sor pods appeared well once again if we go back up we state that there's no evidence of significant spikes in carbon dioxide levels coinciding with relevant periods in sarod evolution okay so there is no support for that Spike okay so we can get rid of this based on this part here the atmospheric carbon dioxide was higher when the largest known sods lived okay we don't know that so we can get rid of C if we take a look at D now we have sods probably would not have evolved to such immense sizes if atmospheric carbon dioxide had been even slightly higher so there's a few things wrong with this okay for one this isn't even supportive of the high hypothesis or the attribution okay so it's not even supportive of that we know the attribution is wrong okay we also know that we never state that sods could not have evolved to such immense size as if atmospheric carbon dioxide had been even slightly higher so there's no evidence for this okay so we can go and get rid of it based on the fact that there just is no evidence okay so our answer there would have to be B so what I want you to take away from this is a couple things for one on this question type which is a fairly common one which Choice logically completes the text I want you to Mark any claims hypothesis attributions conclusions things along those lines I want you to mark them with their coinciding letter um or underline them whatever marking use is up to you okay the next thing is you want to be deliberate about going back to the text okay because often times you saw as we went through these answer choices you'll need to go back to see what logically makes sense and that's especially true for science texts like this okay this is ultimately a science passage okay for science-based passages you will very often you to go back to the text okay find what evidence there is to support what's coming after or what's completing the text here's a second example of how I recommend approaching questions that ask you to logically complete text on the digital sat reading section so I'll illustrate this question 18 in documents called judicial opinions judges explain the reasoning behind their legal rulings and in those explanations they sometimes cite and discuss historical and contemporary philosophers legal scholar and philosopher Anita L Allen argues that while judges are naturally inclined to mention philosophers whose views align with their own positions the strongest judicial opinions consider and rebut potential objections I'm going to mark this with a claim okay it says she's arguing this so you could mark it with an a you can mark it with a c I guess in this case I'll mark it with an a for aru this is her argument okay discussing philosophers who views conflict with the judge's views could therefore what okay so we have discussing philosophers views who conflict with judges views could okay well we know that her argument is that while judges are naturally inclined to mention philosophers whose views aligned with their own positions the strongest judicial opinions consider and rebut potential objections okay so discussing philosophers whose views conflict with judge's views she would you would therefore strengthen their arguments okay so we have option A allow judges to craft judicial opinions without needing to consult philosophical works well it's actually the opposite okay it would force judges to craft judicial opinions with instead of without with needing to consult philosophical work since they would have to consult works that they're not familiar with or ones that they disagree with so they would need to consult them so we can get rid of a okay a essentially has sort of the incorrect relationship in terms of with versus without okay let's go and take a look at B now we have help judges improve Pro the arguments that they put forward in their judicial opinions well we know that that is her argument her argument is that the strongest judicial opinions consider and rebut potential objections therefore discussing philosophers whose views conflict with judge's views could therefore improve the arguments that they put forward in their judicial opinions okay so this is ultimately going in line with what she is arguing okay so our answer there would have to be B I'm going to take a look at C and D as well so we can teach a little bit based on those we have C make judicial opinions more comprehensible to readers without legal or philosophical training well we never discuss legal or philosophical training or the comprehensibility to readers that's not the goal of this the goal isn't um in discussing with conflicting philosophers views the goal isn't to make it more comprehensible to the readers the goal is to make it a stronger argument okay so this would be trying to achieve a separate goal or a different goal from what is actually stated by Anita L Allen okay so this would be if you were not um if you misinterpreted basically the argument that she's trying to make or the goal behind this if we look at D we have bring judicial opinions in line with views that are broadly held among philosophers well for one thing philosophers hold many different views okay so that wouldn't really make a ton of sense but also the goal isn't to bring the judicial opinions in line with the views of philosophers the goal is just to strengthen the argument this all goes back to understanding and identifying Anita L Allen's argument okay her argument once again I will go back up is that well judges are naturally inclined to di menion philosopher whose views align with their own positions the strongest judicial opinions consider and reut potential objections and then when we go on we know that we're specifically looking at and I'm going to underline this again we're specifically looking at this section the strongest judicial opinions consider and rebut potential objections we know we're looking specifically at that because we state that disgusting philosophers who views conflict with judges views could therefore do what okay and since we're talking about how to um since we're talking about views that conflict with the judges okay that's the potential objections that I underlined here so it would have to be that it makes the judicial opinion stronger in order to continue this idea okay so answer there has to be be as far as what I want you to take away from this a couple things I talked about this in the last question I went over that dealt with completing the text but you want to make sure that you're marking any arguments claims hypotheses conclusions with a letter or some sort of other marking so that you know how to go back to that in the text the other thing is if you can I talked about this in a question type that was different than completing the text but but you want to make sure you're understanding where to go back to okay so in this case you saw that we really really focused in on the strongest judicial opinions consider and rebut potential objections okay and the reason is that that is what is directly discussed in this next part discussing philosophers whose views conflict with judges views that is the potential objections so as you can see most of that text pretty much the whole first half were really not very concerned with so generally on the SAT reading section and this is not specific just to this question type if you can limit where you're going back to in the text to just where it is necessary in order to answer the question correctly that will help you there will be times when you need to you know go through more of the text or maybe even all of the text when going through an answer Choice um and that's okay that does happen but on certain questions you can keep the scope of text that you need to refer back to more limited and that will help you save some time here's how I recommend you approach questions on the digital sat reading section that asks you to fill in a quotation to effectively illustrate some sort of claim okay so the first thing that I would do if I had just scrolled down to question 12 is I would identify in this case I need to effectively illustrate a claim I would underline the fact that it's a claim okay so I'm going to mark my claim as I do this readr so we have o Pioneers is a 1913 novel by will a Cather in the novel Cather portrays Alexandra bergson as having a deep emotional connection to her natural surroundings okay the claim here is that bergson has a deep emotional connection to our natural surroundings that's the claim okay so now we just need to go a b c find one that supports that so the question that you need to ask yourself after you read through each answer Choice here is does this support the claim okay or does this illustrate the claim rather okay illustrate does it illustrate the claim so let's go and start with a she had never she had never known before how much the country meant to her okay so this is illustrating that she cares for the country the trapping of the insects down in the long grass had been like the sweetest music she had felt as if her heart were hiding down there okay so it felt as if her heart were hiding down there somewhere with the quail and the Plover and all the little wild things that CED or buzzed in the sun okay so obviously she has an emotional connection here feels her heart is hiding down there under the long shaggy ridges she felt the future stirring so clear that she has a deep emotional connection to Nature from answer Choice a okay so obviously that is illustrating the claim I'll quickly go over b c and d as well because it can be helpful to understand why wrong anes are wrong so we have B Alexandra talked about talked to the men about their crops and to the women about their poultry she spent a whole day with one young farmer who had been away at school who was experimenting with a new kind of clover head she learned a great deal so some people might look at be and say okay it talks a ton about nature that must be the answer but it's not because we have to keep in mind the entirety of our claim if we scroll up we see our claim is that she has a deep emotional connection to her natural surroundings okay answer chice B while it talks about nature it does not show or illustrate that she has a deep emotional connection to Nature it is just talking about her um sort of learning more about nature okay but not showing she has a deep emotional connection to it I can learn about football that doesn't mean I have a deep emotional connection to football okay so that's that's why B would have to be wrong there okay so understand that just because we talk about one of the topics mentioned in the claim does not mean we are illustrating the claim if you look at C we have Alexander drove off alone the rattle of her wagon was lost in the howling of the wind but her Lantern held firmly between her feet made a moving point of light along the highway going deeper and deeper into the dark country okay once again even though we are talking about going into the dark country which can be pertained or could be you know thought of as going deeper into possibly nature if you were to associate country with nature which is a pretty fair Association it does not support once again the fact that she has a deep emotional connection to her natural surroundings okay so you have to make sure that you are illustrating the entirety of the claim and not just talking about one of the topics of the claim which would be nature in this case if you look at D we have it was Alexander who read the papers and followed the markets and who learned by the mistakes of their neighbors it was Alexandra who could always tell you about what it had cost to fatten each steer and who could guess the weight of a hog before it went on the scale closer than John bergson her father himself okay so a couple things I want to point on on this one okay first off at the end here when we talk about how she could guess the weight of a hog before it went on the scales closer than her father himself that's probably indicating that she grew up close to Nature close probably on a farm okay since she's able to guess the weight of a hog better than her father is so presumably she has done a lot of work on a farm so that's kind of what that is indicating but I could once again kind of the same similar example to football right if I had worked on a farm for a long time that does not necessarily mean I have a deep emotional connection to Nature it just means I've worked on a farm for a long time and probably know how much a hog weighs okay so you cannot associate that that does not illustrate having a deep emotional connection with nature okay so that's the problem with d so I think the key thing I want you to take away from um this question and sort of this example is number one the way you approach this identify what you need okay in this case you have to first identify the claims we identify the claim in this case we need to illustrate that claim so we go through a b c and d okay find which one illustrates that and recognize that we need to actually illustrate it we cannot just mention or talk about the topic okay in this case it was nature but it could be another topic it's not enough just to discuss the topic or put the character in a setting where the topic is you have to actually illustrate the entirety of the claim here's a second example of a question where you're asked to provide a quotation to affect itively illustrate a claim okay so this is very similar to the last question in this case we are dealing with a poem however there's also one other thing I want to point out with this question which is why I wanted to include it here so we have question 12 to you is an 1856 poem by Walt Whitman and the poem Whitman suggests that readers whom he addresses directly have not fully understood themselves writing all right well first let's go and identify the claim okay the claim is that the readers who he's addressing directly have not fully understood themselves guys that's the claim they have not fully understood themselves okay now we got to keep in mind this is a poent so let's go and go through our options we also need to understand that he's writing this poem directly to the reader it's called to you okay so we need to understand the perspective of the reader the perspective is he's addressing them directly okay and that's stated up here that he's addressing them directly so perspective is something you need to pay attention to on the SAT reading and writing section so just recognize that if you come across a poem especially you're going to want to be able to recognize perspective um narratives as well but in particular poems okay so let's go ahead and look through our options we have option A you have not known what you are you have slumbered upon yourself all your life your eyelids have been the same as closed most of the time okay you have not known what you are you have slumbered upon yourself okay sleep is sort of a signifier for not fully understanding yourself but if you're looking for something even more explicit you have this first part before the comma you have not known what you are you do not understand yourself okay is essentially what he is saying and when you take into account perspective when he says you have not known what you are he is saying you have not fully understood yourself okay so a is perfect there let's goad and talk about b c and d as well okay so we have option b these immense Meadows these interminable Rivers you are immense and interminable as they well him calling the reader in that case is us because we are the reader here immense is not stating that we have not fully understood ourselves so we can get rid of B that is not illustrating the claim if we take a look at C I should have made my way straight to you long ago I should have blabbed nothing but you I should have chanted nothing but you once again that is not showing that or is not illustrating that we have not fully understood ourselves so we can get rid of C okay now we get into D and D is where perspective really comes into play okay option D States I will leave all and come and make hymns of you none has understood you but I understand you so what many people will do here is they will see none has understood you and they will translate that into thinking that D has to be the answer because if we scroll up the claim is that Whitman suggesting to the readers who he's addressing directly that they have not fully understood themselves but this is where perspective comes into play if I say to you my viewer right now no one has understood you would you interpret that to mean that you yourself have not understood you probably not okay if someone says to me no one has understood you Hayden I would not interpret that to mean that I myself have not understood myself okay so this is where perspective comes into play because he is addressing us directly we need to to recognize and interpret this as no one has understood you that is not the same as saying that you have not understood yourself because of the perspective here okay so that is the problem with answer Choice D okay D is stating I will leave all and come make the hymns of you none is understood you but I understand you okay so ultimately we can get rid of D we see our answer has to be answer Choice a here's how I recommend you approach questions on the digital sat reading section that ask you to use data from either a table graph or any sort to support or weaken any sort of claim or hypothesis or conclusion okay so I'm going to illustrate this with question number 15 the way I would start is I'd start by reading through the passage so I have Alicia Monte cosos Navaro Isabelle stoer and Rosio Perez Bales recently examined several plots within a diverse plant community in southeast Spain the researchers calculated that if individual plants were randomly distributed on this particular landscape only about 15% would be with other plants and patches of vegetation so one thing that will jump out to me here is the fact that it's randomly distributed okay anytime that I see something's randomly distributed I'm usually going to pay attention to it um that goes for the reading section as well as the math section actually um but we'll keep reading they counted the number of juvenile plants of five species growing in patches of vegetation and the number growing alone on Barr and compare those numbers to what would be expected if the plants were randomly distributed okay which we obviously have up there based on these results they claim that plants of these species that grow in close proximity to other plants gain an advantage at an early developmental stage so here we have a claim okay anytime we have a claim hypothesis conclusion anything along those lines I will always mark it okay because that makes it easier for me to come back and find it later so which Choice best describes data from the table that supports the claim so we're looking to support this claim if we take a look at the table now and that is what I will do okay before going to the answer choices I will actually go back to the table now I will note that this is a case where it can be somewhat of a personal preference for me personally I would prefer to go back to the table find what data is supporting this claim and then look through the answer choices for some people they may want to go straight to the answer choices I would recommend that you go to the claim or go from the after reading the claim after reading the prompt going to the table I just find that it makes it easier to avoid getting misled by some of the an choices but um you know you can kind of make your own decision there so let's go ahead and go through this we've got to support the claim that species that grow in close proximity gain an advantage at an early developmental stage we have juvenile plants found growing on bare ground and then patches vegetation for five species we got the five species got the number found in be ground found in patches vegetation we we got the total we got the percent found in patches of vegetation now one thing that we need to keep in mind here is that if they were randomly distributed we'd expect that 15% would be with other plants in patches of vegetation so we would expect that the percent found in patches of vegetation would be 15% okay so 15% and that's for individual plant so it doesn't give a a name on the species so I would just expect 50% in all of these then 15% as we can see we don't have that we' have above 50% all of them which is more than three times what would be expected okay so that's really the evidence I'm looking for is pretty much stating um pretty much all of this column of this table um is obviously more than three times what was expected so let's go down and look at our options okay so we have option A for all five species less than 75% of juvenile plants were growing in patches of vegetation well that is not supporting the claim okay so we can get rid of a we need to focus on the fact that it's three times what would be expected compared to random distribution we got B the species with the greatest number of juvenile plants growing was H sto Stow okay we don't really care um about one particular species versus the other okay we used five species if we look back up at our text but we're not really concerned with a comparison of the species Okay so we've got option C we got for T Li lianes and T morido the percentage of juvenile plants growing in patches of vegetation was less than what would be expected If plants were randomly distributed well we actually see that it's more than what would be expected If plants were randomly distributed so this would fall into the bucket of wrong answer choices that is um the incorrect um I guess in this case it's a a misinterpretation okay because it's actually stating it's really just misinterpreting the data it's stating that it's a less than what would be expected but it's actually more okay so this would just be a misinterpretation of the data we've got option D now for each species the percentage of juvenile plants growing in patches of vegetation was substantially higher than what would be expected if the plants were randomly distributed okay we see that that's true according to the data okay as you can see by going back to the table first and finding what data from the table would support that claim okay I was able to have an idea of what I'm looking for before going into the answer choices here's a second example of how I recommend that you approach questions on the digital sat reading section that ask you to use data for some reason whether that's to support or weaken some sort of claim or in this case to complete an example so first thing I would take a look at is the prompt okay we've already gone over that so from here instead of going straight to the data I'm going to go ahead and go to where I have my passage so we have some researchers studying indigenous actors and filmmakers in the United States have turned their attention to the early days of Cinema particularly the 1910s and 1920s when people like James Young Deere Dark Cloud Edwin Kare lilan St seir known professionally as Redwing were involved in one way or another with numerous films in fact so many films and Associated records of this era have been lost that counts of those four figures outputs should be taken as bare minimums rather than totals it's entirely possible for example that okay we have for example so we need to discuss what we're getting an example of well ultimately we state that um so many films and Associated records have been lost that counts for these figures outputs should be taken as bare minimums rather than to rather than totals it's entirely possible for example that blank okay so we'd be looking to discuss how um it looks like in our table we've got number of films known and commonly credited and then we have years active in the individual credited credited film output keep in mind since this is the credited film output we've discussed how that's a bare minimum not a total and then we're stating it's entirely possible okay since we're saying it's possible that um these are bare since these are bare minimums it would be possible that our numbers would be higher than what's in this table then okay so um which Choice effectively uses data to complete the example okay in this case like on the last question I prefer to go back to the T data table okay and try to figure out how I can use that to in this case I need to complete the example in the past example it was supported claim so to complete the example it's much more difficult to actually come down with an idea of what you're looking for but in this case um looks like we're just going to be looking for an example that provides greater numbers than what's in here for all these for all these uh these rows because what's in these rows is really just to be bare minimums is what we're told not the actual total so we've got option A Dark Cloud acted in significantly fewer films than did St lilan Lilian St Seer Who is credited with 66 performances well that's not providing an example okay keep in mind we need to provide that example because that's what we're told we've got B Edwin CES 47 credit acting roles include only films made after 1934 well if we go up we've got years active 1912 to 1934 for Edwin K uh his 47 acting roles include only films after 1934 well we got 47 acting rol here we see that that's from 1912 to 1934 so B is incorrect according to the data so we can get rid of that we can go down we can look at option C we have Lilian Saint SE acted in far more than 66 films and Edwin K directed more than 58 so Lilian Saint SI we can find where she is we have got 66 here okay this is the amount that she's credited for we know that we're looking for that being a bare minimum and that she actually did more than that so this makes sense next we have Edwin K directed more than 58 we see Edwin K uh was credited as the director for 58 once again we're stating that he did more than that which is in line with an example that these are bare minimums and not totals okay so C looks perfect we'll take a quick look as at d as well D states that James Young Deere actually directed 33 films and acted in only 10 okay we can find James Young Deere we see that he's credited with 33 okay and he's credited as the writer for uh 10 so 33 actor and writer for 10 uh so in this case it's stating that he actually directed 33 films oh okay he stayed as the director for 35 so that'd be less than so that is not an example so that actually be the opposite of what we are looking for so you can put that in the bucket of an opposite um for the wrong answer Choice okay so answer there would have to be answer Choice C okay so the key thing I want you to take away from these last two examples so you have a question like this where you're asked to use data for you know something or another on the SAT reading section that I recommend that you would approach it would be you start by taking a look at the prompt from there go to the passage once you're done with the passage figure out what you need from the data go back to the data once you're done going back to the data have an idea of what you're looking for in your answer choice to either support weaken whatever you need then then go to your answer choices in this section of the course you'll see me solve over 150 practice problems from the released digital SAT practice test for each question I try to explain the strategy I'm using along with any tips tricks or advice I have for similar questions I'm teaching these Concepts through released practice questions because it allows you to not only learn the math required to be able to solve these questions but also learn how to best apply them to the digital sat here's how to answer this sat math question in under 30 seconds the question States the line graph shows the percent of cars for sale at a used car lot on a given day by model year for what model year is the percent of cars for sale the smallest well we see on our y- AIS we have the percent of cars for sale and we just have to find where that's the smallest we see that that's in the year 2014 so our answer is going to be answer Choice C here's how to answer this probability question on the SAT question two states for a particular machine that produces beads 29 out of every 100 beads it produces have a defect a bead produced by the machine will be selected at random what is the probability of selecting a bead that has a defect in this case we are looking for those that have a defect which we know is 29 out of every 100 so we know that probability of that must be in Choice C 29 out of 100 here's how to answer this question about intersecting lines on the SAT question three states in the figure line M is parallel to line n and line T intersects both lines what is the value of x well since M and N are parallel line T is intersecting them we know that X is going to be the same as the angle X I just drew next to that angle 33 now we also know that a semicircle has 180° in it so all we have to do is 180° - 33° and that will give us our answer of 147° as the angle X so our answer is D here's how to find the Y intercept of this graph on the SAT the question States what is the Y intercept of the graph shown all you got to do is find when we're crossing that y AIS where X is zero and we see that that is at 8 so our answer there is going to be 08 here's how to solve this sat math question in under 60 seconds the question States the total cost F ofx in dollar s lease a car for 36 months from a particular car dealership is given by F ofx equal 36x plus 1,000 where X is the monthly payment in dollars what is the total cost to lease a car when the monthly payment is 400 we know the monthly payments are represented by X so we can go and substitute 400 in for x and we will have 36 * 400 + 1,000 and that will end up giving us our answer of $15,400 which is answer Choice C here's how to solve this question about perimeters on the SAT question Six States each side of a square has a length of 45 what is the perimeter of a square well we know squares sides are all the same so the perimeter will just be four times the side length which we know is 45 we can go ahead and put 4 * 45 in our calculator or you can just do it in your head and you're going to get 180 for your answer as the perimeter of the square here's how to solve this sat math question that deals with factoring question seven states what is the positive solution to the given equation in order to solve this we need to ultimately get it set equal to zero so let's go ahead and do that by multiplying both sides by x + 6 once we do that we have x * x + 6 well also go ahead and subtract 55 from each side so we can set it equal to zero and now we have our equation so let's go ahead and distribute this x to this other X to get x^2 and then also plus 6X so now we have x^2 + 6x - 55 is equal to zero now let's go and Factor so I'm looking for factors of 55 that will sum to have positive six so when I do that I can think we've got 11 and five um I need to keep it positive so I'm going to have to have x + 11 and I would have to have x minus 5 now we Factor we have to keep in mind that we can't just pick either one we need to have the positive solution to the given equation so we know that x + 11 will ultimately mean that X could equal -1 but we can't choose that cuz that's negative we need to have x = 5 so our answer there would be five here's how to translate this word problem into an equation and solve it on the SAT question 8 States an object travels at a constant speed of 12 cm/ second at the speed what is the time in seconds that it will take for the object to travel 108 CM well this is pretty easy the distance that you're traveling is 108 CM you want to know how long it's going to take you you are traveling at 12 cm/ second okay you're multiplying by your time in seconds okay we'll have t represented as time in order to solve for T then all you got to do is divide 108 by 12 to get your answer when you do that you're going to end up with your answer of nine which is the answer Choice a here's how to solve this question about comparing the mean of two data sets on the SAT question n States the list gives the values in data sets X and Y which statement correctly compares the mean of data set x with the mean of data set y well let's go and find the means of both we'll start with data set X so the mean is going to be the sum of these numbers divided by four so 5 + 9 + 9 + 13 now I see I have these same numbers in data set y now I also have a 27 addline to data set y now since we've got the same four numbers in data set X as in y and then we are just adding in 27 we know 27 has to be greater than whatever the mean is in data set X because the maximum value in data set X is 13 and 27 is higher than that so it's going to have to bring that mean up therefore we know that data set y has to have a larger mean than data set X without even have to calculate the means just by looking at this so we know our answer there has to be B if you want to calculate the means for this you can but you could also just recognize that 27 is larger than the maximum data set X other than that they're the same therefore data set y has to be a larger mean here's how to solve this sat math question in under 60 seconds question 10 states a rocket contained 467,000 kg of propellant before launch exactly 21 seconds after launch 36215 kg of the propellant remained on average approximately how much propellent in kilograms did the rocket burn each second after launch while our starting amount of propellent is 467,000 we then have to subtract how much propellant remained and then we have to divide all of that by the amount of seconds that this took place which is 21 seconds once we put that into our calculator we're going to end up with the answer Choice a and that'll give us exactly or approximately how much propellent in kilograms the rocket burned each second after launch here's how to use ratios to move faster on the SAT Math section question 11 states if 4x + 2 = 12 what is the value of 16x + 8 whenever I see a question like this I'm always looking for proportions I see 4x + 2 If I multiply that by 4 I get 16x + 8 so all I got to do is multiply 12 by 4 12 * 4 is going to equal 48 So my answer is 48 my answer there is B this way I don't have to solve for so I get it done faster here's how to interpret a common situation on the SAT Math section question 12 States an object is kicked from a platform the equation h 4.9t plus 7 t plus 9 represents the situation where H is the height of the object above the ground in meters T seconds after it is kicked which number represents the height and meters from which the object was kicked okay a common question on the SAT deals with something falling from some certain height whether it's thrown off kicked off launched off things like that and the way that it's usually represented is in an equation like this in this casee we're asked which number represents the height from which the object was kicked well the height at which it is kicked is when it time is at zero right it it's only kicked once the time is zero so that means T would be zero which makes this zero which makes that zero which means that nine is the height when it is first kicked so our answer there has to be D here's the type of question where you should use Desmos on the digital sat question 13 states that F ofx equal 4x^2 - 50x + 126 the given equation defines the function f for what value of x does f ofx its minimum if I saw a question on like like this on the new digital sat I would use Desmos for it 100% I would just check where the minimum is so I'll go and show you how you would do that all you got to do pull up Desmos you can do this on the digital sat it's built into the college boards Blue Book so you put in the equation you look for where the minimum is the minimum is at 6.25 for the x value of the minimum so your answer there would be 6.25 so this is a great example of the type of question where it really does make sense to use Desmos on the new digital sat here's how to set up and solve the system of inequalities question on the SAT question 14 States a small business owner budgets $2,200 to purchase candles the owner must purchase a minimum of 200 candles to maintain the discounted pricing if the owner pays $4.90 per candle to purchase small candles and 1160 per candle to purchase large candles okay I'm using S for small candles I'll use l for large candles what is the maximum number of large candles the owner can purchase to stay within the budget maintain the discount pricing so we only have two candle sizes so we can go ahead and determine the total number of candles would be L plus S I want to quickly point something out you saw as I read through this I was writing out the system of inequalities as I go if you encounter a question on the SAT Math section that is three lines or longer it is most likely going to end up being a question that involves either system of inequalities two equations that you need to set up um possibly something to do with converting units something along those lines but either way my general recommendation is if a question is three lines are longer on the SAT Math section you try to write down units variables and obviously like the code efficients in front of certain units um any sort of constants things like that basically you want to start writing your equation as you read through the word problem because otherwise if I hadn't written down these two inequalities I would have to go back and do a second read through so this is a strategy that I use and that I recommend you use to save time that being said let's go ahead and solve for the number of large candles one thing I want to point out here is you'll notice I'm solving for L right away not s that's because I don't give about S I don't care about s at all right we don't need s we just need l so that's all we're going to focus on solving okay so I'm going to go ahead and subtract uh I'm sorry we're going to subtract L from each side we want to isolate s and the reason why is we want to substitute in for S something with L okay so let's go ahead and get S by subtracting L from both sides we get 200us L is going to be less than or equal to S now we can go and substitute in okay so let's go ahead and substitute that in for S okay so we got 4.9 * s which we know we can represent as 200 minus L okay and keep in mind that we still have a plus 11.6 L right here so let's go and distribute the 4.9 to the negative L into the 200 4.9 * 200 is going to give us 980 okay so equals 980 then we're going to have - 4.9 L and plus 11.6 L which will give us plus 6.7 l in total okay because 11.6 L minus 4.9 L gives us that plus 6.7 L now that all is still going to be 2200 over there we'll subtract 980 from both sides minus 980 that's going to end up leaving us with 1220 20 is going to be greater than or equal to 6.7 L okay from there we would divide both sides by 6 . 7 so we'll go ahead and do that divide both sides by 6.7 okay 1220 ID 6.7 go ahead and put that in my calculator that's going to be 18209 okay 182 point I'll just call it 0.1 okay it's 09 all right now we have to see that L has to be less than or equal to that okay so in order to be less than 1821 we would go to 182 we can't have 0.1 of something okay so our answer there in this case we can't because we can't 0 one of a candle right so our answer there would be 182 so we go ahead and write that down and we'll Circle that so 182 there's our answer here's how to solve this sat math question in under 30 seconds question 15 states in the linear function f f of 0 is equal to 8 and F of 1 is equal to 12 which equation defines F immediately I see I have that F of 0 is equal to 8 which means that my Y intercept is 8 I see all of these are in slope intercept form and I see The Intercept of c and b is not eight so I can get rid of them next thing I see is the difference between a and d is the slope if I look at my slope I'm going over one and I'm going up by four so my slope is four So my answer answer there has to be answer Choice D here's how to interpret this SAT Math problem question 16 states that the function f of w is equal to 6 W ^2 gives the area in the area of a rectangle in square feet if its width is W feet and its length is six times its width which of the following is the best interpretation of f of 14 is equal to 1,176 all right well ultimately this function is giving us our area we know that W represents our width so F of 14 means that our width is 14 ft and then that 1,176 means that when our width is 14 ft our area of our rectangle is 1,176 Ft that's answer Choice a so a is our correct answer there here's how to answer this SAT Math problem about Arc lengths by using ratios and proportions question 17 states that the circle shown has Center o circumference 144 pi and diameters PR and Qs the length of Arc PS is twice the length of Arc PQ so we'll call Arc pqx and the length of Ark PS we know is twice that so we'll call that 2x I'll go ahead and Mark those lengths here okay next thing we are asked is what is the length of Arc QR well Arc QR is going to be the same length as Arc PS so I'm going to go ahead and focus on solving for PS just because it's easier for me to show on this video so if we go ahead and draw this we see that it's X plus 2X so that's going to be 3x we also know our circumference is 144 Pi if our circumference is 144 Pi our circumference is that whole line around the circle right it's all of this that line right there okay so our circumference is 144 4 Pi then that semicircle right that semi Arc semi Arc is going to be 72 Pi okay so then we know that 72 Pi is equal to 3x right because it's the sum of that 2X and that X therefore you would know that PS which is the same as QR okay is 2/3 2/3 of that okay so it' just be 72 Pi just be 72 Pi * 2/3 okay and when you put that in your calculator or you can just do it in your head you're going to end up with 48 pi as the value for Q to R you could have also it by doing that 72 Pi is equal to 3x okay and then solving for x and then taking it in and multiplying it by two but easier ways just to recognize that hey this is a ratio right it's 2/3 2/3 * 72 Pi gets you 48 Pi it's a lot easier than going through and solving for x so I wanted to put the X down there just so you guys could see and understand sort of how it breaks down but ultimately it's a lot better if you can just recognize hey this is a ratio we've got half of this whole circumference is 72 Pi we are taking 2/3 of that to get Arc of QR so answer there is B here's a couple tips for the SAT Math section to help you be more efficient I'm going to illustrate them with question 18 question 18 states a company that provides whe watching tours takes groups of 21 people at a time the company's revenue is $80 per adult so I'm going to represent that as 80a and $60 per child which I'll represent as 60 * C if the company's revenue for one group consisting of adults and children was $1,440 okay so that's going to be the sum of these the value of the number of adults time the cost per adult plus number of kids times cost per kid how many people in the group were children well we know that consists of adults and children so we can represent that as A+ c as you can see I did one read through and I have both my equations so that's tip number one here as you read through an SAT Math problem that is three or more lines as you can see in this case it was six that's why I knew that I wanted to use this sort of this sort of tip or trick anytime you've got an SAT Math problem longer than three lines try to write out the equation or the system of equations as you read through that way you save time by not having to read do a read through right right afterwards to find your variables and things like that okay that being said let's go ahead and keep talking because there's more tips to come here now keep in mind we are asked to solve for how many people in the group were children so you could go through and you could solve for a first and then get to C but you shouldn't do that you should go ahead and solve for C first you want the most direct path to your answer on the SAT Math section because it's a timed exam and you want to be efficient so we're going straight for C we're not we don't want to get a we don't need it so we won't we just don't want to even see it all right so here's what we're going to do we're going to substitute in a value with C for this a value there the way we do that is by subtracting C from both sides to get 21- C is equal to a now we go ahead and sub substitute in okay so it will be 80 * 21 - C + 60 C is equal to 14 we go ahead and distribute our 80 to our 21 and to our C 80 * 21 is going to be 1680 and then we are also going to have Min - 80 C + 60 C is going to equal 14 now we want to start isolating our C so - 80 C and plus 60 C is going to leave us with -20 C okay and we're also going to go ahead and subtract 1680 from both sides okay subtract 1680 from both sides this is going to leave us with 240 or I guess -240 is equal to -20 C now from here we're going to go ahead and divide both sides by -20 -240 ID -20 is going to leave you with your answer of C is 12 so our answer there will be answer Choice C because we have 12 children and as you can see by solving for the number of children first we don't have to go back through and solve for the number of adults we never have to know the number of adults if you wanted to go back through and see obviously you could just put in the number 12 there for for C but uh it's not necessary you don't need to know the number of adults so don't care about it don't need to focus on it just get the number you need to get to and move on to the next question here's how to find x and y intercepts quickly when you have an equation in slope intercept form question 19 States the function H is defined by h x equal 4x + 28 the graph of yal H of X in the XY plane has an X intercept at a and z and a y intercept at 0 B where A and B are constants what is the value of a + b well in this case there's no way to just get to a plus b normally if I see something like that that's what I'd like to do in this case you have to actually find both A and B so in this case let's go and start by finding a we see that a is where our yv value is zero well where our yvalue is 0 we have 4x + 28 is equal to 0 we subtract 28 from both sides and we get -28 is equal to 4X we divide both sides by 4 -28 over 4 is going to equal -7 as the value of x now let's go ahead and solve for our B value and keep in mind that X there would equal that a value okay so a is-7 now let's go ahead and solve for what B is equal to okay B is where our x value is zero so we just put in zero there and we see that we ultimately are going to get 28 okay so we asked for the value of a plus b so we just do 28 + -7 which is the same as 28 - 7 that's going to leave us with 21 so our answer there is a here's an example of an SAT math question that's gotten way easier now that the SAT has gone digital question 20 States one of the factors of 2x CU + 42x 2 + 28x is X plus b where B is a positive constant what is the smallest possible value of B now keep in mind you need the smallest possible value of B and that's important here because there's going to be two possible answers but I want to show you why this question is so much easier now that you have Desmos built into Blue Book on the the digital sat before you would have to factor this out and that could be a bit difficult and there's a lot of room for when you're doing that but now that you have Desmos in the blue book app when you're taking the digital sat you can just put it into Desmos now you have to also understand how to work the problem with Desmos so in this case you know that you need the value X plus b now what that means is that you're looking specifically in this case at the negative X values or the negative X values on in regards to the x intercept right so let me go ahead and zoom in here the reason that we're going to the negative section is because it can't be a positive number because these are ultimately our zeros they're not our values for B okay our zeros here and as you can see the first negative or the first zero there is at8 okay now that does not mean negative 8 is our answer because it's not okay because you have to keep in mind that we're looking for the value of B and X plus b and X plus b since it's one of our factors has to be set equal to zero which means that X is actually going to equal negative B now we know our value for x okay our value for x is ne8 which means that B has to equal positive 8 okay so our answer there will be8 now you really need to make sure that if you are using Desmos which I do recommend you do you do take close account to the signs of values and you understand how to interpret these graphs because if you don't understand how to interpret these graphs but you try to use them it's not going to help you so as you saw when I looked here I had to understand that I'm looking for the value of B okay to get to that I need to understand how a factor works right the factor has to be set equal to zero and then once I find this value of x I have to remember to get that back to be so make sure that when you do use Desmos on the digital sat which I do recommend you do cuz helps a ton and makes you faster less prone to error that you do at least understand how to interpret these graphs here's what you need to know about questions that ask you about the number of real solutions to a quadratic equation on the SAT I'm going to illustrate this with question 21 question 21 states in the given system of equations a is a positive constant the system has exactly one distinct real solution what is the value of a whenever you have a question asking you about two real solutions one real solution is no real solutions or the number of real solutions it's basically testing do you know this crucial Rule and that rule is is B ^2 - 4 a c okay now this works when you have an equation quadratic equation that is set equal to zero okay so a quadratic equation looks like this and it's got to equal out to zero now I'll show you how we get to there in regards to this question in a second but first I want to explain this rule so b^2 - 4 a c if this value is greater than zero that means that there are going to be two real solutions now what if this value is equal to zero in that case there is one real solution and what if this value is less than 0 well if B ^2 - 4 a c is less than Z then that means that there are going to be no real solutions okay so zero real solutions okay I guess I should actually Express that as zero because that's the way it is commonly shown on the is zero real solutions okay with this being said I want to go ahead and go over how we apply this in this question okay so in order to get our b^2 minus 4 a value like I said we have to set it equal to zero in this case it is not set equal to zero yet we have to substitute in this - 1 and2 for y first so then we would end up with - 1/2 = x^2 + 8x + a okay from here I'm going to go ahead and add 1 and a half to each side so that we can get it set equal to zero so we can use this this rule of b^2 - 4 a c okay so then we have that much plus a plus 1 and2 now what I'm going to do is I'm actually going to pick essentially a random variable which I'm just going to call we'll use J now I'm trying to pick one that doesn't sound like a or look like a number let's use uh we're going to use Z okay and I'll try to make it very differentiated okay I'm gonna let Z equal a plus 1.5 all right so now I'm going to go ahead and substitute in Z for a plus 1.5 and you'll see why I'm doing this in a moment here okay so now we have our quadratic equation it's set equal to Z now we can do b^2 minus 4 a c now you may be wondering what's B what's a and what's C well I'll go and show you okay our a value is whatever coefficient is in front of this x squ since there's no coefficient in front of it it's one okay so our a value is one our B value is going to be8 it's whatever is in front of that X okay and our C value is the constant which in this case we're representing a z all right so B is8 so that's going to be squared 8^ squar is 64 okay so b^2 minus 4 * a our a value is 1 okay so we don't need to show that okay and then times C which we're representing as Z to represent that a plus 1.5 all right now we know that there has to be exactly one real solution which means we have to set it equal to zero now it's pretty easy to solve we're going to go ahead and add 4 Z to each side so we'll have 4 Z is equal to 64 we'll divide both sides by four to isolate Z so now we have Z all alone we know that Z is equal to 64 over 4 which is going to equal 16 okay so now Z is 16 well now that we have Z is 16 we can go back up here and we have 16 is equal to a + 1 and A2 I'm going to erase this so you can kind of see what I'm doing back up here 16 is equal to A+ 1 and A2 I subtract 1 and A2 from each side and I get 14.5 is equal to a okay so there's what you need to know about the number of Solutions on the SAT Math section along with this question as an example of how you can apply it here's how to quickly answer this sat math question by understanding zeros question 22 States f ofx is equal to x + 6 * x + 5 * x - 4 the function f is given which table of values represents Y is equal to F ofx minus 3 very important thing to here is to recognize is that f ofx is this equation we have to do that minus 3 there okay so what we can actually call this is I'm just going to scratch this out I'll call it Y and then I'll just add that minus three at the end it's the same thing all right so now we have our new equation Y the next thing that we see is that we have to find the table values that represents it the key thing that I'm looking for here is I want to find where I have a zero in parenthesis which we're going to have when X is sorry let me write that where you can see it uh we're going to have that where X is at6 because 6 plus 6 is 0 we're going to have that where X is neg5 because 5 plus 5 is z we'll have that where X is four 4 - 4 is 0 I'm going look for those X values in my table here I see all of them are in here okay so I know they're all there and any time I have one of these I'm going to have a yv value of3 because 0 * anything is going to end up being zero so then I just end up with 0 minus 3 okay as we can see a has to then be incorrect B has to be correct because it has all of these values of our zeros in this x side of the table and has ne3 for all of them so B is our correct answer here's how to quickly solve this sat math question by understanding the equation for exponential growth question 23 states that for the function Q the value of Q of X decreases by 45% for every increase in the value of x by 1 if Q of 0 is equal to 14 which equation defines Q well Q of 0 being 14 means that our Y intercept where X is0 is going to be 14 which means our initial value is 14 so we can get rid of A and B because their initial values are not 14 next thing we need to recognize is our growth rate okay or our growth factor we have q ofx decreasing by 45% for every increase in the value of x by one if we're decreasing by 45% that means our growth factor is 0.55 okay we're not getting bigger answer Choice D would mean that we are increasing decreasing so that growth factor has to be less than one so our answer there is C here's a trap to avoid on the SAT Math section question 24 States the graph of yal f ofx + 14 is shown which equation defines the function f many people will pick answer Choice C on this question because they'll see the Y intercept is two and pick answer Choice C but that's not correct and the reason why is because you have to pay close attention to the details on the SAT Math section this question States the graph of y = f ofx + 14 is shown and we're asked to define the function f not the function y not y = FX + 14 so the function f has to be down it has to have a y Interceptor that is 14 below where it is on this graph so if we go down 14 from two we have to be at -12 which means our Y intercept has to be -12 and our answer has to be answer Choice a because that's the only answer Choice with -2 as the Y intercept so on the SAT Math section pay very close attention to details with what you're asked to answer with and any equations that you're given any equations or functions that you're given in the context of the question here's how to solve this question about tangents here's how to solve this question about similar triangles and tangents on the SAT Math section question 25 States the side lengths of right triangle rst are given triangle rst is similar to triangle uvw where s corresponds to V and T corresponds to w What is the value of tan of w well the first thing I'm going to do is since I have rst as the triangle and they're similar the tangent values are also going to the same for the corresponding angle so I'm going to go ahead and find that W what is it equal to an rst okay so if I've got V and T correspond let's see s corresponds to V all right so s corresponds to V okay I see that's the middle one that's the middle one and then T corresponds to W okay I see that that's the last one that's the last one that means that R will correspond to you okay but we've got tan of w okay so that's going to be T all right so we have to find tan of T okay I can just write that as then tan of T okay it's the same thing because these are similar triangles going to have the same tan values for the same angle all right so now what is the value of it well let's go aad and draw out this triangle okay cuz that's just going to make it easier to visualize we have a right triangle we have uh we've got rst so let's go ahead and just Mark that rst we know T to R is 52 we know s to T is 48 okay and keep in mind this is obviously not drawn to scale okay it's just a quick sketch because we're only really worried about the actual values not really the the angle measures all right so now we want to know the value of t of w or tan of T all right well we know that the tan is the opposite over our adjacent okay so our opposite from T would be 20 and our adjacent would be 48 so that's going to equal 20 over 48 which we can simplify down and we see we have to because 20 48 is not an answer choice so for simplifying this down we can go ahead and divide them both into four and that's going to give us 5 over 12 as our answer that'd be answer Choice B here's how to solve this sat math question that deals with rearranging variables question 26 States one G of paint will cover 220 Square ft of a surface a room has a total wall area of w Square ft which equation represents the total amount of paint p in gallons needed to paint the walls of the room twice all right so here's how I ended up with this equation one quick note you saw I started writing down variables and uh sort of the coefficients in front of those variables as I read through that's a strategy I recommend that you do anytime that you have an SAT Math word problem that is three lines or longer okay just cuz helps you avoid having to reread as much so just want to make note of that that being said let's go and talk about how I got there all right so we have one gallon of paint is going to cover 220 square feet of the surface okay so we have 220 is the amount of square feet one gallon p is going to cover okay so this gets us the amount of coverage that we're getting now we know that has to equal the area of the wall times two because we're going to do it twice right we're going to paint the walls twice okay so now we have our equation now we see that we need to solve for p so we have to find what P equals now all this question basically hinges on you setting up this equation correctly initially if you don't set it up correctly initially you're not going to get to the right answer so you have to make sure that you understand how the units work right because as you can see here we are ultimately getting to an area by taking the amount of coverage we get per gallon of paint multiplying by the number of gallons now we get our area we're setting that equal to an area as well so checking if your units match is a good way to check your check your work as well so I wanted to point that out okay we're ultimately getting area equals area all right that being said let's go ahead and solve for p now we know that P is going to equal W * 2 all over 220 because we divide both sides by 220 next thing we'll do is we'll go ahead and simplify okay we can divide 2 by two and 220 by two that's ultimately going to give us if we go and cross both those out we'll end up with 110 in that denominator so p is equal to W over 110 our answer there will be answer Choice a here's how to solve this difficult sat math question question 27 States the number a is 110% greater than the number B well that means that a is going to equal 2.1 * B because it's 110% greater than the number B okay keep in mind pay attention to that that greater there that means it's going to be 2.1 * B all right the number B is 90% less than 4.7 well another way to say that is the number B is 10% of 47 okay so that means that b is going to equal 0.1 * 47 which is going to equal 4.7 now we're asked what is the value of a well this is pretty easy to solve for now okay in order to get a we need to know the value of B which we now know is 4.7 so we just do 2.1 * 4.7 if we put that into our calculator we will get 9.87 as the value of a so our answer is 9.87 here's how to answer statistical inference questions on the SAT question one states that there are 55 students in Spanish Club a sample of Spanish club students was selected at random that's important whenever you're doing statistical sampling it must be random sampling in order to provide an accurate statistical inference for you to use later on and as whether they intend to enroll in a new study program of those surveyed 20% responded they intend to enroll always pay attention to if it's they intend or they not to intend because sometimes they will put in something that has only two options and they will give you one of those being they do or the other being they do not and you have to pay attention to what you're given in this case we're given that they do intend to enroll in the study program based on the survey which of the following is the best estimate of the total number of Spanish club students who intend to enroll in the study program in this case this question is super straightforward we have 55 total students were told that of those who responded which was a random sample 20% said they would intend to enroll were asked for those who would intend to enroll so all we have to do is 55 * 0.2 and that'll give us 11 so our answer there would be a here's a tip to help you be more efficient on the SAT question two states Jay walks at a speed of 3 miles per hour and runs at a speed of 5 miles per hour he walks for w hours and runs for R hours for a combined total of 14 miles which equation represents this situation okay well as you can see I've already got my answer without having to read through a second time and the reason why is because I wrote down my variables as I read through as you can see it's a little bit messy because my focus is on reading but I don't have to read through again and the reason you want to do this is because if you were to read through this word problem without writing anything down and then you get to the end and it says which equation represents the situation you now have to go back through you have to look for your numbers you have to look for your variables so what I do when I encounter a word problem on the SAT and you can usually tell pretty much right off the bat if it's a word problem because it'll be usually at least three lines or longer in this case it was four lines you want to write down any numbers they give you and any variables they give you as you go through and you want to try to sort of get it in the equation form that you're expecting and this comes with a little bit of practice but as you can see once I saw we've got walking at 3 miles per hour right running at 5 miles hour I'm guessing it's going to be a summation to get us distance so I went ahead and I put the three here the five here and then once I got my variables went ahead and attach them to the appro appropriate number that I got earlier in the question and then got the equation not having to read through twice so this is a great way to save time on the SAT and I highly recommend doing it here's how I recommend approaching questions about Scatter Plots on the SAT question three states the scatter plot shows the relationship between two variables X and Y a line of best fit is also shown which of the following equations best represents the line of best fit shown what I do in this situation is I take a quick glance at the answer choices to see what format they're in in this case I see they're all in slope intercept form which is going to make this question really easy so let's start by finding our intercept we see our intercept is positive right around three which means we can go and get rid of c and d because they both have negative y intercepts the next thing I'll take a look at is the slope in this case I see my slope is positive if I look at answer choices A and B I see only one of them has a positive slope So my answer has to be answer Choice a here's how to answer this question that deals with y intercepts really quickly on the SAT question States the graph of yal f ofx is shown in the XY plane what is the value of F of0 Well the value of f of Z is just the Y intercept so if we take a look at our graph we see our answer is going to be three so our answer is answer Choice D here's how to answer questions about adding exponents on the SAT question five states which expression is equivalent to and then we have this multiplication question where m q and z are positive what you need to understand in order to answer this question correctly is how to add exponents when you have the same base so to illustrate this let's look at m m ^ 4 * m is equal to M the^ of 5 because it's the same base we add their exponents when we multiply them together same thing with Q we have q to ^ 4 * Q to^ 5 that'll give us Q to the^ of 9 same thing with Z in this case we have Z ^ of -1 * Z to the power of 3 in this case what we have is z to the power of 2 because it's 3 - 1 or in other words 3 + 1 and as we can see our answer then has to be answer Choice B here's how to find the median on the SAT question Six States what is the median of the data shown we're going to start by getting rid of our minimum value then our maximum value then our next minimum value then our next maximum value then our next minimum value then our next maximum value then our next minimum value then our next maximum value to find our answer of 79 now what if we had two values in the middle and we didn't have an odd number total of values we had an even number well in that case let's say for example that we had 79 + 81 as or in this case I guess we'll use 82 since that's the one that's left of it but it's all arbitrary we've already answered this question but I just want to show you what we do in that case in that case we had 79 plus 82 we divide by two we take the average and we use that as the median here's how to solve this sat math question in under 30 seconds the question States what value of x is the solution to the given equation well we got to isolate X then so let's go and subtract 40 from both sides 95 - 40 is going to leave us with 55 is equal to X so the value of x that is a solution to give equation is 55 here's a tip to be way more efficient on the SAT question 8 States the solution to the given system of equations is X Y what is the value of x plus Y what you always want to do on the SAT is look for what you're asked to answer with in this case that's a of X Plus y so does that mean we need to solve for x and y not necessarily and I'll show you why here if I see I have stacked equations like this I'm almost always going to look to add or subtract the bottom equation from the top equation and sometimes that will also mean I need to multiply by some number but in this case I don't need to multiply by a number and what I see immediately is I have 5x and 4x and I have to get x + y so what I'm going to do here is I'm actually just going to add these equations together and that's going to give me x + y because 5x +4x is going to leave me with X and then I have plus Y is going to equal 15 + -2 which is equal to 15 minus 2 which is equal to 13 so our answer there is C and we don't have to solve for x and y because we were able to get the value of x plus y here's an example of how to interpret a word problem on the SAT Math section question n States the given function G models the number of gallons of gasoline that remains from a full gas ttin in a car after driving M miles according to the model about how many gallons of gasoline are used to drive each mile well we know that g of M is how much gas remains in the tank okay presumably since before we have driven any miles this number here is going to end up being zero since M would be zero we would start with 12.1 gallons of gas which means that for every mile M that we drive we are losing 0.05 gallons of gas so our answer would have to be answer Choice a here's an example of how to solve questions that ask you to rearrange variables on the SAT Math section in this case we're asked the given equation relates the positive numbers B X and Y which equation correctly expresses X in terms of being y well in order to get our answer we have to isolate X so let's go ahead and do that by multiplying both sides by y to start and then to get 11x to just X we have to divide both sides by 11 and now we have isolated X so we have y over 11 * 7B which as we can see 11 * 7 is going to give us 77 and we would have y over 77b here's how to solve this sat math question in two different ways question 11 states the graph of the given equations in the XY plane intersect at the point XY what is the possible value of x X now many people would go through and solve this by hand so let's go ahead and do that and then I'll talk about the other way you can solve this one so you have y = 76 and Y X2 - 5 in this case we can go a and plug in 76 for y so we have 76 is equal to x^2 minus 5 the next thing we'll do is we'll isolate that x s value so we'll add five to each side and we'll end up with 81 is equal to X2 from here you should be able to recognize that your answer is going to be positive and negative 9 for the value of x but I'll go and show you how we do that we take the square root of both sides which is going to give us Plus or - 9 is equal to X X the reason why it's plus or minus is because x^ squ if you put in a negative number it will still become positive if you put in a positive number it will become positive because it's being squared so our answer there would be B now here's what I want to show you about this question that's the way I just showed you is one way to do it and it's perfectly fine but there is another way to do it this question is from the digital sat which means you'll have access to Desmos while you are taking the SAT and this is another perfectly valid way to do it you just put in both equations in Desmos and you find where they intersect which in this case we can see here is at9 so both ways are valid the way I would recommend approaching it is with a question as simple as this you can do it by hand if you want to and if you are very confident for example if you're someone who's consistently scoring over 1,400 on SAT practice tests in particular over 700 on the math section and you come across this question you think it's faster for you to do it by hand that's fine you can go ahead and do it if you're someone who's scoring less than 700 on the SAT Math section on practice test I'd use Desmos in my opinion now that you can use Desmos on the digital sat you should be using it fairly often for questions that involve graphing because it helps you avoid human error so even on a question as simple as this if someone wanted to use Desmos I wouldn't fault them at all and I wouldn't tell them not to Desmos is a great tool for the digital sat and you shouldn't be afraid to use it here's how to solve this sat math question about the solution to a system of inequalities the question States the point x and 53 is a solution to the system of inequalities in the XY plane which of the following could be the value of x so in this case we need to solve for x and we already know that this point is a solution so what we're going to do is we're going to take this 53 Y and we're going to as which is a y value we're going to plug it in for y so pretty simple on how we're going to set this up it's going to end up being 40 I'm sorry 4x + 53 must be less than 18 okay now that we've got this set up let's go ahead and isolate X and solve for it so we'll subtract 53 from each side that'll end up leaving us with -35 must be greater than 4X from there we want to isolate X as I said so we divide both sides by four now we see that X must be less than -35 over 4 now what you should be able to recognize here is that 35 over 4 pretty close to 36 over 4 or in other words 9 okay so we know that X has to be less than 35 over 4 which means X cannot be55 or 9 because they do not pass that inequality the only number that does here is answer Choice a here's how to efficiently answer this sat math question about percentages as well as one thing you want to look out for on questions that are simple like this one question 13 states that out of 300 seeds that were planted 80% sprouted how many of these seeds sprouted so it's pretty easy to get to our answer it's going to be 0.8 to represent that 80% we're going to multiply by 300 and that is going to give us our answer of 240 now what you want to watch out for on questions that are as simple as this one as whether or not the SAT is going to put something like this how many of these seeds did not Sprout okay and they would probably underline the word not okay because that would change the math right if you're calculating for the percent or the amount of seeds that didn't Sprout then you would end up with 60 so that is something you want to watch out for on questions on the SAT that are simple like this is whether or not there's something that could trip you up like that here's how to efficiently answer this sat math question question 14 States the function f is defined by F ofx equal 4X for what value of x does f ofx equal 8 well since we're asked to find the value where f ofx equals 8 we go and plug in 8 for f ofx which leaves us with 8 is equal to 4X from there we just want to isolate X by dividing both sides by 4 8 over 4 is equal to 2 which means that the value of x would be two and two is our answer here's how to efficiently answer this sat math question that deals with division and factors question 15 states which expression is equivalent to 8X * x - 7 - 3 * x - 7 all over 2x -4 where X is greater than 7 immediately what I'm seeing is I have x - 7 here and here so what I'm going to see is if I have x - 7 in my denominator which in this case I see I do because I have 2x - 14 and I can change that into 2 * x - 7 so from here what I'm going to do is I'm going to go and rewrite this division problem so you can see what I'm looking for a little bit more neatly the way we rewrite this is 8x * x - 7 all over 2 * x - 7 - 3 * x - 7 all over 2 * x - 7 and now that we've Rewritten this it's very easy to see that these x - 7s are going to cancel out which makes this equation very very simple okay ultimately we have 8x - 3 all over 2 which once again we can rewrite this as 8x - 3 all over 2 which we see as answer Choice B so to answer this question what you really need to understand is one how to factor so you can get that x - 7 out and then second how to sort of change between these similar um sort of forms right of division right you can write 8x - 3 over 2 like this and you can also write it like this so that's really what you need to understand for this question here's how to find the slope of equations in standard linear form and use that slope to answer questions very quickly question 16 States line p is defined by 2 y + 18x = 9 line r is perpendicular to line p in the XY plane what is the slope of line r in order to find the slope of line r we need to first know the slope of line P now the first thing you're going to notice is that we have 2 y + 18x = 9 this is called standard linear form it's when we have our Y and our X on the same side being added together and there equal some constant now because it's in standard linear form we can use the equation M = A over B where a is the value or the coefficient in front of X and B is the coefficient in front of Y so in this case that would be m equals a in this case our a value is 18 so8 over 2 which is going to equal -9 now in order to get a perpendicular slope to -9 you have to do the negative reciprocal so9 is the same as9 over 1 so to do the negative reciprocal we have to change the sign from negative to positive and then we have to flip the fraction to 1 over9 so 1 over9 will be our new slope of line r so we can go slope of R which means that our answer has to be answer Choice C here's an example of why you need to know the exponential growth formula for the SAT question 17 States the given function f models the number of coupons of company sent to their customers at the end of each year where T represents the number of years since the end of 1998 and zero or and T is between 0 and five inclusive if Y is equal to F of T is graphed in the Ty y plane which of the following is the best interpretation of the Y intercept of the graph in this context your Y intercept when you have an exponential growth formula like this is going to be where T is equal to Zer where the exponent is equal to zero and when that exponent is equal to zero 0.65 the^ of 0 is just one and you end up with this Y intercept of 8,000 now in this case we know that that is at the end of 1998 since that's our start year that is where T is zero so from that it's very easy to find the answer so let's go a and read through a through D and let's find the answer a the minimum estimated number of coupons the company sent to their customers during the 5 years was 1,4 and no B the minimum estimated number of coupons company sent to their customers during five years was 8,000 no this is just the value at the beginning of the time so this is the number of coupons that they sent at the end of 1998 uh and then see the number of coupons the company sent to their customers was 1,428 no we know it's 8,000 8,000 is our initial value D the estimated number of coupons the company sent to their customers at the end of 1998 was 8,000 yes D is our answer here's something you need to know about similar triangles for the SAT Math section question 18 states that triangle XYZ is similar to Triangle RS t such that X Y and Z correspond to RS and T respectively the measure of angle Z is 20° and 2 X Y is equal to RS what is the measure of angle T the answer is C 20° now how do you know that right away well this piece of information is completely irrelevant and you don't need to know it in order to know the answer is 20° and here is why you are told that these are similar triangles you are also told that Z corresponds to angle T these two angles correspond to one another which means that they must have the same angle measure so this piece of information does not matter okay all you need is that angle Z is 20 angle T must also be 20 and your answer is C here's what you need to know about systems of linear equations that have no solution on the SAT question 19 States one of the equations in a system of two linear equations is given the system has no solution which equation could be the second equation in the system first thing we need to know is our slope which we see is going to be six okay we see our Y intercept is going to be 18 now the reason we need to know all these things is because in order for a system of linear equations to have no solution they need to have the same slope but a different Y intercept next thing I notice is answer choices a through are all in standard linear form which means that we can use the formula m = a b where m is representing the slope now if we do that for answer Choice a we see that answer Choice a would be6 which would give us positive 6 over one since one is the coefficient FR y so answer choices A and B I see are both going to have a slope of six now they have the right slope but which one of them has the correct Y intercept and by correct Y intercept it means the Y intercept that is different from the one that we are given because if they have the same Y intercept there is infinitely many solutions and as we can see answer Choice a has y being equal to 6X + 18 if we were able to convert it to slope intercept form and in that case it's the same equation as is up here so a is incorrect because that would be the same equation and there are infinitely infinitely many solutions to that now B has a different Y intercept its Y intercept here is going to be 22 so our answer is going to be as Choice B has a different Y intercept with the same slope so there is no Solutions possible here's how to quickly solve this question about area on the SAT Math section question 20 States what is the area in square centim of a rectangle with a length of 34 cm and a width of 29 CM this question is pretty easy all you need to know is the area formula for a rectangle and that's going to be the length times the width these are both the same unit they're both centimeters that's one thing you do want to watch out for on the SAT is if you have different units for one side than the other then You' have to convert units in this case we do not have to do that and it is very simple it is just 29 * 34 we are able to use the calculator on the section this is the digital sat so you're going to be able to use your calculator on both of the sections for the math so you just put it in your calculator you're end up with 986 as your answer here's a bunch of tips that I can illustrate with this question to help you Ace the SAT question 21 states the solution to the given system of equations is XY what is the value of x minus y anytime that you're taking the SAT Math section you always want to pay very very close attention to what you're asked to answer with that is the key to moving faster and being as efficient as possible know what you want to answer with in this case they're asking for the value of xus y so what I would do is if I have a system of equations like this I would look for if there's a way that I can do an addition or subtraction of this bottom equation from the top one in order to get the value of xus y right away and sometimes that may involve multiply one of these equations by some number now in this case I don't see any way that I can quickly get to xus Y doing this so it's not applicable here but we still have the plus minus in order to get the value of x quickly and I'll show you how we're going to do that okay like I said sometimes you're have to multiply in this case I can see that I have y and four y so I'll just multiply this top one by four to get rid of my y so I'll do subtraction here okay so I distribute this four to the Y I get 4 Yus 4 y now my y's are gone okay so I'm going to end up with zero here and then I'm going to have four 4 * 4X 16x - 15x will leave me with just X then 4 * 1 I'm going to have 4 - 8 which is the same as 4 + 8 that's going to give me+ 12 so I can see here that if I subtract 12 from both sides I'm going to end up with X is equal to -12 okay so now that I've solved for X I'll go ahead and solve for y so if x is -2 I'll go ahead and erase up here so we can do this quickly X is -12 I'll substitute that in here so we have -12 and the reason I'm choosing this top equation is because we already have y isolated with no coefficients in front of it so keep in mind that's strategic now that since I need y now I'm not going to pick the Y that has a coefficient in front of it that doesn't make sense to do we want just go ahead and get y right away so we plug in that -2 with multiply it by 4 we get -48 -48 + 1 is going to equal -47 okay so now we want the value of x minus y that's going to be -12 minus -47 okay so keep in mind subtracting a negative it's the same as adding so we're going to have -2 + 47 and that is going to give us our answer of positive 35 here's what you need to know about calculating the number of real solutions for quadratic equations on the SAT Math section question 22 States how many distinct real solutions does a given equation have well in order to solve this we're going to use b^2 - 4 a c because this is a quadratic equation now if the value of b^2 - 4 Z is positive then that means that there are going to be two real solutions now if the value of B ^2 - 4 a c is equal to zero then that means that there are going to be one real solution and I should have said there is going to be one real solution don't at me in the comments okay and then b^2 - 4 a c if that is less than zero then that means that you're going to have no real solutions okay now that we've gone ahead and gone over the value of b^2 minus 4 a c and what that means for the number of real solutions let's go and calculate it so your B value is what's in front of the X your a value is what's in front of your x s and your C value is your constant keep in mind it must be set equal to zero for this to work so b^2 - 4 a c our B value is 10 10^ 2 - 4 * 5 * 16 what is that equal out to that is going to equal out to -2 20 we know is less than zero therefore we must have no real solutions so our answer is going to be d0 there are zero real solutions here's how to convert units on the SAT question 23 States a certain park has an area of 11, 86388 square yards what is the area in square miles of this park and one thing I want to point out here is anytime you have something underl on the SAT it means you need to pay very close attention to it in this case it's because we're converting units from square yards to square miles that being said we are given what one m is equal to in yards and that's 1760 so the key to this question is that you are dealing with square yards not just yards square yards not cubic yards square yards that's the key to this whole thing this makes it super easy as long as you understand that what you're going to do here is you're going to take your 11, 86388 and you're going to divide it by 1760 squared and the reason why you have to square that 1760 is because you are dealing in units of square yards to square miles so you have to square that conversion unit as well well once you do this you just put it in your calculator and you're going to end up with 3.83 so your answer there is going to be answer Choice B here's how to use the circle equation to answer this question on the SAT question 24 states which of the following equations represents a circle in the XY plane that intersects the y- axis at exactly one point well first I'm going to quickly teach the circle equation to anyone who doesn't know it so the circle equation we can write as this x - h^2 + y - k^2 is equal to our radius squ where R is our radius okay now in this situation we would have a center for the circle of h k so as you can see you want to pay attention to the fact that we have those minus signs but our Center is still at H and K so now that we've gone over that I'm going to quickly show you how I would approach this the first thing I would take a look at is what my radius value is for all of these now keep in mind 16 is the radius squared which means that the actual radius here your radius is actually going to equal four okay and that's important because we're only intersecting the y- axis at one point and if you're ever kind of in doubt on a question dealing with sort of circles and graphs go ahead and draw it out it's very useful so I'll go ahead and draw that out to illustrate what I'm looking for here so if I know my radius is four if my x value is anything greater than four and I'll put four here for example I see that my x value for the center right is going to be eight for A and B there's no way that I can reach that Y intercept right no matter where my Y is there's just no way I can get there because my radius is only four so I can get rid of A and B already okay I have to find somewhere where I'm either at four or I'm at4 and the only place that that happens and keep in mind I'm specifically referring to the x coordinate for your Center here and we see the only place that that happens is C and answer Choice D we see that X's Center is at zero now if we had a center at zero we'd end up with a circle that looks like this right and we're crossing that Y intercept twice so our answer there has to be answer Choice C here's a term that you need to know for the SAT Math section question 25 States in triangles ABC and D EF angles B and E each have measure 27 we see that B and E are here okay so they match up in that triangle angles C and F each have a measure of 41 we see C and F they also match up in this triangle which additional piece of information is sufficient to determine whether triangle ABC is congruent to Triangle DF key thing to understand here and pay attention to is the fact that we are asked about congruency which means that they are the same triangles we are not asked about similarity two triangles that are similar can have different side lengths but two triangles that are congruent must have the same side lengths and the same angles now we already know that these triangles are similar because if two out of these three angles are the same that means the third angle is the same in them as well so what we need to know then is if the side lengths are all the same and the way that we can get that we can't get that from just one side length cuz that's only from one of the triangles okay we can't get that from another angle measure we already know they're all the same we do need more information because we need to know whether or not these side lengths are the same and to do that we need to get these side lengths of two corresponding sides which we see we get here in BC if we go up here BC right here these last two letters in EF okaye our answer there has to be C and once again make sure you understand the difference between congruency which is when triangles are the exact same and similarity which is just when they have the same angle measures this is one of the most difficult SAT Math questions and it has less to do with the actual math involved and more to do with the actual logic that's required to set up the problem so with that being said let's go ahe and go over it and let's simplify it down so question 26 States the two data sets of 23 integers each are summarized in the histograms shown for each of the histograms the first interval represents the frequency of integers greater than or equal to 10 but less than 20 so the key thing that we need to understand here is that this line right here right this 30 number is included inside of here right so it's really going whatever is sort of inside of a box keep in mind it's it's sort of the zero through nine it doesn't include that next zero okay so that being said let's keep reading through the second interval represents the frequency of integers greater than or equal to 20 but less than 30 and so on what is the smallest possible difference between the mean of data set a and the mean of data set B so as you can see pretty much sort of a logical sort of question as for the setup of this right so to get the smallest possible difference between these two data sets you want to keep a couple things in mind first of all if you ever have histogram on the SAT you want to pay attention to the shape of them now if you have two of them like you do in this case you want to pay attention to the shape of each of them and as we can see the shape of them is the same there's there's just a shift right so the actual shape is the same as you can see this one right here goes across into nine this goes to seven this goes to four this goes to three same thing over here we have three four seven and nine right we have the same number of bars obviously so these are the same shape but you want to also pay attention to your x-axis as well and as we can see data set B is shifted to the left 10 for each of these right so now in order to set up the smallest difference in means we would actually have to calculate the mean of each right but we don't just calculate the mean because we can't right it's a histogram we know that these numbers fall in between these so the key thing we need to recognize is in order to find the difference we need to know which one's larger and which one is smaller now this data set a it has to be larger because all of these are shifted to the right okay so they can't all fall in the same number because as I pointed out right this 30 and this is true for all of these you know these these uh rectangles or these bars on the graph it's not inclusive of you know this for example right it's it's 20 to 29 that doesn't include that 30 right that 30 is its own and that's what makes it so there has to be a difference here okay so we already know that the answer can't be zero because like I said there has to be a difference um you know because we are dealing with the fact that it's 20 to 29 30 to 39 and so on so if we are shifting one of them you know to to the in this case to the right right if you're doing from B to a it would be to the right if you're doing a to B it would be to the left there has to be some difference there okay so that being said let's go and calculate that difference well if we're going to calculate what the smallest difference is we need the minimum value for data set a and we would need the maximum value for data set B because we are subtracting B from a okay so let's start with getting the minimum value of data set a okay so minimum value of data set a let me go ahead and go up here okay so minimum value of data set a what we would do to set this up is we would start by getting the lowest value from from our first bar right so that's going to be 20 okay so we're getting our minimum value of a so that' be 20 * 3 okay and then we'll have to add on to that 30 * 4 and we'll have to add on to that 40 * 7 and then we'll have to add on to that 50 * 9 okay and then once we get that we're going to have to divide by our total which is going to be 3 + 4 which is 7 7 + 7 which is 14 and then 14 + 9 which is 23 okay so we're going to take all that we will divide it by 23 okay now keep in mind that we're going to also have that division by 23 over in data set b as well all right now we have to calculate our number for data set B and I'm going to have to scroll down a little bit just so you can see all of this getting written out so go ahead and try to scroll down Okay so we're going to have to set up a pretty similar thing right so I'm going to go and put in our subtraction sign and I know it's not super great formatted but that's okay all right so we're going to have minus now we have to do kind of the opposite thing that we just did a so in this case we're taking our maximum values now keep in mind that our maximum values are not inclusive right so this is a range of 10 to 19 okay so we have to take 19 there so that' be - 19 * 3 + 29 * 4 + 39 * 7 + 49 * 9 okay and this is all also over 23 okay and then when we put this into our calculator which is what you would do okay I wrote this out you would just be typing this in in your calculator okay this is ultimately going to get you your answer of one so your answer there is going to be B and that's how you solve this this tricky SAT Math problem here's something you need to know for the SAT and that's how to extract numbers from underneath the square root question 27 States a triangle has legs with lengths of 24 cm and 21 cm if the length of the triangle's hypotenuse in centimeters can be written in the form 3 * theun of D where D is an integer what is the value of D well in order to get in this form of 3 * root D we need to First actually know what the hypotenuses length is so let's go ahead and solve for that so we have a right triangle we know we have lengths of 24 and 21 as our side lengths we need to solve for hypotenuse which we're going to represent as c^ s we're going to use Pythagorean theorem so we're going to go ahead and do 242 + 21^ 2 that's going to equal c^2 okay we know that this is going to equal let's put it in our calculator and we're going to get 1017 okay so we'll take the square root of each side to isolate C okay so we know that c is going to equal that square OT of 107 okay so now that we have that I'm going go ahead and write this out a little bit more neatly we know C is equal to otk of 1017 C is our hypotenuse so that's what we're trying to solve for now we need to ultimately rewrite this in a form where three is extracted okay well underneath the square root in order to extract the value of three we would have to have the value of nine underneath that square root and the way we get that just pretty simple right it's by three squared okay since we have a square root here we'd be squaring three and we would get nine all right so now what we have to do is we have to do 1017 divided 9 and that's going to give us 113 and now what we do is we set this equal to 9 * 113 which as you can see is still going to equal 1017 since we had 10 17 over 9 equal 113 so because of that we now have 9 underneath the square root which means that we can extract three because and I'll just write this over here okay because theun 9 * 113 is the same as < TK 9 * < TK 113 and what is root9 equal to well root 9 is equal to 3 okay so now we've extracted that three and we see we have 3un 113 which is the same format as we got in this question so we know the value of D has to be 113 as well so our answer is 1 13 here's how to solve this sat math question in under 30 seconds question one States what is the solution to the given equation all we have to do here is isolate K by subtracting 12 from both sides 336 - 12 is 324 so we know that K will equal 324 and our answer is B here's how to efficiently solve this sat math question question two states the function f is defined by F ofx equal to X Cub + 15 what is the value of f of two in this case all we have to do is plug in two for x and we're going to get 2 cubed which is equal to 8 and we have to add 15 to that so 8 + 15 will leave us with 23 so our answer is C here's how to interpret this sat word problem question three states that Shawn rents a tent at a cost of $1 per day plus a onetime insurance fee of $10 which equation represents the total cost C in dollars to rent the tent with insurance for D days we know our total cost is going to equal our onetime insurance fee of $10 plus our $1 per day giving us our answer as answer Choice C here's how to quickly solve this sat math question about intersecting parallel lines question four states in the figure shown line M is parallel to line n what is the value of x well we know that this angle of 26 is also going to be the same angle that is right here therefore we know that we have this semicircle of X and angle that is 26° so we can do 180° for that angle of the semicircle minus the 26° and then we're going to get the value of x in degrees which we know will equal 154 so our answer is answer Choice D so I'll go and scroll down so you can see that our answer will be D here's how to be more efficient on the SAT Math section question five states that John paid a total of $165 for a microscope by making a down payment of $37 plus P monthly payments of $16 each which of the following equations represents the situation as you can see as I read through the problem I wrote down the equation that I would eventually come up with so we see that our answer there has to be C now I want to talk about why this is a good strategy and when to use it what I do is when I see an SAT math question with three lines or more then as I read through the question I'll start writing down any coefficients variables or key units that I will need to solve the question so as you saw when I saw I had a total of 165 I knew I was probably going to sum up something else to get to that total of 165 so I wrote down 165 first then as I kept reading I saw I had a down payment of $37 a down payment is a one-time payment so there's not going to be a variable next to it so I went ahead and wrote down 37 okay and keep in mind I'm trying to add up to a total here so I could probably insinuate that I'm going to have a summation after that then we have plus P monthly payments so plus indicating I need to add plus P monthly payments of $16 each in this case p is our variable representing the monthly payments and our coefficient in front of that is $16 each which is how I was able to write out this equation before I finished the question okay so this is a key strategy I recommend you use on the SAT when you have a word problem that is three lines or longer here's how to solve this sat math question in under 60 seconds question 6 states that if Y is equal to 5x + 10 what is the value of y when X is equal 8 well all we got to do here is plug in 8 for X we're going to have 5 * 8 which is going to give us 40 40 + 10 is going to give us 50 and our answer will be 50 here's how to interpret bar graphs on the SAT Math section question seven states the bar graph shows the distribution of 419 cans collected by 10 different groups for a food drive how many cans were collected by group six well let's first take a look at our y- AIS we see we have their number of cans we need to know how many cans were collected by group six so we find group six we see that they collected 40 cans so the answer there is 40 here's how to efficiently solve this sat math question about probability question 8 says the table gives a distribution of votes for new school mascot and grade level for 80 students if one of these students is selected at random what is the probability of selecting a student whose vote for the new mascot was a lion so a couple key things to look for on probability questions number number one is look for the pool that you are selecting from in this case we are selecting one of the students at random keep in mind sometimes they may ask if we are selecting a seventh grader an eighth grader sixth grader if we are selecting one of the students who voted for the badger mascot so you always want to pay attention to the pool that you are selecting from in this case it's just one of the students so that means we're going to be P pulling from this total right here okay now the key thing here is we are looking for uh the probability that student vter for mascot that was a lion okay which we see is going to be this value here so our total probability then is going to be 20 which is the part that we are selecting which is these those students who voted for a lion over the total that we are selecting from which is all of the students so 20 over 80 is going to equal 1 over4 so if we go and scroll down we're going to see that that'll be answer Choice C so c will be our answer there here's how to interpret slope in context for the SAT Math section question n States the graph represents the total charge in dollars by an electrician for X hours of work the electrician charge is a one-time fee plus an hourly rate what is the best interpretation of the slope of the graph well we know that he has a onetime fee which is already represented by our Y intercept and then the slope is representative of his hourly rate okay so we have option A the electrician's hourly rate and that'll be the correct answer there here's how to solve this sat math question that is really a proportions question but disguised as a perimeter question question 10 states that square X as a side length of 12 CM the perimeter of square Y is 2 * the perimeter of square x what is the length in centimeters of one side of square y well couple things to keep in mind here one these are both squares number two the perimeter is going to be the same equation for both of them just with a different value for the side length so if we want to actually double the perimeter all we have to do is actually double the side length and because we know that we know the answer is D having to do very little math here keep in mind we didn't actually have to calculate the perimeter for either Square X or Square y because we're able to recognize that the equation for the calculation of the perimeter is the same the only difference is the actual side length so if we wanted to double the output of the perimeter or double the perimeter value in this equation all we have to do is double that side length because the equations are set up the same here's how to quickly solve this math question question by understanding slope and Y intercepts question 11 states what is the equation of a line that passes through the point 05 well the point 05 means that we have a y intercept of five because that x coordinate is zero so that is where we are crossing the Y AIS and is parallel to the graph of y is equal 7x + 4 in the XY plane well if we're parallel to the graph of y = 7x + 4 that graph has a slope of seven and since we're parallel to it we also must have a slope of seven so we know that our slope must be 7x okay so slope equals 7x we know our Y intercept must be 5 okay so our y inter intercept must be 5 therefore we know that our equation has to be B yal 7x + 5 here's how to efficiently solve this sat math question by understanding how to calculate slope and why intercept quickly question 12 states in the linear function h h of 0 is 41 we know that when we have H of 0 f of 0 g of 0 any function where we have that Zer as our x coordinate then we are getting our Y intercept so in this case our Y intercept is 41 then we have H of 1 is 40 immediately uh I'll go and finish reading the question first which equation defines h well immediately what I see here is that we are moving over one okay so if we go over one we see that we are going down by one from 41 to 40 okay so netive 1 over 1 is going to be our slope okay so a ne1 coefficient for our slope so now we have our Y intercept of 41 we have our slope of negative 1 it's very easy to find Define this equation all right so we're going to have that Negative X as our slope so our B is incorrect because it doesn't have that 41 as our Y intercept okay so a is our correct answer there we've got Negative X is the slope plus 41 Y intercept answer there has to be answer Choice a here's how to quickly solve this sat math question by understanding the equation for exponential growth question 13 states the function f of T is equal to 60,000 * 2 the Power of T over 410 gives the number of bacteria in a population T minutes after an initial observation how much time and minutes does it take for the number of bacteria in the population to double well we know that we are doubling when we have this two to the power of one this two is our growth factor this 60,000 is our initial amount and this T over 410 is representing how often we are doing this doubling okay and we will double every 410 minutes okay because at 410 minutes we'll get our first double and then if we go up another 410 then we'll get our second double okay in this case we are asked for the amount of time it takes for the population to double only one time so T would be 410 and our answer will indeed be 410 here's how to translate graphs up on the SAT Math section question 14 States the function f is defined by f ofx is equal to x - 6 * x - 2 * x + 6 in the XY plane the graph of yal G ofx is the result translating the graph of y f ofx up four units so keep in mind our F ofx graph is already defined up here what is the value of G of0 in other words that's the Y intercept of G ofx okay now keep in mind that g ofx is f ofx translated up four units so we have to start by finding what the Y intercept is of F ofx and then add another four units on top of that since G of X is a translation up four units of it all right so let's go ahead and solve for first the Y intercept of f ofx so we know that the Y intercept is where X is z so let's go ahead and plug in 0 for X so we'd have 0 * or 0 - 6 and then 0 - 2 and then 0 + 6 okay this is all going to equal out to -6 * -2 which will give us pos2 pos2 * 6 which will give us 72 okay so now we have our Y intercept for our F of 0 right now G of0 is what we need to solve for here and we know that's going to be up four units so that means that g of0 will equal F of 0 which we know is 72 + 4 which means that g of 0 will equal 76 and our final answer will be 7 6 here's how to efficiently solve this sat math question question 15 states a candle is made of 17 ounces of wax when the candle is burning the amount of wax in the candle decreases by 1 o every 4 hours if 6 ounces of wax remain in this candle how for how many hours has it been burning okay so we know that we start out with 17 ounces we know that we are going down by 1 qu ounce every hour so in this case I'm having X represent hours and the way that I got this minus 1 quar x is by the fact that we're losing 1 oun every 4 hours that means every hour we are losing 1 quarter of an ounce all right so from here the way I'm going to set up my equation is actually setting it equal to how many ounces are remaining okay so the amount of ounces that are remaining I'm going to call F ofx okay and that's going to equal our initial amount minus how much we're losing every hour and keep in mind hour I'm representing as X here all right so now from here we want to find if 6 ounces remain okay so that would mean that we have six remaining and that's going to equal our starting amount minus 14 x now we want to solve for what time for how many hours it's been burning so we want to solve for x now that we have this equation we'll go ahead and subtract 17 from both sides that's going to end up giving us -11 is equal to - 1/4x from there we will multiply both sides by -4 in order to get rid of this minus one4 okaye so we multiply both sides by -44 * -11 is going to give us POS 44 is equal to X so our answer will be 44 here's how to rearrange variables on the SAT Math section question 16 States the given equation relates to numbers J K and M which equation correctly expresses K in terms of J and M all right so we got to solve for what K is equal to so to do that we're going to isolate it by subtracting 14 J from both sides so we'll subtract 14 J from both sides okay so now this is gone next thing we have to do is divide both sides by five to isolate K all right so now we're going to end up with K is equal to M - 14 J all over 5 okay and keep in mind that we divided that by five all right so let's find which equation matches up with RS we see that's going to be answer Choice a so a will be our answer there here's something you need to know about similar triangles for the SAT Math section question 17 States triangle fgh is similar to Triangle J KL where angle F corresponds to angle J and angles G and K are right angles if s of f is equal to 308 over 317 what is the value of s of J okay well we know that F and J are referring to the same angle these are similar triangles they have all the same angle measures because they have the same angle measures the value for their signs are going to be the same when it's the same angle that is inputed in these parentheses which we see it is okay J and F are the corresponding angles then these similar triangles okay as you can see up here it says F corresponds to angle J therefore they're going to have the same sign values and our answer for the S of J will also be 308 over 3177 here's how to efficiently set up and solve this sat math question question 18 states the product of two positive integers is 546 if the first integer is 11 greater than than twice the second integer what is the smaller of the two integers okay so you want to solve for the smaller of the two integers well in this case since we have greater and smaller I'm going to use G and S as my variables okay so G and S we know 546 is going to equal the product of these two variables G and S we also know that the first integer which we're representing as or actually I guess let's use F and S for the first and the second okay so we're going to use F and S all right so we know that the first integer is equal to 11 plus twice the second integer okay that's 2 s now we want to solve for the smaller we want to solve for S here so to solve for S I'm going to go ahead and plug in F into this top equation okay we know f is also represented as 11 plus 2s so we're going to end up with 5 46 is equal to 11 + 2 s * s we'll go ahead and distribute our s and then we're going to end up with 11 s + 2 s^2 okay from here we want to set this all equal to zero so we can solve for S so we're going to subtract 546 from both sides to get 0 is equal to 2 s^2 + 11 s - 500 and 46 now this question is from the digital sat which means that you have access to Desmos Within the testing environment okay it's through bluebuck which is the sort of the software that they're using to test um for you to take the SAT the digital sat so at this point what I would do is I would actually plug this into my graphing calculator so I going to show you what I did so I put it in my graphing calculator and now it's very easy to actually solve for where it equals zero because it equals zero where it crosses the xaxis and as you can see there's two points but we only are able to use one of them and the reason why is because we have to remember that the product is of two positive integers so yes there are two values where s will equal where this equation here will equal zero But ultimately there's only one that is a positive value and that is going to be at 14 okay so 14 is going to have to be your answer for the value of s okay so our answer there is 14 which is answer Choice B here's an example of an S math question where I would use substitution to solve the question quickly question 19 states which point XY is a solution to the given system of inequalities in the XY plane so I've got4 for my x value I'll go ahead and plug that in up here okay -4 + 7 is ultimately going to give me a value of7 my y value 0 is 0 less than or equal to7 no so a is wrong B I go ahead and put in a zero for the value of x this time and a -14 for the value of y is -14 less than or equal to 7 yes that's true let me check my next Point okay I'd have -14 again for the value of y I've got zero here all right is -1 less than or equal to -4 no B's wrong next one I jump up onto C I plug in zero for X again okay so I'm going to end up with s I'm going to end up with1 and then this time I have 14 for my value of y is 14 less than or equal to 7 no it is not so C is wrong our answer there would have to be D I will check it just to make sure that I did this correctly and as you should if you get to a question like this and if you're using substitution on a question I actually do recommend that unless you're in a massive time crunch you do actually check the last answer choice just to make sure you didn't mess up because as you can see I just did like Mental Math pretty much six times so odds making a mistake for me aren't high but for the average test taker like you could have made a mistake even I could have made a mistake uh I definitely just came across really arrogant but I'm just going to keep going anyways I plug in 14 for the value of x so 14 + 7 that's going to be 21 uh and then right here for the value of y 0 is 0 less than or equal to 21 yes plugging in zero again plugging in 14 here I'm going to end up with -28 minus 1 uh so that'd be -29 okay as we can see -29 is less than or equal to zero so our answer there would be D so I guess the quick lesson here is if you're doing substitution try to move quickly once you do three answer choices you should still check the fourth one because there's a chance you made a mistake so that's something I do on the SAT Math section even as someone who scored perfectly on back toback math sections I would still check that answer D just to make sure I didn't make a mistake on the mental math because as I said I did six basically six sort of situations of mental math before getting to answer Choice D so there is a chance that you know anyone could make a mistake there so wanted to quickly go over that question on substitution and with that being said let's move on here's how to solve this difficult sat math question efficiently question 20 States what is the smallest Sol solution to the given equation to start I'm going to get rid of these square roots by going ahead and squaring both sides from there I'm going to end up getting x - 2^ 2 which is going to end up equaling 30X + 34 now from here I want to ultimately get this set equal to zero so I can solve for x so to do that I'm going to go and expand x - 2 2 to do that I use the foil method so I'm going to end up with x^2 - 4x + 4 is equal to 3x + 34 now like I said I want to get the set equal to zero so that I can ultimately solve for it okay so setting equal to Z I'm going to get x^2 - 4x but I also have to subtract 3x from both sides to get it set equal to zero so that's going to give me - 7x total and then I have that four but I have to subtract 34 so that's going to give me minus 30 now from here this is from the digital sat so you could plug this into Desmos and then solve for x but in this case I want to just go ahead and show you how you could also solve for this by hand since that would be the little bit more difficult way to do it but it could possibly be a little bit quicker depending on whether you're skilled at factoring like this if you're not Skillet factoring you can go ahe and use Desmos like I said perfectly valid way of doing it but in this case I'll talk to you about how to factor this so 30 you want to think about what multiplies together to get -30 that adds to get -7 so immediately I would think -10 and positive 3 so I would end up with x - 10 and then x + 3 okay so that's set equal to zero now from there I've got two possible solutions one would be X is equal to 10 and one would be X is equal to -3 now keep in mind that we have to have the smallest solution to the given equations now the smallest solution here isg -3 because it's obviously negative and the other value is positive so our answer here would be -3 now if you were to graph this out you also still need to pay attention to the fact that you need the smallest solution to the given equation so make sure on the SAT that you always pay really close attention to what you're asked to answer with because if you don't you're probably going to miss points here's how to efficiently solve this multi-step sat math question question 21 states that the regular price of a shirt at a store is $11.70 the sale price of a shirt of the shirt is 80% less than the regular price and the sale price is 30% greater than the store's cost for the shirt what was the store's cost in for the shirt okay so we want to solve for the stores cost well we know that the price the regular price is 11.7 we know it's on sale for 80% so let's go and solve for the sale price because in order to get the stores cost we need to first know the sale price so the sale price is 11.7 time 0.2 because the shirt is 80% off all right so now we have the sale price that's going to equal our sale price so I'm just going to write that as sale well we also know that the sale price is equal to well it's 30% greater than the store's cost so we want to solve for the store's cost so the store's cost time 1.3 is going to give us the sale price well we already know the sale price and we want to solve for cost we know that the sale price ID 1.3 will equal our cost we have our sale price up here so we can go ahead and go like this 11.2 or I'm Sorry 11.7 divid by 02 or I'm sorry 11.7 time 0.2 that is our sale price we then divide that by 1.3 and we get our cost okay so now we can go ahead and plug this into our calculator and let's see what we get so we got 11.7 * 0.2 / 1.3 and that'll give us our answer of 1.8 is equal to the cost so 1.8 is our answer there here's how to efficiently solve this sat math question about density question 22 states that a sample of Oak has a density of 807 kg per cubic meter the sample is in the shape of a cube where each Edge has a length of 0.9 m to the nearest whole number what is the mass in kilograms of this sample all right so we know our equation for density is mass over volume is equal to our density in this case we total our density is 87 kg per cubic meter make sure we're paying close attention to units in this case it's kilog per cubic meter we also see we're dealing in meters and we're asked for answer in kilograms so we're not going to be dealing with any unit conversion so that makes this a lot easier now we know that our mass is what we're trying to solve for okay so we know our mass then is going to equal 87 times our volume now we have to solve for our volume we know that is from a cube which has each length of 0.9 Metter now keep in mind our equation for volume of a cube would be the Cube's Edge length cubed okay because all these all these side lengths are the same in a cube all right so ultimately that's going to be 0.9 cubed all right so now we've got our equation let's go ahead and put it into our calculator and we will get our answer so we're going to do 87 multili .9 cubed and that'll give us our answer of 588 for the value of our Mass so our answer is answer Choice a here's how to avoid a common misconception on the SAT question 23 States for X is positive the function f is defined as follows F ofx equal 2011% of x which of the following could describe this function many people would be tempted to pick increasing exponential here because they see this 2011% but that's not correct the correct answer here is increasing linear and the reason why is because if f ofx is equaling 2011% of X it's going to scale linearly with X and here's why if you were to write this out as an equation it would be f ofx is equal to 2 1 * X because think about it if x is one and F ofx is 200 and and I'll just draw this as a table actually really quick okay we'll do X X is 1 and X is 2 you'll kind of be able to see how this works okay so our y value when X is one in this case would be two well what's our y-value when X is 2 then well that would be 4.02 now what about when it's three well then it' be 6 and as you can see each time we are increasing by 2.01 so this is linear increasing okay so if you see a question like this on the SAT don't fall for the misconception of it being exponential when it's actually linear and if you want something to help you figure out if it is exponential or linear try making a table with three values and that should help you figure it out here's how to solve this difficult sat math question that deals with Transformations left and right of graphs question 24 States the rational function f is defined by an equation in the form F ofx = ax plus b where A and B are constants the partial graph of y f ofx is shown if G of X is equal to F ofx + 4 which equation could Define G the key thing to help you solve this quickly is to understand that when G of X is equal to f ofx plus 4 that is a transformation of the graph of f ofx to the left by four units okay now if it was x minus 4 it'd be a transformation to the right four units but since we know it's a transformation to the left four units this going to make this question a lot easier now as you can see I'm making a DOT up here at the point -10 And1 and the reason why I'm doing that is because if you take a quick glance at your answer choices it's going to help you see that getting to the point of Nega -1 for your yv value or your G of x value should be pretty easy because all of your numerators are six so in order to find that value you have to find the answer choice that will get you to a g of x value of1 okay cuz that's that y value when X is -14 and you may be wondering how I get to that -4 number but I'll quickly show you okay if we're transforming this by going to the left four okay I'll go ahead and draw1 -123 -14 okay then this dot has to shift over to that4 okay so the new point will need to be at -4 and-1 so as you can see what I did is I just put those points in and now I'm just going to check my answer choices and find which one has that correct I see in option A that' be 6 over -14 which does not equal ne1 I see in B I'd have 6 over -10 which is also not equal to1 I see in C that I would have 6 over -14 + 84 + 8 is -6 that' be 6 over -6 which is equal to -1 so I see C would be my answer I can quickly check D the D I see is actually just going to be G of X is equal to 6 so that could never be the correct answer okay so my answer there would have to be answer Choice C here's how to solve questions about adding fractions on the SAT Math section question 25 states which expression is equivalent to and then you've got kind of this mess of fractions that you're adding together with a bunch of variables but I'm going to simplify this down for you and show you how you can do this pretty easily what you ultimately need to first get as a common denominator in both of these fractions I see I have x - 8 here which means I'm probably going to be looking at x- 8 as one of the factors in this right here so let's go and see if we do have that as a factor okay we see that x^2 y - 8X y can also be re written as let's see x - 8 * XY all right so that's going to be the same so from there we see that this right here we don't really need to do anything to but what we do have to do is with this y + 12 over x - 8 okay we ultimately need to multiply this by XY over XY okay so now we have to go ahead and distribute our XY to 12 and also to Y once we do that we're going to end up with x y^2 + 12x y okay and since we have same denominators here we can go ahead and add this y * x - 8 well we know that y * X is going to give us another YX so plus another XY and then we'll also have a y * - 8 which will give us a minus 8 y okay and keep in mind that this is still all over that denominator of x - A8 * XY well let's go ah and simplify this down that's going to end up being x y^ 2 let me go ahead and write that a little bit neater x y^ 2 + 13 XY since we are combining these two terms okay and then we also have - 8 Y and keep in mind this is all still over that denominator of x^2 y - 8 all right from here we go ah and find which answer Choice matches this we see that'll be answer Choice C so c will be our answer there here's why you need to pay attention to details on the SAT Math section question 26 states that the table shows the results of a poll a total of 803 voters selected at random were asked if the candidate they would vote for in the upcoming were asked which candidate they would vote for in the upcoming election according to the poll if 6,424 people would vote in the election by how many votes would Angel crw be expected to win the key thing with the SAT Math section in general is you need to know what you need to answer with in this case it is by how many votes Angel Cruz would be expected to win so it's not how many votes Angel Cruz would get it's not how many votes his competitor would get it's by how many votes he would beat his competitor by so it's the difference between the two so because it's the difference between the two what we ultimately want to do is we want to take this poll and we want to find the difference between those two so we're going to do 483 minus 320 we have to put that all over the number of people who are in the poll which is 83 okay and the next thing we have to do is we have to multiply that number by the amount of people who are actually going to be voting in the election because we're wanting to write how many votes they are expecting him to win by right the difference in the expectations of what will happen with the actual number of people which is 6,424 okay so I'll go ahead and multiply that by 6424 all right now we'll put this into our calculator and get the answer so the answer is 1,34 which we see is going to be answer Choice B here's how to use Desmos to be more efficient on the digital sat question 27 states that the graph of x^2 + x + y^2 + y is equal to 199 over 2 in the XY plane is a circle what is the length of the circle radius with a question like this there's a lot of room for error if you try to do it by hand so I highly recommend using the graphing calculator that's available on the digital sat to do this so the graphing calculator on the digital s sat pretty much works just like desmo so I'll go ahead and give you a look at how I would set this up it's really simple all I would do is put in this equation into the graphing calculator and since I'm looking for the circle's radius I would first find two points that are really easy to calculate so I see I have one here at the x coordinate 0.5 and the y-coordinate 9.5 and then I just find the opposite coordinate right so I just go straight down and I see I have at negative 0.5 so the same x coordinate my y-coordinate is 105 so that difference is from 9 1/2 down to -102 so that means that I know my diameter is 20 go ahead and write that we know that our diameter is 20 so 20 is equal to D we know that our radius then has to equal 10 and we're asked for to answer with our radius so that gives us our answer right there the answer is 10 here's how to quickly solve this SAT Math problem question one States Isabelle grows potatoes in her garden this year she harvested 760 potatoes and saved 10% of them to plant next year how many of the harvested potatoes did Isabelle saved plant next year all you got to do is take your total amount of potatoes multiply that by the percentage that she saved which represent as a decimal of 0.1 you're going to get your answer of 76 which is answer Choice B here's how to find the Y intercept of this graph on the SAT question two states what is the Y intercept of the graph shown we find where it crosses that y AIS and we see that at two so our answer there will be 02 which is answer Choice B here's how to convert units on the SAT Math section question three states what length in centimeters is equivalent to a length of 51 M where 1 met is equal to 100 cm well we know that we have 51 M which I'm going to represent with meters is M for that unit it's not a variable but it's the unit okay now we want to get rid of meters so what we're going to do is we're going to multiply by the fact that we have 1 meter per 100 cm now notice how my number of meters is going to cancel out and the unit that I'm going to be left with is centimet so as we can see 51 * 100 is going to leave us with 5100 CM so our answer is answer Choice C here's how to quickly solve this sat math question about distance question four states a bus is traveling at a constant speed along a straight portion of a road the equation D is equal to 30t gives the distance D and feet from a road marker that the bus will be T seconds after passing the marker how many feet from the marker will the bus be 2 seconds after passing the marker well all we have to do is plug in two for T since T represents the number of seconds after passing the marker and that'll give us our distance D that we are from the marker so D will equal 30 * 2 in this situation since we are doing the distance 2 seconds after passing the marker and that will give us 60 so our answer there will be answer Choice C here's how to simplify on the SAT Math section by Distributing a negative sign question five states which expression is equivalent to 20 w- 4 W + 3w what you'll do here is you'll distribute that negative sign to that 4 W and that 3 W and that'll leave you with 20 wus 4 wus 3w that's ultimately going to end up being the same as 20 W - 7 W which is 13 W so our answer there is answer Choice B here's how to use proportions to solve this sat math question faster the question is if 6 Plus xal 9 what is the value of 18 + 3x immediately I recognize that 6 + x if we multiply it by 3 we get 18 + 3x so all we got to do is take this 9 and multiply by three which will give us 27 as our answer so if you see a question like this on the SAT see if you can multiply it by something to get what's right here and that will help you get to your answer faster without having to solve for your variable X here's how to quickly find the x coordinate of a Vertex of quadratic if you take a look at this question it states the given equation relates the variables X and Y for what value of x does the value of y reach its minimum well in this case we see we have a quadratic x^2 - 14x + 22 now what you have to do then is you have to take the value of B over 2 a and that will give you the x coordinate of your vertex now in this case we're asked for the value of x where y reaches its minimum now y will reach its minimum at the x coordinate of the vertex so all we got to do is do B over 2 a well our B value is -14 so we have4 which will give us POS 14 over 2 * a we see in this case our a value is just 1 so 14 over 2 will give us a value of 7 so our answer there has to be seven here's how to find an equivalent expression for a question like number eight which expression is equivalent to 9 x^2 + 5x in this situation I see I can pull out an X by factoring so if I do that I'm going to end up with x * 9x + 5 okay let's see if we have that anywhere we see we do have that as option A so that' be our answer I'll quickly show you why b c and d are wrong as well okay obviously 5 * 9 gives us 45 that's not found anywhere 9 * 5 again okay that's not found anywhere and then right here we'd end up with an X cubed value okay so as we can see our answer there would have to be D okay you can tell that just by factoring but I want to go and show you why BC and D are wrong as well here's how to quickly solve this question about finding angle measures in a triangle on the SAT question 9 States in triangle ABC the measure of angle B is 52 the measure of angle C is 17 what is the measure of angle a well we know that the sum of all the angles in a triangle must add to 180 so all we have to do here is do 180° - 17° - 52° and that will give us the value of angle a and 50 + 17 is going to give us 69 180 - 69 will give us 111 so our answer there would be answer Choice D here's how to quickly solve this sat math question question 10 states the graphs of the equations in the given systems of equations intersect at the point XY in the XY plane what is the value of y all right it's pretty easy to solve for y here all you got to do is go ahead and substitute xal 8 and for X we know 8^2 is 64 so we're going to end up with Y is equal to 64 + 8 which we know is going to equal 72 so our answer there is D here's how to answer scatter plot questions on the SAT Math section question 11 states a scatter plot shows the relationship between two variables X and Y a line of best fit is also shown which of the following equations best represents the line of best fit shown so immediately what I'm going to look for is my Y intercept which I see is right around 13 and A2 then I'm also going to look at my slope which I see is negative so I see that I have positive slopes in answer choices C and answer choices a so I can get rid of them I see I have the wrong Y intercept answer Choice D So my answer there has to be answer Choice B here's a trick to make your life easier on the SAT when dealing with square root Ro question 12 States the function f is defined by FX 8 * X for what value of x does FX equal 48 well let's go and start by writing out our equation so we're going to have 48 is equal to 8 < tkx now you could go ahead and square both sides but I don't recommend doing that because you're going to end up with a really large number instead what I recommend doing is dividing both sides by 8 to start 48 over 8 is going to leave you with 6 is equal to the square < TK of x from here now is a great time to go ahead and square both sides because you don't have to square the value of 48 now you end up with 36 is equal to X so your answer there is going to be C here's how to efficiently solve this geometry problem on the SAT question 13 states a circle has Center o and points R and S lie on the circle in Triangle o RS the measure of angle R is 88 and what is the measure of RS o in degrees all right let's draw this out cuz it's going to make it a lot easier to visualize okay we've got this Center o and we've got R oos which is 88° so r o key thing we need to understand here is that the side length from R to O and O to S are going to be the same length now that's important because we can go and put in this 88° for this angle measure now we want to know what the measure of angle RSO is so let's go ahead and draw this triangle okay now as you can see we have an isoceles triangle now an Isles triangle means that these two sides are the same which also means that the angle o RS and the angle RSO are the same so now since we know all of the degrees in a triangle will sum or I'm sorry all of the angles in a triangle will sum to 180° we do 180° we'll subract subract the 88° that we have in this angle here and then we will divide it by two since we know that we have two of these angles that will have the same measure okay and once we do that we'll get that angle RSO so 180 minus 88 is going to leave us with 92 92 divided 2 is going to leave us with 46 as our answer for angle RSO here's how to efficiently solve this sat math question question 14 States what is the sum of the solutions to given equation well let's go ah and distribute our X ultimately we're going to want to set this equal to zero so let's go ahead and just try to do that right so we'll distribute this X we're going to end up with x^2 + x - 56 is equal to 4x^2 cuz we're going to distribute that 4X and then we will have - 28x all right let's go ahead and set it equal to zero to do that I'm actually going to subtract everything on my left side because I don't want to deal with subtracting a 4x^2 because then I have a negative coefficient in front of my x squ value and just a piece of advice I would generally try to avoid having a negative coefficient in front of your x squ value just something that that I would usually recommend right and it's also easier to subtract you know just a coefficient of one than it is one of four so anyways that's why I'm choosing to do it this way so we'll go ahead and do this we'll have to add 56 okay so we're going to end up getting a 4x^2 - x^2 it's going to leave us with 3x^2 we have - 28x which we also have to subtract another X that's going to end up leaving us with a - 29x and then we also have this plus 56 so plus 56 okay now from here you have a couple of options you could try to factor this out or you could just use Desmos a situation like this honestly I would just use Desmos you're dealing with 56 29 3 you might be able to factor something out there but there's really not necessary so let's go ahead and use desmal to solve this so as you can see in the graph we've got two solutions and keep in mind we have to answer with the sum of the solutions so the first solution that we have is at 2.66 7 so in other words if we convert that into thirds that would be 8 over three okay so we have 8 over three and then we also have seven okay if we convert 7 into thir that'd be 21 over 3 so 8 + 21 is going to give us 29 over 3 as our final answer there okay so 29 over3 is the sum of the solutions now once again as always on the SAT Math section you have to be very pay very close attention to what you're asked to answer with in this case it is the sum of the solutions so that's how we get to that 29 over three so always make sure you're paying close attention to what you're asked to answer with on the SAT Math section in this case the answer 29 over3 here's a trick you can use to save time on the SAT Math section question 15 it says the solution to the given system of equations is XY what is the value of 5x on the SAT you always want to pay attention to what you're asked to answer with in this case it's the value of 5x we don't necessarily have to actually solve for x to get our answer we just need to know the value of 5x so the reason that's important is because if you see stacked equations like this on the SAT you're typically going to look to add subtract or substitute something in in order to get to the value as or answer with because like I said you don't always actually have to solve for x and you don't always have to actually solve for x and y so in this case what I'm actually going to be looking to do is substitution because I see I have y is equal to 3x and I see I have a 2X here I know 2x + 3x is it's going to give me 5x so when I substitute in that 3x for y I end up with 5x is equal to 12 and I know my answer has to be C and I never had to actually find the value of x here's how to solve this question about volume on the SAT question 16 States a cube has an edge length of 41 in what is the volume in cubic inches of the cube one thing you want to pay attention to on the SAT Math section is units in this case you see they're both Inches so it's very easy okay all you have to do is take your 41 in for your Edge length and raise it to the power of three Okay so 41 raised to the power of 3 you put it in your calculator and you're get answer choice to D 6892 the reason we're raising it to the power of three is because a cube has a length width and height that are all the same so the volume is just 41 cubed here's how to answer this question about population growth on the SAT Math section question 17 States the given function P models the population of LOL T years after a census which of the following functions best models the population of LOL M months after the consensus the key thing to understand here is that this equation up here P of T is representing the population T years after consensus but we have to convert this into months after the consensus so to do that we need this T to turn into that t needs to turn into an m/ 12 that way at 12 months we have 12 over 12 which is one year which would be the same as T being one one year so we can go ahead and get rid of A and B next thing we can look at is the difference between C and D now we have to keep in mind we aren't needing to divide our growth factor at all because think about it if we divide 1.06 over 12 we now have a decreasing population because that's going to result in a value that's less than one and that's not the case we know know our population is increasing every year okay our growth factor Remains the Same all we're changing is the unit of time so we have M over 12 to account for the fact we are changing from years to months our growth factor Remains the Same and our initial population Remains the Same and our answer is D here's a trick to use on the SAT Math section to be way more efficient if you take a look at question 18 it says the solution to the given system of equations is XY what is the value of y on the SAT Math section especially whenever you see stacked equations like this always pay really close attention to what you're asked to answer with in this case it's the value of y now whenever I stacked equations like this what I'm usually going to look to do is either substitute if I have something like y equals and then something that doesn't include another variable but in this case they both have varibles there's an X and Y in each of these equations so instead of substitution I am looking for addition and subtraction of adding or subtracting this bottom equation from the top one now sometimes that'll require me to multiply the bottom and the top equation by some number in this case it does I'm going to multiply this bottom equation by three and the reason why is because once I do that and I distribute this three to all these numbers I will end up with 6x and then I can subtract my bottom equation from my top and I'll end up with 6x - 6X I'll be able to get rid of my x's I'll have 7 y - 6 Y and that will leave me with my value of y so let's go ahead and do that we're going to end up with 6x - 6X X's are gone 7 y - 6 Y which means that we have one y left and then we have 28 minus 30 which leaves us with -2 and our value of y is -2 and our answer there is a so there's some advice on how you can deal with stacked equations on the SAT and work them to your advantage to be more efficient here's here's how to solve this sat math question in under 60 seconds question 19 States the minimum value of x is 12 less than 6 times another number n which inequality shows possible values of X well we know that the minimum value of x which means that X must be greater than or equal to this number okay and it's 12 less so it's going to be minus 12 6 times another number n so 6 * n and as we can see this perfectly matches up with answer Choice B so B will be our correct answer there here's how to efficiently solve this sat math question question 20 States data set a consists of the height of 75 buildings it has a mean of 32 M data set B consists of a height of 50 buildings and has a mean of 62 met data set C consists of the heights of 125 buildings from data sets A and B what is the mean in meters of data set C okay so ultimately for this question we need to calculate the mean of data set C well we know that that is a composite of the data set A and B together so what we need to do is we need to get the total amount of height in meters from data sets A and B combined so to do that we're going to take the 75 buildings that are in data set a multiply it by the mean of 32 and that'll give us that total height from data set a we then have to add onto that the total height from data set B which is going to be those 50 buildings multiplied by those 62 meters of those 50 buildings so from there we then have to divide by that 125 buildings total so here we're getting our total height in our numerator and the number of buildings in the denominator and that will ultimately get us to our answer once we put in our calculator let's see what we get of 44 so 44 is our answer here's three different strategies that you can use to solve question 21 and stick around to the end because at the end I'm going to discuss how to know which strategies you should be using on certain questions when there's different ways that you can get to the right answer all right so let's go and read through the question the graph of 9x - 10 y = 19 is translated down four units in the XY plane what is the x coordinate of the x intercept of the resultant graph so a couple things that jump out right away if we're looking for the x intercept we know that's going to be where Y is zero we need to find the x coordinate of that x intercept we're going down four units and we also want to make note that this is in standard linear form not slope intercept form Okay so let's start with the first and probably the most commonly used approach that would be converting this into slope intercept form then translating it down those four units so let's go ahead and do that if We're translating this into if we're converting this into slope intercept form the way that I would approach it is we're going to have 9x - 10 Y is equal to 19 I would isolate y in this case I would actually add 10 y to the right and left sides and I subtract 19 so I'd end up with 9x - 19 is equal to 10 y I divide both sides by 10 and I'd end up with 9 10 x - 19 over 10 all right now keep in mind that we are ultimately going to translate this graph down four units in the XY plane so if We're translating it down four units we would subtract by 40 over 10 okay is equal to Y now we want to find where our x intercept is well our x intercept is going to be where Y is equal to Zer so we can now set this equal to zero now from here I'm going to combine this9 over10 and this -40 over10 into 59 over 10 then I'll add it to both sides and I'll end up with 59 / 10 is equal to 9/ 10x okay now from here all we got to do is multiply both sides by 10 and we get 59 is equal to 9x from there to isolate X we see that X would equal 59 over 9 okay so 59 over 9 is our right answer but that's just one of the ways to get there let's talk about the other two different ways to get there okay so one of them is pretty similar to the way that we just did but probably a couple less steps okay and this is kind of for people who are a little bit more advanced in math who maybe are able to sort of pick up on something like this a little bit quicker okay let's say that we have 9x - 10 y = 19 all right now yeah if We're translating this down four units okay then that's the same as doing 9x - 10 y + 4 in parentheses equals 19 okay and this just kind of saves a couple steps right we distribute that 10 over we're going to end up with 9x - 10 Y and then - 4 is equal to 19 all right so from here once again like I said before our X intercepts where Y is equal to Zer so this would ultimately and I'm just going to kind of bring this up here okay we put in zero for y we end up with 9x - 40 it's equal to 19 we add 40 to both sides we get 59 is equal to 9x we divide both sides by 9 and once again we get that same answer of 59 over9 okay so now there is also a third way to solve this okay I want to make a point at the end that'll help you with other questions on the SAT too so the Third Way is kind of a halfway point between this one and the other one but it's more so like the the first step that we did so let me go ahead and pull up Desmos because this is for the digital sat so you do have access to Desmos in your testing environment so the way that I would do this using Desmos is I would pretty much convert it into slope intercept form and then I would put it into Desmos and use that to get to the rest of the answer so as you can see if you do that you look for where it equals zero and that's at 6556 which is 59 over 9 now the disadvantage of using Desmos is it's not going to give you a perfect fraction but most of the time it's pretty easy to figure it out this is probably one of the more difficult cases where it's something being divided over 9 and it's a little bit more difficult to discern what the fraction is but most of the time it's usually something over three or over five or over four and it's pretty easy to do but now that we've talked about the three different methods that you can use for solving this question I want to talk about how you know which method you should use just generally on certain questions because there are often times certain shortcuts you can use and many times maybe not many times but some people may not know those shortcuts exist so are they worth learning when should you use them how much focus should you put into using shortcuts versus using Desmos I think it's something we really do need to talk about because with the digital sat everything is very different and I think it really comes down to how comfortable you are using sort of shortcuts like the one I showed you in the second way of solving this where you know that it's translated y + 4 right if you don't know those shortcuts you know rely more on Desmos convert things into slope intercept form there's so many different maybe not so many but there's sometimes a couple different ways to get to an answer and you ultimately need to use what you're most comfortable with now is it good to still learn shortcuts yes because it can save you time so especially if you're someone who struggles with time it's probably worth learning them but if you're someone who can move really fast by converting things into slope intercept form and using Desmos then do it and maybe don't worry as much about learning these shortcuts my job is to give you as many tools as you can to be successful but ultimately you do need to pay attention to what you're most comfortable with there are certain times where the method that I use I'll show you two different methods and you may choose one that I don't necessarily prefer to use and that's okay but you ultimately should be focused on what you're most comfortable with what you're fastest with what you're fastest and most accurate with so you kind of got to make a judgment call for yourself my job is to give you as many strategies as you can to be successful if you find that some of them are a little bit too advanced for you that's okay notice how you could get to this answer using slope intercept form and Desmos right so it's possible to still do highly well extremely well in the SAT Math section and not know every shortcut but like I said if you do struggle with time it is worth knowing those shortcuts so I guess to wrap all this up and to bring it to a conclusion I'm going to give you the tools and you know as many different ways to solve things as I can I'll give you what I recommend I'll try to give you strategies but you also need to take into account your personal situation how comfortable you are using certain strategies and that'll help you do the best that you possibly can on the SAT so there's my little rant for this question here's how to answer this question about the exponential growth formula on the the SAT question 22 States two variables X and Y are related such that for each increase of one in the value of x the value of y increases by a factor of four when x equal 0 yal 200 which equation represents the relationship well this piece of information right here is giving us our initial value when x is 0 Y is 200 so we need to have that y equals 200 so we can go ahe and get rid of A and B because they both don't have the correct initial value now as for our growth factor we know our growth factor is four it's stated pretty explicitly right here for every increase in the value of x by one we increase our value in y by a factor of four now we have to keep in mind we are going to raise this to the power of X because this is exponential growth every time we increase the value of x by 1 we increase y by a value by a factor of four that is exponential growth down to the definition so we know our answer there has to be answer Choice a d and there's a quick review on exponential growth for you here's how to solve one of the most difficult SAT Math questions in a standard way and a way to finess the question if you're not sure how to do the standard way all right so question 23 States one solution to an equation can be written as 1 plus root K where K is a constant what is the value of K so the key part to this is you seeing that you have 1 plus theare root of K and recognizing that you're probably going to be dealing with some sort of squares there all right so the next thing you really need to understand is how to ultimately get this into the point where you're completing a square right and if this sounds complicated it kind of is but at the end I'll show you a way that you can finesse this so just just hang with me here all right so you're going to start by adding 9 to both sides you'll end up with x^2 - 2x is is equal to POS 9 now what you ultimately want to get and what your goal is here is since you saw you have this you want to get to a point where you have X something squared set equal to some constant okay and the reason why is because I guess I'll just get to that kind of as I go through this but you you'll see why you want to get there and that's what I'm trying to get to all right so we have x^2 - 2x equal to 9 now like I said I want to get to X something squar now x^2 - 2x I know x - 1^ 2 isn't going to quite get me exactly x^2 - 2x it would give me X 2 - 2x + 1 so what do I have to do here well I've got to add one to both sides so if I add one to both sides I'm going to end up with x^2 - 2x + 1 is equal to 9 + 1 which is 10 well now from here I can set that equal to that x -1 squared so now I'm where I want to be okay because from here I'm going to go and take the square root of both sides and now I have root 10 and now keep in mind that root 10 is plus or minus okay because we are taking the square root of it so be plus or minus root 10 it's going to equal our X - 1 okay now from here we go ahead and add one to both sides we get 1 plus orus < TK 10 is equal to X okay now if we look at the format for the solutions right we need to be writing it as 1 plus root K well we see that one of our Solutions here would be 1 + < TK 10 okay so we know our answer for the value of K is 10 okay so our answer there would be B now let's say you don't know how to do this which honestly like it's one of the most difficult SAT Math questions so it wouldn't be that surprising okay if you don't know how to do this and you get to the SAT and maybe you are able to do it in practice but on the SAT you just kind of Panic or you're running out of time here's an alternative method that you can kind of finesse to get to the right answer all right so I'm going to use Desmos here and keep in mind the reason I'm using this is because on the new digital sat you pretty much have access to Desmos within Blue Book the testing platform so you'll be able to use this so what I'm going to do here is I plug in my equation now keep in mind this is set equal to zero right I'll go ahead and cir that so you see what I'm referring to right we're set equal to zero so we want to find where we are equaling zero okay so where we are crossing our xais now if we take a look we see that we cross our xaxis at 4162 now what else do we know and I'm going to go ahead and erase this since we have that the solution must be 1 + otk K and we know that our solution is equal to 4162 because we see that on Desmos we can do this we've got 4.1 62 we subtract one from that we get 3162 we know that that's got to equal the square root of some number K now since this is multiple choice we could actually just plug in these numbers and get to our right answer but I want to talk about what if this was free response you can still finesse it even if it was free response and here's how the way I would look at this is I know that the square root of 9 is three and I see that we need to get a little bit higher than that so then what I would do is I would put in the square root of 10 and keep in mind this might not work if you dealing with numbers that are like the square root of 500 but that question typically wouldn't be asked on the SAT because that would be extremely complex and if you already have a question as complex as this you're probably going to be dealing with a with a K value that's not you know extreme right so I see 3162 I know that n if I take square root of that it's three I go up one I take square root of 10 and I get 3162 so that's how you can finesse this even if it's not multiple choice obviously since it's multiple choice you could just go ahead and plug in um the eight the 10 the 20 and see which one works and you'd get 10 so I wanted to go a and show you this because it's a great example of how you can use the digital SATs Desmos is basically being built in to your advantage um and if you have a graphing calculator it's the same thing so hopefully this was helpful and hopefully you understand better how you can finesse the SAT if you do forget how to do things you know the normal way quote unquote here's something you need to know about standard deviation for the SAT Math section I'm going to illustrate this through question 24 the dot plots represent the distributions of values in data sets A and B which of the following statements must be true then we have two statements here one being the median of data set a is equal to median of data set B and then two being the standard deviation of data set a is equal to the standard deviation of data set B now whenever you have anything like a a histogram or Scatter Plots or two data sets you always want to compare the shape of them to each other okay or the values of them to each other if it's the case that they are just listed out in numerical form but in this case we have the shapes so we want to compare the shapes of these two together and as you can see they are the same except for these two dots in data set a we see that there's three dots here for 13 but in data set B there's only one okay so we looking at this as the only difference now as far as as the medians we see that since everything else is the same right we would cross out these and we would end up getting a median of 13 and then over here in data set B we'd also get a median of 13s their medians are the same okay so we know that one is true let's see if we can answer it just based on that we know that one must be true uh doesn't look like that will get us there on its own so let's go and look at number two standard deviation of data set a is equal to standard deviation of data set B well we know that that can't be true and here's why okay even though these things have the sh the mostly the same shape this difference of two more values being centered around the median is going to make it so that the standard deviation of data set a is lower than that of data set B okay they can't be the same in order for the standard deviations to be the same they have to be the same right they have to be the same data sets for the most part generally on the SAT that's that's pretty much the case Okay because they don't really get too in depths into the actual equation for standard of deviation they pretty much just want you to be able to visually tell in terms of standard deviation so yeah what you need to know here is that since we're adding more concentration around the median around the mean value okay that means that our standard deviation is going to be lower in data set a okay so the answer here is that one is true number two is false okay so that would be which of the following must be true the answer is a one only here's how to solve this really difficult SAT Math Problem the first way being how you can finesse it since it's a multiple choice and the second way I'll show you how you can solve it on the off case that you come up with a question like this that is a free response answer so that being said let's go and get into it question 25 States an Isles right triangle has a perimeter of 94 plus 94 < tk2 in what is the length in inches of one leg of the triangle okay so ultimately the length of one leg is pretty easy to find and the reason why is it's an isoceles right triangle so Isles right triangle I'm going to draw this out as I recommend you do with questions about triangles and circles on the SAT we've got these two side legs will be the same because like I said Isles now that means it's going to be a 45 4590 triangle okay therefore we know our hypotenuse will be X < tk2 where X is the value of one of the legs okay from here let's go and set up our equation we know our perimeter is 94 + 94 < tk2 we know that's going to equal 2x + x < tk2 okay we get that by taking X Plus X Plus X < tk2 okay from here I'm looking to solve for x right so I'm going to go and factor out X from my right side I'm going to get x * 2 + < tk2 okay now to ultimately solve for x then I just divide both sides by this 2+ < tk2 okay so now I have isolated my X this is over 2 + < tk2 now since this is multiple choice what I would do at this point is I would just go ahead and put this right here in my calculator I'd get whatever it is as a decimal and then I would just check a through D and find the answer that is the fastest way to do it since it's multiple choice so that's what I would 100% recommend and I would without a doubt with no question that's what I'm doing if it's multiple choice which it is in this case so that's a strategy you should use on multiple choice however this question or one like it could come up as a free response question and the way that they would do that since it's dealing with a square root is they would probably say they would do something like this they would put like some variable underneath the square root and say What's the value of D and the answer um so I am going to show you how you solve this in case you come across one of these that is free response so let's continue this question okay so we know that X is equal to this right here now we need to ultimately get this so it's actually a number right we need to get it so that it's something we can put in on fore response now to do that we have to multiply by 2 minus < TK of two okay so you multiply by 2 minus < TK two and the reason that we have to do this is because we have 2 plus < tk2 here and by taking the difference of these squares it's going to help us get rid of the square root that's in the denominator all right so let's go ahead and do this okay we're going to have this 2 * 2 and I'll do the the denominator first so we have this 2 * 2 that's going to give us four okay we're going to have four time let's see we're going to have this plus < tk2 * 2 and we're going to have this minus < tk2 * two so keep in mind those are going to cancel that's why we're doing this we're doing the difference of these squares okay so that square root is now going to get cancel out okay one thing we will still have is this < tk2 * this negative < tk2 which will give us a minus two right so we're going to end up with a 4 minus 2 minus 2 okay now in our denominator I'm sorry our numerator we also have to do this right so we have to take the same thing and we have to foil it out all right so we got 94 * 2 we know that's going to be 188 so we got 188 we've also got 94 < tk2 * 2 so that's going give us plus a 1 < tk2 we've also got a 94 * < tk2 which will give us Aus 94 < tk2 okay and I know I'm running out of room there so I'm actually going to erase this and bring it up okay so as you can see I folded out I brought it up here so you can see it a little bit better and it's a little bit bigger now from here we can go ahead and see that we have 188 minus 188 okay so those are going to cancel so I'm just going to go ahead and erase those okay we still have this plus 188 < tk2 - 94 < tk2 that's going to leave us with a positive 4 < tk2 so now we have 94 < tk2 over 2 94 over2 will leave us with 47 and now we are left with our answer of 47 < tk2 so that's how you solve it if it is free response okay the key thing being right here down in your denominator you have to multiply by flipping the sign within that parenthesis okay in order to get that difference of squares okay so that's the key to solving this if it is free response remember though if it's multiple choice do not do this it will take way too long just put it in a calculator and then PL in a through D and find the right answer here's how to solve SAT Math questions that deal with the number of real solutions question 26 states in the given equation C is a constant the equation has exactly one real solution what is the value of C well if you're unfamiliar with how to calculate the number of real solutions you're going to use this formula called B squ minus 4 a c okay and keep in mind you use this when you have a quadratic equation like here set equal to zero okay and in this equation your a Valu is what's in front of your x squ value your B value is what's in front of X and then your C value is your constant which in this case is just being represented as C now if b^ s - 4 a c is greater than Z then that means that there are two real solutions that mean there are two real solutions in this case we want one real solution so when b^2 minus 4 a is equal to Z that's when we get one real solution okay now there is a third case which is where B ^2 - 4 a c is less than zero and in that case there are no real solutions or in other words there are zero real solutions okay now in our case we know that we have to set this equal to zero since we're looking for where there is one real solution well we know our a value is going to be9 we know our B value is 30 and we obviously have C so B value is 30 we're going to take that we're going to square it so we have 30 2 - 4 * a we know our a value is 9 * C which we're just representing as C and that's got it all equal Z 30 s is going to be 900 so we have 900 minus 4 * 9 which is going to end up being POS 36 so POS 36 C is going to equal zero from here we'll subtract 900 from both sides and we'll end up with 36 C is equal to 900 and then from there we'll divide both sides by 36 to get that c is equal to 900 or I'm sorry 900 divided 36 okay now 900 divided 36 is going to give us - 255 so we know our value for C must be -25 this SAT Math problem may seem scary but it's actually really easy and today I'm going to explain why question 27 states in the given system of equations p is a constant if the system has no solution what is the value of P so this is a system of linear equations and in order for a system of linear equations that have no solution the slopes must be the same but the Y intercepts must be different now these are going to be in standard linear form now they aren't really in it yet but we're going to put them in it and that'll make it a lot easier so let's start with the top equation now standard linear form is where you have a coefficient in front of your Y and then a coefficient in front of your X and it's set equal to a constant all right so let's go ahead and do that we'll start with equation one which I'm just going to Mark with a one right here now we have 3 over2 Yus 1 4X = 2/3 - 3 2 y now we need to move this right here over here and we're going to do that by adding it since it's minus 3 over2 y we're going to add 3 over2 y to both sides now that's going to end up leaving us with 3 over2 y + 3 over 2 Y which will ultimately simplify down to 3 y so now we have 3 y - 1 4X is equal to 2 over3 for our first equation now like I said we have to have the same slope so let's go Ahad and find the slope for this first equation well when we have standard linear form which where we have a coefficient in front of our Y and a coefficient in front of our X set equal to a constant our slope is going to equal a b where okay and M is going to represent our slope where the a value is the value that is in front of our X which in this case is NE 1 over4 okay so we're going to end up with positive 1 over4 because we have negative negative 1 over4 which gives us that postive 1 over4 we're going to divide that by b b value being three so we're going to divide that by three now keep in mind when you are dividing by three right divide by 3 over 1 okay we multiply by the reciprocal right so that'd be the same as multiplying by 1/3 okay so that makes it a lot more simple so we got 1 over 12 now okay so now we know that our slope is 1 over 12 now like I said we need to have the same slope in this next equation in order for there to be no Solutions all right so let's get to that same slope once again we want to put it in the same form so let's go ahead and bring this py over by subtracting it okay so we're going to end up right here this is be our second equation 12x we have this + 3 over2 which we can actually just go and move to the other side so we'll move it to the other side okay but we're going to have minus py okay and we have 9 / 2 - 3 over2 okay which is UL going to leave us with 6 over2 which is 3 so we just put that equal to 3 okay so now we got to solve for what p is well we know we need to get the same slope so we're going to have 1 over 12 1 over 12 must equal now we got negtive a our a value here is2 so that' be negative -2 okay and then we have to divide that by our B value so we have to divide that by this negative P so we have to divide that by P over 1 now like I said we can just change this Division and multiplication by doing multiplying by 1 over P so multiply by 1 P multiply it by 1 P okay so now we see that these negative signs are going to cancel so we'll just go ahead and get rid of those negative signs all right so now we have ones in all of our numerators and then we have 12 is equal to 2 p so we have 12al 2 p we divide both sides by two and we're going to end up getting that six is equal to P so we see our answer there will be six so even though this problem looks really scary it's actually pretty simple it's just a matter of knowing how to set it up understanding standard linear form how to get your slope and the fact that in order for there to be no solution you have to have the same slope and a different Y intercept which as you can see here we do have different y intercepts as well here's how to interpret bar graphs on the SAT Math section question one States a group of students voted on five after school activities the bar graph shows the number of students who voted for each of the five activities how many students chose Activity three in this case we'll take a look at our y- axis we see that that's number of students therefore we want to know the number of students who voted for Activity 3 we find that bar and if we go ahead and go across we see it's somewhere around 30 38 or 39 which we see is answer Choice B here's how to answer this sat math question about percentages in under 60 seconds question two states what percentage of 300 is 75 all you got to do is do 75 / 300 and then that will get you your decimal to convert that to a percentage you multiply it by 100 and that would get you 25% so your answer is answer Choice a here's how to solve this sat math question in under 60 seconds the question States what is a solution to the given equation in order to solve this we need to isolate X we'll start by multiplying both sides by 25 next thing we have to do is get X all alone so we have to take the square root of x^2 which means we also have to take the squ otk of 36 * 25 this leaves us with X is equal to the square < TK of 36 * 25 which will equal out to 30 so we know our answer there is going to be answer Choice B here's how to efficiently solve this s math question the question States three more than 8 times a number X is equal to 83 which equation represents the situation so one thing you'll not is as I read the question I started writing down the equation I notice we have three more that means 3 plus something 8 * a number which is represented as X so Plus 8 x is equal to 83 we're ask for the equation we've already got it so 3 + 8x = 83 we see that we have that in answer Choice D so D will be our correct answer there here's how to interpret this word problem on the SAT question five states Hannah deposited a fixed amount into her bank account each month the function f of tal 100 + 25t gives the amount in dollars in Hannah's bank account after T monthly deposits what is the best interpretation of 25 in this context well we know F represents the amount in her bank account this 100 since it doesn't have any variables next to it is her initial amount and then she's adding on $25 every month so that that 25 is the amount that she's depositing every month so we have option A with each monthly deposit the amount in hanah's bank account increases by $25 yes that is a correct interpretation so our answer is a here's how to quickly solve this sat math question and a trick to check your work question Six States a customer spent $27 to purchase oranges at $3 per pound how many pounds of oranges did the customer purchase well we know that she spent $27 so that's $27 now we have to divide that by that $3 per pound okay so that's $3 per pound I'll represent pound as lb okay now what we see here is that our dollars are going to cancel and what we're left with is 27 over three which is 9 Pound okay so we have N9 pound and obviously you're seeing that this is the correct sort of equation to set up because we end with pounds we want know how many pounds of oranges the customer purchased so that's one way you can check is by making sure you end with the correct units um and as you can see our answer there will be nine here's a tip to help you be more efficient on the SAT Math section and how to apply it so when you glance at question 7 you see it's going to be more more than three lines now because it's more than three lines I'm probably going to be dealing with some sort of equation or system of equations or system of inequalities what I'm going to do is as I read through I'm going to start writing down coefficients and variables so that I can kind of get my equation on my initial read through hopefully which should save me time so let's go and read through now here about nine storage bins that were each the same price he used a coupon for $63 off the entire purchase the cost for the entire purchase after using the coupon was $27 okay and we know that he got $63 off and it's nine times some variable we'll see if we get what that is what was the original price and dollars for one storage bin we're not given it so we'll just call that X okay so now we have to solve for x x is the cost per storage bin um so all we got to do here is isolate X We'll add 63 to both sides okay we're going to end up with 90 is equal to 9x we divide both sides by 9 and that will give us X is equal to 10 so our answer there will be 10 so as you can see by writing down our coefficients and variables on our initial read through we're able to save time because we don't have to go back and find these coefficients and variables we're able to get that equation set up immediately after our first read through avoiding a second read through and saving us time here's how to turn a table into a linear function on the SAT question 8 States for the linear function f the table shows three values of X and their corresponding values of f ofx which equation defines F ofx in this case all my answer choices are in slope intercept form so what I'll start by doing is finding Intercept in this case since I'm given the x coordinate of zero I know that my Y intercept will be at 29 which means I can get rid of B and I can get rid of D next thing I'm looking at is slope okay I see that when I go over one I go up by three which means my slope is going to be 3x my answer there there will be answer Choice a here's how to quickly solve this LCT math question about similar triangles question 9 States right triangle pqr and S are similar where P corresponds to S if the measure of angle Q is 18° what is the measure of angle s okay so we know Q is 18° okay we also know then that t is going to be 18° since these are similar triangles okay now we want to solve for the measure of angle s the measure of angle s is the same as the angle measure of P so what we can do here since this is a right triangle okay we know that 90 is going to equal our angle measure s so S Plus our angle measure that is 18° so that would be angle measure t Okay so plus 18° 90° = S Plus 18° that means that s is going to equal 90 minus 18 90 - 18 will leave us with 72° so 72° will be our answer for the value of angle s so our answer is B here's how to answer this question about Scatter Plots on the SAT question 10 states a scatter plot shows a relationship between two variables X and Y which of the following equations is the most appropriate linear model for the data shown in this case since we're looking for a linear model I'm going to go ahead and find about where the Y intercept is it's right around 10 I see my slope is going to be negative so if I'll go down to my answer choices anything with a positive slope I can get rid of so that means answer choices answer choices a I can get rid of and answer Choice C I can get rid of because they both have positive slopes then I'm looking at my Y intercept my Y intercept needs to be right around positive 10 uh which I see I have in answer Choice D so D we have that positive Y intercept somewhere around 10 then we also have that negative slope of around one so D will be our correct answer there here's how to quickly solve this sat math question question 11 states the given equation describes the relationship between the number of birds B and the number of reptiles r that can be cared for at a pet care business on a given day if the business cares for 16 reptiles on a given day how many birds can it care for on this day well we know we can plug in 16 for R then if we plug in 16 for R we're going to end up with 5 * 16 which will equal 80 so then we would have 80 is equal to 80 okay which means that the value of B has to be zero okay so our answer is a here's a trick to help you move faster on the SAT Math section if we take a look at question 12 it asks what is an equation of the graph shown if I glance at my answer choices I see all my y intercepts are the same so I'm really worried about my slope here I see my slope is negative which means I get rid of anything with a positive slope the next thing I see is I've got to calculate the negative slope and see what it is well I see that right here I go down by two and I go over by two now the key thing that they're testing you on is whether or not you're taking a look at what the units are okay because if you look here even though we only have one dash that we are changing we are actually moving over to the right by two units so the key thing here is to make sure that you're paying attention to what your units are on your x axis and your y AIS so as we can see we are going down by two and we are going to the right by two which means that our actual slope here is just okay so our answer there is C here's how to answer this sat math question super quickly question 13 states if x over 8 is equal to 5 what is the value of 8 overx since we know that X over 8 and 8 overx are just flipped all we got to do is take this 5 over one flip it to 1 over five and that'll be our answer here's a trick to help you be way more efficient on the SAT Math section question 14 States the solution to the given system of equations is X Y what is the value of y the key thing to pay attention to on questions like this is what you're asked answer with in this case it's the value of y which means there's a chance we don't have to calculate the value of x if we take a look at this system of equations whenever you see stacked equations like this you want to look to add or subtract this bottom equation from the top one and sometimes that might be mean that you have to multiply the bottom or the top equation by some number in order to get to the value you want to answer with which in this case is y so to get y we want to get rid of X so let's take a look if we can do that well if we multiply this bottom equation by four we're going to end up with 24x and then we can go ahead and subtract this bottom equation from the top equation and then we'll be left with a Y value and then a constant so let's go ahead and do that so we're going to have 24x - 4 * 6X so - 24x our X's are then gone then we have y - 4 y because we have to distribute this four so y - 4 Y is going to leave us with -3 Y is equal to 48 - 4 * 72 which when we put in our calculator will give us -240 so from there we isolate y by dividing both sides by -3 so we can go ahead and divide both sides by -3 and that's going to leave us with positive 80 as the value of y so our answer there is 80 here's a trick to solve this sat math question way faster question 15 states line T and the XY plane is a slope of 1/3 and passes through the 910 which equation defines line T first thing I'm seeing is I've got this slope of 1/3 which means I can get rid of answer choices A and B and I'm left with c and d the only difference with the two being their y intercepts now since I know that this is ultimately going down and I've got these points 9 and 10 if I plot that point just roughly I know my Y intercept is going to to have to be uh somewhere above 10 right because we got to be going down throughout this time so because we have these points that's why we know that thus our answer cannot be C because C would require us to have a flat line in order to hit that point so we know that that cannot be true and we know our answer there has to be answer Choice D here's how to interpret exponential growth word problems on the SAT Math section question 16 States the function f ofx is equal to 206 time 1.34 is the power of X models the value in dollars of a certain bank account by the end of each year from 19 57 through 1972 where X is the number of years after 1957 which of the following is the best interpretation of f of 5 is approximately equal to 243 in this context well we know that that 243 is ultimately what the value of f of 5 is therefore that 243 is the amount that is in the account after 5 years after 1957 so that would put us at 1962 okay so let's go and find the answer choice that matches up with that interpretation we have option a value of the bank account is estimated to be approximately $5 greater in 1962 than in 1957 no B the value of the bank account is estimated to be approximately $243 in 1962 yes 1962 is 5 years after thus the F of5 and it's equal to that $243 in value here's how to quickly answer this sat math question using proportions question 17 States for a certain rectangular region the ratio of its length to its width is 35 to 10 if the width of the rectangular region increases by 10 by seven units how must the length change to maintain this ratio Rao okay so what we know here is that our length is going to equal 3 1/2 * our width and the way we get that is by having 35 over 10 right if you were to rewrite 35 over 10 you get 3 and A2 all right so now from here we want to know if we increase our width by seven units how much will our length change well we can just use this proportion right here so all we would have then is 3 1/2 * 7 which will equal 242 so we know that we must increase by 24 1/2 since we are increasing ining our width we must also increase our length in order to maintain that ratio or proportion so our answer there is B here's how to break down hard sat math problems to make them easy and simplistic question 18 states Square P has a side length of X in square Q has a perimeter that is 176 in greater than the perimeter of square P the function f gives the area of square q and square in which of the following defines F okay well we know that ultimately the perimeter of square Q is going to be 4X Plus 176 I'll write that is equal to perimeter of square Q okay now the key thing here is we need to understand what we have to solve for and that's the area of square Q so in order to find the area of a square we need to know the side length so in order to find the side length here what we can do is we can take this perimeter and we can divide it all by 4 so if we go and take 4X plus so 4x + 176 and we divide all of that by 4 that's going to leave us with x + 44 as the value of the side length now the area of the square then is going to be the value of the side length squared so we know our answer there will be answer Choice a here's how to quickly rearrange variables on the SAT question 19 States the given equation relates to the distinct positive real numbers WX and Y which equation correctly expresses W in terms of X and Y well in this case all we got to do then is isolate W as you can see in all our answer choices so what we'll do here is we'll go ahead and divide both sides by two when we divide this side by two we see we have 2 * 7 which is going to equal 14 so we can go and cancel both these 14s now we're left with X over Y is equal to theun of w + 19 so we're going to goad and square this side so we can get that W out from underneath that square root and since we're since we're squaring that side we also have to square this side so what we're going to end up with then is going to be X over y^2 is equal to W + 19 to isolate w we got to subtract 19 from both sides so we're going to end up with W is equal to X over Y and that's all going to be squared minus 19 if we look at our answer choices we see that that's going to be answer Choice C so c will be our answer for question 19 here's something really simple about circles that you need to know for the SAT question 20 States 0 is the center of a circle the measure of Arc RS on the circle is 100° what is the measure in degrees of its Associated angle RS now what you need to know here is that if you have an an arc for example RS and you have its Associated angle that Associated angle is going to be the same degrees as the arc so the answer here is just 100 and if you want to see this sort of drawn out I'll do that really quick okay we have Center o and we're drawing r o s so R to O to S okay we're told that the Arc RS is 100° well that means that the angle also has to be 100° here's how to quickly solve this difficult sat math question question 21 states the expression and then I'm not going to say that but you can read it is equivalent to a x^ B where A and B are positive constants X is greater than one what is the value of a plus b pay really close attention to here this is free response it'd be very easy for someone to answer with the value of a or b or a times B we need to answer with a plus b okay that means said let's go ahead and solve so what I see here is that I'm taking the fifth root and then the eighth root so I've got a six and then we've got fifth root of 3 raised to^ 5 which would leave us with just three since that's 5 over 5 which is to the power of one okay so I'll just write that as power to one so you understand that next thing we have is X to 45 over 5 okay so x to the 45 over 5 is the same as x to the power of 9 okay so we have x^ of 9 now we have to multiply that by this otk 8 * or root8 and then 2 the^ of 8 which is the same as 2 the^ of 8 over 8 or 2 to the^ of 1 and we have to multiply that by x to the power of 1 over 8 all right so from here it's pretty simple we're going to take this 6 * 3 * 2 and 6 * 3 gives us 18 18 * 2 gives us 36 so now we have 36 okay so now we have 36 now the next thing we've got is this x^ of 9 * x^ of 18 so what I'm going to do is I'm going to go and convert this 9 into something where the denominator is8 as well so I'll do 9 * 8 and that's going to give us 72 so we have X to the^ of 72 over 8 and now I can go ahead and add 72 and 1 to get me x^ power of 73 over 8 okay now we know that our value for a is going to be 36 okay so a will equal 36 and we know that our value for B is going to equal 73 over 8 so from here what we have to do is we have to sum these two values together now in order to sum these together I need to convert this 36 into also being over8 so I'll go ahead and convert that so that's going to be 36 * 8 which will give us 288 288 over 8 so now we have 288 + 73 288 + 73 is going to leave us with 361 all over 8 so our answer there is 361 / 8 here's how to answer this difficult question about calculating the area of a triangle on the SAT question 22 States a right triangle has side lengths of 2 < tk2 6 < tk2 andun 80 what is the area of the triangle in square units key thing we have to figure out here is what is the hypotenuse out of these three lengths because we know the formula for the area of a triangle is equal to/ 12 the base times the height so what I notice here is that I've got 2 < tk2 6 < tk2 so this is obviously the greater so we know one of our legs would be that 2 < tk2 now between 6 < tk2 andun 80 what I know is if I take six and I Square I get 36 okay so what I could do is I could rewrite 6 < tk2 is equal to < TK 72 and I getun 72 because I take 6 squar that gives me 36 and then I multiply that by that two okay so I know that ultimately this root 80 is what will be hypotenuse so therefore I know that my base and my height values can be represented then as that 2 < tk2 and then that 6 < tk2 okay from here it's really easy because we see this two is going to cancel with this two and we're going to be left with a is equal to 6 * < tk2 * < tk2 which we know will end up equaling 6 * 2 which will equal 12 okay so our answer there' be answer Choice B here's how to solve one of the most difficult questions on the SAT Math section and even though I think this question is kind of pointless and stupid I'll still show you how to solve it question 23 States the expression 4x^2 + BX - 45 where B is a constant can be Rewritten as HX + K * X Plus J where H K and J are integer constants now if you ever come across on the SAT them saying that something is integer constants that probably means it's going to be required in order for you to solve the problem so pay close attention to it which of the following must be an integer so once again if they're telling you that something needs to be an integer pay attention to that always so in this case what I'm going to do is I'm going to start by expanding this right here this HX plus K * X Plus J I'm going to expand it out um because as you can see we're going to need to end up getting the values for you know H uh k um possibly J as well in order to get our answer so let's go ahead and do that so I'm going to end up with 4x^2 + BX - 45 is going to equal and now we'll go ahead and expand on this we'll have H x^2 hx2 and then we'll have plus KX and then we'll also end up with a plus jhx as well so we're going to have plus J J HX + KX and then we'll have a plus k j as well from this K * J okay so from here let's go ahead and try to simplify this right side um so we'll still have hx2 but I see I have this common factor of X so I'm going to go ahead and pull that out so we'll end up with plus x * JH + K and then plus KJ all right from here let's start getting what things equal we see that we're going to have a -45 is equal to the value of K * J the other thing that we see is that we have this BX not necessarily anything we can really do with that at this point we know that four is going to equal the value of H since we have 4x^2 and hx2 so we also know that four would equal the value of H uh from here this is the point where it really becomes important to pay attention to the fact that H K and J have to be integers um because they have to be integers I can then state that uh K must equal -45 over J if we see this that 45 over J then we know that that's an integer if we also see that J is equal to -45 over K we know that that would have to be an integer as well and then obviously if we see you know the value of just H so let's go and run through these we have option A B over H obviously we don't have the value of B so that's not going to be our answer uh at least you know not at this point B uh B over K once again I'm not really looking for the value of B down here 45 um over H we know H is 4 45 over 4 isn't an integer um it is a decimal but it's not an integer and then we have C 45 k um which we know would actually have to be our correct answer here and I'll go and explain why right like I said we have J is equal to5 45 K we know that J is an integer just because there's a negative doesn't mean that it's not an integer right so our answer there would have to be answer Choice D because this ultimately has to be um negative and then 45 overk has to be an integer keep in mind that if we haveg -3 for example that's an integer as well so our answer there would be D and that's how you solve this really difficult SAT Math problem here's how to efficiently solve this difficult SAT Math problem question 24 states in the given system of equations a is a constant the graph of the equations in the given system intersect at exactly one point anytime you're told that a system intersects at exactly one point or exactly two points or that it never intersects pay close attention to that in the XY plane what is the value of x always pay close attention what you're asked to answer with as well in this case it is the value of x okay so that means we might not actually have to solve for a okay we just need to solve for the value of x all right so immediately what jumps out to me is I have y equals and Y equals so I'm going to go ahead and substitute this 3x + a over here for y then I'm going to work to set it all equal to zero and the reason why I want to set it all equal to zero is because I want to end up using B ^2 minus 4 a c is equal to Z because if this value is equal to zero then that means that we have one real solution or in other words we intersect at exactly one point so that's ultimately what I'm trying to get uh in terms of the form so I want to set it equal to zero to do that I'm going to have 2x^2 and then I have this minus 21x but I also have to subtract 3x from both sides so once I do that that's going to end up leaving me with -4x and then I have plus 64 but I also have to subtract a from both sides so that's going to give me plus 64 minus a now what I'm going to do here is I just want to deal with a c value I don't actually want to deal with 64 minus a so I'm just going to go plus C and then I'll State up here that c is equal to 64 minus a all right from here we know that our B value is -24 so we'll have -4 ^ 2 - 4 * our a value which is 2 * C and we know that's all has to equal zero for there only be one real solution now -42 is going to give us 576 when we put it in our calcul we have 576 minus 8 C is equal to 0 we can rewrite this as 576 is equal to 8 C by adding 8 C to both sides which therefore means that c is going to have to equal that 576 / 8 which is going to equal a value of 72 okay so now I'm going to go ahead and erase the value of C here and I'm going to put in 72 we'll put in that equals 0 as well and then I'm going to erase everything down here okay so from here we're going to look to factor out what we can and solve for the value of x so I see that 2 is a common factor in all these so I'll factor out of two I'll be left with x^2 - 12x + 36 is equal to zero from there I'm looking for numbers that multiply to get uh 36 that will have a sum of -12 um so from there I'm looking at 6 as the value for that so that would be x - 6 * x - 6 okay now we Factor this out we see that X will have to equal 6 so our value uh for the value of x then would be six so our answer there would be C here's something you need to know about Isles right triangles for the SAT question 25 States an Isles right triangle has a hypotenuse of length 58 in what is the perimeter and inches of this triangle all right so let's go ahead and write this out anytime you're given a triangle or a circle questions on the SAT it's usually helpful to write it out so we're given our hypotenuse now keep in mind that since this is an isoceles right triangle we know that it's a 454590 triangle which has this special property where the side length x will be the same side length since isoceles and then the value of the hypotenuse would be x * < tk2 now this is important because when we have our given hypotenuse of 58 in I would elect to rewrite this actually as and I'll just write that this is equal to 29 * < tk2 * < tk2 and you'll see why I'm writing that in a second here so * Ro tk22 * < tk2 now the reason I'm choosing to write it like that is because then we know that our values down here would be 29 time < tk2 since they just don't have that extra root2 added on to them and since their isoceles they're going to be the same now from here we want to find the perimeter so the perimeter is pretty easy to do we're just going to add in all these side lengths we'd have 29 * < tk2 and we'd actually multiply that by two since we'd be adding it to itself that's the same as multiplying by two which is ultimately um I'll go over what that'll equal out to in a second but we also have to add on to that then our variable of hypotenuse which we know is 58 okay so from here we have 29 < tk2 * 2 that's going to end up leaving us with 58 < tk2 plus 58 as a value of our perimeter which we see is going to be equal to answer Choice C so c will be our correct answer there here's how to solve one one of the most difficult questions on the SAT question 26 states in the XY plane a parabola with vertex 9 and -14 intersects the xaxis at 2 points if the equation of the parabola is written in the form y a X2 plus BX plus C where a B and C are constants which of the following could be the value of a plus b plus C now keep in mind we always want to pay attention to what we're asked to answer with in this case that is the value of a plus b plus C so we need to know the value of all three values so first thing we know is our vertex so if we're given our vertex on a parab question like this we're probably looking to use vertex form now vertex form be Y is equal to a * x - h^ 2 + K where our vertex is where vertex is h k all right well we know our vertex let's go ahead and substitute in so we're going to have y is equal to a x - 9^ 2 - 14 okay from here we want to get these values a b and c which means we need to get into the form of ax^2 plus BX plus C so to do that let's go a and expand this x - 9^ 2 so we're going get Y is = a * x^2 - 18 - 18x and then we would have + 81 - 14 or that'd be plus 81 um yeah plus 81 - 14 all right so now from here we need to distribute this a so we got to distribute the a to the x^2 to that 8X and to that + 81 so I'm going to go ahead and race what we have here so we're going to have y is equal to ax^2 - 18 a x + 81 a - 14 all right so now from here what I'm going to look to do is get the values of a b and c so let's start with a so we know that a is going to equal just a it is what it is now B is going to equal this value of -8 ax or8 a since that that X is included right here so8 a our C value is going to equal 81 a -4 so -4 all right so from here I want to sum these all together so a + B+ C is going to equal a - A + 81 a - 14 now from here what we're going to look to do is go and combine these a terms so what we'll have then is a minus 18a which will give us7 A7 a + 81 a will give us positive 64 a so we'll have 64 Aus 14 now what I'm immediately noticing and that I want to look at is we have to keep in mind that this intersects the xaxis at two points now because we're intersecting the x-axis at two points but we know our vertex has a y-coordinate that's below that x-axis we know that we must open up so our Parabola must look like this like a smiley face you must open up to cross that x-axis well that means that the a value must be positive so if our a value must be positive then we're going to have 64 times some positive number let's just pick 0.01 just as an example here okay and then we have to subtract 14 from it so we know that we can't ever get below ne4 we can't even reach -14 right because this is going to be some positive number we're subtracting that4 so we can't get to4 we can't get to9 and we can't get to -23 okay we would have to have that value be -12 that's the only possible value so our answer has to be D here's something you need to watch out for on the SAT question 27 States function f is defined by f ofx = a^ of x plus b where A and B are constants and the XY plane the graph of yal f ofx - 15 as a y intercept of 099 over 7 where the product of or the product of A and B is 65 over 7 what is the value of a so a couple things you need to look out for here number one what are you asked to answer with in this case it's a value of a so that's the only thing we should really focus on solving unless there's something we need to solve before in order to get to the value of a next thing we are given that the product of A and B is 65 7 so let's go and write that a * B is equal to 65 over 7 now the main thing you need to watch out for in order to avoid getting stuck on this question or getting it wrong is the fact that we have y is equal to FX minus 15 if you ever have a transformation like this on the SAT you really need to pay attention to it because if you don't you're probably going to end up getting it wrong so in this case we have F ofx equal to a to^ of X plus b well we know that y then must equal a a^ x + b - 15 okay and that's a really important distinction now that we have the value of y let's go ahead and substitute in our points so we have this point of X being 0er so that would equal then a to the^ of 0 plus b - 15 is going to equal that value of 99 over 7 so we have 99 over 7 now from here what we're going to look to do is solve for the value of B and then we can use B in order to get the value of a using this equation equ up here so to solve for b we can go ahead and write this and I'll try to write it out a little bit bigger up top so as you can see we had a^ of 0 and any number to the power of 0 is 1 so that leaves us with this - 1 + B minus 15 now from here what I'll do is I'll go ahead and add one or add 7 over 7 to both sides now once I add 7 over 7 to both sides I'm left with 92 over 7 is equal to B minus 15 I'll do the same thing with that 15 so I'll add 15 * 7 over 7 to both sides if I put my calculator here 15 * 7 that's going to give me 105 okay so if I add 105 over 7 to both sides that's going to end up leaving me with B is equal to 13 over 7 all right so now that I have my value of B I can go back and I can solve for the value of a now how can we do that well if we go ahead and divide both sides by B here we would get a is equal to 65 over 7 * B okay well we know that the value of B is 13 over 7 so if we go ahead and plug that in for the value of B 13 over 7 we see that these sevens are going to cancel we're going to be left with 65 divided by 13 which is going to equal five so our answer for the value of a which we're asked to answer with always check that is five here's how to quickly interpret this line graph question one States the line graph shows the estimated number of chipmunks in a state park on April 1 of each year from 1989 to 1999 in our Y axis we see we have the estimated number of Chipmunks xaxis We have year based on line graph in which year was the estimated number of chipmunks in the state park the greatest what we see that the greatest or maximum point is right here which we see is going to be in the year 1994 so our answer there is B here's a tip for unit conversion questions on the SAT question two states a fish swim a distance of 5,14 yards how far do the fish swim in miles what you're going to do is you're going to take your number of yards 5,14 and we'll use y to represent yards here we want to multiply in a way that gets rid of the Yards we want our yards on the bottom we want that 1760 yards per one mile with yards in the bottom now as you can see our yards will cancel and we left with our distance in miles which when we put this into our calculator will give us 2.9 miles and as you can see our only unit that is left is Miles here's how to solve this sat math question in under 60 seconds question three states which expression is equivalent to 12 x Cub - 5 x Cub key thing here is since you have X cubed and X cubed you just do that 12 - 5 that's going to leave you with 7 x cub and your answer there is going to be C here's a tip for the SAT Math section question four states what is the solution XY to the given system of equations if you see that you have 5 yal x you can go ahead and take this X and you can substitute in that 5 y this will help you solve y afterwards you can solve x so let's go and do that 5 y + y will give us 6 Y is equal to 18 from there we divide both sides by six and we'll see that Y is equal to three now at this point we have to go ahead and take we can actually just take a look at our answer choices and see that our answer has to be a and the reason our answer has to be a is that's the only answer Choice with three as our y value so as you can see you don't always have to solve for both X and Y sometimes you can solve for just one of the variables here's how to quickly solve this sat math question question five states the point 82 in the XY plan is a solution of which of the following systems inequalities well we have our X point of 8 and our y point of two so let's go ahead and check well if we plug in 8 for X we have 8 is greater than Z that's true now is 2 greater than Z that's also true so our answer has to be a here's something you need to know about absolute value for the SAT Math section if you take a look at question six it says what is one possible solution to the given equation well here we have the absolute value of x - 5 is equal to 10 so the way that we're going to set this up is first by doing x - 5 is equal to 10 when we do that we see if we add five to both sides we'll get x equal to 15 so one of the possible answers here is 15 but there is another possible answer when you have absolute value like you here another way or your other answer here would Bex - 5al to 10 from there you distribute that negative sign to your X and also to your minus5 that's going to end up giving youx + 5 is equal to 10 you would subtract five from both sides and you would getx is equal to 5 and then from there you would get that X is equal to5 so neg5 could be your the other answer to this question here's how to efficiently solve this math question question seven states the function gives the total number of people on a company retreat with x managers what does the total number of people on a company retreat with seven managers well in this case we just plug in seven for X so we would have F of seven is going to equal 7 * 7 + 1 7 * 7 is 49 49 + 1 is 50 so our answer there is 50 here's how to quickly solve this sat math question by plugging and chugging question 8 states which table gives three values of X and their corresponding values of H ofx for the given function all right so the first thing I'm going to notice is that all of these have these X's of one two and three so it's goingon to be pretty easy to solve this I'll start by plugging in one for x if I put in one for X I have 1^2 minus 3 I know 1^2 minus 3 is going to give me a value of -2 therefore I can get rid of a b is still possible answer because that is true C I can get rid of and then D is also possible answer because that's true next thing I'm going to do is I'm actually going to jump to three just because I know it's really easy 3^ s - 3 well 3 squ is 9 9 - 3 would be 6 so I see that I have three and six which is true if I look here three and three isn't true and three and three isn't true my answer there has got to be answer Choice B and the reason just to point this out really quickly the reason I chose three is because I saw that two and one here are both the same okay because two and one were the same and B and D and those were the two that I had it narrowed down to there was no point in checking them I went ahead and moved on to using the x value of three here's something you need to know about when the exponent is zero for the SAT question 9 States the function f is defined by F ofx equal 270 * 0.1 the^ of X what is the value of f of 0 well if we plug in 0 for X we have 0.1 raised to the power of 0 now 0.1 ra to the power of 0 is like any number raised to the power of 0 it's going to equal one therefore you're going to end up with 200 70 * 1 which is just going to equal 270 and your answer will be answer Choice D here's something you need to know about margin of error for the SAT question 10 states to estimate the proportion of a population that has a certain characteristic a random sample was selected from the population based on the sample it is estimated the proportion of the population that has the characteristic is 0.49 with an estimated margin of error of 0.04 based on the estimate and the margin of error which of the following is the most appropriate conclusion about the proportion of the population has the characteristics a couple things I want to point out here number one we are taking a random sample it's very important we take a random sample because if we don't we can't apply it to the general population it has to be a random sample in this case it is so that's perfect now the next thing we need to knowe is that the estimated proportion of the population that has a characteristic is 0.9 with an Associated margin of error of 0.04 so what that means is answer Choice a it's plausible that the proportion is between 0.49 and 0.53 and you get that by adding 0.04 to 0.49 and subtracting 0.04 to 0.49 so our answer there has to be answer Choice a here's a tip to help you move faster on the SAT if you encounter a word problem you see it's more than three lines try to write out the equation or system of equations or system of inequalities that comes up in the question as you read it on your first read through that way you don't have to do a second read through when you're done reading the question so let's go ahead and Show an example a moving truck can tow a trailer if the combined weight of the trailer and boxes is no more than 4600 lb well that means that 4600 lb must be greater than or equal to the combined weight of the trailer and the boxes now what is the maximum number of boxes this truck can tow in a trailer with a weight of 500 lb if each box weighs 120 lb so we'll use uh B for the number of boxes okay now we have to keep in mind here that we just got to solve for b so we'll just subtract 500 from both sides that's going to end up leaving us with 4100 must be greater than or equal to 120b we'll divide both sides by b or I'm sorry divide both sides by 120 okay 4100 / 120 we can put that in our calculator when you put put that in your calculator you're going to get 34 repeating okay now keep in mind that B has to be less than that so the maximum number of boxes would be 34 so our answer is a this sat math question is a great example of when it can be a great idea to use Desmos on the digital sat question 12 States what is the positive solution to the given equation well what I would do here is I would take this and set equal to zero so I'd have -4x ^2 - 7x + 36 is equal to zero now from here what I'm going to do is I'm just going to go ahead and put it in Desmos and then I'm going to solve for what the positive solution is by looking at where it equals zeros or in other words where it crosses the x-axis now keep in mind we need the positive solution so the positive solution here we see is 2.25 or in other words 9 over4 so our answer there is going to be answer Choice B here's how to quickly answer this probability question on the SAT question 13 states the table summarizes the distribution of color and shape for 100 tiles of equal area if one of these tiles is selected at random that's a key component here what is the probability of selecting a red tile express your answer as a decimal or fraction not as a percent all right so ultimately here we are selecting a red TI we see the total number of red tiles is 30 and this is out of a total of 100 so that' be 30 over 100 which we'll calculate out as a decimal of 0.3 so our answer there is 0.3 here's something you need to know about parallel lines for the SAT Math section question 14 States for the given function f the graph of yal f ofx in the XY plan is parallel to line J what is the slope of line J well since they're parallel they have to have the same slope which means that line J must have a slope of two here's how to quickly solve this math question that deals with proportions and differences question 15 states a proposal for a new library was included on an election ballot a radio show stated that three times as many people voted in favor of the proposal as people who voted against it so we have three times the number that who voted against it which I'll represent as an a is equal to the number who voted in favor of it social media post reported that 15,000 more people voted in favor of the bill or of The Proposal then voted against it okay so we also know that the number of people who voted in favor is equal to the number who voted against it plus 15,000 based on these data how many people voted against the proposal so in this case you want to solve for a what we already have what f is equal to so we can go and substitute in so we would have f is equal to a + 15,000 so a + 15,000 from here I'll go ahead and isolate a by dividing both sides by three so I'll have a is equal to a over 3 + 15,000 over3 which would simplify down to 5,000 from there I'll go and subtract a over3 from both sides a minus I'll just write this out a minus a over 3 is going to equal out to 2 a so 2/3 * a which is equal or which is equal to 5,000 still next thing we'll do is we'll multiply both sides by 3 over2 so we'll multiply both sides by 3 over2 okay keep in mind that 5,000 * 3 over2 will give us 7500 so we'll have 7500 then is equal to a so our answer there is answer Choice a here's something you need to know about intersecting parallel lines on the SAT question 16 states in the figure lines M and N are parallel if x = 6 k + 13 and Y = 8 K - 29 what is the value of Z so always pay attention to what you're asked to answer with in this case that is the value of Z well to calculate the value of Z we need to know what this angle right here is now we know that that angle has to be the same as the value of angle Y and the value of angle X so we can go and just put y as the angle measure there as well so what we ultimately need to do is we need to get 180 which is the value of this semi Arc right and we'll take that or that you know that angle measure right 180 we have to then subtract angle Y and that'll give us angle Z so we need to solve for angle y first well in order to solve for angle y we know that X and Y are equal to each other so we'll set these two together and we'll solve for K and that'll give us the value of angle y so we have 6K plus 13 is equal to 8 Kus 29 now from here I'll go ahead and subtract 6K from both sides once we do that we'll be left with 2K on our right side we'll go Ahad and add 29 to both sides so we can start isolating K even further that's going to leave us with 42 is equal to 2K we'll divide both sides by two and we'll get that K is equal to uh 21 so K would equal 21 from there we can go ahead and solve for the value of y all right so we have K is equal to 21 so we have then the value of uh we'll solve for x just because it looks like it's a bit easier so we'd have value of x is going to equal 6 * 21 + 13 okay 6 * 21 is going to give us 126 126 + 13 is going to give us 139 then we have to do 180 minus 139 to get the value of Z and that's going to leave us with 41 so right answer there is C here's a trick to help you on the SAT Math section question 17 states in the given equation p is a constant the equation has no solution what is the value of p in this case as to answer with the value of P always pay attention to what you're asked to answer with and pay attention to key information for instance the equation has no solution well because it has no solution we know it's set equal to a constant we also know that we have X and a value that will ultimately be with X so because of this if there's any sort of number next to X then we know that we're going to have at least one solution so in order there be no Solutions we need to get this set equal to zero so ultimately what we need then is -3x + 21 PX to equal 0 well in order for that to be the case we can go and add 3x to both sides we'll get that 3x has to equal 21 * P * X we see our X's will cancel and we'll be left then with 3 is equal to 21 p in order to solve for p will'll divide both sides by 21 we'll see that P is equal to 3 over 21 which we know is equal to 1 over 7 so our answer has to be B here's a trick you should know about quadratics for the SAT question 18 states the function f is defined by the given equation for what value of x does f ofx its minimum well if you have a quadratic like this your value of x at which F ofx will reach its minimum or maximum will be the midpoint between the 2x intercepts we see here our X intercepts are going to be 10 and -3 and the way that we get those is by taking a look at xus 10 setting that equal to zero adding 10 to both sides and then you see xal 10 same thing that you'll do for x + 13 you subtract 13 from both sides when it's set equal to zero and you get that xal 13 now from here we're going to take our two x intercepts we are going to sum them together and then we'll divide by two to get theid mid point of them and that'll be the value of x where f of x reaches its minimum in this case that's going to give us -3 over2 so our answer will be D here's a tip that's extremely helpful for the SAT and that is the vertex form of a quadratic and I'm going to illustrate this with question 19 the question States the function f ofx is equal to 1 n x - 7^2 + 3 gives a metal Ball's height above the ground F ofx in inches x seconds after it started on a moving track where X must be between 10 and Z which are both inclusive which of the following is the best interpretation of the vertex of the graph yal F ofx in the XY plane this question is way easier if you understand what this vertex form is well vertex form at its simplest would be f ofx is equal to a which can be some coefficient x - h^ 2 + K where your vertex vertex is going to be H comma K so as we can see in this case our vertex would be at 7 for our x value okay so I'll write seven I'll just rewrite this okay our vertex would be at seven and three okay so that's going to be where our vertex is so understand vertex form is going to help you a lot now we have to keep in mind that seven is not any sort of height seven is just the time since it's that x value now the actual height here is three now the other thing we need to understand is whether this is a function that is opening up or down and you get that from the a value okay and our a value is positive which means that our graph is going to open up like a smiley face now because that's the case we know that that vertex will be a minimum it'll be a minimum point or a minimum height so if we look at our answer choice we have option A the metal Ball's minimum height was 3 in above the ground we know that'll be the correct answer because we ultimately have that minimum height at 73 3 being the number of inches that is above the ground here's how to quickly solve this sat math question about triangles question 20 States in Triangle jkl cosine of K is equal to 24 51 and angle J is a right angle what is the value of the cosine of L well with triangles in cires questions I always recommend to go ahead and just draw them out because it is very helpful to visualize okay in this case we know that we have a right triangle we also know that angle J is going to be the right angle so we can go and put J here and then we'll put k l now we're asked for the value of cosine of L okay we know that the cosine is our adjacent over our hypotenuse all right so in order to calculate this we need to know the values of the hypotenuse and the adjacent one now we also know that the value of the cosine of K is 24 over 51 okay well if the cosine of K is 24 51 we know our hypotenuse is 51 we know that the adjacent side length is 24 so from here what we'll do is we'll do 51 2- 2 4^ s is equal to LJ this line squar all right now what we can do then is we'll just take the square root of all this and the square root of LJ squ and that'll just give us the value of the length LJ okay so once we do that if we put that in our calculator that is going to give us a value of 45 for LJ so we have 45 here now now we're asked for the value of cosine of L so we can go ahead and have the adjacent which is 455 over our hypotenuse of 51 so 45 over 51 which can be simplified down if we divide both sides by 3 to 15 over 17 or you could also put it in your calculator and if you do that you're going to get a value of 0.82 okay so answers are here and here and you could also take uh the value of 08823 and that would be accepted as well by the SAT here's how to solve this sat math question that deals with an equation that has no real solution in question 21 it says in the given equation B is a positive integer the equation has no real solution what is the greatest possible value of B so a couple key things here if you're told that an integer is positive or negative always pay attention to it next thing we know that we have no real solution so we're asked for what the greatest possible value of B is what you need to understand here is that for a quadratic to have no real solution the value of B ^2 - 4 a c be less than zero so from here let's go ahead and get the values of B A and C and we'll plug them in so we know that our value of B here is just B okay it's just what's in front of the X so we have B ^2 then - 4 * a we know our a value is going to be - 1 so I'll just change this to a +4 and then I have multiplied by C our C value is 676 all right from here we have four * - 676 and that'll give us a value of 274 so we're going to have B ^2 then minus 2 or I'm sorry yeah 274 okay we know that this has to be less than zero so from here I'll go aad and add 274 to both sides and I'll end up with B ^2 must be less than 274 at this point we take the square root of both sides to isolate B so once we do that we're going to be left with B must be less than 52 now keep in mind your answer for the greatest possible value of B is not 52 because we have to have a b value that is less than 52 and it has to be a positive integer so the next highest positive integer that is less than 52 is 51 okay so the max maximum possible value of B is 51 here's how to solve this tricky sat math question question 22 States if a new graph of three linear equations is created using the system of equations shown and the equation x + 4 y = 16 how many solutions XY will the resulting system of three equations have well let's start by going ahead and plotting this third equation so we see we have x + 4 y = -16 now I'm going to go and convert that into slope intercept form so it's easier to graph so what I'll do is I'll start by subtracting X from both sides that'll give me 4 y = x - 16 from there I'll divide both sides by four and that's going to give me Y is equal tox over 4 or in other words 1/4x and then I have that much- 16 over 4 which is equal to minus 4 so I'll go ahead and plot that on this graph okay so I have this minus 4 and then I'm going up by about a quarter per so I'll just go ahead and go over four and then I go up by one all right and if I go ahead and do that I'll just kind of draw a rough line because we don't need it to be perfect and as we can see if we extend these lines okay here's where our Crossings will be now as you can see there's not any single point where all three of these lines intersect now there are points where two of the lines intersect but there is no point where all three intersect at one time so the answer here is zero many people would be tempted to pick something like one or maybe two but the correct answer is zero because it's about where all three of these lines intersect at a single point and that never happens here's something you need to know about the formula for exponential growth on the SAT question 23 States the function f gives the value in dollars of a certain piece of equipment after X months of use if the value of the equipment decreases each year by p% of its value the previous year what is the value of P now keep in mind we're talking about how much it decreases each year now what you want to take a look at is your growth factor here now your growth factor is 0.64 which means we are decreasing in value by 1 minus 0.64 which is 0.36 or in other words 36% so our answer here is C and one thing I do want to point out here is that many people might be tempted to take a look at this uh X over 12 and think that that changes something here but it doesn't okay you were ultimately decreasing each year still by that Z or by 036 right since we have this growth rate of 0.64 which means we are decreasing by 36% every year here's something you need to know about medians and ranges for the SAT question 24 States The Dot Plot represents 15 values in data set a data set B is created by adding 56 to each of the values in data set a which of the following correctly compares the medians and ranges of data sets A and B well we know that if we add 56 to each of the values in data set a we ultimately are just going to change these values but we're not actually going to change the range or in other words the distance from the minimum to the maximum we are just going to change what value the minimum is and what value the maximum is but not what the range is or the difference between the two so our range will stay the same so we can go and write that range is going to stay the same I'll just represent that as range is equal now the next thing we need to take a look at is the medians well obviously if we're adding 56 to each of these values they will ultimately change for example 22 plus 56 would then become 78 and then we'd have 79 and then right here we'd have 80 81 and 82 so ultimately obviously our median then is going to increase significantly okay so our median will increase but our range will stay the same okay so option A we have the median of data set B is equal to the median we know that's not true option b we have the median of data set B is equal we know that's not true option C the median of data set B is greater than the median of data set a we know that's true and the range of data set B is equal to the range of data data set a we know that is true so our answer is C here's why you need to know the equation for circle on the SAT question 25 States the equation x^2 + y - 1 = 49 represents Circle A Circle B is obtained by shifting Circle A down two units in the XY plane which of the following equations represents Circle B so first I want to show you what the circle equation is the circle equation would be something like is the circle equation is this x - h^2 + y - k^ 2 is equal to R 2 where R is your radius K is the center y value and H is the center x value so in this case your Center would be h k all right now that I've shown you the circle equation let's go and talk about how you can quickly answer this as long as you know the circle equation well all you're doing here is you're just shifting Circle A Down by two units so you're not affecting you're not affecting the x value of the center and you're not affecting the radius so those need to stay the same and just on that you can get rid of a and you can get rid of C now as you can see the next difference is going to be obviously the K value now you have to understand that if you're sh Shifting the circle down by two units you need to know that that minus K means your Center is at K so if you need your Center to move down then you have to ultimately add to K because if you want to move that Center down two units you have to add two because there's that minus sign in front of K all right so then what you do is you take this minus one you add two and you get y + one so your answer there has to be answer Choice D here's how to solve this very difficult sat math question about surface area question 26 states that two identical rectangular prisms each have a height of 90 CM the base of each prism is a square and the surface area of each prism is K CM squar if the prisms are glued together along a square base the resulting prism has a surface area of 92 47 K CM squ what is the side length and centimeters of each square base all right well we know that the surface area of each prism and keep in mind it says they are identical rectangular prisms we know the surface area of each is going to be K CM squar so we know the total surface area if they were kept separate would be 2K cm squ and we also know that when they are glued together then the total surface area of everything then becomes 92 over 47k which is obviously less than 2K right so the difference there is what we want to find so it' be 2K - 92 47 K now we know that that's ultimately going to equal 2 * the area of each of those squares so that would be 2 * s^ 2 where s is going to represent our side length of the square which is what we want to solve for here all right so let's go ahead and get a value for K here because we're going to need a value of K to then plug into another equation so as far as what the other equation to be let's go and find what that is so we know that we have a height of 90 CM on the rectangular prisms and we know that side length is going to be S we'll represent that as s so we then know that the surface area for the individual rectangular prism will then be represented as 90 which is the height times our side length which we're going to represent as s so in other words we can write that as 90s * 4 since we have four of those side lengths for each part of that rectangle okay so 4 * 90s and then we would have that much plus 2 s^ 2 okay because we also have to account for the Square on the top and the bottom of the rectangular prism and that's all going to equal K all right so if we can find the value of K then we can substitute in so let's go ahead and do that 2K - 92 over 47k will leave us with 2 over 47k and then from there we need to solve for K so we'll multiply both sides by 47 over2 now once we do that we'll obviously end up with k then is going to equal we'll have these two cancel out so we'll have 47 s^2 okay so let's write that neatly K is equal to 47 s^2 all right now let's go ahead and substitute in for K so we have 47 s 2 now I'm going to scroll down so that we can continue writing out this question so from here 4 * 90s will give us 360s we have this plus 2 s^2 and we have this 47 s^2 what I'm actually going to do here is I'm going to start moving everything over to this right side so we can get it set equal to zero now the reason that I want to move everything over to the right side is that I have a positive coefficient in front of s s just because that generally makes questions easier so let's go ahead and do that by subtracting 2 s^2 from both sides and subtracting 360s from both sides once we've done that we see that 0 is going to equal 45 s^2 - 360s from here we can factor out 5s from both that 45 s^2 and that - 360s so once we do that we'll have 0 isal to 5 S * 9 s minus looks like that's going to be 360 / 5 will give us 72 so from here we'll go ahead and set this equal to zero again so now we're going to have 0 is equal to 9 s - 72 from here we'd add 72 to both sides once we do that we're going to have 72 is equal to 9s we divide both sides by 9 72 over 9 is going to leave us with 8 and we see that 8 will be our value for S which we see is going to be answer Choice B so B would be our correct answer here for question number 26 here's how to answer this difficult sat math question about percentages the question States 210 is p% greater than 30 what is the value of P well we know that we start with with the value of 30 then we want to multiply by 1 because if we don't increase at all we still need to multiply by one plus the percent that we are going to increase by so that would be p over 100 now we know that we ultimately need to equal that to 110 from here we distribute our 30 which is our initial value to 1 plus however much greater we are increasing whatever that percentage is so that will give us 30 plus 30 over 100 which can be represented as 0.3 * P that's all going to equal 210 from here we subtract 30 from both sides and we're going to get that 0.3 p is equal to 180 from there we'll divide both sides by 0.3 180 / 0.3 is going to leave us with 600 for the value of P so the value of p is going to be 600 now one thing that you really need to pay attention to here is the wording okay the wording is that it is p% greater than 30 that's really important because you don't know if sometimes they'll say hey P is uh it's p per greater than 30 sometimes they'll say it's p per of 30 sometimes they will say uh it's p% less than 30 so always pay close attention to the wording um with percentages questions because if you don't pay attention to the wording of percentages questions you're going to get it wrong it's really really important now what we're going to do is try to get you some practice for the digital sat reading and writing section so this will be digital SAT practice test 2 module one what we're going to do is I'll give you about 60 seconds to answer a question once that 60 seconds is up I'll go through how I would approach and answer the question and then we'll move on to the next question so with that being said I'm going to go ahead and start the stopwatch and you'll have 60 Seconds To answer question number one starting now now okay that's 60 seconds is now up so I'll go ah and go over question one so if we look at the prompt for this Which choice completes the text the most logical and precise word or phrase so this is going to be a reading type of question so what I'm going to do is I'll start by reading through and I'll try to fill in this blank as I go through so we have as Mexico's first president from an indigenous Community Bonito Warz became one of the most blank figures in the country's history among the many significant accomplishments of his long tenure in office Warz Consolidated the authority of the national government and advanced the rights of indigenous people all right so we have he has many significant accomplishments so positive connotation and then we have the advance the rights of indigenous people all of this is positive connotation okay so I'd be looking at one of the most um uh positive figures in the country's history something with a positive connotation so for now I'll just fill in uh one of the most um we'll just do positive okay ultimately it's kind of tough to fill that word in there with something because it's pretty broad as far as what it could be let's go and take a look at our options we've got option A unpredictable we we have no indication that it was an unpredictable presidency um if you look at B important K important would make sense because we go on and discuss how he had many significant accomplishments and we discuss those accomplishments if you look at C secretive there's nothing indicating that it was secretive if we look at D ordinary there's nothing indicating it was ordinary in fact there is things that point to it being not ordinary we state that there were many significant accomplishments of his long tenure in office and he Advanced the rights of indigenous people really the key part here is that there were many significant accomplishments so we would say that he was one of the most important figures in his country's history so our answer would have to be B all right let's go ahead and move on to question number two so once again I'll give you 60 Seconds To answer question number two starting now e all right so there's your 60 seconds now I'll go over question two and how I would approach it once again we have Which choice completes the text most logical and precise word or phrase so I'll try to fill in this blank before taking a look at the answer choices we have due to their often strange images highly experimental syntax an opaque subject matter many of John Ash Barry's poems can be quite difficult to blank and thus are the object of heated debate among Scholars all right what we're stating basically three things strange images highly experimental syntax opaque subject matter that would make it difficult to understand okay so the poems can be difficult to understand would basically be what I'd be looking to fill in that blank with if we look at our options we wouldn't State Delegate okay we're not stating that we're delegating any sort of work of the writing or the reading anywhere so that wouldn't make sense compose well we're not talking about them being composed okay they've already been composed okay they can be difficult to to blank unless are the object of heated debate among Scholars it's not that they can be difficult to compose and are the heated debate among Scholars it be that they're difficult to understand so compose would make sense there if look at C interpret okay they're difficult to interpret unless are the object of heated debate among Scholars that would make sense they're difficult to interpret because there are strange images highly experimental syntax and opaque subject matter if you look at option D R now we wouldn't say it's difficult to renounce them and L their object of heated debate among Scholars it's that they're difficult to interpret because of these three things listed at the start so our answer would have to be C all right let's move on to question number three we have uh once again I'll put 60 seconds on the clock okay starting now e right that 60 seconds is now up so let's go over question number three once again same prompt so the way I approach this is try to fill in the blank before taking a look at the answer choices that way I avoid being swayed between answer choices and also getting stuck between two okay so if you look at question three the Cambrian explosure gets its name from the sudden appearance and Rapid diversification of animal remains in the file record about 541 million years ago during the Cambrian Period some scientists argue that this blank change okaye we need to describe the change in the fossil record might be because of a shift in many organisms to body types that were more likely to be preserved well we state that it's a sudden appearance and Rapid diversification of animal remains in the fossil record okay so rapid diversification sudden appearance this is all things that are indicating that this happened all at once okay so we could argue um trying to think of a word that would fit all at once okay if you are in a situation like this and you don't really know you know an exact word to place it's okay to just have a general idea obviously you wouldn't State this all at once change but if you're kind of stuck as far as exact word to place there it's okay to just kind of have an idea in your head and you may not even necessarily need to fill it out but just at least have an idea in your head so in this case looking for something that's just indicating that it's it's all at once if we look at our options we have option A catastrophic well that would have a negative connotation we're not looking for something with a connotation we're looking to something that indicate that this happening all at once if you look at option b elusive elusive wouldn't make sense okay elusive would be more so used to describe something that's sort of hard to hard to reach or hard to to catch basically basically if we look at abrupt okay abrupt would make sense abrupt would be a sudden change okay it's the sudden appearance and Rapid diversification of animal remains so abrupt would make sense okay that would be a really really good way to fill in that blank so we can switch that to abrupt okay and then we have option D imminent well we wouldn't say that it's an imminent change it would be an Abrupt change because it's happening all at once okay so our answer there would have to be answer Choice C right let's take a look at question four okay once again I will give you 60 Seconds To answer question four starting now e okay that's 67 second is now up so I'll go over question number four once again same prompt so I'll be looking to fill in this blank during a 2014 archaeological dig in Spain Vincent LOL and his team uncovered the skeleton of a woman from L algar an early Bronze Age Society buried with valuable objects signaling a high position of power this finding May persuade researchers who have argued that Bronze Age societies were ruled by men to blank that women may also have held leadership roles while they're uncovering a skeleton from a woman um in an early Bronze Age Society who was buried with valuable objects signaling a high position of power okay so these researchers who believe that bronze AG societies were ruled only by men would have to now acknowledge that women may have also held leadership roles okay so I'd fill in this blank with acknowledge which is a very large word so I'm not going to write it in because I can't fit it there but looking for something that basically mean acknowledge we have option A which is wave well we wouldn't state that they um would wave that women have also held these leadership roles okay that doesn't fit there if we look at option b concede okay that would make sense okay in order for these men to acknowledge you keep in mind that they argued that Bronze Age societies were ruled by men now they would have to acknowledge that women have also held leadership roles in other words they would also have to ConEd that women have also held leadership roles they have one belief now and now we have evidence that points to the fact that that belief is not true and in fact only part of it is which is that the belief that men held these leadership roles exclusively but now we have evidence pointing that women also did so they have to concede that women also did okay so B looks perfect if we take a look at C okay that wouldn't allow them to refute that women also held leadership roles because they already believe um right now they believe that women did not hold these leadership roles okay now in light of this new evidence this would not make them refute it this would make them acknowledge it so C would be the opposite of what we're looking for and then we can't require anyone um if we go and read through the sentence this finding May persuade researchers who have argued that Bronze Age societies were ruled by men to require that women may have also held leadership roles you can't require anyone to believe anything K you'd have to have them concede that women may also have held these leadership roles in light of this new evidence okay so our answer there would have to be B all right let's go ahead and take a look at question five okay once again I'll give you about 60 seconds and then I will go over the question so stopwatch Starts Now e okay that's 60 seconds so now I'll go ahead and go over this question right so we've got same prompt as we've had before so we'll start from the top within bailing whale species some individuals develop an accessory spleen a seemingly functionless formation of spinetic tissue outside the normal spleen given the formation's greater prevalence among Welles known to make deeper Dives some researchers hypothesize that its role isn't blank rather the accessory spleen May actively support diving mechanisms okay I would fill this in with meaningless okay it's not meaningless it must serve some sort of function because the whales that dive deeper have there's a higher prevalence of the spleen there the accessory spleen okay so it can't be meaningless it would have to be um something that actually helps them function so you look at our options we have a replicable which wouldn't make sense here B predetermined okay it can't be predetermined if you look at option C operative okay we have to keep in mind that it is operative but right here we have isn't okay that its role isn't operative we know that we're making the argument actually that it does have a function okay and that it would actually help them operate in terms of diving Down Deeper okay so we would say that it isn't latent okay in this context Laton would basically just mean meaningless in this context okay so this is a words and context question be able to recognize that in the context here would' be stating that this accessory spleen isn't meaningless it must serve a function because there is a higher prevalence among um whales that are diving deeper there's a higher prevalence that they have this accessory spleen all right let's go a and go down to question number six now okay once again I'll give you 60 seconds okay so I'll goe and start the clock right now e all right that's 60 seconds so now I'll go and go over the question so we've got question number six once again same prompt so according to a US tax policy expert state taxes are blank other factors when considering an interstate move even significant differences in state taxation have almost no effect on most people's decisions so that's key there differences in state taxation have almost no effect on people's decisions well differences in employment opportunities housing availability and climate are strong influences all right so we would state that state taxes are blank other factors when considering an interstate moved we would probably state that are considered less than other factors so something along the lines of considered less than other factors so we've got option a consistent well we wouldn't State it's consistent with other factors we know that it's considered less than other factors B representative of well state taxes aren't representative of climate housing availab availability and employment opportunities we got to get rid of B if you look at C overshadowed by okay well that would make sense considered less than and overshadowed by would make sense in this context because we'd be stating that in both of those state taxes are overshadowed by these other factors okay and that's supported in the text when we state that significant differences in state taxation have almost no effect on most people's decisions differences in employment opportunities housing ability and climate are strong influences so C looks perfect we can take a look at a d IR relevant to we don't actually make the claim that state taxes are irrelevant to other factors when considering an interstate move okay we state that there's almost no effect but not that it's completely irrelevant okay so the best answer here would be C the main focus here isn't whether or not state taxes are irrelevant it's that they're overshadowed by these other considerations so our answer there would have to be C all right let's go on to question number seven once again I'll give you 60 Seconds To answer question number seven starting right now e all right 60 seconds is up so now I'll go and go over this question Okay so we've got the author's claim or in this case we've got once again same prompt which chice completes the text with the most logical and precise word of phrase the author's Claim about the relationship between neanderthals and Homo sapiens is blank as it fails to account for several recent archaeological discoveries okay we would assume then that the claim is um weak basically since it fails to account for several recent archaeological discoveries to be convincing his argument would need to address the recent finds of additional homed fossils such as the latest Den denan specimens in homo longi okay so I would say that the uh Rel relationship or the claim is weak because it fails to account for several recent archaeological discoveries we've got option A disorientating we wouldn't state that the claim is disorienting okay disorienting would be basically like if someone got you know punched in the face then you know that would obviously be disorientating disorienting uh if we look at option b tenuous okay in this context tenuous would basically mean weak so that looks really really strong if you look at option C nuanced we wouldn't say that the author's claim as nuanced because it fails to account for several recent archaeological discoveries because it's failing to account for these discoveries we would make we would call it weak not nuanced so we can get rid of C there if you look at option D on original whether or not it's original or unoriginal um isn't really affected by whether or not it fails to account for new discoveries okay that is what makes it weak or strong it'd be strong if it accounts for the new discoveries and it would be weak if it doesn't and in this case it does not so answer there would have to be answer Choice B all right let's move on to question number eight once again I'll give you 60 seconds to answer eight and then I'll go through let me zoom out a little bit so you can see the entirety of the question all right so time starts now e all right that 60 seconds is now up so I'll goe and go over the question Okay so we've got question number eight following text is from Georgia Douglas Johnson's 1922 poem benediction okay in this case we see that our prompt is Which choice best states the main purpose of the text so I'll look to identify the main purpose before taking a look at the answer choices let's go ahead and go through we have go forth my son winged by my heart's desire great reaches yet unknown await for your possession I may not if I would retrace the way with you my pilgrimage is through but life is calling you okay so what jumps out to me is this part here my pilgrimage is through okay obviously just kind of as a summary here uh we have someone basically talking to their son saying hey go forth uh winged by my heart's desire okay so she wants her son to go forth um sounds like explore Adventure stating my pilgrimages through in other words this person's probably old possibly on their deathbed or close to to um sort of leaving this Earth um and they're stating that life is calling you so really it kind of seems like a wait for your possession it's basically encouraging their child um that the world is is up to theirs to go and sort of capture not necessarily um a way of conquering but just in the sense of you know you can go and and make what you want of the world so obviously we have um this parent expressing that they want their their child to go and explore and have Adventure in their life is what I would say the main purpose is we option A to express hope that a child would have all the same accomplishments as his parent did okay well in fact we actually see it's the opposite okay I may not if I would ret trace the way with you my pilgrimes through life is calling you great reaches yet unknown await for your possession okay in this case we're not stating that you know whoever is writing this wants their child to have the same things or the same accomplishments as they did in fact they're encouraging them to to go explore presumably beyond what the parent um has already done or has already seen if you look at option b to suggest that raising a child involves many struggles we really don't mention any struggles here so that wouldn't really make sense if we take a look at C to warn a child that he will face many challenges throughout his life once again through this we don't really see any indication of struggle or challenges being mentioned okay so we can get rid of C as well if we take a look at option D we have to encourage a child to embrace the experiences life will offer okay and once again that kind of goes back to that main purpose that I was talking about where we have a parent encouraging their child to go adventure to go explore to go embrace the experiences that life will off will offer okay so D would be perfect there okay so for question 9 I'm going to go and give you 60 seconds starting now now e okay that 60 seconds is now up so I'll go and go over number nine the following text or I guess I'll start with the prompt okay so starting with the prompt we have Which choice best describes function of the underlined sentence in the text as a whole okay so I'll take as I go through this I'll to identify uh the sentence that comes before what function it serves with the sentence that is underlining and then also how that connects with the sentence that comes after what's underlined so the following text is adapted from Indian boyhood in 1902 Memoir by oaza a saan Dakota writer in the text OA recalls how women in the tribe harvested maple syrup during his childhood now the woman began to test the trees moving leisurely among them ax in hand and striking a quick blow to see if the sap would appear the trees like people have their individual characters some were ready to yield up their life blood While others were more reluctant now one of the Birch and basins was set under each tree in a hardwood chip driven deep into the cut which the aak had made from the corners of the chip at first drop by drop then more freely the out trickled into little dishes this is basically all about the women sort of harvesting the sap from the trees okay we see that they test the trees to see if the sap would appear and then after this we have sort of this representation of lifeblood as the sap so when we state that some were ready to yield up their lifeblood we're basically stating that some were ready to give sap While others were more reluctant or in other words some were not ready to give sap um and then we talked about how Birch Basin are set under each tree hardwood ship driven in deep into the cut to which the a made so in terms of the function of the underlying sentence here basically just looks like it's talking about how some of the trees were giving sap some were not okay so a little bit tough to sort of decipher without taking a look at a through D so let's go ahead and take a look at a through D now so we have option A portrays the range of personality traits displayed by the woman as they work okay that's way off from pretty much everything in the text okay we know that it's really just focused on the fact that um some of these trees that the women are are chopping into are giving sap and some are not look at option b it foregrounds the beneficial relationship between humans and maple trees okay we're not really focused on the beneficial relationship between humans and maple tree so that doesn't make sense we look at C demonstrates how human behavior can be influenced by the natural environment it does not demonstrate that if we take a look at option D it elaborates on an aspect of the maple trees that the women evaluate okay the aspect being the ones whether or not it's ready to give sap or whether it's not ready to give sap okay so that would be one of the aspects that the women evaluate on the maple trees okay so D would be perfect there okay so text one is a little bit cut off but as you can see there is I'm going to go ahead and start the clock I'm going to give you in this case I'll give you about 90 seconds to answer this question since it's a bit longer e e okay that 90 seconds is now up so I'm going to go ahead and go over this question so we have a case where we have text one and text two what I'm going to do is I'm going to start at the prompt we have based on the text how would barenfeld and colleagues text 2 most likely respond to the conventional wisdom discussed in text one so as I read through text one I want to identify the conventional wisdom and I'll mark it with a CW for conventional wisdom ecologists have long wondered how thousands of microscopic phytoplank and species can live together near Ocean surfaces competing for the same resources according to Conventional wisdom one species should emerge after out competing the rest so I'll mark that CW so why do so many species remain it col just many efforts to explain the phenomenon still haven't uncovered a satisfactory explanation so now we want to know how the authors of text 2 would respond to that conventional wisdom ecologist Michael barenfeld and colleagues have connected phytop Plankton's diversity to their microscopic size because these organisms are so tiny they are space relatively far apart from each other in ocean water and moreover experience that water as a relatively as a relatively dense substance this in turn makes it hard for them to move around and interact with one another therefore says barfield's team uh direct competition among phitop planktons probably happens much less than previously thought Okay so we would address the conventional wisdom that species should that one species should emerge after out comping the Rest by stating that they are not in competition with each other as a result of the water density so we have option A by arguing that it's based on a misconception about phytol plant and species competing with each other okay yes the misconception being that they actually aren't going to be in competition with each other because of this water density okay we state that direct competition among phop happens much less than previously thought or in other words we could also state that it happens much less than it's thought by this conventional wisdom okay so a looks really really strong we can take a look at BC IND as well B states by asserting that it fails to recognize that routine replenishment of ocean nutrients prevents competition between phytol species well we're not focused on the routine replenishment of ocean nutrients okay we're focus on actually the the water density okay so B does it really make sense there if we take a look at C by suggesting that their own findings help clarify how phytop species are able to compete with larger organisms we're talking about competition uh between these species we want one species to emerge so it's not about competition with larger organisms we actually also state that they're insulated from competition okay that direct competition probably happens much less than as previously thought so we want to focus on that aspect we look at d by recommending that Mor ecologists Focus their research on how competition among phytop and species is increased with water density okay well they're not recommending that Mor colist Focus their research on this okay so we can get rid of d as well okay so our answer there would have to be answer Choice a all right moving on to question number 11 I'm going to give you guys about 60 seconds for this question e okay that 60 seconds is now up so I'm going to go over question number 11 all right so I'm going to go ahead and go to my prompt to start we have according to the text why would a helicopter built for Earth be unable to fly on Mars okay so a helicopter built for Earth why can't it fly on Mars in 2014 ailia Quan and her team at Nasa set out to build a helicopter capable of flying on Mars because Mars's atmosphere is only 1% as dense as Earths the air of Mars would not provide enough resistance for the rotating Blades of a standard helicopter for the aircraft to stay afat okay so this is ultimately why a helicopter built for Earth would not be able to fly on Mars we'll just quickly keep reading to see if there's any more context we need for 5 years Quan's team tested designs in a lab that mimicked Mars's atmospheric conditions the craft the team ultimately designed can fly on Mars because its blades are longer and rotate faster than those of a helicopter of the same size built on Earth all right so as far as why a helicopter built on Earth can't fly on Mars it's because Mars is atmosphere is only 1% as dense as Earth's and the air of Mars wouldn't provide enough resistance to the blades got option A because Mars and Earths have different atmospheric conditions yes that's perfect okay in particular because Mars atmosphere is only 1% as dense as Earth okay we can quickly take a look at BC and D as well okay B would state that because the blades of helicopters built for Earth are too large to work on Mars we know that the helicopter that's built from Mars actually has larger blades than those on Earth so that would be the opposite take a look at C because the gravity of Mars is much weaker than the gravity on Earth we never discuss gravity on either Planet if we look at D because helicopters built for Earth are too small to handle the conditions on Mars okay well that's just not factually correct okay according to the text and the text is very very clear on this it's because Mars and Earth have different atmospheric conditions all right let's go and go on to question number 12 okay once again I'm going to give you guys about 60 seconds for this question okay starting right now e all right that 60 seconds is now up so I'll go and go over question number 12 in West Africa jalis have traditionally been keepers of information about family histories and records of important events they have often served as teachers and advisers too new technologies may have changed some aspects of the role today but jaist continue to be valued for knowing protecting their people's histories okay and I should have gone to the prompt first okay we're looking for the main idea okay so I should have gone to this prompt first instead of started reading but we're looking for the main idea all right so main idea here looks like is we describe the role of the jalis which is uh being keepers of information about family histories and records of important events serving as teachers and advisers and then from there we kind of shift into stating that new technologies have changed some aspects of the role so if I was to State the main idea it would be describing what the jaist um do what they are right which is there are people who are keepers of information about family histories and records of important events and I would also then state that new technology are changing some aspects of the role but that they're still keeping their main responsibilities the same okay and being valued for knowing and protecting fam's history so we have option A even though there have been some changes in their role okay as a this as a result of new technology so that part makes sense I'll a te there for the first part for True jails continue to preserve their community history okay that part is true as well okay so we put a check mark by a we can take a look at BC and D B States although jist have many roles many of them like teaching best there's no textual support that they like teaching best C JS have been entertaining people within their communities for centuries well we need to keep in mind we need the main idea of the text okay option C focuses too much on the first half and it doesn't address at all the second half if we look at option D technology can now do some of the things jalice used to be responsible for this is the opposite of C this is focusing too much on the second half and not enough on the first half okay there has to be a keep in mind it's the main idea not just what's the idea of the last half or the first half all right let's go on and go on to question number 13 so once again I'm going to give you 60 seconds for question 13 starting now and I will zoom out so you can see the rest of this question all right 60 seconds is now up so I'm going to go ahead and go over question 13 so I start with the prompt Which choice best states the main idea of the text so I'll try to come up with the main idea before I go through my answer choices we've got in 1934 physicist Eugene wigner posited the existence of a crystal consisting entirely of electrons and a honeycomb like structure the so-called wigner Crystal remained largely conjecture however until Fang Wang and colleagues announced in 2021 they' captured an image of one the researchers trapped electrons between two semiconductors and then cooled the apparatus causing the electrons to settle into crystalline structure by inserting an ultrain sheet of graphine above the crystal the researchers obtained an impression the first visual confirmation of the wigner crystal so all this is basically about confirming that the wigner crystal exists okay so if you look at option A researchers have obtained the most definitive evidence to date of the existence of the wigner crystal that looks perfect we can take a look at BC and D as well B States researchers have identified an Innovative new method for working with unusual crystalline structures okay this is way too narrow okay for one I'm not I don't even need to know whether it's sure or not because it's focused way too narrowly on one section of this text and not on the main idea which is about confirming the existence of the wiger crystal if we look at C graphine is the most important component required to capture an image of the wigner crystal well graphine I believe is only mentioned at the end here stating that by inserting an ultra thin sheet of graphine above the crystal the researchers obtain an impression first visual confirmation the wigner crystal that's way too narrow okay we need the main idea not a narrow part from one sense look at D it's difficult to acquire an image of a Winer Crystal because of the Crystal's honeycomb structure once again this is too narrow okay we need to focus on the main idea not just one or two sentences within the text so our answer that would have to be a all right here's question number 14 give you guys uh we'll give you guys 90 seconds for this one e e okay the 90 seconds is now up so I'm going to go ahead and go over this question so we're going to start by taking a look at the prompt so which Choice best describes data from the graph that support the researcher's conclusion so I need to First identify the researcher's conclusion then I look for the data in the graph that supports it so let's start with the text considering a large sample of companies economics expert Maria Guadalupe Julie wolf and raguram ran assessed the number of managers and leaders from different departments who reported directly to a CEO according to the researchers these findings suggest that AC cross seers analyz there is a growing interest among CEOs in connecting with more departments in their companies okay so our conclusion is that there's a growing interest among CEOs in connecting with more departments in their companies so I'm looking specifically at department leaders here not necessarily managers okay so I'm looking at this black part of these graphs I see that we are increasing substantially um through from 1991 to 1995 and then from 1996 to 2001 and then from 2001 to 2008 okay and this is the average number of individuals directly reporting to the CEO we go from about 3.2 or so up to about 6.8 okay so pretty much a double if you look at option A we have the average number of managers and department leaders reporting directly to the CEO didn't fluctuate from 1991 to 1995 to 2001 2008 period that's not true according to the data if we look at B the average number of managers reporting directly to their CEO was highest in the 1996 2001 period that's not true according to the data if we look at C average number of department leaders reporting directly to their CEO was greater than the average number of managers reporting directly to their CEO in each of the three periods studied were're not concerned with comparing managers to departments we can get rid of that if we look at D average number of department leaders reporting directly to their CEO Rose over the three periods studied yes okay keep in mind we need to ultimately support the researchers conclusion which is that among CEOs there's a growing interest in connecting with more departments in their companies so we're really not concerned with the manager is mostly just the department leader so answer there would have to be D all right let's go and move on to question number 15 and I'll Zoom back in so you guys can see this a little bit closer okay so for number 15 um I'll give you guys another um 90 seconds for number 15 okay so start the clock now e e okay so that's been a minute 30 so I'm going to go and go over question number 15 so once again I'm going to start with my prompt which finding if true would most directly undermine Foster's hypothesis so I need to identify the hypothesis and then we'll look for an answer that undermine it when digging for clams their primary food sea otters damage the roots of eelgrass plants growing on the sea floor near Vancouver Island and Canada the otter population is large and well established yet the eelgrass metals are healthier than those found elsewhere off Canada's Coast to explain this conservation scientist Aaron Foster and colleagues compared the Vancouver Island Meadows to Meadows where otter are absent or were reintroduced only recently finding that the Vancouver Island Meadows have a more diverse gene pool than the others do Foster hypothesize so now we have the hypothesis I'll mark that with an H that damaged to E Grass Roots increased the plants rate of sexual reproduction this in turn boosts genetic diversity which benefits the metals Health overall we need something that undermines that hypothesis we have option A at some sites in the study illg grass Meadows are found near Otter populations that are small and have only recently been introduced okay so we have e grass metals are found near Otter populations that are small and have only recently been re introduced that's not undermining the hypothesis okay so you can get rid of a take a look at B at several sites not in the in the study there are large wellestablished sea outer populations but no eelgrass Meadows okay well this is not going to undermine the hypothesis this also really wouldn't confirm the hypothesis either okay this is just neutral so we can get rid of it if we look at C at several sites not included in the study IL grass Metal's Health correlates negatively with the length of residence and the size of SE otter populations well we know that our hypothesis would be that as the otter populations would increase that would create more damage to the eelgrass roots would increase the plants rate of sexual reproduction which would boost gentic diversity and boost the Metal's health so if the Metal's health is correlating negatively with their length resonance on the side of otter that goes directly against the hypothesis and would undermine or weaken the hypothesis so C is perfect there we can take a look at d as well at some sites in the study the health of plants unrelated to e grass correlates negatively with the length of residence and size of otter populations okay so health of plants unrelated to eelgrass this is the key part it's the plants that are unrelated to the Eel Grass our hypothesis is specific to the eel grass so talking about the health of plants that are unrelated really isn't going to undermine the hypothesis so our answer there would have to be answer Choice C all right question 16 I'm going to give you guys 60 seconds starting now e that 60 seconds is now up so I'll go over number 16 we have Which choice most logically completes the text as our prompt so I'll take a quick look at this sentence thus those who primarily view Zelda as an inspiration of f Scott's writings and then something that comes after so Scholars have noted that AB Scots Fitzgerald's writings were likely influenced in part by his marriage to Zelda Fitzgerald but many don't recognize Zelda as a writer and her own right indeed Zelda authored several Works herself such as the novel save me the Walts and numerous short stories thus okay so this is basically a transition word kind of indicating that because of what came before thus what came after so what came before is Zelda basically being her own writer so not just someone who influenced her husband's work but had writings in her own right okay so thus those who primarily view Zelda as an inspiration for fot Gerald writings I'm guessing what comes after would be something stating basically that they're missing the the um sort of writings that she had herself we option A Overlook the many other factors that motivated F Scott to write okay once again that's not really in line with thus as the transition here okay because we're using thus there we need to focus on what came before it okay which is the fact that she was a writer herself so not overlooking the other factors that motivated up Scot look at B risk misrepresenting the full range of Zelda's contributions to literature okay those contributions would be the works that she wrote herself which we actually discussed in that previous sentence okay so be looks super strong we can take a look at C and D as well C May draw inaccurate conclusions about how F Scott and Zelda viewed each other's works okay that's really never discussed in the text if we look at D tend to read The Works of fcot and Zelda in an overly autobiographical light that one's just a pretty random answer Choice KR answer there would have to be answer Choice B all right I'm going give you guys 90 Seconds To answer question number 17 which is on the left side of the screen e e okay that 90 seconds is now up so I'm going to go over this question we have Which choice most logically completes the text so I'm going to take a quick look at the sentence that we'd be completing they have they found that tauris hatchlings show a significant preference for the image suggesting that what okay so the towards hatchling show significant preference for an image among social animals that care for their young such as chickens monkeys and humans newborns appear to show an innate attraction to faces and face like stimuli elizabeta verace and her colleagues used an image of three black dots arranged in the shape of eyes and a nose or mouth to test whether this trait also occurs in testudo tortoises which live alone and do not engage in Parental care this is a contrast from social animals that care for their young so that would be parental care up there all right so we've got which live alone do not engage in Parental care they found that tus hatchlings showed a significant preference for the image suggesting suggesting what well we have that the animals that have parental care and that are social animals they also showed this innate attraction to the faces and face like stimuli and so do these ones that don't have parental care so this attraction does not um depend on Parental care or not is basically what I'd be looking for if you look at Option a face like stimuli are likely proceed ceed as harmless by newborns of social species that practice parental care but as threatening by newborns of solitary species without without parental care well we see that it's not threatening okay so this is really just an incorrect interpretation of what was stated okay we know that it's actually stated that it is they are perceived as nonthreatening okay they actually um like them right it states that if we go up uh whether this trait they found taurtis hatchling showed a significant preference for the image okay so obviously not threatening if we take a look at B researchers should not assume that an innate attraction to face like stimuli necessarily an adaptation Rel to social interaction or parental care okay yes we should not assume that it's dependent upon social interaction and parental care because we have these these tortoises which do not have this parental care or social interaction they also have this innate attraction so it does not depend on social interaction or parental care let's take look at C and D as well C States researchers can assume that the attraction to face like stimuli that is seen in Social species that practice parental care is learned rather than inate we can't assume it's learned because those that don't receive parental care also have this innately if you look at D newly hatched t ttis say show a stronger preference for face like stimuli than adult tortoises do well there's just that's not discussed at all okay so that's very very random okay so answer would have to be answer Choice B all right question 18 I'm going to give you 60 seconds for starting now e okay any anyone who wants to take another 30 seconds here go ahead and do that this is a bit of a longer question all right let's go and go over question number 18 now so I end up giving you guys another about 30 35 seconds because this is a little bit of a longer question so let's go over over it okay so we have Which choice logically completes the text we take a look at this last sentence we have thus some Scholars have concluded what okay so we need to figure figure out what the conclusion would be from this text compiled in the late 1500s largely through the efforts of indigenous scribes contus Mexicanos is the most important collection of poetry and classical nautal the principal language of the Aztec empire the poems portray Aztec society before the occupation of the Empire by the army of Spain and marginal notes in canis Mexicanos indicate that much of the collection's content predates the initial Invasion nonetheless some of the poems contained in audiable references to beliefs and Customs common in Spain during this era th some Scholars have included what we know that most of the poems or the bulk of it is sort of predates um the invasion of the army of Spain okay but still there are some pieces of if we go up marginal notes indicate that um most of the collection predates the initial evasion some of the poems contain an arable references beliefs and Customs common in Spain during this era okay so we're ultimately suggesting that there must have been something that was most likely added after this evasion to um this this book or this collection of poetry so we have option A well its content largely predates The Invasion which is true according to the text canas Mexicanos also contains additions made after the invasion that would make sense since there are in arable references to beliefs and Customs common in Spain during this era okay so that looks true as well so a looks super strong we take a look at BC India as well B States although those who compiled contarus Mexican were fluent and now all they had limited knowledge of the Spanish language okay that's not what we would conclude based on this text take a look at C before the Invasion by Spain The Poets of the azc Empire borrowed from the literary traditions of other societies okay there's really no support for this anywhere okay ultimately we know that it states that um the poems portray AIC Society before the occupation of the Empire by the army of Spain the marginal notes indicate much of the collection's content predates the initial Invasion okay there's nothing suggesting that The Poets of the atic Empire borrowed from literary traditions of other societies there's nothing suggesting that they even had access to literary Traditions from other societies we look at d the references to beliefs and customs in Spain should be attributed to a coincidental resemblance between the societies of Spain and the aztech Empire okay there's nothing to really support that either okay because if we go up it states that much of the collection's content predates the initial Invasion nonetheless some of the poems contain audable references to police and customs in common and Customs common in Spain during this era okay the key part here is much of the collection's content predates the initial Invasion okay that would suggest that there is some of it that came after the invasion or in other words was added on later as we see in answer Choice a okay so it's not strictly that all the content was pre-invasion it states much of it was pre-invasion but not all of it okay so our answer would have to be a all right for number 19 I'm going to give you guys 60 seconds starting now e all right let's go ahead and go over question number 19 okay so I'm going to start with the prompt Which choice most logically completes the text okay we have the results of the study therefore okay so I want to know what the results of the study are and what they're pointing to as some sort of conclusion here so we have in a study of the cognitive abilities of white-faced monkeys uh cus mature researchers neglected to control for the physical difficulty of the tasks they used to evaluate the monkeys the cognitive abilities of monkeys given problems requiring literal little dexterity such as sliding a panel to retrieve food were judged by the same criteria as were those monkeys given physically demanding problems such as unscrewing a bottle and inserting a straw okay so ultimate we have a problem with the study okay it's that they the researchers neglected to control for the physical difficulty of the tasks they use to eval Val the monkeys basically this means all of the data is pretty much thrown out the window okay when you fail to control for the physical difficulty on these tasks you're not going to get any sort of accurate study on the cognitive abilities of cus IM mature so basically the results of the study are that it's really messed up so if we take a look at option A it could suggest that there are differences in cognitive ability among the monkeys even though such differences may not actually exist okay that'd be perfect okay because we may see that there you know shows up in the data that there's some difference in cognitive ability specifically because some of these tasks are much easier than others and that's not being controlled for okay so a is absolutely perfect we can take a look at BC and D as well B states are useful for identifying tasks that the monkeys lack the cognitive capacity to perform but not for identifying tasks that the monkeys can perform well we actually would be able to use it for identify tasks that the monkeys um can perform because obviously we do still have uh the data on that okay we do know which tasks they are able to perform so we do have that data so we wouldn't say that it's not useful for that so we can get rid of B if we take look at C and also just keep in mind that if you have a question like this you really need to be looking for you know what's the biggest takeaway okay so the biggest takeway here is that because we failed to control um therefore we may have false conclusions that could arise in the data or false you know evidence okay so if we take a look at C should not be taken as indicative of the cognitive abilities of any monkey monkey species other than c immature well it shouldn't even be indicative of the cognitive abilities of CM mature because once again that data is not going to allow us to make any conclusions because we didn't control for the physical difficulty of the tasks if you look at D reveal more about the monkey cognitive abilities when solving artificial problems than problems in the wild well it's not even revealing really anything about solving artificial problems because once again we did not control for the different difficulty of the tasks okay so our answer there would have to be in Choice a all right so we've now made it to the writing questions at this point I'm going to go ahead and give you 45 seconds to answer question number 20 e all right that 45 seconds is up so now I'm going to go ahead and go over question 20 so let take a look at the prompt we have Which choice completes text so conforms the conventions of Standard English if we look at our options we've got enter to enter having entered and entering okay so off the bat to me this is looking like a question where it's going to be a non-finite versus finite verb choice so if we take a look we have to survive when water is scarce embryo is inside African turquoise killfish eggs keep in mind that inside is a preposition so we can get get rid of this prepositional phrase we know our subject will be embryos so if embryos blank a dormant state known as diapause okay our options are of to enter well to enter would be a non-finite infinitive okay so we can get rid of B we need to have a finite verb in order to have a complete sentence okay so we need a verb that is doing the action of the embryos okay so embryos enter a dormant state known as diapause will have to be our answer here I'll touch on c and d as well here okay C and D are both non-finite participles okay we need a finite verb in order to have a complete sentence our answer has to be a all right let's go ahead and move on to question number 21 okay for question number 21 I'm going to give you guys about 45 seconds as well starting right now e okay that 45 seconds is now up so we have Which choice completes the text for conforms conventions of Standard English if I look at my options here I've got has double had double doubles and will double so I'm looking basically at what tents I'm in so let's go and go through paying attention to our tents formed in 1967 so already we're starting off in the past tense to Foster political and economic stability within the Asia Pacific region the association of Southeast Asian Nations was originally made up of five members once again we have was originally okay so dealing in the past tense we have Thailand Philippines Singapore Malaysia and Indonesia by the end of the 1990s the organization blank its initial membership so we have option of has doubled okay well has double does not indicate that this has already happened in the past and that it has finished so we can get rid of a if we look at B we have the past perfect of had doubled okay which would indicate that this has happened in the past by the end of the 1990s the organization had doubled its membership okay so it's happened in the past and it is done and over if we look at option C doubles that's present tense and then we have option D will double which is future tense okay we know that we are dealing the past tense this has already happened okay by the end of the 1990s organization had doubled its initial membership our answer there would have to be B okay for question number 22 I'm going to give you 45 seconds starting now okay that 45 seconds is now up so let's go over number 22 so I take a look at my prompt we got the standard prompt of Which choice completes the text so it conforms the conventions of Standard English in this case if I take a look at my answer choices I've got differences in punctuation so I'll probably be looking at figuring out what's an independent clause what's a dependent clause if I have any phrases okay so let's go ah and read through we've got the intense pressure found in the deep ocean can affect the structure of proteins and fish cells distorting the protein shape the chemical trimethylene and oxide Teo counters this effect ensuring that proteins retain their original configurations okay so that's an independent clause prior to any sort of punctuation so basically right there we get an independent clause next we have Teo is found in high concentrations in the cells of the deepest dwelling fish well that's also an independent clause okay so connecting them with a period is fine if we look at our other options we have no punctuation which isn't okay we need to have something connecting these two independent clauses we can't only use a comma without one of the Fanboy so we can get rid of C if we look at D we have and but we don't have a comma so our answer there has to be a to connect these two independent clauses all right for question number 23 I'm going to give you 45 seconds starting now e all right that 45 seconds is now up so I'll go over question 23 once again we have the prompt Which choice completes text for conforms the conventions of Standard English if I look at my options I've got experience had experience experience is and be experiencing so looks like I'm dealing with tense so that's what I'll be looking for as I read through food and The Sensation of taste are Central to Monique trang's novels in the book of salt for example the exiled character of Ben connects to his native Saigon through the food he prepares while in the bidder and the month the character of Linda blank a for s atasia whereby the word she hears of O taste all right so I'm looking at parallelism here I've got exiled character of Bin connects is the verb there to his native saon through the food he prepares so dealing the present tense while in bitter in the month bitter in the mouth the character of Linda we also need to have present tense here as well a form of sasia whereby the words she hears evokes taste okay so I'm looking for present tense so I'm going to get rid of A and B I can also get rid of D okay my answer would have to be C we need to maintain that present tense parallelism all right moving on to question number 24 I'm going to give you guys 45 seconds for this question as well starting right now e all right that's 45 seconds right there so let's go and go over question 24 inventor or we'll start with the prompt which chice completes text so it conforms to conventions of Standard English I look at my options we look for the differences differences are in Threads whether or not it's possessive now keep in mind these all have a period at the end of them okay so it's not going to end up being possessive so just based on that I can get rid of a and d and then if I look at the different is it's do we have multiple screws or do we have only one screw okay and it's the screws thread so it is possessive we just need to know how many screws we have so we have inventor John freedom and created a protyp of the F first flexible straw by inserting a screw so singular screw into a paper straw and using dental floss binding the straw tightly around the screws threads and then when the floss and screw were removed once again singular screw the resulting Cor corations in the paper allowed the straw to bend easily over the edge all right so we know there's only one screw okay so we can't have screws with an S and then an apostrophe it would just be screw apostrophe s threads okay and threads obviously can't own anything since there's a period right after it so our answer there would have to be C all right I'm GNA give you 45 seconds for question 25 starting now all right time's up so let's go and go over question 25 so we've got Which choice completes text what conforms conventions of Standard English and then we've got differences in punctuation and possibly having and after materialism so in her analysis of Edith Wharton's House of Mirth 1905 scholar Candace Wade observes that the novel depicts the upper classes of New York Society is consumed by the appetite of a soulless materialism okay so that we start out with an independent clause up to materialism then we have an AP assessment given that the house of Mer is set during the guilded age a period marked by the rapid industrialization economic G and widening wealth dispar disparities okay well an apt assessment is ultimately a supplementary noun phrase that's describing okay the this part right here basically the the observation right scholar Candace way observes the no depicts the upper classes of a New York society as consumed by the appetite of a Soul's materialism an apt assessment okay which is referring back to the assessment that is made by Candace Wade okay so we have a supplementary noun phrase we can't connect that with a semicolon so we can get rid of a we can't connect it with just an and okay we would use a comma okay we would connect that supplementary noun phrase with a comma okay we do need to have some sort of punctuation so our answer there has to be C we connect that supplementary noun phrase to the main Clause using a comma all right now I'm going to go ahead and give you guys 45 seconds for question number 26 starting right now e okay 45 seconds is now up so I'm going to go over question 26 once again we have to conform to conventions of Standard English I see we have pre and rather with some different punctuation one thing that I'd be looking for anytime I have a transition word next to where I might be ending or starting an independent clause is do I need that transition word to be within the first clause or within the second Clause um so in this case we'll be looking for rather okay so whether we have a contrast in the first clause or the second clause next thing we need to look at is punctuation okay so do we need a semicolon basically because we have semicolon here and here versus no semicolon and a and b let's go Ahad and read through to humans it does not appear that the golden orb weaver spider uses camouflage to capture its prey all right so that's an independent clause and we're not contrasting anything within that independent clause to anything that came before it or anything like that so we wouldn't want to put rather within that independent clause so looking at the differences between C and D here we can go and get rid of C because we don't want rather to be within in this same independent clause now let's read on and see if we have another independent clause after this we have the brightly color we have the brightly colored arachnid seems to wait conspicuously in the center of its large circular web for insects to approach so that is another independent clause okay now keep in mind that that's a contrast to what came before okay because we have two humans it doesn't appear the gold orb weave weaver spider uses camouflage to capture its prey and then we have rather the brightly colored arat nid seems to wait conspicuously in the center it's large circular web for insects to approach okay so we do have a contrast okay and this contrast begins in the second independent clause so since we do have independent clauses we can't disc connect them with commas okay so our answer there would have to be D we want that transition after the semicolon we do need to use a semicolon here to separate these independent clauses okay I'm going to give you 45 seconds to answer question number 27 starting now e okay that 45 seconds is now up so let's go ahead and go over question 27 so in terms of our prompt we have Which choice completes the text conforms the conventions of Standard English if I look at my options I'm looking at do we have possession from plias to sediment and also is Plas singular or plural and then the next difference is does rocks own mysterious migration okay and also how many rocks are there so let's go and look through 27 in death Valley's national parks racetrack paa so paa singular and because p is singular I can actually go ahead and get rid of d and a so let me go ahead and do that okay so now we're between B and C difference being is rocks possessive okay so let's read on we have in a flat dry lake bed are 162 rocks some weighing less than a pound but others almost 700 lb that move periodically from place to place seemingly of their own valtion race track like trails in the Rocks uh race track like trails in the Rocks mysterious or in the pla's sediment Mark the Rocks mysterious migration okay so it's the Rock mysterious migration so it is possessive so we can get rid of answer Choice B and our answer would have to be answer Choice C okay I'm going to give you guys 45 seconds now to answer question number 28 starting now okay time's up let's and go over question number 28 so once again for a prompt we need to conform to the conventions of Standard English if we look at our options we've got gingerbread and then different forms of punctuation and then option C with no punctuation so let's go and read through in crafting or fantasy fiction Nigerian born British author Helen oen has drawn Inspirations from the classic 19th century fairy tales of the brothers Grim her 2014 novel boy snow bird for instance is a complex retelling of the story of Snow White while her 2019 novel gingerbread offers a delicious Twist on the classic tale of Hansel and gredle yeah there's no need for punctuation here okay ultim we have our subject her 2019 novel gingerbread and then we have our verb offer so when you have your subject right next to your verb there's no need to have punctuation between them okay so options a b and d are all just trying to mess with you you don't need any punctuation there you're just having your subject and then the verb follows immediately after you don't need punctuation answer there is going to be C okay I'm going to give you guys 70 seconds for question number 29 e e okay time is up let's go and go over at number 29 so the way I would approach this is take a look at my prompt in this case we have the student wants to explain an advantage of the microbes so as I read through the notes I want to look for what the advantage is of the microbes we're researching a topic of students taking the following notes Nasa uses Rovers large remote vehicles with wheels to explore the surface of Mars na NASA's Rovers can't explore regions inaccessible to wield Vehicles rovers are also heavy making them difficult to land on the planet surface microbes robotic probes that weigh as little as 50 milligrams can be deployed deed virtually anywhere on the surface of Mars okay so an advantage would be they can be deployed almost anywhere on the surface of Mars compared to Rovers which cannot because they're are areas that are inaccessible to wield Vehicles micro probes have been proposed as an alternative to Rovers okay so we need to explain an advantage we have option A despite being heavy Rovers can't land successfully on the surface of Mars that's not explaining advantage of micro probes option b micro probes which weigh as little as 50 milligram could explore areas of Mars that are inaccessible to NASA's heavy wheel Rovers yes that is explaining an advantage of the microbes we can go micro probes we can go and take a look at C and D we've got NASA currently uses its Rovers on Mars but Micro probes have been a proposed alternative once again that's not explaining an advantage of the micro probes and then D though they are different sizes both micro probes and Rovers can be used to explore the surface of Mars that's not expressing an advantage of the micro probes okay so answer there would have to be B okay I'm going to give you guys uh 25 seconds or not sorry not 25 I'm going give you guys 60 seconds for question number 30 starting now okay 60 seconds is now up let's go and go over question number 30 so we take a look at my prompt student wants to introduce Paradise to an audience unfamiliar with the novel and its author okay keepy part here is audience unfamiliar with the novel and its author so I'll need to introduce uh both the novel and the author so we've got uh which what topic seems the following notes uh a g was awarded the 2021 Nobel Prize in literature G was born in zanzi bar in East Africa and currently lives in the United Kingdom many readers have singled out G's 1994 book Paradise for praise Paradise is a historical novel about events that occurred in Colonial East Africa option AG who wrote Paradise and later was awarded the Nobel Prize in literature was born in Zan bar in East Africa and currently lives in the United Kingdom that doesn't really introduce Paradise we can get rid of a if we take a look at B many readers have singled out AG's 1994 book paradise's historical novel about clone of East Africa for praise that doesn't introduce AGS we can get rid of B if we look at C A much praised historical novel about Colonial East Africa Paradise was written by AG G winner of the 2021 Noel prize in literature so we introduce G with or AG with this right here and then we also introduce the book by saying that it's about Colonial East Africa and that it's received much praise and it's a historical novel so in this case we're introducing them both if we take a look at D we have Paradise say a historical novel that occurred in Colonial East Africa AG's Homeland that's not introducing who AG is so our answer there would have to be answer Choice C all right now for question number 31 I'm going to give you guys 60 seconds starting right now for all right that 60 seconds is now up so let's go and go over question number 31 so I'm going to take a look at my prompt Which choice most effectively uses information from the given sentences to emphasize the relative sizes of the two capitals populations so key thing here we want to emphasize the relative sizes of the capital populations so we've got UL bantar is a capital of Mongolia the City's population is 97,000 it contains 32% of mongolia's population Hano is capital of Vietnam its population is about 8 million um and it contains 8.14% of Vietnam's population we have option a mongolia's capital zulam bantar which has 900,000 people in Vietnam's capital is Hanoi which has about 8 million people so the problem with this is it doesn't emphasize the relative size of the two capitals populations keep in mind the relative sizes are this 8% of Vietnam's population and that 32% of mongolia's population we take a look at B the populations of the capitals Mongolia and Vietnam are 900,000 and 8 million respectively once again that does not talk about the relative size if we take a look at C even though Hanoi population about 8 million is larger than ulam bantar population about 900,000 ulam banar's accounts for more of its country's population so this does talk about the relative size if we take a look according to the data is Zulan bantar account for more of its country's population relatively yes it does that looks factually correct as well if we take a look at D comparing Vietnam and Mongolia 8 million is uh 8.14% of Vietnam's population and um okay this isn't even talking about the capitals this is just stating these numbers which it's meaningless without talking about the capitals because in our prompt we state that we want to emphasize the relative sizes of the two capitals populations we want to mention that it's the capitals populations given in D which we don't so our answer there would have to be answer Choice C all right let's go a move on to question number number 32 okay for this question I will give you guys 60 seconds as well starting right now for all right 60 seconds is now up okay so let's go ahead and go over this question so we're going to start with the prompt student wants to explain how the House of Wisdom preserved the world's knowledge okay so as we go through we want to focus on how the House of Wisdom preserved the world's knowledge so specifically methods if we can see any we've got one of the histories one of History's Greatest libraries with the House of Wisdom in Baghdad Iraq it was founded in the 8th centur country with the goal of preserving all the world's knowledge Scholars at the house of wisdom collected ancient and contemporary texts from Greece India and elsewhere and translated them into Arabic becausee this would be how writings included those of Greek philosopher Aristotle and the Indian mathematician ariata the House of Wisdom used Chinese papermaking technology to create paper versions to be studied and shared so this would also be discussing how so these two are are how they did it we've got option A House of Wisdom was known for bringing together Knowledge from around the world including from Greece India and China okay what they're known for isn't explaining how they did it so you can get rid of a if we look at B found Iraq in the 8th Century the House of Wisdom employed many scholars as translators okay that's also not telling us how they did it it's telling us what they did employing people as translators but it's not telling us how they actually preserved the world's knowledge okay keep in mind we need to explain how they preserved the world's knowledge always pay attention to that prompt look at C writings from the Greek philosopher Aristotle and the Indian mathematician ariata were preserved at the house of wisdom once again that does not explain how they're preserving the world's knowledge if you look at D the House of Wisdom collected writings from different countries and created paper versions in Arabic to be studied and share that is explaining how they are preserving the world's knowledge so the answer would have to be D okay now we've got our last question question number 33 I'm going to have to uh scroll down it looks like um I'm just going to scroll down I'll cut off a little bit on the top but it's just the generic part so it's okay okay so here I'm going to give you guys 60 seconds to answer this question as well starting right now for this one's a little bit so I decided to give you guys 70 seconds instead of 60 but that being said let's go and go over it so first thing I'm going to do take a look at my prompt student wants to make a generalization about the kind of study conducted by Glickman Brown and song so what I'm focusing on here is we need to make a generalization about the kind of study that was conducted all right so let's go and read through our notes we have British museums John lenon Paul McCartney shared writing credit for numerous Beetle songs many Lennon McCartney songs were actually written by either lenon or McCartney not by both exact authorship of specific parts of many Beetle songs such as the verse for in my life is disputed Mark Glick Mark Glickman Jason Brown and Ryan song statistical methods to analyze the musical content of beetle songs They concluded that there is 18.9% probability that McCartney wrote the verse for in my life stating that the verse is consistent with lenon songw writing style all right so ultimately what's the kind of study that's conducted well it's using statistical methods to analyze musical content of Beetles song so we want to generalize it so we wouldn't really want to apply it specifically just to The Beatles we want to generalize it as they use statistical methods to analyze um musical content or if there's nothing about musical content then just that they use statistical methods to to study something so if we go down we've got our options we got option A based on statistical analysis Glickman Brown and song claimed that John Lennon wrote the verse of in my life okay well that's too specific we need to make a generalization about the kind of study okay so while we do introduce the kind of study here we're not generalizing it so you can get rid of a if we take a look at B there's only an 18.9% probability that Paul McCartney wrote the verse for in my life John lenon is the more likely author that doesn't even introduce the type of study so we can get rid of B if we look at C it is likely that John Lennon not Paul McCartney wrote the verse for in my life once again that does not mention the study so far the only ones that mentioned in the study would be a if we take a look at D researchers have used statistical methods so now we are talking about the study here to address questions of authorship within the field of music so this is providing that generalization about the kind of study okay the kind of study being statistical methods and then the generalization being we're using it to address questions of authorship within the field of Music which is what occurred here but now we are generalizing it to music as a whole and not just the Beatles so our answer there would have to be D okay now I want to get you guys some practice on the digital SATs math section so what I'm going to do is I'll give you a certain amount of time for each of these questions once that times up I'll go over the questions so that being being said let's go ahe and get started with question number one I'm going to give you guys 20 seconds for this one starting now all right 20 seconds is up so let's go and go over it so what is 10% of 470 all you got to do is 0 .1 for that 10% and then multiply that by 470 and that'll get you 47 so our answer there would have to be answer Choice B all right let's move on to question number two okay for question number two I'm going to give you guys 20 seconds as well starting now all right time's up let's go and go over it Okay so we've got which equation has the same solution as given equation if we take a look at our answer choices we have 4X equals so we just want to isolate 4X so we'll subtract 6 from both sides 18 - 6 will leave us with 12 so we have 12 is equal to 4X so our answer there would have to be answer Choice C all right let's move on to question three okay for question number three I'm going to give you guys uh 20 seconds as well starting right now all right so that 20 seconds is up so let's go and go over it so we've got total cost in dollars to rent a surfboard consists of a $25 service fee so that service fee is a onetime charge and a $10 per hour rental fee so plus 10 time H the person rent a surfboard for T hours so we can substitute T in for H and intends to spend a maximum of 75 so this total cost must be less than or equal to 75 to rent the surfboard which inequality represents the situation we see that that have to be answer Choice D all right let's go and move on to question number four okay for question number four I'm going to give you guys 20 seconds as well starting right now all right 20 seconds is up so let's go and go over number four so you got the function G is defined by G of X = x^2 + 9 for which value of x is G of x equal to 25 we'd have 25 is equal to x + 9 subtract 9 from both sides that get you 16 is equal to x^2 from there we're going to take the square root of both both sides to isolate the value of x < TK of 16 would be four so we have four is equal to the value of x we're asked to answer the value of x so our answer there would have to be answer Choice a all right moving on to question number five for question number five I'll give you guys 20 seconds as well starting now all right time's up so let's go over question five each face of a fair 14-sided die is labeled with a number from 1 through 14 with a different number appearing on each face if the dies rolled one time what is the probability of rolling a two well only one of these faces has a two so if we're only rolling it once the probability of rolling it to would be one out of the 14 different sides so there would have to be answer Choice a all right moving on to question number six for question number six I'm going to give you guys or was that oh six is right here okay so question number six I'm going to give you guys 20 seconds as well starting now all right 20 seconds is now up so let's go to go over the question Okay so we've got a printer produces posters at a constant rate of 42 posters per minute so we can do 42 posters per minute so P per M at what rate in posters per hour does the printer produce posters anytime something's underly pay attention to it so we need to convert this to hour so we'll multiply by the fact that we have 60 minutes per every one hour our minutes are going to cancel out and we'll be left with our amount of posters per hour so we can put this in the calculator it's just 42 * 60 and that'll give us 2520 okay so our answer there would be 2520 all right question number seven so for question number seven I'm going to give you guys 20 seconds as well okay starting right now all right 20 seconds is up so let's go and go over the question Okay so we've got function f is defined by the equation f ofx is equal 7x + 2 What is the value of f ofx when X is equal to 4 so we just plug in four for the value of x 7 * 4 is 28 28 + 2 leaves us with 30 so the value of f ofx when X is equal to 4 would be 30 once again you take the four multiply by that s gives you 28 28 + 2 gives you 30 okay question number eight I'm going to give you guys uh 30 seconds for this one starting now all right time's up let's go go over the question so we've got teachers creating an assignment worth 70 points the assignment will consist of questions worth one point and questions worth three points which equation represents a situation where X represents the number of one point questions so we have 1 X and Y represents the number of threo questions so plus 3 y okay so our total amount of points is 70 and that's got to equal the number of one point questions plus the number of threo questions times three points okay so if we look at our options we have to have answer Choice D all right moving on to question number nine okay for question number nine I'm going to give you guys 30 seconds as well starting now okay time's up so let's go over number nine right triangles LMN and pqr are similar where l and m correspond to p and Q respectively angle M has a measure of 53° what is the measure of angle Q all right so we can go ahead and draw this out okay we've got l and m corresponding to p and Q so we know L is corresponding to p M corresponds to Q we're asked for the measure of angle Q we know that the measure of angle m is going to be the same as the measure of angle q and we're told that the measure of angle m is 50° 53° therefore the measure of angle Q would also be 53° so the key thing to identify here is the fact that since we have um l and m corresponding to p and Q means M corresponds to Q so we don't actually have to do any math here we know that they have to be the same because they're similar triangles okay I'm going to give you guys 30 seconds for question number 10 starting now okay time's up let's go and go over question number 10 so we've got the solution to the given system of equations is XY what's the value of x we've got stacked equations so I'm going to look to add subtract or substitute in this case we have y is equal to -3x I want to get to the value of x as fast as I can so I'll substitute in this -3x because then I have 4X minus 3x which would leave me with just X so then I have X is equal to 15 so what's the value of x it have to be 15 so our answer there would have to be C okay moving on to question number 11 for this one I'm going to give you guys uh 30 seconds as well starting now all right time's up so let's go and go over question we've got which of the following equations is most appropriate linear model for the data shown in the scatter plot I'm going to take a look at my Y intercept I see it's somewhere between 9 and 10 I'll take a look at my um slope my slope's negative okay so if I look at my options I can get rid of c and d because they have positive slopes I can get rid of a since it's got a negative Y intercept we know our Y intercept is positive so our answer there would have to be B all right let's go move on to our next question okay for our next question I will give you guys 30 seconds as well okay so you get 30 seconds starting right now all right time's up let's go and go over the question so we've got the graph of y f ofx is shown where the function f is defined by F ofx = ax CU plus BX S Plus c x plus d where a b and c d are constants for how many values of X does f ofx equal Z well F ofx will equal Z where we cross our x intercept or where we touch sorry I should say where we touch our x intercept okay so if we look at our zeros we've got one right here we've got one right here and we've got one right here so we have three zeros okay once again I want to repeat that you have F ofx equal Z where you touch that x axis okay we touch the x-axis in three different points so we have three zeros so our answer there would have to be C okay moving on to question number 13 for question number 13 I'm going to give you guys 30 seconds as well so 30 seconds starting now all right so that's about 30 seconds so let's go and go over question number 13 we've got Vivian bought party hats and cupcakes for 71 so we've got our total cost is 71 we've got each package of party hats costs $3 so I'll mark that as $3 per package of hats so I use H for hats and each cupcake costs $1 so I'll use plus C for cupcake Vivian bought 10 packages of party hats how many cupcakes did she bought well let's go and substitute in 10 for H because that's how many packages of hats she bought okay we need to solve for the amount of cupcakes she bought well 3 * 10 is 30 so we'll do 71 minus 30 71 minus 30 will leave us with 41 is equal to the number of cupcakes so our answer there would have to be 41 all right moving on to question number 14 okay for question number 14 I'm going to give you guys 30 seconds to answer that one as well starting now all right 30 seconds is up so let's go and go over it we've got what is one of the solutions to the given equation in order to get my solution I'm going to look to factor this okay so I'll do z uh we have looking at numbers that multiply to -4 that'll add to 10 okay so numbers that multiply to -4 would be uh 2 and then positive uh posi 12 okay that would be how we could Factor this we'd have Z + 12 and Z minus 2 as you can see -2 * 12 gives us -4 and then we have plus 12 z- 2 Z which gives us that plus 10 Z and then we have z^2 as well all right so as far as possible solutions here you'd have Z is equal to two as one of the solutions and the other solution you could have would be Z is equal to -12 now keep in mind in this case you're just asked for one of the solutions so I would just answer with two here okay you could also have answered with -12 um sometimes they'll ask you to answer the positive solution or the negative solution or something like that so always pay attention to that but in this case they're just asking for one of the solutions so you could have -2 and you could have positive2 all right going on to question number 15 for question number 15 I'm going to give you guys uh 40 seconds on this one starting now all right time's up let's go and go over the question so we've got bacteria growing in a liquid growth medium there were 300,000 cells per milliliter during an initial observation number of cells per milliliter doubles every 3 hours so we've got our initial amount 300,000 that's doubling okay so doubling means our growth factor is two that's happening every 3 hours okay so denominator in our exponents three and the numerator will be how many cells per milliliter will there be 15 hours after the initial observation so 15 over3 would be that exponent 15 over 3 we know is equal to 5 so we could rewrite this as 2^ 5 okay so now we just put this into our calculator and that would give us 9, 600,000 okay so that would be answer Choice D all right moving on to question number 16 okay so for question number 16 I'm going to give you guys uh 30 seconds on this one okay so 30 seconds starting now all right time's up let's go and go over the question so which expression is equivalent to and then we' got this equation here so if we look at our options okay we can see that we're ultimately going to be pulling out 6x^2 y^2 in all these so let's go ahead and do that if we pull out 6 x^2 y^2 from this number here we'd be left with x ^ 6 okay so we're going to have X to ^ 6 as one of our factors then if we take a look at if we pull out 6 x^2 y^ over here we'd have to multiply by two to get that 12 so we'd end up with x^ of 6 + 2 and then getting multiplied by 6 x^2 y^2 okay so if you look at our options here we can go ahead and see what matches up with that we see B doesn't match up neither does a neither does d our answer there has to be answer Choice C x^ of 6 + 2 * 6 x^2 y^2 okay moving on to question number 17 okay for question number 17 I'm going to give you guys uh let me zoom in a little bit okay there we go all right for question number 17 I'll give you guys um 40 seconds for this one all right time's up let's go over the question Okay so we've got the neighborhood consists of a 2 hectare Park and a 35 hectare residential area the total number of trees in neighborhood is 3934 equation 2x + 35 y = 3934 represents situation which the following best interpretation of X in the context well we know we have our total number of trees okay so we ultimately need to sum this we've got a two hectare Park so this x then must be the number of trees per hectare in the park okay so average number of trees per Hector in the park that would be answer Choice a so a would have to be our answer there all right let's go and move on to question number 18 okay for question number 18 I'm going to give you guys um 45 seconds for this one okay starting right now okay and I'll zoom out so you can see the whole thing there's question 18 all right time's up let's go and go over the question Okay so we've got graph shows relationship between number of shares of stock from company a which is represented as X and Company B which is represented as y that Simone can purchase which equation could represent the relationship all right I see my Y intercept is going to be at 40 okay keep in mind we also want to check that we've got Z and zero here which we do okay we see that our X intercepts at 60 our slope is going to be -40 over 60 which is the same as -2/3 okay so let's go look at our options we have option A Y is equal 8x 12 we can get rid of that cuz it has a positive slope same thing with c c also has a positive slope so we can get rid of it next thing we're looking at is B and D okay so for B and D one thing that we can do here it looks like um looks like they would have different y intercepts so we could use that um as one of the ways to do it so let's actually go ahead and do that so we could do 480 over 12 will get us the value of our Y intercept okay so let's go ahead and do 480 over 12 and that would be 40 okay and then if we look at option D we would have 480 over 8 which would give us 60 okay we know that our Y intercept is at 40 so our answer would have to be answer Choice B okay moving on to question number 19 okay for question number 19 I'm going to zoom in a little bit and I'll give you guys 30 seconds for this one so 30 seconds starting right now all right time's up so let's go and go over the question we' got Circle A has radius of 3 n and Circle B has a radius of 129 n where N is a positive constant the area of Circle B is how many times the area of circle a all right well to get the area of a circle we would do pi r 2 so we have pi times our radius which is 3 n all being squared divided by or hang on it says area of circle B okay so Circle B is 129n okay so we got how many times the area of circle a so how many we have the area of circle B is how many times the area of circle a we need the radius then of Circle B to start and we'll square that and we put that all over the radius of piun * radius squ okay our radius here is 3 n squ ultimately that would equal out to Pi um * 129 2 * n^ 2 all over Pi so as you can see our pies will cancel out so we can just get rid of them then we'd have 3^ 2 * n^2 the N SS will also cancel out so then it's just 1292 over 3^ 2 so you can put that in your calculator once we do that that will ultimately give us a value of 1849 so that would have to be answer Choice d okay moving on to question number 20 all right for question number 20 I'm going to give you guys uh we'll do 30 seconds for this one as well okay so 30 seconds starting right now all right 30 seconds is now up so let's go and go over the question so we've got the frequency table summarizes the 57 data values in the data set what is the maximum data value in the data set okay keep in mind we need the maximum data value in the data set not the value with the highest frequency so some people would be inclin Ed to answer 11 because it has the highest frequency but that's not the question we're asked we're asked what's the maximum data value in the data set we see that the maximum data value would be 14 okay so our answer would have to be 14 all right moving on to question number 21 for question number 21 I'm going to give you guys uh 45 seconds for this one okay so 45 seconds starting now e all right time's up so let's go and go over the question Okay so we've got a circle in the XY plane has a diameter with end points 24 and 214 an equation of the circle is x - 2^ 2 + y - 9 = r s where R is a positive constant what's the value of R all right so we need to solve for our radius here okay if I'm given two different end points for a diameter I know that I can solve for the diameter and then just divide by two to get my radius now what I look for if I'm given two end points like this is I'm going to look for if the X values are the same or the Y values are the same in this case the X values are the same which means that if we were to plot this okay we'd have two and four and we' have two and 14 okay and these are just going to be just a straight line down okay so let me just redraw that dot okay just be a straight line down okay and as you can see the difference there is 10 okay so our diameter is 10 so we can write 10 is equal to the diamer therefore the radius then would have to be five okay so our answer there would have to be five so the big tip I have for you here is if you're given end points like this for a circle try to see if the X values are the same or the Y values are the same because that makes it super super easy all right that being said let's go and move on to question number 22 all right for question number 22 I'm going to give you guys 40 seconds for this one starting right now all right all right time's up let's go and go over question number 22 so we've got angle measure uh the measure of angle R is 2 pi over 3 radians measure of angle T is 5 pi over 12 radians greater than the measure of angle R what's the measure of angle T and degrees anytime something's underlined on the SAT Math section pay attention to it okay so in this case we've got angle T 5 pi over 12 radians greater than the measure of angle R so we have to add in the measure of angle R to add a fraction like this I need the same denominator okay so I'll go ahead and multiply the numerator and denominator of this fraction by 4 to get to 12 so that would give us 8 pi over 12 okay this would ultimately give us a value of 13 pi over 12 radians to convert radians to degrees what we're going to do is we'll take that 13 pi over 12 radians multiply it by the fact that we have 180° per Pi radians we see our pies are going to cancel out 13 over 12 * 180 will give us 195° so our answer would have to be answer Choice C okay and I just noticed that part of my camera was blocking so let me scroll down so as you can see once again 13 piun / 12 multip by 180° over Pi radians gets rid of our radians and we're left with 195° all right let's go ahead and move on to question number 23 okay so for number 23 I'm going to give you guys 30 seconds for this one starting now all right time's up let's go and go over question number 23 we got a certain town has an area 4.36 square miles what is the area in square yards of this town so to convert from square miles to square yards what we have to keep in mind is that this conversion is for only miles and yards so to do square miles of square yards we have to keep in mind that we have to square this value so what we do is we have 4.36 square miles now we have to multiply that by 1760 squared okay and if you are someone who gets confused when dealing with converting units I'll show you a way that you can check your work kind of as you go you have 4.36 miles okay you want to or square miles let me write that as square miles square miles okay so actually just write that as mil with a a two as the exponent okay now we want to get to square yards to do that we would want to multiply by the number of square yards we have per square mile so we can write yard squared per mile squared okay now our conversion unit is just 1 mile to 1760 yard so we'd actually have to do 1760 squared yard squared and then we'd have to have a 1 per 1 M squar okay so as you can see here you're going to have to do 4.36 * 1760 s when you put that in your calculator you're going to get 135 5 536 and you can also see that your square miles cancel here and you're left with square yards okay so your answer there's got to be answer Choice D we can go ahead and move on to our next question okay and once again I kind of noticed that my camera is blocking it so there you can kind of see it more clearly all right let's go down to number 24 okay for this question I'm going to give you guys uh we'll do 60 seconds actually we'll do 75 seconds for this one this one's a little bit a little bit longer so 75 seconds on this one starting right now for for all right time is up let let's go and go over question number 24 so we got for line H table shows three values of X and their corresponding values of Y Line K is the result of translating line H down five units in the XY plane anytime you have translations or Transformations always pay attention what is the x intercept of line K well let's start by getting our equation for line H to start so we see that we are going over by five so our denominator for our slope would be five and we are going up by 30 okay so 30 over 5 we can simplify that down to positive 6 so we know our slope for line H is 6X so we've got Y is equal 6x let's go and find our Y intercept okay since we know our slope is 6X we can do 6 * 18 okay in order to figure out how much we went up going from 0 to 18 so if we add a new point 0 right here okay we see that we've got to go back by the value of 6 * 18 which is 108 and that'll leave us with 22 okay so now we've got 22 there so we know that we have y is equal to 6X + 22 okay from here we need to translate this down by five units to get the value of line H because this equation we have right now is for line K so that would mean that line H is going to be Y = 6x + 17 now keep in mind that we want to find the X x intercept of line K our x intercept is where Y is z so we can put in a0o for y and we have 0 is equal 6x + 17 we'll subtract 17 from both sides then we get that -17 is equal to 6X then we divide both sides by 6 and we get -7 over 6 is equal to the value of x which we see must be answer Choice D all right that being said let's go ahead and move on to question number 25 for question number 25 I will give you guys um we'll do 60 seconds for this one as well actually we're going to do um we'll do 90 seconds for this one so 90 seconds e e all right 's up let's go and go over it in the XY plane the graph of the equation yal x^2 + 9x - 100 intersects the line yal C at exactly one point what is the value of C so for a question like this the first thing I Look to do is find my vertex now in this case we don't have vertex form so what I'm going to do is I'm going to plug into Desmos since I don't see a very easy way to factor this so I'll go ahead and put it in Desmos and then I will see what my vertex is there okay now keep in mind this is specifically for the digital sat that you have access to a graphing calculator within Blue Book the testing environment you also if you are taking the sat on paper you could use your graphing calculator to do this if you have a ti84 for example you could plug this in and find the vertex okay in this case if we take a look at the graph we have a Vertex at 79.7 for the y-coordinate now keep in mind we're really only concerned with the y-coordinate because we need this to intersect the line Y equals c at exactly one point so the value for C then would have to be that uh 79.7 okay so we need 79.7 we take a look at our answer choices we've got answer Choice B which obviously is not equal to that same with answer Choice D now between C and A we know that option A would have to be negative something below 00 okay this would have to be below 00 right there okay so once again option A would have to be less than 79.7 okay so what ultimately would have to equal 79.7 that would have to be answer Choice C okay so C would have to be our answer there for number 25 all right let's go ahead and go over number 26 now okay so I'll give you guys um a certain amount of time let me go a and remove Desmos from my screen and we'll scroll down all right so number 26 is right here okay for this question I'm going to give you guys uh we'll do two minutes for this one okay because this one's a little bit of a longer one let me go ahead and switch the sides at my cameras on so you can see the question and I'll give you guys two minutes starting right now e for all right that two minutes is up okay I will note that this question is one that that is um pretty timec consuming if you don't know what to look for so if you weren't able to get it done in 2 minutes you might have still been able to get it right in more time but you do need to be able to move fast on the digital SAT Math section order to get a really good score so let's go and go over how you can do this much more efficiently so here's the way I would approach question number 26 so we've got for each real number R which of the following points lies on the graph of each equation uh of each equation in the XY plane for the given system sorry about that want to make sure I was recording still and I am all right so we've got uh 2x + 3 y equal 7 10x + 15 Y is equal to 35 so what I'm look to do here is see if something is a solution to this first one if it's also a solution to this second equation okay so if we take a look we've got 2 * 5 gives us 10 3 * 5 gives us 15 and 7 * 5 gives us 35 so that means that since we're multiplying this top equation all by five anything that is a solution to this top equation or anything that's a solution to this bottom equation will also be a solution for the other equation okay so as long as something is a solution for one of the equations it's a solution to both all right next thing I'm going to look at is you pretty much just have to use substitution here in order to get a through D um but you want to be smart about the order that you do substitution so what I mean by that is since I have a two as my coefficient in front of my X I'm going to look for X values that have a denominator of two which I see is the case in answer Choice B okay the next thing I look at is in terms of Y okay I've got 3 y so where do I have a denominator of three and that y-coordinate I see that's in the answer Choice C okay so from here what I'll do is I will go like this I would go one two and then between d and a I would take a look at option D and I'd probably go D before a so I'd probably go 1 two 3 and then four and the reason why is because we've got this 35 as this constant we're dealing with fives okay none of that really makes much um it doesn't make the math very easy it makes it much more difficult if we look at down here we've got this being over two that just seems easier to deal with then over five and then constants as well so this is the order i' approach these in so basically if you're wondering you know what you should do to order um as you saw first start out with where you're going to have things cancel out for example two in this numerator will cancel out these twos in the denominators um and then from there obviously B and C they both have that just one's X one's y I would from there just go in the order that they're listed so I do the first one first so in this case let's go and start with B so we' plug in two so we'd have 2 * -3 r/ 2 + 7/2 and these twos will cancel out with this two that's the coefficient so that's going to end up leaving me with -3 r + 7 and then we have R for the value of y so we'd have + 3 * R so now we've got -3 R and plus 3 R that'll give us 0 R so then we just have 7 is equal to 7 okay is that true that is true okay so we know that since this a solution for the first one it's also a solution to the second one since the second equation is just the top one multiplied by five okay so we know our answer there would have to be answer Choice B okay so basically big things to take away here number one make sure that if you have equations like this okay see if you know one is just getting multiplied by some constant to get the other because then if something's a solution to one of them it'll be the solution to the other one and you have to check them both which saves you cuts the time in half basically and then the next thing be smart about the order that you go through your answer choices when you have a substitution question okay try to use hints from the the question because often times you can you know go through certain answer choices much faster it's much easier for me to check the value of one and two or in other words of B and C because I know that these coefficients are is going to end up canceling out with what's in the denominator so way faster to check those than it is to check these other ones so it makes sense to start with the ones that are easier to check all right that being said let's go ahead and move on to question number 27 so for question number 27 I'm going to give you guys 90 seconds okay so 90 seconds starting now e e all right 90 seconds is now up so let's go and go over this question Okay so we've got perimeter of an equilateral triangle is 624 CM the height of the triangle is kk3 CM where K is a constant what is the value of K all right we've got an equilateral triangle let's go and draw it anytime you have a triangle or Circle question I do recommend that you try to draw it out okay so that this is equilateral which means all sides of the same length we've got our height which is kot3 so I'll write that as K tk3 okay we've got 90° angles right here and then we've got a 60° angle here a 60° angle here and then we have two 30° angles up here okay so what I'm going to do is I'm going to actually draw this out bigger so you can see this better okay so I'm going to redraw this and I'm only going to draw one of the sides just to make it easier okay so we're just going to draw one of these so that we can draw it bigger all right so once again we've got K < tk3 and then we've got 90° angle here 60° angle here and a 30° angle here so what you see is you got a 60 30 90 triangle okay so 6039 triangle and also just remember too that I guess I will just redraw this just for clarity that this is just one part of it that we're looking at okay and same thing 6030 all right so from here at 6030 90 triangle what you want to recognize is if we have kot three across from our 60 that means across from our 30 we would have K and then our hypotenuse would be 2K okay this is just the rule of a 60 30 90 triangle you could think of K if you were to replace it with X as well it just goes for any variable all right with that being said now we have 2K there we know it's equilateral which means all side lengths are the same which means that we have 2K on this side as well and then we would have um you know K there and K there and that means that this whole side length would be 2K as well so as you can see our perimeter for this equilateral triangle it's 62 2 4 cm but it's also 6K so we can write this as 624 cm is equal to 6K from here we can just go and divide both sides by six to get the value of K and when we do that we're going to end up with 104 as the value of K so the value of K would be 104 you've now reached the point in the course where it is time for you to take your first full length digital SAT practice test to do this I recommend that you download Blue Book using the instructions on the college board's website and take digital SAT practice test number four while simulating the testing environment as best you can if you're if you are able to take the practice test at a similar time of day to which you will be taking the actual digital sat I recommend doing that as well after completing the practice test the next task in this course will be to review every question you got wrong I will discuss specifically how I recommend you review your test after you have finished it for now I'm going to start a 2our and 14-minute timer for you to take practice test 4 e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e now that you've completed the practice test I want you to go to the college board's website and open up your results for every question you got incorrect read through the entire answer explanation for both the correct and incorrect answers and identify what mistake you made as well as how you will avoid making that mistake on future questions it may be helpful to write this down or create a PowerPoint with screenshots of every question you got wrong for future reference and studying depending on how many questions you got wrong this review may take a while that is okay make sure to finish the entire review before proceeding on to the rest of the course I'm going to allocate 2 hours here for you to review Once the timer is finished the next portion of the course will begin e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e 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