I've gotten perfect 800 scores on back-to-back SAT Math sections and in this video I show you 54 practical tips and strategies I've curated for the digital SAT Math section each demonstrated on an actual question from digital SAT practice test one for more digital SAT prep content make sure to like this video And subscribe to my channel and with that being said let's dive into the video here's how to answer this sat math question in under 20 seconds question is what is 10 of 470 we can take 10 and express it as a decimal of 0.1 and then multiply it by 470 and that'll give us our answer of 47 so our answer will be answer Choice B here's a trick that'll save you time on the SAT Math section question 2 says which equation has the same solution as the given equation if we take a quick glance at our answer choices we see we have 4X in every single one of our answer choices which means if we look at our equation on top we have 4X plus 6 equals 18 all we have to do is subtract 6 from both sides and we're left with 4X is equal to 12. now we don't actually have to solve for x because we have 4X in every answer choice so our answer is answer Choice C here's a tip to be more efficient and on the SAT Math section if you glance at the answer choices of question 3 you'll see that all of them are going to be inequalities so as you read through this word problem you want to go ahead and write out the inequality to save you time so if we go and start from the beginning the total cost in dollars to rent a surfboard consists of a 25 service fee so we can go ahead and write down that 25 and that's a one-time charge because the service fee and a ten dollar per hour rental fee so we're gonna have plus 10 H we'll use H to represent hours a person rents a surfboard for T hours so we have to replace H with TDOT and intends to spend a maximum of 75 dollars to run the surfboard so they are going to spend a maximum of 75 so this total has to be less than or equal to 75 we find which inequality represents the situation and as we can see that is going to be answer Choice D so D would be our answer there here's how to solve this sat math question in less than 30 seconds the function G is defined by G of X is equal to x squared plus nine for which value of x is G of x equal to 25. well since we have the G of X equaling 25 we go ahead and plug that in for G of X now we have 25 is equal to x squared plus nine now we're going to subtract 9 from each side so we can start isolating that x squared value now we have 6 18 is equal to x squared to isolate X we need to take the square root of x squared and the square root of 16 the square root of 16 is 4 which means 4 will equal x and our answer will be a here's how to solve this probability question on the SAT question 5 States each face of a fair 14-sided die is labeled with a number 1 through 14. with a different number appearing on each face if the die is ruled one time what is the probability of rolling a 2 well only one of the 14 faces has a 2 on it so the answer has to be 1 over 14 which is answer Choice a here's a trick for converting units on the SAT question 6 States a printer produces posters at a constant rate of 42 posters per minute at what rate in posters per hour does the printer produce posters so what we're going to do here is we're going to convert from 42 posters per minute which I'll represent as P per M and we have to convert that into posters per hour so we're going to do is we're going to multiply by 60 minutes per hour so as you can see our minutes which I'm representing as M are going to cancel here and we'll be left with posters P per hour H so 42 times 60 is going to equal 2520 posters per hour so our answer is 2520. here's how to solve this sat math question in under 40 seconds question 7 States the function f is defined by the equation f of x equals 7x plus 2. what is the value of f of x when x equals four well all we have to do is plug in 4 for X so we do 7 times 4 plus 2. 7 times 4 is going to be 28 28 plus 2 will be 30 30 is going to equal our value of f of x and be our answer here's how to solve this sat math question in under 60 seconds question 8 States a teacher is creating an assignment worth 70 points the assignment will consist of questions worth one point and questions worth three points which equation represents the situation where X represents the number of one point questions and Y represents the number of three-point questions we know our total number of points is going to be 70. so it's gonna have to equal out to 70. now for every X question we get right which is every one point question we get one point so we have X Plus now our three point questions which are represented as y so X Plus 3y must equal 70 and our answer will be D here's how to answer the similar triangles question on the SAT question 9 States right triangles l m n and pqr are similar where l and m correspond to p and Q respect actively angle M has a measure of 53 degrees what is the measure of angle Q so what we see here is since we have similar triangles where l and m correspond to p and Q we also know that n must correspond to R okay we see that angle M has a measure of 53 degrees okay and then we're asked for the measure of angle Q we see that M corresponds uh to angle Q since they're similar triangles so they're going to have the same angle measure okay so that 53 degrees that we are given for the angle M must also be the angle measure of angle Q so our answer will be B here's a trick for the sac math section question 10 states a solution to the given system of equations is X Y what is the value of x whenever you see stacked equations like this on the SAT it's usually a sign that you're going to be able to add subtract or substitute one of the equations with the other in order to get your answer faster in this case we're asked for the value of x and we're given that Y is equal to negative 3x so what we're going to do is we're going to substitute in that negative 3x for y in this below equation so now what we're going to have is we're going to have 4X plus y when we know Y is negative 3x so 4X minus 3 X is equal to 15. now we know that 4X minus 3x is X which means that X must equal 15 and our answer is answer Choice C here's how to answer scatter plot questions on the new digital sat question 11 states which of the following equations is the most appropriate linear model for the data shown in the scatter plot what you're going to want to do here since we're looking for a linear model to represent the scatter plot let's go ahead and draw a line just to give you a rough reference as you can see we have a negative slope which means that answer choices C and D cannot be true since they have positive slopes the next thing we'll look at is the differences between s choices A and B which are their y-intercept we see that we have a positive y-intercept of right around 10. so if we look at answer Choice a it would have a y intercept of negative 10 which cannot be correct and our answer Choice must be answer Choice B here's how to answer this polynomials question on the SAT question 12 States the graph of y equals f of x is shown where the function f is defined by f of x equals ax cubed plus BX squared plus CX plus d where a b c and d are constants for how many values of X is f of x equals zero well all we have to do is find where f of x equals zero and count the number of points we see we have one here one here and one here so our answer will be 3 which is Ann's Choice C here's a tip to be more efficient on the SAT Math section if you see a word problem like this you're going to want to start writing out the equation as you read it so watch How I do this problem question 13 states Vivian bought party hats and cupcakes for 71 dollars so 71 is going to be the total amount she spends each package of party hats costs three dollars so three dollars times our number of packages of party hats which I'll represent as p and each cupcake costs one dollar so you could make it plus 1C but since a one in front of C is redundant we'll just get rid of the one so now we have our equation well if she bought 10 packages of party hats that means 10 is equal to P so we can go and substitute that in so now I'll go ahead and erase that P and I can put in 10 so we know that's the amount that she had bought of those party hats we have three times ten we know that's going to equal 30. so we're gonna have 71 is equal to 30 plus C now we want to isolate C to solve for it to do that we're going to subtract 30 from each side 71 minus 30 is going to leave us with 41. so now we have 41 is equal to C and our answer will be 41. here's an example of when you should use your graphing calculator on the SAT Math section if you take a look at question 14 it states what is one of the solutions the given equation now you could solve this without a graphing calculator by factoring but it's really a smarter choice just to go ahead and use the graphing calculator now as you can see here this is Desmos and you're going to have essentially a version of Desmos on the Bluebook sat on the new digital sat now what I recommend doing is you just go ahead and put in this equation into the graphing calculator now keep in mind you want to substitute out Z or any other variable they put in there for x and once you do that you see that you have your equation graphed out and then since it's set equal to zero all you have to do is find where it equals zero you can see that's at negative 12 and at 2. so you have two potential answers here one is negative 12 and that would be correct and the other answer is 2 and that would also be correct so you could put in one of either of those answers but I want to quickly touch on why I think it's smart to use the graphing calculator here instead of actually Factor this out yourself if you're factoring this out yourself the chances of you making a mistake go up versus if you use a graphing calculator now keep in mind using the graphing calculator that's built into the digital sat only takes a couple of seconds right and factoring May save you a couple of seconds but in my opinion it's not worth the risk of you actually making a mistake doing multiplication or doing addition or doing subtraction anything along those lines in my opinion with questions like this it's just much smarter to go ahead and use the graphing calculator you avoid making many many errors that can be made when factoring so with questions like these just use the graphing calculator here's how to solve this sat math question about exponential growth question 15 states that bacteria are growing a liquid growth medium there were 300 000 cells per milliliter during an initial observation the number of cells per milliliter doubles every three hours that's important how many cells per milliliter will there be 15 hours after the initial observation so our starting amount is three hundred thousand so let's go ahead and write that down now we're going to be using the equation for exponential growth keep in mind we are doubling every three hours since we're doubling a two is what's going to go in these parentheses now we are going to raise it to the power of 15 over 3 and I'm going to explain why here and it's very important pay attention because this equation is commonly tested on the SAT Math section so the reason we are raising it to the power of 15 over 3 and keep in mind we're raising this 2 to the power of 15 over 3 is because we are doubling every three hours since we're doubling every three hours that gives us that three in that denominator of that exponent now we're asked how many there's going to be after 15 hours which is why we have that 15 in the numerator okay so now as you can see we have our equation we put this in our calculator and we get our answer of D 9.6 million here's how to solve this question about simplifying exponents on the SAT question 16 states which expression is equivalent to 6X to the power of 8 times y squared plus 12x squared y squared what you're going to do here is you're going to look for common factors that you can pull out of each of these so as we can see we have y squared in both of them we also have 6 and 12 which we can pull out a 6 from 12. we also have x to the power of 8 and x squared okay so the way that we're going to do this is we're going to pull 6 out we're going to pull x squared out and we're going to pull y squared out now we still have to multiply get this equation still okay so what do we have to multiply by here well we're going to need x to the power of 6 still to get to that x to the power of 8. keep in mind that this x squared times this x to the 6 is what's going to give us x to the power of 8. we're still going to have that y squared we have that 6 out front so now we have our first term now we know that we also have to have another term so we have six here but we have 12 up here okay so to get to that 12 there we're gonna have to add 2 and we still have x squared and Y squared here as well so we see that we're ultimately going to end up with 6X squared y squared times x to the power of 6 plus 2 which we see is going to be answer Choice C here's how to better interpret word problems on the SAT Math section question 17 States a neighborhood consists of a two hectare Park and a 35 hectare residential area the total number of trees in the neighborhood is 3934. the equation 2x plus 35y is equal to 3934 represents the situation which of the following is the best interpretation of X in this context well what we have to look at here is what does this total represent well it represents the total amount of trees now we also have to look at what gets us to that total okay we have 35 times y well 35 is our area but we have to multiply by the number of trees per unit of area now keep in mind we're asked to solve for x here so we're looking at the amount of trees per hectare in the park okay so X must be the the average number of trees per hectare in the Park which is answer Choice a here's a tip to solve SAT Math Questions when your answer choices aren't in point-slope form if we take a look at this question it says the graph shows the relationship between the number of shares of stock from company a which is represented as X and the number of shares of stock from Company B which is represented as y that Simone can purchase which equation can represent this relationship and we see we have company B and Company a and obviously we have the correct correspondence of x to a and Y to B so that's good to know now in this case I see that A and C both are in point-slope form so I'm going to go ahead and just check if they're correct since that's the easiest thing to do so here I see that both of these have y-intercepts that are not correct I have 12 and 8 but the actual y-intercept is 40. so I can go ahead and get rid of a and I can get rid of C now you could go ahead and convert B and D into point-slope form and there's not an issue with that but it does take longer than what I'm about to show you instead what you could do is you could know that the slope which will represent is m is equal to negative A over B when we have our equation set up like this where we have a coefficient in front of X plus a coefficient in front of y equals some kind constant now the next thing I'm going to do is I'm going to check what my slopes are for each one okay so for answer Choice B here we see that our slope would be negative 8 since 8 is our a value over 12. okay and then for our D value we see that we would have negative 12 over 8. now I'm going to see what my actual slope is okay my actual slope is I go down 40 and I go over 60. so that'd be negative 40 over 60 which we know we can simplify to negative 4 over 6. Okay negative 4 over 6 is equal to negative 8 over 12 when we simplify negative 8 over 12. so our answer there is going to be answer Choice B here's how to solve this I'll say t math question in under 60 seconds question 19 States Circle A has a radius of 3 and then Circle B has a radius 129 and where N is a positive constant the area of circle B is how many times the area of circle a well let's start by finding the area of circle B then so Circle B has a radius of 129 n now keep in mind the formula for the area of a circle is pi r squared we know our radius is 129 n and all of that is going to get squared now we have to divide divide that then by the area of circle a to find out how many times bigger it is so we know that the radius of circle a is 3n squared now keep in mind that n here is going to end up being squared in both the top and the bottom okay so first thing it's very obvious that those Pi's cancel so most people will get that now the next thing we need to understand is that 129 squared times N squared is equal to what we have here of 129 times N All To The Power of 2. Now on the bottom then we end up with 3 squared times N squared as well and we see that those n squareds are going to cancel okay that's really important to know because now the question becomes very easy we can just plug it into our calculator and when we plug into our calculator 129 squared divided by 3 squared which we can also just know is 9 then you're going to end up with answer Choice D here's how to avoid this tricky question on the SAT question 20 States the frequency table summarizes the 57 data values in a data set what is the maximum data value in the data set now most people when they look at this might think that the answer is 11 because it has the highest frequency and they think that that's the maximum since it's the highest value in the frequency section of the table but that's incorrect the actual answer here is 14. now the reason why is because they're asking for the maximum data value they're not asking for the highest frequency value okay that would be 11 because the data value there is 11 but they are asking for the maximum data value which means our answer has to be 14. here's how to answer this question about circles on the SAT question 21 says a circle in the X Y plan is a diameter and then points 2 4 and 214 an equation of the circle is x minus 2 squared plus y minus 9 squared equals r squared where R is a positive constant what is the value of R okay what you need to understand here is that this is a question dealing with the circle equation so it's important you know the circle equation going into the SAT because it is tested fairly often now as far as how you answer this it's actually pretty easy as long as you can recognize this simple trick when you're given a circle question you're given endpoints often times there are endpoints that are specifically designed to make the question easier so you want to look at them pretty closely and here what we notice is that we have an x coordinate that is the same in both of these sometimes it'll be a y coordinate that is the same in both but I either way try to find if you can see either the x coordinates are the same or the Y coordinates are the same because it'll make the question a lot easier in this case since our x coordinates are the same we're going to look at how far apart are our Y coordinates and we see that from 4 to 14 as a difference of 10. now keep in mind that the circle has a diameter with these endpoints okay so if the circles like this and this is our diameter between our points and it's 10 well that means our radius must be 5 because our diameter is Double R radius okay so the value of R and keep in mind that this is the equation of a circle okay where R is representing our radius and we're asked for the value of R not r squared the value of R then must be five okay so our answer is 5. here's how to solve questions that ask you to convert from radians to degrees on the SAT question 22 States the measure of angle R is 2 pi over 3 radians the measure of angle T is five pi over 12 radians greater than the measure of angle R what is the measure of angle T in degrees so we have to start by finding the measure of angle T and radians and then after that we'll convert to degrees so we know that the angle R is 2 pi over 3 radians now we have to add on to that the Phi 5 pi over 12 radians since 5 pi over 12 is the amount of radians that we are greater than the angle measure of R to get to angle T from here we need to have a common denominator in order to add these fractions so to do that I'm just going to go I see 3 and 12. I'm just going to go ahead and make it 12. I know that you could sort of simplify it but I'm not going to so I'm going to multiply 3 by 4 to get to 12 and I'm going to multiply with 2 by 4 which will give me 8. so now I have 8 pi over 12. now I can go and add these together and I'm going to see that's going to give me 13 pi over 12. now from here I need to go ahead and convert 13 pi over 12 in 2 degrees now this is really easy but some people can get tripped up on it if they don't know this trick in order to convert from radians to degrees you need to multiply by 180 degrees over Pi radians now keep in mind that we have radians as our units in here with this 13 pi over 12. so to get rid of those radians we have to have radians in the denominator right here which is why we have Pi on the bottom okay so when we go ahead and do this we're going to end up getting rid of our PI on each one sorry I did not mean to erase that let me go and put that back okay we're going to end up canceling out those pies and we're going to end up with 13 times 180 over 12 which we're going to go ahead and put into our calculator and once we do that we're going to see that that turns out to be 195 degrees which is answer Choice C here's how to answer questions about converting units on the SAT question 23 States a certain town has an area of 4.36 square miles what is the area in square yards of this town now when you're converting area as your unit you have to keep in mind that you end up squaring it right since we have square miles and square yards so when we make this conversion of one mile equaling 1 760 yards what we have to actually do is we have to take our first our 4.36 square miles and then we have to actually multiply that by 1760 squared since we're converting from square miles to square yards we have to square the unit that we are converting okay and when we do that we put it in our calculator and we end up with an answer of answer Choice D 13 million five hundred and five thousand five hundred and thirty six here's how to solve this difficult sat math question question 20 24 States for line H the table shows three values of X and their corresponding values of Y Line K is the result of translating line H down 5 units in the X Y plane what is the x-intercept of line K well in order to get to line K we need to first know the equation for line H let's go and find that so let's start by finding our slope we see that we go over 5 and we go up 30. so we have 30 over 5 as our slope so let's go ahead and write that down we're going to get 30 over 5 which we know is equal to 6 is equal to our slope which we'll call M now in order to solve for our full equation we're going to go ahead and put in some of these points to get our y-intercept okay so we see that X is 18 when Y is one so Y is 130 so we're going to have 130 is equal to 6 times 18 plus some constant B now let's go ahead and solve for this so 6 times 18 is going to give us 108 so let's go ahead and subtract 108 from each side here 130 minus 108 is going to leave us with 22 is equal to B okay so now we have our equation Asian so let's go ahead and write out our equation all right so we have y is equal to 6 X Plus 22. now we don't use this to find our answer reacts we have to keep in mind that line H is translated down five units so if we're going down five units instead of plus 22 we would have plus 17. okay so let's go ahead and put in that plus 17. okay so now we have our equation for line H now we can go and find our x-intercept well where's our x-intercept that is where Y is equal to zero so let's go ahead and take out y we'll put in 0. now all we got to track 17 from both sides okay when we do that we're going to end up with negative 17 is equal to 6X now we're going to go ahead and divide both sides by 6 and we're going to get that X is equal to negative 17 over 6 which we see is going to be answer Choice D here's a great example of an SAT question that is made way easier by using the graphing calculator that is available on the digital sat question 25 says in the X Y plane the graph of the equation y equals negative x squared plus nine x minus 100 intersects the line Y equals c at exactly one point what is the value of C now the key thing here is that intersects at exactly one point which is what is going to allow us to do this super easily using Desmos so as you can see what I did here is I went ahead and I plugged in this equation into Desmos now as you can see from this negative x squared and also from the graph it's going to open down so in order for us to to intersect at exactly one point with the equation y equals c that's going to have to happen right at this maximum value so if we take a look at the graph all we got to do is find that point we see that point is negative 79.75 we just have to match that up with one of our answer choices now now I see with our answer choices they're all negative but this is obviously going to be way too small value negative 100 we know is not equal to negative 79.75 negative 481 over 4 would be something below negative 100 so it can't be correct and our answer would have to be C here's how to make this really difficult sat math question much easier if you take a look at question 26 States for each real number R which of the following points lies on the graph of each equation in the X Y plane for the given system now if you see stacked equations like this oftentimes you'll be looking to sort of add or subtract to get to your answer but in this case I'm were asked for which of the following points lies on the graph of each equation what we're actually going to do is check if if something lies in the first equation if it also will will be a solution to the second equation so the way we're going to do this is in this case we have 2X plus 3y equals 7 we have 10x plus 15y equals 35. I'm going to look for proportions or ratios here I see that to get from 7 to 35 I'd be multiplying by 5. I see to get from 2 to 10 I'd multiply by 5. I see to get from 3 to 15 I would multiply by 5. so in this case I know that since all of those numbers if they're multiplied by 5 will get me that next equation I know that if if a solution's set it works on the first equation it will also be true on the second equation right so now in this case I only have to actually check on one of the equations and if it is true then it means that it will work for the other equation as well so that's going to save me half the time now the next important thing to help you here is the order at what you're going to track these because the reason this question is so difficult is because it's time consuming it's not necessarily that is is extremely complex but the real only way to check these is substitution which is obviously not ideal at all substitution takes a very long time but thankfully we already gotten rid of half the work let's let's be smart about the way we go about this so what I'm going to look for here is which of these answer choices I would start with because if you start with the wrong answer choices oftentimes it's going to be a little bit more lengthy to figure out that it's actually wrong and the reason why is because typically the correct answer choices will just fit nicely it's just kind of the way it works usually most of the time not always but most of the time so the way that I'm going to choose which answer choice to actually substitute in first here is I'm going to look for things that will cancel out okay so the first thing I'm going to do is since I see three out of my four answer choices are dealing with sort of denominators of two or three I'm going to be working with this first equation okay and I would usually pick that one anyway just because it's smaller numbers than sort of 10 15 and 35 so that's where I'm going to be checking these possible solutions now the next thing I'm going to look at is which ones will cancel out nicely right and the way that I look at that is I'm going to look for X values that are divided by 2 since I have this 2 and look for y values that are divided by 3 because I have that three okay so I see here by X guys are over two okay so that is one that I would probably start with and if I look at b or I'm sorry if I look at number c i see that in this y value I have ones that are over three so that's the one that I would check next and then I have DNA and I'd probably just check D third and then a fourth I'm checking a fourth because it's the most complex I'm checking D third because it doesn't have something that nicely cancels out okay so from here this is the order that I would check these in on a substitution question now from this point I would just go ahead and start substituting so let's go ahead and do that so we're going to have 2 multiplied by negative three R over two plus seven over two and then we are also going to have that plus 3 times y we know that Y is going to be R so plus 3r is going to equal 7. now let's find out if this is true so we can go ahead and cancel this 2 out with this 2 and that 2 out as well with this two because we know that we would distribute this okay so once we do that we end up with negative three r plus seven and then plus 3r is equal to seven now we have a negative three R and A Plus 3r which will cancel out to 0. so we're going to end up with 7 is equal to 7 okay we end up with 7 is equal to seven now is that true yes so is that a solution yes so is our answer B yes here's a really difficult sat math question made super easy question 27 States the perimeter of an equilateral triangle is 624 centimeters the height of the triangle is K times root 3 centimeters where K is a constant what is the value of K well if we go ahead and draw this out it's going to make us a lot easier to visualize so we have our equilateral triangle we have our height which is going to form a right angle there since it's equilateral we know that we have side lengths 60 and 60. and we also know that since we have a 90 degree angle and a 60 degree angle this angle has to be 30 degrees the next thing we know is that our perimeter is 624 okay and that's perimeter since we have an equilateral triangle if we divide it by 3 we're going to get our side lengths so that's going to be 208 as our side length now the next thing to note is that we have our height K times root 3. now this is important because when we have a 60 30 90 triangle we know that the value here must actually be K and the reason why if I go ahead and draw this out very quickly okay is that that in a 60 30 90 triangle which I'll go ahead and just put those numbers there so you can recognize them and you should try to memorize this for the SAT if you have side length x there you're going to have side length x times root 3 there and you're going to have 2X here so in order to actually solve for the value of K I just have to divide this 208 by 2 to get the value of K right here okay so 208 over 2 is going to leave me with 104 as my answer and I'll just go ahead and put 104 as the value of K here's how to solve this oddly worded sat math question question 1 states that Tilly earns P dollars for every W hours of work which expression represents the amount of money in dollars till he earns for 39 W hours of work well we know that she's earning P dollars per every W hours of work and we know that we can set that proportion equal to the amount that she's earning per 39 W hours of work and now on our numerator we'll just have that labeled as X and that's what we need to solve for here so to isolate X we'll multiply both sides by 39w to isolate X so now we have 39 W time times P all over W is equal to X now we see our W's are going to cancel and we're going to be left with 39p keep in mind that that is p so I'm gonna put it parentheses just to make it clear so 39 times p is equal to X and we see that that is going to be answer Choice a here's how to solve this seemingly simple SAT Math problem question 2 States for a training program one rides his bike at an average rate of 5.7 minutes per mile which function m models the number of minutes it will take one to write X miles at this rate now the reason this question can be Troublesome for some people taking the SAT is because it really does deal in details so let's go ahead and focus on the details that we need to pay attention to in this case we are asked for the model of the number of minutes it will take to ride X miles at this rate now we have to keep in mind that our units were given for our rate is 5.7 minutes per mile so this is actually very easy but you have to pay attention to the details like I said now we're modeling the amount of time it takes him to ride x amount of miles so we're already given that ratio and our answer is d m of x equals 5.7 X you have to make sure here that you're paying attention to the details because some people or to fall for the misconception that you have to convert minutes per mile into miles per minute or miles per hour and you do not need to do that in this case your answer is here's an SAT Math tip that can save you a ton of time question 3 states the solution to the given system of equations is X Y what is the value of y since we want to solve for y and we see that we have stacked equations we're going to look for a way to get rid of the X to do that in this case I see we can add these two equations together because 3x plus negative 3x is going to give us 0x so we're going to end up with then is y is equal to 12 plus negative 6 which is the same as 12 minus 6 which is 6. so our answer there will be B for the value of y here's how to solve this sat math question in under 60 seconds question 4 States the equation gives a speed s in miles per hour of a certain car T seconds after it began to accelerate what is the speed in miles per hour of the car five seconds after it began to accelerate well given our equation we want to know how fast is it going five seconds after it begins to accelerate we know that the amount of time after it begins to accelerate is represented as T so we plug in 5 for T and we're going to have our speed is equal to 40 plus three times five three times five is going to be fifteen fifteen plus forty is going to equal 55 and our answer will be answer Choice D here's how to solve this question that deals with the Pythagorean theorem on the SAT question 5 States for the right triangle shown a equals 4 and b equals 5 which expression represents the value of C well when you're given a triangle question on the SAT it's often helpful to go ahead and label your sides so as you can see we go ahead and do that we're asked for the value of C we're going to use the Pythagorean theorem which means that we're going to take a squared plus b squared and make it equal to c squared and when you do that you're going to get your value of C as the square root of 4 squared plus 5 squared which we see is going to be answer Choice D here's how to solve this sat math question in under 60 seconds the question Six States what is the solution to the given equation we have 4X plus 5 equals 165 we want to isolate X so we're going to subtract 5 from both sides we're going to end up with 160 is equal to 4X then we'll divide both sides by 4 to isolate X when we do that we have 160 over 4 which is going to end up giving us 40 as our value of x right our answer there is 40. here's how to solve this sat math question in under 30 seconds the question States the x-intercept of the graph is X 0 what is the value of x in this case since we're asking for value of x and zero we know that our y coordinate is 0 at y being zero we have our x value of 7 so the value of x is seven here's how to solve this sat math question that deals with slope intercept form the function f is defined by f of x equals 1 10 x minus two what is the y-intercept of the graph of y equals f of x in the X Y plane well all that this means is you have an equation y equals 110 x minus 2. all you got to do is find the y-intercept your y-intercept is where X is zero if you substitute in 0 for X you're going to end up with Y is equal to negative 2. so as you can see your answer has to be where x is 0 and where Y is negative 2 and your answer has to be answer Choice B here's how to solve this sat math question that deals with Transformations question nines is the function f is defined by f of x equals seven X cubed and the X Y plane the graph of y equals g of X is the result of Shifting the graph of y equals f of x down two units which equation defines the function G well the function G of X is the same as f of x except we are moving it down two units which means that g of X will equal seven X cubed minus two we can see that that is answer Choice D here's how to solve this system of equations question really easily the question states which ordered pair X y's assume solution to the given system of equations now as we can see we have one equation x plus seven equals ten we know that in that case we can subtract 7 from both sides and we're going to get that X is equal to 3. now that we have the value of x we can go ahead and plug that in on our second equation we will end up with three plus seven squared which is equal to 10 squared which is equal to 100 is equal to Y so we know that it will have to be 3 and 100 which is answer Choice a here's how to solve this sat math question that deals with adding and subtracting variables with exponents the question states which expression is equivalent to 7x cubed plus 7x in parenthesis minus 6X cubed minus 3x what we're going to do here is distribute this minus sign to both of that 6X cubed and that minus 3x once we do that we're going to go ahead and combine like terms so we have 7x minus negative 3x which is the same as plus 3x and then we also have a 7x cubed minus 6X cubed now keep in mind that these are going to get some together I just didn't have room on one line to write them but that is ultimately going to give us 10x plus our X cubed value for a total of X cubed plus 10x which we see as answer Choice a so a is our answer there here's how to solve this sat math question in under 60 seconds question 12 States the function p is defined by P of n is equal to 7 n cubed what is the value of n when P of n is equal to 56 well when P of n is equal to 56 means we just substitute in that 56 for p of n in our equation and we get 56 is equal to 7 n cubed next thing we're going to do is try to isolate n because that's what we need to solve for is the value of n now we got 56 over 7 that's going to leave us with 8 is equal to n cubed now from here you should hopefully be able to recognize that if we take the third root of each side we'll be able to isolate the value of N and we will also have the third root of 8 which is 2. so 2 is equal to the value of N and our answer will be a here's how to solve SAT Math questions that deal with intersecting lines this question states in the figure shown line C intersects parallel lines s and t What is the value of x well since we have parallel lines s and t with something intersecting them we know that this angle next to X also has to be 110. the next thing that we can notice is that since we have the straight line here that has to sum to 180 so we can go and do 180 minus 110 and that will give us our answer for the value of x as 70 degrees so our answer will be 70. here's how to solve questions that ask you to find the mean of a data set on the SAT question 14 States a list of 10 data values is shown what is the mean of these data since the SAT has gone digital you will be able to use a calculator on each part of the test as of the filming of this video so in that case if you're asked to find the mean I will 100 recommend that you use a calculator exclusively because you can and it makes much more sense to find the mean of a data set using a calculator rather than doing it by handwritten math because you're less likely to make an error so what you would do is you would take all of these values and you would sum them together and then you you would take that sum and you would divide it by the number of values and that will get you your mean so that is how you would solve this question and once you do that you will end up with an answer of 10. here's how to answer this question that asks about the exponential growth formula on the SAT question 15 states the equation E of T is equal to 5 times 1.8 to the power of T gives the estimated number of employees at a restaurant where T is the number of years since the restaurant opened which of the following is the best interpretation of the number five in this context the number five is our initial value it is our starting value it is the amount that when T is 0 we will have because any number raised to the power of zero is one so this is our initial amount and that is a very important thing to know for the SAT Math section let's go and run through our answer choice we have a the estimated number of employees when the restaurant opened that is the correct answer here's how to solve this sat math question super quickly question 16 States what is the minimum value of the given function we have G of x equals x squared plus 55. now since we have an x squared value we don't have any sort of minus 5 x value or anything like that we know that any number that is squared is going to be positive and that's just being added to 55 so our minimum value will be 55. now if you come across a question like this and it's a little bit more complicated for example say that the question was something like x squared minus 12x plus 55 then in that case what you should do is you should go ahead and graph it use on the digital sat you pretty much have access to Desmos within sort of the testing environment and you should use that and then just find the minimum on the graph but in this case this is a trick you can use since you know that x squared will always be positive you're not subtracting anything as X changes so in this case this is a trick you can use to move faster here's something you need to know about exponential and linear functions for the SAT question 17 States each year the value of an investment increases by 0.49 percent of its value the previous year which of the following functions best models how the value of the investment changes over time now since it is dependent on the value of the investment the previous year since we are going up by 0.49 percent each here that is exponential growth so that is increasing exponential now I want to cover these other three options as well so you know them and you can answer them correctly on the SAT if they come up on a different question so let's go over it increasing exponential in this case since we're going up by 0.49 of our previous year's value the number that would be within our exponential growth equation for the growth rate would be 1.0049 now what if that number instead of being above one what if it was below one right let's say that our rate instead of being that our rate was 0.09 well 0.09 is a decreasing exponential function so in that case it would be a now what if instead of being dependent on the previous year's value it was independent of the previous year's value so in that case let's say that we just went up by 50 so we went up by 50 each day right it's a dollar sign we're going up by 50 hours each day well that would be increasing linear and what if we were going down by 50 each day that would be decreasing linear if we are not dependent on the previous year's value then it's likely going to be then it will be linear now if we are dependent on the previous year's value then it will be exponential and then you can use the rate of growth to determine if it's increasing or decreasing here's how to solve this sat math question about percentages question 18 states the population of Greenville increased by seven percent from 2015 to 2016. if the 2016 population is K times the 2015 population what is the value of K well if we're increasing by seven percent then the way we would represent this is the 2015 population which we're just going to label as P multiplied by K which is how many times we are bigger than the 2015 population will give us our new population now we have to solve for K and we know we're increasing by seven percent since we're increasing by seven percent we would represent that as 1.07 so our answer will be answer Choice C here's how to answer this tricky sat math question about exponents the question states which expression is equivalent to a to the power of 11 over 12 where a is positive it now the first thing I would immediately check for is if we have a to the 11 over 12 just Rewritten in the same format which would be the 12th root of a to the 11th power but we see that that's not the case so instead what we're going to do is we're going to go ahead and multiply by 12 over 12 to this exponent up here and the reason why we're doing that is because I see that all of these have 132 on the power on the you know what a is being raised to the power as and I know to get to 132 I ultimately have to multiply by 12. so we're going to go ahead and multiply by 12 over 12. now why is this okay well it's okay because we're multiplying by one so we're taking that 11 12 we're multiplying by 1 so it would stay the same we're just making it a larger number so when we do that 11 times 12 we know is going to equal 132 and we know in our denominator 12 times 12 will equal 144 so now we're going to find our answer Choice it will be answer Choice B which is 144th root of a to the power of 132. here's how to solve this sat math question that deals with an inequality the question States an event planner has planning a party a costly event planner a one-time fee of 35 dollars now keep in mind when you're dealing with a word problem like this you want to start writing out equations as you come across the number so in this case we have a one-time fee of 35 dollars that's not reoccurring so I can just go ahead and add that to rent the venue and uh to rent the venue and 10 25 per attendee so it's gonna be our cost will be plus 10.25 per attendee which I'm just going to call a for now unless I'm given a variable it needs to be the event planner has a budget of 200 what is the greatest number of attendees possible without exceeding the budget so since we cannot exceed the budget it has to be less than or equal to 200. now from here I want to go ahead and solve for the maximum amount of attendees I can have without going over so I need to solve for a so I'm going to subtract 35 from both sides that will cancel to zero subtract 35 here okay so now I'm going to end up with 10.25 a and then 200 minus 35 is going to end up giving us 165. from here I will divide both sides by 10.25 okay so I divide both sides by 10.25 now 165 divided by 10.25 is going to give me 16.09 now since I know I can't have you know a partial amount of a person and I can't go over my budget since that gives me 16.09 I know that a must equal 16 okay and I got that by using my calculator on the new digital sat you can use your calculator on the section so our answer will be a is equal to 16 so our answer would just be 16. here's how to solve this sat math question that deals with absolute value question 21 states of the absolute value of 4X minus 4 is equal to 112 what is the positive value of x minus 1. now keep in mind here that when you have an absolute value question like this you can have two answers for the value of x but in this case we are asked for the positive value of x minus 1. so there is only one right answer here but there are two answers for the value of x so let's go ahead and to talk about why that is and how you can approach this question so the first thing I would do is I would do 4X minus 4 is equal to 112 then I will add 4 to both sides add afford both sides this will cancel to zero 112 plus 4 will give us 116 so I can just go ahead and write this as 4X is equal to 116 and then from there I divide both sides by 4 and we're going to get that X is equal to see what that is in my calculator that'll be 29 okay so X is equal to 29. now we see that if we plug in 29 for X we're going to get 29 minus 1 that's positive that's 28. so 28 will be our answer okay so 28 is our answer now I want to show you what would happen if we came across the negative number first okay because the other way to get X because there are two values that X can be here is you would do negative and I'm just going to actually erase this so you can see how you do this right so you saw me get one of the values of X there is another value of x however because when you have absolute value like this you also have to do this to find the other solution okay so negative 4X minus 4 you distribute your negative sign okay and notice how I'm Distributing that negative sign to everything that was within that absolute value and that gets us negative 4 4X plus 4 is equal to 112 we will subtract 4 and we will get 108 okay so now we have negative 4X is equal to 108 I'm just going to go ahead and write that neater negative 4X is equal to 108 we divide both sides by negative 4 divide both sides by negative 4. okay and we see that X is going to equal 108 divided by negative 4 which if we go ahead and put that in our calculator 108 divided by negative 4 that's going to give us negative 27 okay and then in that case you would see negative 27 minus 1 is negative 28 that is not a positive solution which is why our answer there has to be 28 okay so it's important that you understand absolute value on the SAT Math section which is why I wanted to go over this even though we got to the answer sooner without having to get this other value for x here's how to solve this difficult sat math question that deals with volume question 22 states that a cube has an edge length of 68 inches a solid sphere with a radius of 34 inches is inside the cube such that the sphere touches the center of each face of the cube to the nearest cubic inch what is the volume of the space in the cube that is not taken up by the sphere and just a quick note anytime you have something that is underlined on the SAT pay close attention to it because they are underlining it for a reason because in a sense it's almost trying to trick you they're telling you hey this is important it sticks out from the rest because it is different and you need to pay attention to it so anytime you see that pay close attention to it now since we're asked to find the volume of the space in the cube not taken up by the sphere we have to calculate first the volume of the cube then we have to subtract the volume of the sphere so let's start with the volume of the cube we know that the cube has an edge length of 68 inches so what we're going to do is we're going to have 68 inches now the volume of a cube okay all the side lengths are the same so that's going to be 68 to the power of 3 is the volume of the cube now let's subtracting the volume of the sphere so the volume of a sphere is four thirds times pi times the radius cubed we know our radius is 34 inches so I'll go ahead and put 34 in parentheses cubed now all you have to do is put this into your calculator and you will ultimately get your answer of 149 700 196 so our answer there will be answer Choice a here's how to solve this question on the SAT about circles super easily question 23 States what is the diameter of the circle in the X Y plane with this equation now if you know the circle equation you know that this value of 16 is equal to the radius squared now if 16 is equal to the radius squared all you have to do is take the square root of the radius squared to isolate the radius the square root of 16 we know is four so we know that 4 is equal to the radius to get the diameter we know that the diameter which we'll just call d is equal to two times the radius so that's going to be 2 times 4 which will equal 8 and our answer there will be answer Choice B here's a trick to make this difficult Sac math question super simple question 24 States for the exponential function f the value of f of 1 is K where K is a constant which of the following equivalent forms the function f shows the value of K as the coefficient or the base well in this case all of our ant's choices are in the exponential growth formula or the exponential growth equation so our coefficients are going to be 50 80 128 and 204.8 now in order for the value of f of one to be that in a situation where we have exponential growth like this we need to have the exponent be zero because if the exponent is zero and we're multiplying it by 1.6 that's going to give us one which means that our value will just be that of the coefficient so f of x will equal the value of the coefficient when X is equal to 1 which is what we need so all we got to do is is due find the answer choice where we are raising it to the power of zero so one plus one would be two so we can go ahead and get rid of a if we just have one that's not zero if we have one minus one we get that equal to zero as the exponent so our answer there has to be answer Choice C and I will just quickly show you how this works just to prove it to you in case you are in disbelief 128 times 1.6 raised to the power of zero well 1.6 to the power of 0 is going to be one so that will equal 128 when we have F of 1. we know that we have 128 as our coefficient therefore our answer has to be C so there's just some quick proof in case you were doubting me here's a really difficult sat math question made super simple just by knowing the exponential growth formula so question 25 States a model estimates that at the end of each year from 2015 to 2020 the number of squirrels in population was one hundred and fifty percent more than the number of squirrels in the population at the end of the previous year the model estimates that at the end of 2016 now the reason that I'm underlining this is because I noticed that here we had 2015 to 2020 now we have 2016. so we are moving one year in to this growth there were 180 squirrels in the population which of the following equations represents this model where n is the estimated number of squirrels in the population T years after the end of 2015 and T must be less than or equal to five key thing here is they're kind of trying to throw you off with ants choices C and D because we are modeling it after the end of 2015 and that 180 number that they gave us is at the end of 2016. so that's one year in so our initial value is not 180 our initial value is 72. now as far as the rate of increase they're also trying to throw you off with answer Choice a because they know that you're going to see that 150 percent and think oh that's just 1.5 but it's not you have to keep in mind that it's 150 more than the number of squirrels in the population at the end of the previous year right so if we're multiplying by let's say we're increasing by 50 then it would be 1.5 but we're not increasing by 50 we're increasing by 150 which means we have to multiply that by 2.5 so our answer has to be B so if you know the exponential growth formula this question is really easy if you don't don't you're probably going to get it wrong here's one of the most difficult SAT Math Questions made super simple question 26 states that in the given pair of equations A and B are constants the graph of the pair of equations the X Y plane is a pair of perpendicular lines which of the following pairs of equations also represents a pair of perpendicular lines so the key thing here is that you understand what perpendicular lines mean it means that these slopes are negative reciprocals of each other so for example if we look at our equations that we are given we have 5x plus 7y equals one ax plus b y equals one now the slope of this first one I'm going to call M our slope so m is going to equal negative A over B now the form negative A over B works when you have the form of a coefficient in front of X plus a coefficient in front of Y is equal to some constant which we have in both of these equations we can use it okay so that means that our slope is going to equal let me go ahead and get that it's going to equal negative 5 over 7 right now our slope for this bottom equation is going to be m is going to equal well that's going to have to equal 7 over 5. and how do we know that well we need the opposite sign and the reciprocal okay so that's going to have to be 7 over 5. let me go and write that a little bit bigger so you can see it better 7 over 5. okay and I'll just draw the arrow that that's there all right well if that's going to be 7 over 5 we know that our a value then well that must be negative 7. okay and the reason we don't ask me negative seven is because we know that the formula for our slope is negative A over B in this form okay and we know our B value then has to be five okay so I'm just going to go ahead and write that down that our B value is going to equal 5. because we need to know that in order to solve this now the other thing that I think is important to notice here and that will ultimately help you solve this extremely quickly once you know this trick is that if you look at our equations up top here we have negative 7x plus 5y is equal to one now what I want you to notice here is that when you're dealing with perpendicular lines in this format of you know the the format where you have them set equal to a constant right notice how we have 5x and 5x and then notice how we have 7y and 7y obviously they are changed places right that that coefficient of seven has now changed from being attached to the Y to being attached to the X and then we have One Singular change in sign so that change in sign it can be out in front of this a value or it could also be in front of the B value but either way we have that one change in sign so now that we've noticed that we can pretty much solve these pretty quickly right so if if we look at answer Choice a if we were to plug in for a we know our value of a is negative seven so we can go ahead and do that so negative seven we know that we have the sign change right we're switching from that 70 in front of the Y being in front of X that part's good but then we have minus 2 times B we know that our B value is five right so we're going to end up getting minus 10y now the problem with that is that we change both sides we can only change one of the signs so a is going to be wrong and then we look at B we've got 10x plus 7y and then down here we know that our a value is negative seven so once again we're changing the sign that looks good and then we got plus 2 times B we know B is five so that's going to end up giving us plus 10 y right and now we see that both of the the you know the coefficient in front of X is now in front of Y coefficient that was in front of Y is now in front of X and we only changed one of the signs so that means that B has to be our correct answer okay so I know it took a little while for me to explain that but I wanted to make sure that you guys understand how this works and why this works because once you understand this trick you can then apply it and it becomes very very quick to find the right answer and also I will just note that this is one of the more difficult questions on the SAT so being able save time by understanding this trick is going to be very very beneficial especially for students who are looking to score high on the math section in particular above 700. here's what you need to know about calculating the number of real solutions on the SAT Math section along with a problem to help you apply it question 27 says in the equation above C is a constant the equation has no real solutions if C is greater than n what is the least possible value of n well let's start by discussing how you know the number of real solutions the way you know that for a quadratic equation like this is by using the value of B squared minus 4AC now one thing I want to have you make note of is that in the quadratic equation it is set equal to zero that's very important okay so B squared minus 4AC if that value is greater than zero then that means that you're going to have two real solutions which I'll represent as RS now if B squared minus 4AC is equal to zero then that means you're going to have one real solution now if you can kind of figure out where I'm going with this B squared minus 4AC if that is less than zero then you're going to have no real solutions okay so now that we know this and we know that in our question we are asked to find the equation having no real solutions if C is greater than n we know that we can go ahead and set up this equation so we know our a value is one we know our B value is going to be negative 34 and we know our C value is just going to be represented as C in this case so we have B squared we know B is negative 34 so we'll go ahead and take that and square it we're going to subtract 4 times a a is 1 and then we'll multiply it by C next thing we have to do is we have to set that as less than zero so negative 34 squared is going to become 11 I believe let me just quick check on the calculator 1156 1156 okay so 1156 minus 4C it's going to be less than zero I'm going to go ahead and add 4C to each side okay so I'll add 4C to each side and then next thing I'm going to do is I'm going to divide by 4 in order to isolate C so we can get it all alone so let's go ahead and do that we'll divide both sides by four we'll get that c must be greater than 11 56 over 4 which is going to be 289. all right so now that we have this we know that c has to be greater than n okay and we know that n if we go ahead and let me just draw this right this inequality is going to equal this other inequality of C being greater than n well in that case n is going to have to equal 289 okay so our answer for the least possible value of n is 289. if you enjoyed this video please like subscribe and consider sending a super thanks to help support my channel additionally please drop a comment below letting me know what videos you want me to make in the future and if you are looking for additional Educational Services that it offer please check out my website Hayden roadie.com