GED Math Power Rules and Problem-Solving Strategies

I know how frustrating and expensive and time consuming it can be to have to keep retaking GED math over and over and over again so my wish is to help everybody watching this pass so that they could move ahead to bigger and better things in life like college or a better job know that I heard from a student who suffered from epilepsy but eventually she persevered and she burst into tears of joy when she finally passed and I want that kind of success for you too which of the following is false is it a 44 raised to the first power equals 44 B 789 raised to the zero power equals 1 C 5 to the ninth divided by 5 to the fourth power equals five to the 13th power what about D eight raised to the power of five times eight raised to the power of three equals eight raised to the power of eight four e eight raised to the fifth power times eight raised to the fifth power equals parentheses eight times eight parentheses raised to the fifth power so try to figure this out which one of the following is false okay so let&#39;s go over how to do a question like this a 44 raised to the first power equals 44. so this is a power rule that you&#39;ll just want to memorize uh if you don&#39;t believe me you can just check this in your calculator any number raised to the power of one just gives you that number it doesn&#39;t matter if it&#39;s 987 whatever pick any random number raise it to the power of one that&#39;s just equal to that number in this case 987 so here 40 34 raised to the first power is equal to 44. so sorry I should cross this out because this one is this is correct which means that it can&#39;t be the right answer because we&#39;ve tried to find which one is false so that&#39;s why I crossed it out now B here 789 raised to the 0 power equals one this is another power rule that you should know okay 789 or any number for that matter raised to the zero power is going to give you one doesn&#39;t matter what it is you can pick 23 raised to the zero that&#39;s going to be one just put any number in your calculator pick something at random and raise it to the zero power and the answer is going to be one so this is a true statement meaning it can&#39;t be the correct answer here because we need to know which one is false so I&#39;m going to cross B out as well okay so let me skip C here hint hint uh let&#39;s look at D here okay so if we have two of the same bases what we can do is we can add the exponents so 8 raised to the fifth power times eight raised to the third power since the bases are the same really this is the same as doing eight raised to the 5 plus 3. which is equal to eight raised to the eighth power okay so what I want you to remember is that any number if the bases are the same and you&#39;re multiplying all right you just tap to add the exponents up so e is also a true statement if you have the same bases the same exponents all right in this case eight times five eight raised to the fifth power times eight to the fifth power that&#39;s just the same as parentheses eight times eight parenthesis raised to the fifth power we&#39;re we already said that D is correct so that leaves us with c c is false here all right and Y is C false well it looks like what we did here was five to the ninth divided by 5 to the fourth it looks like we added the exponents and really you need to subtract so if you&#39;ve got something like this a division problem where both the bases are the same this 5 to the ninth divided by 5 to the fourth that is really the same as 5 raised to the nine minus 4 power all right and 5 minus uh not five raised to the nine minus four what is nine minus four that&#39;s five so this is really the same as five raised to the fifth power Hello friends I&#39;m Michelle some of you recognize me from purely persistent and I&#39;m going to answer a couple of these questions here with Parker the price of Sadie&#39;s meal before tax and tip was 18.32 cents Sadie paid seven percent tax then added a fifteen percent tip to the total how much did Sadie pay per meal please round your answer to the nearest cent okay so first thing we&#39;re going to do is take our 18.32 cents and we&#39;re going to times that by seven percent which is really just .07 okay and we get here one dollar 28 cents that&#39;s how much she&#39;s paying in tax but we&#39;re going to add the total so we&#39;re going to take this 1832 and add that to the tax whoops 32 and we get 19.60 now Sadie&#39;s a nice person and she&#39;s providing the tip after text not before text so we&#39;re going to take our tax let&#39;s change colors here we&#39;re going to go 19.60 times the tax which is 15 so 0.15 and we get 2.94 and it does have a little bit after that but we&#39;re just rounding okay so we&#39;re going to take the 1960 and the 294 and add them together so bring this down here 1960 add them together and we get 22.54 and as you can see here the answer is C I used a calculator which made this a little bit easier you can do it by hand but really knowing how to do the calculator is critical for the GED or hiset test what is the approximate value of side C of the triangle a 18.2 b 8.6 c 3 or d74 or is it e 5476 now in case you&#39;re on a cell phone or a small device where this is hard to read this number is seven this number is five and this says C so let me turn it over to you I&#39;ll have you try this out if you&#39;d like to so you can pause the video and then we&#39;ll go over it okay so hopefully you had a chance to try this out here and for a question like this you&#39;re going to want to use the Pythagorean theorem formula which is a squared plus b squared equals c squared so this formula is going to guide us through the question here so as we can see in the formula this side of the triangle is our a so over here that corresponds to 7 so I&#39;m going to plug 7 into the formula for a so I have 7 squared plus what plus b squared now this side of the triangle down here is side B and on my triangle for the example here I see that side B is 5 so I&#39;m going to put 5 into the formula here in place of B 7 squared plus 5 squared equals c squared 7 squared is equal to 49 and 5 squared is equal to 25 so we have 49 plus 25 equals c squared so if you add these up 49 plus 25 and you can use the calculator if you want to that&#39;s going to be 74. so 74 equals c squared now whenever I teach a Pythagorean theorem question like this there are some common mistakes that students make here so I&#39;m just exploiting these again I&#39;m not trying to you know pick on anybody here I&#39;m not trying to make anyone feel bad I just want to make sure that you know how to do this right so that if you get a question like this on your test you&#39;ll maximize your score so you don&#39;t have to spend time and money retaking the test over and over again so that&#39;s why I am you know really trying to drill this point home if you thought D was the correct answer here you did one really good thing the thing that you did right was you got to this step right here so pat yourself on the back for making it this far and getting to 74 equals c squared but just know that we&#39;re not quite done here because we&#39;re asking we&#39;re asking the question to find side C this is telling me here that 74 equals c squared so this step here we found c squared but we need to find C all right so again if you made it this far and you thought D was the right answer good job you were on the right track but there&#39;s still a little bit more to the question here so another common mistake would be to get to this step here and then to think that the way to get c squared is that you have to do 74 squared so if you did 74 squared you probably thought that e was the right answer here okay and this is a really really common mistake so by by all means do not feel bad whatsoever if you made this mistake because over my many years of doing this on YouTube I&#39;ve been doing this since I think 2017 on YouTube I tutored for several years before that but I&#39;ve been on YouTube and since I&#39;ve been on YouTube I&#39;ve seen people make the same mistake over and over and over again and a lot of questions where I teach this problem it seems like somebody always does this and and tells me about it in the comments the way that you do this you don&#39;t want to do 74 squared okay you don&#39;t want to do that so that&#39;s actually Incorrect and again I&#39;m not picking on you if you made this mistake I&#39;m just pointing this out so you know the correct way to do this once you get to this step is you have to take the square root of both sides you have to take the square root that&#39;s going to undo this power of 2. so we would then find that the square root of 74 if you use your calculator comes out to a number very close it&#39;s 8.6 and then a bunch of other numbers after that it&#39;s like 8.60 and a bunch of other numbers here but we don&#39;t care about those other numbers because we just have to find the approximate value of side C and we&#39;ll see that 8.6 is approximately equal to side C so B is the correct answer here a sub shop serves custom made Subs where guests select cheese vegetables in meat to be added to their sub if there are four cheeses available and customers May pick any two cheeses for their sub how many different combinations of cheeses are possible a eight b six C 99 or D 24. so let&#39;s have you pause the video if you&#39;d like to try this one out and then when you&#39;re ready we&#39;ll go over how to do it okay so this question is a combinations question and the part of the question where it says how many different combinations of two cheeses are possible this word combination should be a clue to you uh that you want to use this formula here and it is n factorial divided by R factorial times n minus r factorial and you might be wondering what in the world does this mean so don&#39;t worry this is not as complicated as it might look so basically here it tells us that customers May pick two cheeses so the total number of choosing objects in the set is just going to be two so R is going to equal 2. n is the total number of objects and since here there&#39;s four cheeses available n is going to be 4. but it&#39;s not as simple as just plugging 4 into the formula for n and 2 into the formula for R this exclamation mark here or exclamation point whatever you want to call it it means that instead of just putting 4 into the formula for n and being done with it you actually have to do 4 times 3 times 2 times 1. now I&#39;m not going to write the times 1 here because anything times 1 is just going to be itself same with the bottom of the of the formula here too instead of just plugging 2 into the formula for R you would have to do 2 times 1. now since 2 times 1 is just 2 I&#39;m just going to leave that as 2 here now for the parentheses here we have to start off by doing n minus r so what is n minus r well 4 minus 2 is just two and let me simplify this even further so what is 4 times 3 4 times 3 is 12 what is 12 times 2 12 times 2 is 24 and 2 times times 2 down here on the bottom is 4 so we can simplify this to 24 divided by 4 and what is 24 divided by 4 24 divided by 4 is 6 so B is the correct answer here what is the slope of the line represented by the equation 6X plus 7y equals 9. so let&#39;s have you pause the video this would be a good time to try this out and if you get stuck don&#39;t worry we&#39;re just going to go over it and let&#39;s have you try it all right so hopefully you had a chance to try this out so for most slope questions this is going to be the formula to guide you through them and right here for this question we need to recognize this formula in order to get the question right the formula is y equals m x plus b this little M here this is the slope so in this formula if we want to find the slope of the line we basically need to figure out what is the value of M the first move that I&#39;m going to make here is I want to get the 7y itself on the left hand side of the equation so I&#39;m going to subtract 6X from both sides of my equation here now the reason I&#39;m subtracting is because it&#39;s positive 6X so I have to do minus 6X to get the 7y by itself on the left hand side of the equation now in math whatever you do to one side you also have to do to the other so I also have to subtract 6X on this side too so when I rewrite I&#39;m left with 7y equals minus 6 x plus nine okay so hopefully this makes sense so far now we don&#39;t want 7y we just want y so since it&#39;s 7 times y the opposite of times is division and so I&#39;m going to divide to get y by itself but whatever I do to one side I also have to do it to the other so I have to divide everything on the right hand side by 7 as well so I&#39;m going to do negative 6 divide negative 6 divided by 7 positive 9 divided by seven all right the sevens are going to cancel out on the left hand side and I&#39;m just left with y equals negative 6 over 7 X plus nine over seven now if we were asked to find the y-intercept the y-intercept would be this 9 over 7 here but we&#39;re not asked to find that we&#39;re asked to find the slope so remember the slope is this little M it&#39;s the number in front of the X so this negative 6 divided by 7 here this is our slope and that corresponds to answer Choice C so C is the correct answer to this question okay the next question says solve 4x squared plus 5x minus 9 answer choices are x equals negative 9 over 4 and x equals one b x equals negative 19 over 4 and x equals fifteen c x equals negative 12 and x equals 5 or d x equals negative 4 and x equals negative fifteen so let&#39;s have you try this out it does doesn&#39;t hurt to try if you don&#39;t know how to do it don&#39;t worry you&#39;re going to learn how to do it here so let&#39;s have you pause the video and try it out this is what we call a quadratic equation when you have a quadratic equation like this the first number in that equation is whatever is in front of this x squared is what we call a and whatever is in front of our X is what we call B and whatever&#39;s left out here is what we call our C and so what we&#39;re going to do is we&#39;re going to factor this quadratic equation and what you do is you think about it this way you you make a little X or a diamond like this whatever you want to call it and on the top part of the diamond you&#39;re going to write a times C and down here is gonna is gonna just go B so let&#39;s start by doing that so we know here that our a is four and we know that our c is negative 9 right because we remember we have to take that minus sign into consideration so here&#39;s our a here&#39;s our C so what is 4 times negative nine four times negative 9 is negative 36. so I&#39;m going to put this here in the top of my X now what do we plug in down here that&#39;s just our B so the B is whatever is in front of our X which is five so I&#39;m going to put a 5 down here now you might be wondering well so what what is this accomplished well let me tell you we have to find two numbers that will multiply together to give us negative 36 but they have to add up together to be 5. so a good way to start would be let&#39;s just list out numbers that you could multiply together to get negative 36. so one would be let&#39;s think of pairs of numbers that would multiply together to give us negative 36 and one pair would be 6 and negative 6. so if you do 6 times negative 30 times negative 6 you&#39;re going to get negative 36 but if you add these up what is 6 plus negative 6 well that&#39;s actually going to be zero so this pair is not going to work because we need something that&#39;s going to give us 5. so what about negative 9 and positive four negative 9 times 4 is going to give us negative 36. so it passes the first test now let&#39;s add these up negative 9 plus 4 is going to give us negative 5 not just 5. so this isn&#39;t going to work because this is going to be negative 5. so now let&#39;s try it the other way around let&#39;s try positive nine and negative 4. so positive nine times negative 4 is going to give us negative 36. now let&#39;s add these up 9 plus negative 4 is really the same as 9 minus 4 which is going to be positive 5. so this is the pair that we want to use so I&#39;m going to put one number here and I&#39;m going to put the other number right here that doesn&#39;t matter you could write 9 here and negative 4 here doesn&#39;t matter we&#39;re just kind of doing this just to keep track of the numbers so now what I&#39;m going to do and this is the part of problems like this that often confuses people all right so don&#39;t worry if you&#39;re confused we&#39;re going to work this out right now all you want to do is just pick one of these numbers let&#39;s start with negative four and I want you to write X minus 4. if it was a positive 4 you would do X plus 4 but since it&#39;s minus 4 you write x minus 4. now you go back to the original question and you look what number was in front of the x squared the number in front of the x squared is 4. so we have to take this negative 4 and we have to have to have to divide it by four all right so what is negative 4 divided by 4 that&#39;s going to be negative 1. so I could rewrite this as X minus 1. and I&#39;m setting this equal to 0 here and I want to find X so x minus 1 equals zero if I want to find X in other words if I want to get X by itself I have to cancel out this minus one and I do that by adding one and whatever I do to one side I have to also do it to the other so I would get x equals 1. as one of the solutions to the equation now so I I dealt with my negative 4. so now let me deal with the positive 9. so we&#39;re going to start by writing X Plus 9. okay but now I have to look back here at the number that&#39;s in front of the x squared it&#39;s 4 so I have to do 9 divided by 4. and I have to set this equal to 0 here all right so without simplifying this we don&#39;t have to do any math here because we can look at the answer choices and see that they&#39;ve left their answers as fractions so there&#39;s no need to plug this into your calculator or anything like that what you can do now is let me try to bring this up a little bit that&#39;s going to bring the whole problem up okay let me clear some room out so basically what I want to do is I need to get the X by itself so I need to subtract nine over four from both sides of my equation here okay so when I rewrite this I would get X equals negative nine over four all right and so the answer is going to be a because my Solutions are x equals negative 9 over 4 which is right here and x equals 1 which I found down here okay the next question says what is 70 of 350 is it a 230 B 75 C 245 or D 390 and let&#39;s have you pause the video give this one a try and then when you&#39;re ready we&#39;ll go over it okay so there are different ways to solve percent questions and I&#39;m going to show you one method here I think this method is pretty easy um at the end of the day you have to do what works with you what works best for you it says 70 here in the question so that tells me that I&#39;m going to go into this formula and I&#39;m going to replace the percent sign with the number 70. it says of 350. so I&#39;m going to take 350 and I&#39;m going to plug it into the formula here in place of of so what&#39;s going to go into the formula for is well that&#39;s actually what I&#39;m trying to find because it&#39;s asking me what is so I don&#39;t know what goes in is so I&#39;m just going to put an X in here and now we&#39;re going to basically plug the numbers in and we want to rearrange this so that we&#39;ve got X by itself on one side of the equation and that&#39;s going to tell us what number is is so since it&#39;s x divided by 350 and I want to get the X I want to multiply by 350. now why would I do that well watch this if I have 350 divided by 350 that&#39;s going to equal 1 1 times x is just X so I&#39;ve effectively got the X by itself on the left hand side but whatever I do to one side I also have to do it to the other side all right so I have 70 divided by 100 times 350 now okay so now what I want to do is you can just put this in your calculator if that&#39;s easiest for you and if I do that the answer is going to be C 245. what is the equation of a line that passes through the points 1 negative 10 and 2 8 is it a y equals 12x plus 28 b y equals 18x minus 28 c y equals 8X minus 2 or d y equals 9x plus 74. let&#39;s have you pause the video and give this one a try and as always if you get stuck don&#39;t worry about it we don&#39;t care for right now whether you get this right or wrong it&#39;s all about the knowledge so let&#39;s have you pause the video and try it out okay so there&#39;s two formulas that we want to use to figure out this question the first is the slope formula m equals Y2 minus y1 all over X2 minus X1 so when we put a 1 here to indicate that you want to start with this formula here and you want to calculate the slope and then once we know the slope we&#39;re going to use that and plug it into the point-slope equation which we&#39;ll use second all right so if you&#39;re completely lost don&#39;t worry let me show you the first step here so the first step is to calculate the slope so what I have to do is I&#39;ve got to look at my pairs here I have 1 and negative 10. now the first number in a pair is always an x coordinate so this one I&#39;m going to call this X1 and this negative 10 I&#39;m going to call that y1 because the second number is always y now let me look at this pair right here so this too what do you think I&#39;m going to call that well I&#39;m going to call that two X2 and this a I&#39;m going to call the eight Y2 so simply put all I&#39;m going to do is I&#39;m going to take my Y2 which is 8 and I&#39;m going to plug it into the formula here where it says Y2 and I&#39;m going to take my y1 which is negative 10 and I&#39;m going to plug that into the formula here for y1 what do you think I&#39;m going to do after that well I&#39;m going to take my two which I labeled as X2 plug it into the formula for X2 and lastly I&#39;m going to take my X1 which I labeled the one right here and I&#39;m going to plug that into the formula for X1 okay so let me show you how I would do this so m equals Y2 minus y1 so what do I put in for Y2 well remember I&#39;m going to put 8 in for Y2 so it&#39;s 8 minus my negative 10. so here&#39;s a little trick here minus a minus is the same as plus so instead of doing 8 minus negative 10 I can just write it as 8 plus 10. all right and I&#39;m going to divide that by X2 minus X1 so X2 is 2. and X1 is 1. so it&#39;s 2 minus 1. 8 plus 10 is what 8 plus 10 is 18. two minus 1 is just 1 18 divided by 1 is just 18. so what did I figure out well I just figured out that my slope is equal to 18. now what I&#39;m going to do is I&#39;m going to take this m this 18 and I&#39;m going to substitute it into the formula here in place of M so let me now use the second equation so it&#39;s y minus y1 so what do you think I&#39;m going to plug in for my y1 well since I labeled negative 10 as y1 I&#39;m going to plug that in so it would be y minus negative 10. now remember I said minus a minus is the same as plus so really I&#39;m just going to write that as y plus 10. so this is equal to my slope which I just calculated was 18. times x minus X1 and my X1 is 1. so I have x minus 1. so there&#39;s two ways to do this now you could start by handling the 10 over here or you could start by Distributing the 18. so I&#39;m going to start by Distributing the 18 just personal preference so I would do 18 times x which is going to be 18x then 18 times negative 1 which is going to be negative 18. so I have y plus 10 equals 18 X minus 18. now you could have also dealt with the plus 10 first I decided to deal with that last but what I&#39;m trying to do here I need to get y by itself on the left hand side of the equation so I have y plus 10 the opposite of plus is minus so I do 10 minus 10. whatever you do to one side you also have to do to the other so I&#39;m going to subtract 10 over here from the 18. all right we&#39;ve got to work with like terms here so I can&#39;t do 18x minus 10 because the 10 doesn&#39;t have an X but I can do minus 18 minus 10. okay and so now what I&#39;m going to get if I rewrite this I am going to get y equals 18 x minus 20 eight So my answer is going to be B determine the mean median mode and range for the following data set 8938 into so let&#39;s hope you pause the video trying to figure this one out and then when you&#39;re ready we&#39;ll go over it okay so let&#39;s go over how to do this and to start we&#39;re going to first figure out the mean so the mean simply means the average so to find the average I want to add up all the numbers in the number set and then I&#39;m going to count up how many numbers there are in the number set total and I&#39;m going to divide by that number and if it sounds like I&#39;m speaking uh a different language like from another planet or something don&#39;t worry because I&#39;m going to show you how to do this mean median mode and range questions are fair game for science for Math and for social studies so you&#39;re probably going to get something like this at some point on your test all I&#39;m doing here to calculate the mean is I want to take each number as you can see I&#39;ve got my eight I&#39;ve got my nine all right I&#39;ve got my three I&#39;ve got my eight and my two I&#39;m just adding up all the numbers and then I&#39;m gonna count up how many numbers there are there&#39;s one two three four five that&#39;s where I put the five downstairs here so you add up all the numbers in the data set and you divide by five and if we do this if we put it in our calculator we&#39;re gonna find out that the mean is equal to six okay so to start off we know that the mean is six so now let&#39;s go to the median so what a lot of people do sometimes I&#39;ve seen when I did a lot of in-person tutoring I saw a lot of students do this and a lot of people will look at three and they&#39;ll say okay well three is the middle number so it must be the median and they&#39;ll think D is the right answer and there&#39;s first of all let me say that if you made this mistake you know don&#39;t worry about it right now I&#39;m not picking on you by any means I just want to make sure that you know how to do this so that way on your test you can get as many points as possible and you can move on faster but just know that it&#39;s I like the thought process I like that you probably remembered that the median had something to do with the middle number and so you looked for three and you saw that hey three is right in the middle here so I like the thought process but we have to take that take it another step further and what you have to do first is you have to put the numbers in order from smallest to largest all right so 8 is actually the median here so let&#39;s talk about the mode next the mode is the most occurring number in the data set get it mode most the mode is the most occurring number in the data set so we see that 8 shows up twice all the other numbers only show up one time so 8 is going to be our mode the biggest number is nine the smallest number is two so if I subtract them 9 minus two is seven here so the range is seven so the answer that&#39;s going to be correct here the mean should be 6 the median should be eight the mode should be eight and the range should be seven so answer Choice a is the correct answer please answer the following question without using a calculator so what I&#39;m going to do is order of operations and so we have please excuse my dear Aunt Sally so the please the p is parentheses e exponents multiplication and division those guys are buddies addition and subtraction those guys are also Buddies first thing I&#39;m going to do is what is in the parentheses so here I have 20 minus 10 is just 10 squared and I like to rewrite everything 10 minus 8 is 2. next exponent so we have our 10 squared so really that&#39;s just 10 times 10. which is 100 and again rewrite all of it multiplication and division so I have 4 times 2 which is 8. addition and subtraction go from left to right and just go on through so I have 100 plus 18 is 118 minus 8 118 minus 8 is 110 and look here&#39;s our answer B 110. okay the next question says which table represents a function is it A B C or D let&#39;s hope you pause the video give this one a shot you never know and then we&#39;ll go over it okay let&#39;s talk about functions now so a function relates in input to an output and to teach this I&#39;m going to show you in imaginary soda machine here that functions very unlike a soda machine would in real life so with this imaginary soda machine let&#39;s say that every time you put one dollar into the machine you always get out of sprite all right and let&#39;s say every time you put two dollars into the machine you&#39;re always going to get out a Diet Coke now let&#39;s say every single time you put in three dollars you get a vitamin water and the point here with this imaginary soda machine is that one dollar will only ever get you a Sprite so every time you put one dollar into the machine you&#39;re always going to get a Sprite same with the two dollars two dollars will always get you a Diet Coke you&#39;re not going to put in two dollars and get a monster you&#39;re not gonna put in two dollars and get a water you&#39;re not gonna put two dollars and get a vitamin water two dollars will only ever give you a Diet Coke okay so this is parallel to or this is a metaphor for what happens with a function in math I Think metaphor is the word I want to use here I don&#39;t know but the point is that this example here with the soda machine is very similar to how a uh to what we&#39;re trying to do here with understanding which table represents a function so in other words with a function in math each input has exactly one output you&#39;re never going to put you know the same input into the machine and get two different outputs all right just like you&#39;re not not going to put in three dollars and get out a monster and a Coke and a Sprite you&#39;re only going to get one output every time so if we look at a here the x&#39;s and well the X is not just an A in every case the X&#39;s represent the inputs what you&#39;re putting into the function and the Y&#39;s represent the output okay so here this is telling us that if we put in negative 2 as an input we get 3 as an output but also if we put negative 2 in as an input we get 18 as an output so you could put negative 2 in and there&#39;s two different outputs well this is not going to be a function because remember that would be like putting three dollars into the machine and getting a Sprite or a monster or a vitamin water so what about two here we see that if we or what about B we see that if we put in 2 as an input we get three but it also shows us that if you put 2 in 8 is also an output so this is not going to work all right again that&#39;s like trying to put a dollar in and getting a spray to Coke a monster or this or that no it doesn&#39;t work that way the function machine function soda machine every time you put that dollar in you only ever get that Sprite so what about C here well it looks like for C we put in two we get three as an output we put in negative five we get three as an output we put in negative one we get 8 is an output we put a negative two we get 18 as an output so for each input there&#39;s exactly one output now I know what you might be thinking you might be thinking well how come we have two output three negative five output three well the outputs can be the same we don&#39;t care if the outputs are the same we just don&#39;t want we just want for every input there has to be one output all right it&#39;s okay to get the same output for different inputs so in other words it&#39;d be okay let&#39;s say maybe you put in three dollars you get a vitamin water you put in five dollars you can also get out of Vitamin Water there&#39;s two different inputs five and three are both different inputs but it&#39;s okay if they have the same output so it&#39;s okay if two and negative 5 have the same output but it wouldn&#39;t be okay if for example over here 12 and 12 have different outputs that wouldn&#39;t match all right that would not work so C is the correct answer okay the next question says multiply 3x minus y times four X plus seven Y and we&#39;ve got answer choices a b c and d so so let&#39;s have you pause the video give this one a try and then when you&#39;re ready unpause the video and we&#39;ll go over how to do it so to get a question like this right we&#39;re going to use What&#39;s called the foil method and it stands for first outer inner and last so let me break down how to do this in case you haven&#39;t studied this or in case it&#39;s been a while so I want to look at each set of parentheses and I want to look at the first number in the first set of parentheses and then in the second set of parentheses I want to look at the first number there too so I&#39;ve got three and I&#39;ve got four so I want to start by multiplying the first number inside each of the parentheses so what is 4X times 3x well that is going to give me 12x squared so don&#39;t forget that instead of just doing 3 times 4 we also have to do x times x x times x is going to be 12x squared so that takes care of the first so now we want to do the outer so for the outer I want to start with this 3x here and I&#39;m going to go over here and I&#39;m going to do 3x times 7y so what is 3 times 7 well 3 times 7 is 21. and what is x times y well x times Y is best left as just x times y so that takes care of my outer so now I want to look at the inner two numbers here in this case I&#39;ve got negative 1y or just negative Y and I&#39;ve got 4X so what is negative 1 times 4 negative 1 times 4 is just negative 4. what is x times y x times Y is just simply x y all right so since we&#39;ve got 21xy and we&#39;ve got minus 4xy I&#39;m going to Blind them up on top of each other here and this will become 17 because 21 minus 4 is 17. so I can really rewrite this as 12 x squared minus 17 X y so I&#39;ve done my inners now the L stands for last so the last two numbers that I haven&#39;t multiplied yet that&#39;s what I&#39;m going to do last which would be negative Y and 7y so negative 1 times 7 is negative seven and Y times Y is y squared so I&#39;ve got negative 7 y squared and this whole thing is going to match up with C so C is the correct answer to this question what is the slope of a line that is perpendicular to 7x plus 4y equals twelve is it A B C or D let&#39;s have you pause the video try this out and then when you&#39;re ready we&#39;ll go over it okay so again we want to start since this is a slope question we want to start with this formula y equals m x plus b and the first thing that we&#39;re going to do here is we&#39;re going to figure out what the slope of that line is so we&#39;re going to take this formula and we&#39;re going to rearrange it into the form y equals MX plus b and we&#39;re going to find the slope but we&#39;re not done yet there&#39;s another step we have to do since we want to know about perpendicular for this question so what I&#39;m going to do here is I want to start by getting the Y by itself so let me just right off the bat get rid of this 7x so since it&#39;s positive 7x If I subtract 7x I&#39;m going to cancel this out but whatever I do to one side I also have to do it to the other so I&#39;m going to have to subtract minus 7x from the other side as well and I still have that positive 12 there so I rewrite this as 4y equals negative 7x plus 12. now I want to deal with this 4. so if I want to get rid of the force it&#39;s 4 times y 4 divided by 4 is just 1 1 times Y is just y but now what I have to do is divide both numbers here by 4. since whatever I do to one side I also have to do it to the other so I could rewrite this as y equals negative 7 over 4 X plus 12 over 4. now 12 divided by 4 is the same as 3 but we don&#39;t have to do anything with this 12 divided by 4 so I&#39;m just going to leave it like this what we really care about is this number right here which is our slope the negative 7 over 4 is the slope but since we need to figure out what is the slope of the line that&#39;s perpendicular we have to flip this upside down and change the sign so whenever you find the slope and you need to know what is the slope of a line that&#39;s perpendicular to that equation you have to take the opposite reciprocal so that&#39;s a fancy word for flip it upside down so instead of 7 over 4 I make it 4 over 7 and since it was negative 7 over 4 I make this positive so you take the opposite reciprocal the opposite this is negative it becomes positive and you flip it upside down so it becomes four over seven so the correct answer here is a Nick is shipping one package that weighs 10 pounds in eight boxes that all weigh the same in total the shipment is 118 pounds what is the weight in pounds of each box is it A B C or D you know the drill by now let&#39;s have you pause the video give this a shot and then we&#39;ll go over how to do it all right thank you for sticking with me so far into the video so basically here what we need to do is we want to write an equation here so it tells us that he&#39;s got one package that weighs 10 pounds and 8 boxes but we don&#39;t know how much each box weighs right that&#39;s what we need to find but we know that there&#39;s eight of them so let&#39;s say eight times B where B represents the weight of just one box right so since all boxes weigh the same if we find what that weight is it multiplied by 8 it tells us the weight of eight boxes we add that to the weight of the package and that will add up to be 118 right because it tells us in total the shipment is 118 pounds so we have this equation here and all we have to do now is we have to solve this equation for B all right so what&#39;s and when I say solve the equation by B all I mean is we have to get B by itself on one side of the equation so first I would subtract 10 from both sides of the equation 10 minus 10 is 0 118 minus 10 is 108. so I can rewrite this now as a b equals 108. and again the name of the game here is to get B by itself so it&#39;s 8 times B what do I need to do here well I need to divide by 8 because if we&#39;ve got 8 times B the opposite of times is division 8 divided by eight is one one times B is B so the eights are really canceling out here but whatever I do to one side I have to do it to the other so I have to do 108 divided by 8. and if we throw that in our calculator we&#39;ll see that b equals 13.5 pounds and so we know that c is the correct answer here the next question says what is the value of f of x equals 9x cubed minus 2 when x equals negative three is it a negative 9 38 B negative 2 45 C 241 or D 928 so that&#39;s up for you that&#39;s up to you to decide I&#39;ll let you pause the video give this one a shot and then as always we&#39;ll go over how to do it okay hopefully you had a chance to try this so whenever you see a question like this I know this can seem kind of confusing but all you&#39;re really being asked to do here is to substitute negative 3 into the equation for x so if I were to rewrite this I would rewrite it as 9 times negative 3 raised to the third power minus 2. and negative 3 so what is negative 3 cubed well that&#39;s the same as negative 3 times negative three times another negative 3. so negative 3 times negative 3 would be positive nine but then when I multiply Pi multiply positive 9 by negative 3 what I get is negative 27 so I would rewrite this again now as 9 times negative 27 . minus 2. and if you plug this in your calculator here 9 times negative 27 minus 2 the answer is going to be B negative 245. simplify 15x plus 13 times x minus 1 in parentheses please put your answer in the box below now I know you obviously can&#39;t literally write your answer in this box below but just imagine you could and let&#39;s have you pause the video give this one a try and then as always we&#39;ll go over it okay so the trick here is you have to distribute this 13 so you would distribute it to the X and then you distribute it to the minus 1 and yes you do have to take this minus sign into consideration so rewriting this I would have 15 x plus 13 X because 13 times x is 13x then I have 13 minus 1 which would be minus 13. so now what I want to do is I want to add up the like terms so 15x and 13x since they both have X&#39;s I can add them up and that would be 28 X minus 13 and since the 13 doesn&#39;t have an X there I can&#39;t subtract 28x minus 13 so I just leave it here and this is all I can do I can&#39;t simplify any further than this so this would be the correct answer the next question says what is the area of the following triangle now this side says 7 this side says 50 and this is a question mark I didn&#39;t give you the side for the question here I&#39;m reading this to you in case you&#39;re on a phone or a small screen device so in case it&#39;s hard to see these numbers and I&#39;ve given you answers a b c and d now let me warn you this is a hard question so if you get stuck on this one don&#39;t worry about it okay don&#39;t beat yourself up because this is in my opinion the hardest one on this test so far so let&#39;s have you pause the video give it a try and then it like I said don&#39;t worry if you don&#39;t get this right you&#39;re you&#39;re going to learn from it we&#39;re going to go over it okay so to get this question right uh there&#39;s actually a few things that you have to be aware of here and the first is that this is a triangle question and we have this little 90 degree angle this little box down here which represents a 90 degree angle which means that this is a right triangle so we may be able to use the formula for the Pythagorean theorem which is a squared plus b squared equals c squared now this formula is not directly going to give us the area so why am i showing you this formula here well we we don&#39;t know what this side is equal to right this side is one big question mark and we know that side a is 7 and we know that side C the biggest side of the triangle is 50. um but we don&#39;t know what this side is however we can figure it out all right so the other formula that is going to be relevant to this question though is the formula for the area of a triangle so I&#39;m going to put an a to represent area I&#39;m going to put a little T here to represent triangle so this stands for the area of the triangle that&#39;s equal to the base times the height of the triangle all divided by 2. another way to write this would be half times the base times the height okay that is another way of writing the exact same thing so however you want to look at it base times height divided by two or half times base times height is two ways of saying the same exact thing so these are the two formulas that are going to be relevant here and this formula up here this a squared plus b squared equals c squared we&#39;re going to use this formula to figure out what the unknown side of the triangle is then once we know what both sides of the triangle both sides down here of the triangle are we can do base times height divided by 2 and get the answer all right so if if it seems like this is really complicated this is really confusing let me break it down and put some real numbers to this and hopefully it&#39;ll make more sense so we&#39;re going to start with this formula right here like I said now 7 we can conveniently plug into the formula for a and 50 we can plug into the formula for side C which would look like this 7 squared plus b squared and I&#39;m leaving this as B squared because we don&#39;t know what this side is down here so let&#39;s say that this side is B we don&#39;t know what B is so I&#39;m just going to leave it right here all right and that is equal to 50 squared okay so what is 7 squared 7 squared is 49 so I&#39;m just regretting this as 49 plus b squared and what is 50 squared 50 squared is 2500. all right so now what I&#39;m doing and what I&#39;m going to do is I&#39;m going to take this 49 and I want to get rid of it so I want to subtract by 49 from both sides or in other words I want to take 49 subtract from both sides all right now why am I doing this all right why am I doing this I&#39;m doing this because I want to find B squared by itself and if I figure out what B squared is I can take the square root of both sides and if I do that I&#39;m going to be able to figure out what the missing side of the triangle is why do I want to figure out what this missing side of the triangle is because then I can go up here and use the second formula and that&#39;s going to give me the answer so now we figured out what B squared is B squared equals 2451. so what I want to do is take the square root of both sides of our equation here so the square root of B squared just gives me B the square root of 2451 is 49 point five so we now know that the missing side of our triangle is equal to 49 .5 so why is this information helpful what&#39;s my next step well what I&#39;m going to do now is I&#39;m going to take the base and substitute it into the formula for B and I&#39;m going to take this 7 plug it into the formula for the height so let me rewrite this now so we know that the base is equal to 49.5 and the height is equal to seven and if I divide by 2 what does this tell me well it tells us the area of the triangle because formula two is the formula for the area of the triangle so that&#39;s going to give me a if I put this in my calculator so basically just a quick recap because this is kind of hard what I had to do here is I had to take a Formula 1 the Pythagorean theorem a squared plus b squared equals c squared I had to take the 7 in the 50 and I had to use them by putting them into this formula here and I had to solve for b once I found b b told me what this side of the triangle was equal to in other words B was the base of the triangle once I had both the height of the triangle and the base of the triangle I plugged them both into the formula for the area of the triangle I did the base times the height divided up by 2 and a is the correct answer for which value or values of X is the function f of x undefined if f of x equals 72 plus x divided by X plus 12 is it a x equals 0 b x equals negative 12 let&#39;s see x equals 19 or d x equals negative 20. so now would be a good time to have you pause the video give this one a shot and then we&#39;ll go over how to do it okay so these questions do come up on the test and this is an important topic to understand um but this can be a little confusing for some people so let me break it down like this when we see this notation F parenthesis X all that means we just read this as f of x and the f is the name of the function now it could be G it could be H typically it&#39;s just going to be F but just know that it could be G of X2 that does happen but this out here this letters just will be called the name of the function now what about the x or whatever&#39;s in the parentheses that is what we call the input so we already kind of talked about this concept a little bit if you remember when we did the function soda machine question where I went off on a big spiel about uh putting inputs into the machine and getting out an output well here the x is just the input all right we&#39;ve got f is the name of the function the x is our input and all of this stuff out here this is our output okay and the idea with this question is that we need to figure out which value of x is going to make the function undefined now there are two cases when a function is undefined okay the first is when you have to divide by zero so I&#39;m going to abbreviate this I&#39;m just going to put div for division divide by zero okay you can never divide by zero and if you don&#39;t believe me just take out your calculator and just pick any random number let&#39;s just do 10 put 10 divided by 0 in your calculator and your calculator is going to give you an error message because you can never divide something by zero now you can go the other way you could do 0 divided by 10 and the answer would just be zero okay but you can never do you can never have uh anything that you&#39;re actually dividing by zero that&#39;s going to give you an error all right the other case is when you have a negative under a square root all right so let me just put this like I&#39;m going to abbreviate this negative number under a square root all right so if you&#39;re you&#39;re taking notes this would be a good thing to add so the two cases that are going to make a function undefined if you have a zero in the denominator in other words if you&#39;re trying to divide by zero or if you have a negative number underneath the square root okay and so I should also mention that whenever you have a fraction like this the top part of the fraction is what we call the numerator and the bottom part is what we call the denominator so here what I&#39;m going to do is I&#39;m going to take the denominator and I&#39;m going to set it equal to 0. so I have X plus 12 and I&#39;m just going to set this equal to 0 and I want to solve this equation for x again when I say solve the equation for x that&#39;s just you know a fancy way of saying I want to get X by itself on one side of the equation so I have X plus 12. I want to do the opposite of addition here which is subtraction and that&#39;s going to get the X by itself on the left hand side but in math whatever you do to one side you always have to do it to the other so I have to subtract 0 I could do 0 minus 12. so subtract 12 to the other side too so I I end up with x equals negative 12. now what does this tell me Well if you go back to the original question 72 plus x divided by X plus 12. if you put in negative 12 for X here it&#39;s going to make the bottom number zero all right so watch this if I do 72 and then instead of X here I write negative 12 and then down here on the bottom I do instead of writing X here I write negative 12 plus 12 all right negative 12 plus 12 is going to be 0. all right and so we have 72 minus 12 divided by 0 and this is an error because we can&#39;t divide by zero if x is negative 12 the function is going to be undefined because if x is negative 12 e would have a situation here where you&#39;re trying to divide by zero and that is an illegal move in math you&#39;re not allowed to do this in math it won&#39;t work so basically B is the correct answer here so to Simply put if you get a question like this you just take the denominator here take the bottom take everything from the bottom and just set it equal to zero and solve for x and the majority of time that is going to give you the right answer which answer Choice represents the inequality graphed on the number line a x is less than negative 2 b x is less than or equal to negative 2 c x is greater than or equal to negative two or D X is greater than two let&#39;s have you pause the video try to figure this out and then when you&#39;re ready we&#39;ll go over how to do it and again no worries no pressure let&#39;s just see how it goes all right let&#39;s talk about this one so note here that the arrow starts at negative two and it goes to 5 and it just kind of keeps going and also note here that at negative 2 we have a closed Circle the closed Circle tells us that negative two is going to be included in the range of values here so if I were to draw a little stick figure person right here above negative two note here that if the person were to Walk This Way to the right what happens to the numbers well they go from negative one to zero to one to two and so on and so forth so we see here that the numbers get bigger as we go to the right as we Follow the arrow from negative two to five the numbers are getting bigger so let&#39;s look at a a is telling us that X is less than negative two well if that were the case then the arrow would be pointing this way to the left the arrow would be going through the smaller numbers the numbers that are decreasing which is now what we see and that&#39;s the same with b b tells us X is less than or equal to negative two that is also not the case so A and B are out here now D tells us X is greater than two and this is also not the right answer because the arrow doesn&#39;t start here at 2 or it says X is greater than positive two the arrow doesn&#39;t start here at 2 and keep going it starts back here at negative two all right so note here that the right answer is X is greater than or equal to negative two and this answer includes the negative 2 and the range of values here that&#39;s why it&#39;s not just X is greater than negative 2. it&#39;s X is greater than or equal to negative 2 because the closed Circle tells us that negative 2 is included in the range of values so this question let&#39;s have you try this without a calculator it says between which pair of decimals should 5 8 be placed on a number line is it a 0.4 and 0.5 is it B 0.5 and 0.6 is it C 0.6 and 0.7 or D 0.7 and 0.8 so again let&#39;s have you try this without a calculator you could pause the video give it a shot and then when you&#39;re ready we&#39;ll go over how to do it okay so to answer a question like this what the first step I would recommend is to look at the fraction and just figure out is this greater than or less than half okay that&#39;s always a good first step here now to do that you look at the bottom number in the fraction the bottom number is eight and so what is half of eight well half of eight would be four so I have the fraction 4 over 8 here and I want to compare four over eight to five over eight now really the key to getting this question right is to understand the skill that when two fractions have the same denominator you can figure out which one is the bigger fraction by which one has the bigger numerator so in other words here these fractions both have an 8 downstairs in the denominator so I look up top here and I see we&#39;ve got 5 8 and we&#39;ve got 4 8 well 5 is bigger than four so 5 8 is bigger than 4 8 and since 4 8 is equal to half we know that 5 8 is greater than half so 5 8 is greater than half and why does this matter well it matters because half as a fraction is equal to 0.5 as a decimal all right so again all I did here is I looked at 5 over 8 and I I thought about the fact that if it was 4 over 8 it would be equal to half but it&#39;s 5 over 8 so I know that this fraction is going to be greater than 0.5 all right 5 over 8 is greater than half half is equal to 0.5 so this lets me take answer Choice a out of the question here so if you don&#39;t if you&#39;re having a little trouble following what I just did it might be a good idea to just rewind the video watch it maybe slowly just just think about it here because this is an important skill and if you got that then great job the next thing I would do is we want to figure out we know that 5 over 8 is bigger than 0.5 but we next want to see is it greater than or or less than 0.6 if 5 over 8 as a 5 over 8 converted to a decimal is bigger than 0.6 then we would know that b is the wrong answer here so how do we do that well let&#39;s compare five over eight let&#39;s compare that to 0.6 and then if we need to we&#39;ll compare it to 0.7 so how do I write 0.6 that&#39;s a decimal how do I write that as a fraction 0.6 is equal to 6 over 10. all right so now what I want to do is I want to get a common denominator so we&#39;ve got 5 over 8 and 6 over 10. so what I&#39;m going to do is I&#39;m going to say hey 6 over 10 has the 10 in the denominator so I&#39;m going to multiply both the top number and the bottom number of 5 over 8 by 10. and if I do that I get 50. over 80 now down here I have 6 over 10. I look up at the the five over eight fraction I see that there&#39;s an 8 in the denominator so I multiply the top and the bottom number of this fraction by 8. and again all we&#39;re trying to do is we we need to compare five over eight and six over ten and I need to get a common denominator and then we&#39;re going to see which fraction is bigger so 6 times 8 is 48 and 10 times 8 is 80. so now we can compare the two fractions 50 over 80 is bigger than 48 over 80 because 50 is bigger than 48. so which fraction is bigger is 5 is it 5 over 10 or 6 over 10 or I&#39;m sorry is it 5 over 8 or 6 over 10 which one is bigger well we know that once we got a common denominator we saw that 50 over 80 was bigger than 48 over 80. so this tells us that 5 over 8 is greater than 6 over 10. so let&#39;s rule B out here because we know that when we take 5 over 8 and compare it to 6 over 10 5 over 8 ends up being the bigger number so we know that 5 8 cannot be between 0.5 and 0.6 so now let&#39;s look at 0.7 so 0.7 how can I write that as a fraction well I can write that as a fraction because point seven is equal to 7 over 10. so now what I want to do is I want to compare 5 over 8 to 7 over 10. so I want to get a common denominator all right so how am I going to get a common denominator here all right what what I want to do is I want to multiply the top and the bottom number of 7 over 10. both by eight now seven times eight is what 56. 8 times 10 is 80. all right so what is a bigger number 56 or 50. well hopefully you see that 56 is a bigger number so basically you know we can see here that 48 over 80 is smaller than 50 over 80. but 56 over 80 is bigger than 50 over 80. so again if we go back to our original fractions here we see that 5 8 is bigger than 6 over 10 but it&#39;s smaller than 7 over 10. so therefore we know that c is the right answer because we know that 5 8 is smaller than 0.7 but it&#39;s bigger than 0.6 all right so this question is a little tricky maybe watch this one again if you had trouble with it because this is an important skill to understand the next question which of the following is true A B C or D let&#39;s have you pause the video think about this one and then when you&#39;re ready we&#39;ll go over how to do this question okay so this question is just testing you on how well you understand basic math signs and symbols and their translations so let me put this big table up on screen here and if you had trouble with this question it would be it wouldn&#39;t hurt to pause the video and put these down in your notes basically this if I read a out loud if I translate the symbols to math words this would say 88 is greater than 109 which is false that is not true um C would read as 109 is less than 88 and 109 is bigger than 88 so C is wrong now B would read as 88 does not equal 109 which is true so B is the right answer here and like I said if you had trouble with this don&#39;t worry about it for right now we&#39;re just practicing definitely study this table that I have on the screen and then when you&#39;re ready we&#39;ll go on to the next question if the area of a circle is 200 what is the diameter please rate your answer in the box below now you obviously can&#39;t write your answer in the box below through the screen but imagine if you could and I want you to pause the video try to figure this one out this is a tough one uh whenever you&#39;re ready we&#39;ll go over it and like always don&#39;t worry uh if this question&#39;s hard uh we&#39;re just going to learn how to do it okay so let&#39;s learn how to do this question now um so the formula is of a circle it&#39;s area of a circle equals pi r squared so we need to use this formula to get the right answer now R is the radius of a circle so the radius of a circle and this is a pretty bad drawing of a circle it actually looks more like an orange but hopefully my bad drawing skills help help make this more memorable for you but if I were to measure half of the circle that&#39;s what we call the radius and if I were to measure the entire circle and this actually is an even worse Circle but just pretend this is a circle you have to be really open-minded to watch my videos because some of my examples are just very out there but imagine this was a circle if I measured across the entire circle that would be the diameter so we can say that the radius is half of the diameter and the diameter is double the radius all right so the point here is what we&#39;re going to do is we&#39;re going to use the formula for the area we&#39;re going to figure out what the radius is and we&#39;re going to double it that simply tells us what the diameter is so fortunately we already know the area of the circle it&#39;s 200 so I can say let me write it over here 200 equals pi are r squared so we can divide by pi on both sides and why would I want to divide by pi on both sides well the reason is because I want to get the radius by itself so I want to kind of clear the Pi&#39;s out of the row here now another thing that you should know is that Pi is uh you can think of it as being equal to 3.14 it&#39;s actually not it&#39;s equal to 3.14 and then a ton of other numbers but you could just think of it roughly as being equal to 3.14 although technically it&#39;s not uh but that&#39;s beside the point here coming back to question here you know we can cancel the pies out here over here we have 200 Pi all right now you could take this pie out and replace it with 3.14 all right uh if you want to but I&#39;m just going to leave it as the pi symbol for right now and when I rewrite this so that we can see it more clearly here I rewrite it we&#39;ve got 200 divided by pi equals r squared so even if you&#39;re completely lost or have been up until this point in the video I want you to ask yourself right now 200 divided by pi equals r squared how would I solve this for R and we&#39;ve talked about this in the example with triangles I think it was earlier in the video and now we have a it&#39;s a different scenario but it&#39;s a very similar idea so the answer is that if we want to get just R we have to take the square root of both sides all right the square root of r squared is just equal to R so we now have the square root of 200 over pi is equal to the radius and we don&#39;t want to find so we need to find the radius but the final answer we need to know what the diameter is for the final answer here so fortunately we already know that the radius is equal to half of the diameter and that the diameter is equal to twice the radius so if I double this number here the square root of 200 over Pi if I double that it&#39;s going to give me the diameter so I would say that the diameter is a 2 times the square root of 200 divided by pi so if I put this in my calculator and I do uh the square root of 200 divided by pi multiplied by 2. the answer you should have would be 15.96 maybe you rounded it a little bit different I don&#39;t really care for now I just want you to have either gotten this 2 times the square root of 200 divided by pi or 15.96 or an answer very close to this if you round it a little bit differently and you might be wondering on the test how will the answer choices be are the answer choice is going to have the pi symbol and the answer or are they going to be a numerical value like this the answer is that it depends on how they do the test it might be a number they might also leave Pi on the answer choices it could be either way so be ready for for both and and really either way you just have to remember Pi is 3.14 again that&#39;s not technically mathematically correct there&#39;s a bunch of other numbers on it too but all you really need to remember is it is 3.14 for the purposes of the GED test and I know this is a hard question so you know give yourself on the a pad on the back just for trying this if you got it right fantastic work if not fantastic job for trying Mr Burns wants to take his wife and children to the movies both children are under 13 years old each child will bring one friend along of the same age the ticket prices are shown in the table below children under 13 years old five dollars each for a day show seven dollars each for a night show then we have over here adults and teens 13 years old and up twelve dollars each for a day show and 15 each for a night show now if Mr Burns is buying the tickets how much money will they save on the cost of the tickets if they attend a day show instead of a night show please disregard sales tax in your answer a 44 dollars B 58 C 14 or d 16 let that be pause the video try to figure this out and then when you&#39;re ready we&#39;ll go over it okay so basically here let&#39;s take stock of how many people we have here so a represents adults so we have two adults here we&#39;ve got Mr Burns and his wife and as far as the children go we know that he has two children and because it tells us that both are under 13 and each child is going to bring one friend of the same age so as far as children that are under 13 we know that we&#39;re going to have four here so what we have to do here is we have to calculate the cost in total that he&#39;s going to pay for a night show and the cost for a day show and we&#39;re going to subtract them all right so let&#39;s start with night here so to calculate the cost at night we would have to say well there are two adults going and at night the cost for an adult is 15 bucks so I would want to do 2 times 15. now I&#39;m going to add that to the cost of the children so how much does he have to pay for the children well think about it there are four kids that he&#39;s going to be taking to the movies and the cost for one kid would be seven dollars all right so we would do seven times four here and if you just plug this all into your calculator you&#39;ll see that the cost for a night show is gonna be 58 dollars so that&#39;s how you would do night now the process for day is basically the same thing here except it&#39;s going to be different numbers so again we have to add up the cost of the adults and the cost of the children but this time we&#39;re looking at the prices from the day so there&#39;s again there&#39;s two adults there&#39;s him and his wife and the cost for one adult for a day show would be twelve dollars and we&#39;re gonna now add the cost that he&#39;s going to pay for the children so again we have four children still and the cost for one child child would be five dollars all right so again we can plug this in the calculator do two times twelve plus four times five and we&#39;ll get forty four dollars so now what we have to do is we have to take the cost of a Night Show in total which is 58 and the cost in total of the day show which is 44 and we have to subtract them and if we subtract them we get C as our answer Kate&#39;s parents let her start her own lemonade stand to sell lemonade to the neighbors during which period did our earnings increase the most a April through may be June through July C May through June or D March through April and we have a graph over here it says Kate&#39;s Lemonade Stand profits from January through July now on our vertical axis we see the monthly earnings on the horizontal axis we see the months and so I&#39;ll turn it over to you to pause the video give this one a shot and then we&#39;ll go over how to do it okay so one of the key words in this question is the word increase and we want to look on the graph meaning the blue line here and we want to look at each period here and find the one that had the biggest increase so let me first identify the period April through May so I find April down here and I find May right here so to determine what&#39;s happening what happened between April and May the only thing that I need to look at is what&#39;s happening on the line in between the months through April and May now if you were to imagine a little stick figure person starting at the leftmost part of the line and imagine this blue line here is a hill if the person were to follow the line which direction would they be going well hopefully you can see that if they just ran on this line they&#39;d be going downhill that means that there is a decrease between April and May and so we can take April and May answer Choice a out right away because we&#39;re trying to find the period that had the biggest increase so what about June through July so to do that let me start by finding June and obviously you&#39;re not going to be able to write lines like this on your test but I&#39;m just kind of showing you how to check the period through June and July all you have to do is check what&#39;s happening on the graph in between June and July so detection in July I don&#39;t care about what&#39;s happening with the graph over here I just need to look between this two period this this period right here now again if we imagine that we had a little stick figure person and the person was going to start at the leftmost part of the graph and follow the line they would be running downhill which means a decrease so from June to July we know that there was a decrease so we can take B out as well here so let&#39;s check answer Choice C May through June so again find you want to First identify the part of the graph that is going to be relevant to answering the question so here&#39;s May and June looks kind of like right here okay so now here&#39;s the point that we want to get at here so from May through June if we start over here at the leftmost part of the line which would be May and now what if our stick figure person were to just follow this line right here which direction would they be going well now we can see the person would have an uphill battle right here they&#39;d have an uphill climb so we do see that there would be an increase from May to June but let&#39;s look at March and April 2. so if we look here&#39;s March here&#39;s April so if we just focus on what&#39;s happening with this part of the blue line right here between March and April and we give it the stick figure test if the stick figure starts right here at March and just follows the line towards April they would also be going uphill so we know that there was an increase in March and April but the question is which had the the biggest increase well one other way to think about this is which Hill would be harder to climb this little Hill right here or this big hill right here well just by the eyeball test it looks like the hill for me to June would be harder to climb all right and we can verify this with numbers too so let me get the stick figures out of the road here and I&#39;ll show you what I mean so let&#39;s look at May here so may is about here all right so what&#39;s the numerical value for May so if I start at May and I kind of draw a line all the way over here I see that I would land somewhere in between ten and five but closer to 10. so let&#39;s say that it was maybe eight dollars in May all right and again I can&#39;t tell the exact number but I&#39;m just guessing it&#39;s about eight so let&#39;s look at June so right here was June that looks like it&#39;s exactly at 25. so here&#39;s 25 right here let me just Mark that down all right and so if we look at March and April March right here if I look over here on the left I see that that is maybe two dollars maybe something like that so let&#39;s say in March she made two dollars and from April which is right here if I trace April over here I see that it&#39;s almost it&#39;s not quite 10. so let me just call that nine now I can subtract the values here so I can do what is 25 minus eight so 25 minus 8 is 17 so I see that there was a 17 dollar increase from the start of the month that may till June she had a 17 increase and if I look at where she was at in March and look at where she was at in April and I do 9 minus two nine minus two is seven so it looks like she had a seven dollar increase from March to April so clearly the biggest increase was C so what I want to want you to take away from this is that you know you can do a question like this in two ways you can actually put numbers to it or you can just kind of use the eyeball test and the eyeball test of just thinking you know hey this is going downhill so I don&#39;t have to look at that this is going uphill this is going uphill this hill is bigger so the biggest increase was May through June two different ways to do it up to you to decide which way makes the most sense to you Ryan invested twelve hundred dollars for two months at a 10 interest rate how much interest did he earn on his money Parker must know me well because I love questions dealing with money and interest as my students know this is the way to make you really really rich so compound interest a beautiful thing but we&#39;re actually doing simple interest here so what we&#39;re going to do is we&#39;re going to take 1200 and we&#39;re going to divide that by 10 percent okay so let&#39;s just think if I take 12 and I just move the decimal point over that&#39;s dividing it so that gives us a hundred twenty dollars which is actually not per month it&#39;s per year it&#39;s called annual percentage rate maybe you&#39;ve heard that that means that the 120 is actually broken down into 12 months so we&#39;re going to divide the 120 by 12 and we get a nice easy 10. so he&#39;s making ten dollars per month how many months is he doing it two right so we&#39;re going to say ten dollars times two equals twenty dollars so he is making twenty dollars in simple interest G wrestled in eight matches he scored two one eight zero twelve four one and twelve points during each match respectively what was Jay&#39;s average number of points scored in these eight matches rounded to the nearest whole number a 9 e 5 C 2 or is it D12 let&#39;s have you pause the video give this one a shot and then when you&#39;re ready we&#39;ll go over how to do it okay so we&#39;re trying to find the average here and we&#39;ve talked about mean earlier in the video and we said that mean means the average and so mean and average are two words for the same thing but that&#39;s all we&#39;re doing here is we&#39;re finding the average and the way that we do that is we want to add all the numbers up and then what we&#39;re going to do is we&#39;re going to divide by the total number of numbers in the set okay so all I&#39;m doing here is again I took all of these numbers here gonna add them all up which I&#39;m doing up here and I&#39;ll throw a parentheses around all of this and so I&#39;d add all these numbers up and then down here I&#39;m going to divide by the total number of numbers and so we know that he wrestled in eight matches and we have eight numbers here right one two three four five six seven eight so all you do is you put this add these all up in your calculator you can divide by eight and the answer you should get is five so hopefully that makes sense

I know how frustrating and expensive and time consuming it can be to have to keep retaking GED math over and over and over again so my wish is to help everybody watching this pass so that they could move ahead to bigger and better things in life like college or a better job know that I heard from a student who suffered from epilepsy but eventually she persevered and she burst into tears of joy when she finally passed and I want that kind of success for you too which of the following is false is it a 44 raised to the first power equals 44 B 789 raised to the zero power equals 1 C 5 to the ninth divided by 5 to the fourth power equals five to the 13th power what about D eight raised to the power of five times eight raised to the power of three equals eight raised to the power of eight four e eight raised to the fifth power times eight raised to the fifth power equals parentheses eight times eight parentheses raised to the fifth power so try to figure this out which one of the following is false okay so let&amp;#39;s go over how to do a question like this a 44 raised to the first power equals 44. so this is a power rule that you&amp;#39;ll just want to memorize uh if you don&amp;#39;t believe me you can just check this in your calculator any number raised to the power of one just gives you that number it doesn&amp;#39;t matter if it&amp;#39;s 987 whatever pick any random number raise it to the power of one that&amp;#39;s just equal to that number in this case 987 so here 40 34 raised to the first power is equal to 44. so sorry I should cross this out because this one is this is correct which means that it can&amp;#39;t be the right answer because we&amp;#39;ve tried to find which one is false so that&amp;#39;s why I crossed it out now B here 789 raised to the 0 power equals one this is another power rule that you should know okay 789 or any number for that matter raised to the zero power is going to give you one doesn&amp;#39;t matter what it is you can pick 23 raised to the zero that&amp;#39;s going to be one just put any number in your calculator pick something at random and raise it to the zero power and the answer is going to be one so this is a true statement meaning it can&amp;#39;t be the correct answer here because we need to know which one is false so I&amp;#39;m going to cross B out as well okay so let me skip C here hint hint uh let&amp;#39;s look at D here okay so if we have two of the same bases what we can do is we can add the exponents so 8 raised to the fifth power times eight raised to the third power since the bases are the same really this is the same as doing eight raised to the 5 plus 3. which is equal to eight raised to the eighth power okay so what I want you to remember is that any number if the bases are the same and you&amp;#39;re multiplying all right you just tap to add the exponents up so e is also a true statement if you have the same bases the same exponents all right in this case eight times five eight raised to the fifth power times eight to the fifth power that&amp;#39;s just the same as parentheses eight times eight parenthesis raised to the fifth power we&amp;#39;re we already said that D is correct so that leaves us with c c is false here all right and Y is C false well it looks like what we did here was five to the ninth divided by 5 to the fourth it looks like we added the exponents and really you need to subtract so if you&amp;#39;ve got something like this a division problem where both the bases are the same this 5 to the ninth divided by 5 to the fourth that is really the same as 5 raised to the nine minus 4 power all right and 5 minus uh not five raised to the nine minus four what is nine minus four that&amp;#39;s five so this is really the same as five raised to the fifth power Hello friends I&amp;#39;m Michelle some of you recognize me from purely persistent and I&amp;#39;m going to answer a couple of these questions here with Parker the price of Sadie&amp;#39;s meal before tax and tip was 18.32 cents Sadie paid seven percent tax then added a fifteen percent tip to the total how much did Sadie pay per meal please round your answer to the nearest cent okay so first thing we&amp;#39;re going to do is take our 18.32 cents and we&amp;#39;re going to times that by seven percent which is really just .07 okay and we get here one dollar 28 cents that&amp;#39;s how much she&amp;#39;s paying in tax but we&amp;#39;re going to add the total so we&amp;#39;re going to take this 1832 and add that to the tax whoops 32 and we get 19.60 now Sadie&amp;#39;s a nice person and she&amp;#39;s providing the tip after text not before text so we&amp;#39;re going to take our tax let&amp;#39;s change colors here we&amp;#39;re going to go 19.60 times the tax which is 15 so 0.15 and we get 2.94 and it does have a little bit after that but we&amp;#39;re just rounding okay so we&amp;#39;re going to take the 1960 and the 294 and add them together so bring this down here 1960 add them together and we get 22.54 and as you can see here the answer is C I used a calculator which made this a little bit easier you can do it by hand but really knowing how to do the calculator is critical for the GED or hiset test what is the approximate value of side C of the triangle a 18.2 b 8.6 c 3 or d74 or is it e 5476 now in case you&amp;#39;re on a cell phone or a small device where this is hard to read this number is seven this number is five and this says C so let me turn it over to you I&amp;#39;ll have you try this out if you&amp;#39;d like to so you can pause the video and then we&amp;#39;ll go over it okay so hopefully you had a chance to try this out here and for a question like this you&amp;#39;re going to want to use the Pythagorean theorem formula which is a squared plus b squared equals c squared so this formula is going to guide us through the question here so as we can see in the formula this side of the triangle is our a so over here that corresponds to 7 so I&amp;#39;m going to plug 7 into the formula for a so I have 7 squared plus what plus b squared now this side of the triangle down here is side B and on my triangle for the example here I see that side B is 5 so I&amp;#39;m going to put 5 into the formula here in place of B 7 squared plus 5 squared equals c squared 7 squared is equal to 49 and 5 squared is equal to 25 so we have 49 plus 25 equals c squared so if you add these up 49 plus 25 and you can use the calculator if you want to that&amp;#39;s going to be 74. so 74 equals c squared now whenever I teach a Pythagorean theorem question like this there are some common mistakes that students make here so I&amp;#39;m just exploiting these again I&amp;#39;m not trying to you know pick on anybody here I&amp;#39;m not trying to make anyone feel bad I just want to make sure that you know how to do this right so that if you get a question like this on your test you&amp;#39;ll maximize your score so you don&amp;#39;t have to spend time and money retaking the test over and over again so that&amp;#39;s why I am you know really trying to drill this point home if you thought D was the correct answer here you did one really good thing the thing that you did right was you got to this step right here so pat yourself on the back for making it this far and getting to 74 equals c squared but just know that we&amp;#39;re not quite done here because we&amp;#39;re asking we&amp;#39;re asking the question to find side C this is telling me here that 74 equals c squared so this step here we found c squared but we need to find C all right so again if you made it this far and you thought D was the right answer good job you were on the right track but there&amp;#39;s still a little bit more to the question here so another common mistake would be to get to this step here and then to think that the way to get c squared is that you have to do 74 squared so if you did 74 squared you probably thought that e was the right answer here okay and this is a really really common mistake so by by all means do not feel bad whatsoever if you made this mistake because over my many years of doing this on YouTube I&amp;#39;ve been doing this since I think 2017 on YouTube I tutored for several years before that but I&amp;#39;ve been on YouTube and since I&amp;#39;ve been on YouTube I&amp;#39;ve seen people make the same mistake over and over and over again and a lot of questions where I teach this problem it seems like somebody always does this and and tells me about it in the comments the way that you do this you don&amp;#39;t want to do 74 squared okay you don&amp;#39;t want to do that so that&amp;#39;s actually Incorrect and again I&amp;#39;m not picking on you if you made this mistake I&amp;#39;m just pointing this out so you know the correct way to do this once you get to this step is you have to take the square root of both sides you have to take the square root that&amp;#39;s going to undo this power of 2. so we would then find that the square root of 74 if you use your calculator comes out to a number very close it&amp;#39;s 8.6 and then a bunch of other numbers after that it&amp;#39;s like 8.60 and a bunch of other numbers here but we don&amp;#39;t care about those other numbers because we just have to find the approximate value of side C and we&amp;#39;ll see that 8.6 is approximately equal to side C so B is the correct answer here a sub shop serves custom made Subs where guests select cheese vegetables in meat to be added to their sub if there are four cheeses available and customers May pick any two cheeses for their sub how many different combinations of cheeses are possible a eight b six C 99 or D 24. so let&amp;#39;s have you pause the video if you&amp;#39;d like to try this one out and then when you&amp;#39;re ready we&amp;#39;ll go over how to do it okay so this question is a combinations question and the part of the question where it says how many different combinations of two cheeses are possible this word combination should be a clue to you uh that you want to use this formula here and it is n factorial divided by R factorial times n minus r factorial and you might be wondering what in the world does this mean so don&amp;#39;t worry this is not as complicated as it might look so basically here it tells us that customers May pick two cheeses so the total number of choosing objects in the set is just going to be two so R is going to equal 2. n is the total number of objects and since here there&amp;#39;s four cheeses available n is going to be 4. but it&amp;#39;s not as simple as just plugging 4 into the formula for n and 2 into the formula for R this exclamation mark here or exclamation point whatever you want to call it it means that instead of just putting 4 into the formula for n and being done with it you actually have to do 4 times 3 times 2 times 1. now I&amp;#39;m not going to write the times 1 here because anything times 1 is just going to be itself same with the bottom of the of the formula here too instead of just plugging 2 into the formula for R you would have to do 2 times 1. now since 2 times 1 is just 2 I&amp;#39;m just going to leave that as 2 here now for the parentheses here we have to start off by doing n minus r so what is n minus r well 4 minus 2 is just two and let me simplify this even further so what is 4 times 3 4 times 3 is 12 what is 12 times 2 12 times 2 is 24 and 2 times times 2 down here on the bottom is 4 so we can simplify this to 24 divided by 4 and what is 24 divided by 4 24 divided by 4 is 6 so B is the correct answer here what is the slope of the line represented by the equation 6X plus 7y equals 9. so let&amp;#39;s have you pause the video this would be a good time to try this out and if you get stuck don&amp;#39;t worry we&amp;#39;re just going to go over it and let&amp;#39;s have you try it all right so hopefully you had a chance to try this out so for most slope questions this is going to be the formula to guide you through them and right here for this question we need to recognize this formula in order to get the question right the formula is y equals m x plus b this little M here this is the slope so in this formula if we want to find the slope of the line we basically need to figure out what is the value of M the first move that I&amp;#39;m going to make here is I want to get the 7y itself on the left hand side of the equation so I&amp;#39;m going to subtract 6X from both sides of my equation here now the reason I&amp;#39;m subtracting is because it&amp;#39;s positive 6X so I have to do minus 6X to get the 7y by itself on the left hand side of the equation now in math whatever you do to one side you also have to do to the other so I also have to subtract 6X on this side too so when I rewrite I&amp;#39;m left with 7y equals minus 6 x plus nine okay so hopefully this makes sense so far now we don&amp;#39;t want 7y we just want y so since it&amp;#39;s 7 times y the opposite of times is division and so I&amp;#39;m going to divide to get y by itself but whatever I do to one side I also have to do it to the other so I have to divide everything on the right hand side by 7 as well so I&amp;#39;m going to do negative 6 divide negative 6 divided by 7 positive 9 divided by seven all right the sevens are going to cancel out on the left hand side and I&amp;#39;m just left with y equals negative 6 over 7 X plus nine over seven now if we were asked to find the y-intercept the y-intercept would be this 9 over 7 here but we&amp;#39;re not asked to find that we&amp;#39;re asked to find the slope so remember the slope is this little M it&amp;#39;s the number in front of the X so this negative 6 divided by 7 here this is our slope and that corresponds to answer Choice C so C is the correct answer to this question okay the next question says solve 4x squared plus 5x minus 9 answer choices are x equals negative 9 over 4 and x equals one b x equals negative 19 over 4 and x equals fifteen c x equals negative 12 and x equals 5 or d x equals negative 4 and x equals negative fifteen so let&amp;#39;s have you try this out it does doesn&amp;#39;t hurt to try if you don&amp;#39;t know how to do it don&amp;#39;t worry you&amp;#39;re going to learn how to do it here so let&amp;#39;s have you pause the video and try it out this is what we call a quadratic equation when you have a quadratic equation like this the first number in that equation is whatever is in front of this x squared is what we call a and whatever is in front of our X is what we call B and whatever&amp;#39;s left out here is what we call our C and so what we&amp;#39;re going to do is we&amp;#39;re going to factor this quadratic equation and what you do is you think about it this way you you make a little X or a diamond like this whatever you want to call it and on the top part of the diamond you&amp;#39;re going to write a times C and down here is gonna is gonna just go B so let&amp;#39;s start by doing that so we know here that our a is four and we know that our c is negative 9 right because we remember we have to take that minus sign into consideration so here&amp;#39;s our a here&amp;#39;s our C so what is 4 times negative nine four times negative 9 is negative 36. so I&amp;#39;m going to put this here in the top of my X now what do we plug in down here that&amp;#39;s just our B so the B is whatever is in front of our X which is five so I&amp;#39;m going to put a 5 down here now you might be wondering well so what what is this accomplished well let me tell you we have to find two numbers that will multiply together to give us negative 36 but they have to add up together to be 5. so a good way to start would be let&amp;#39;s just list out numbers that you could multiply together to get negative 36. so one would be let&amp;#39;s think of pairs of numbers that would multiply together to give us negative 36 and one pair would be 6 and negative 6. so if you do 6 times negative 30 times negative 6 you&amp;#39;re going to get negative 36 but if you add these up what is 6 plus negative 6 well that&amp;#39;s actually going to be zero so this pair is not going to work because we need something that&amp;#39;s going to give us 5. so what about negative 9 and positive four negative 9 times 4 is going to give us negative 36. so it passes the first test now let&amp;#39;s add these up negative 9 plus 4 is going to give us negative 5 not just 5. so this isn&amp;#39;t going to work because this is going to be negative 5. so now let&amp;#39;s try it the other way around let&amp;#39;s try positive nine and negative 4. so positive nine times negative 4 is going to give us negative 36. now let&amp;#39;s add these up 9 plus negative 4 is really the same as 9 minus 4 which is going to be positive 5. so this is the pair that we want to use so I&amp;#39;m going to put one number here and I&amp;#39;m going to put the other number right here that doesn&amp;#39;t matter you could write 9 here and negative 4 here doesn&amp;#39;t matter we&amp;#39;re just kind of doing this just to keep track of the numbers so now what I&amp;#39;m going to do and this is the part of problems like this that often confuses people all right so don&amp;#39;t worry if you&amp;#39;re confused we&amp;#39;re going to work this out right now all you want to do is just pick one of these numbers let&amp;#39;s start with negative four and I want you to write X minus 4. if it was a positive 4 you would do X plus 4 but since it&amp;#39;s minus 4 you write x minus 4. now you go back to the original question and you look what number was in front of the x squared the number in front of the x squared is 4. so we have to take this negative 4 and we have to have to have to divide it by four all right so what is negative 4 divided by 4 that&amp;#39;s going to be negative 1. so I could rewrite this as X minus 1. and I&amp;#39;m setting this equal to 0 here and I want to find X so x minus 1 equals zero if I want to find X in other words if I want to get X by itself I have to cancel out this minus one and I do that by adding one and whatever I do to one side I have to also do it to the other so I would get x equals 1. as one of the solutions to the equation now so I I dealt with my negative 4. so now let me deal with the positive 9. so we&amp;#39;re going to start by writing X Plus 9. okay but now I have to look back here at the number that&amp;#39;s in front of the x squared it&amp;#39;s 4 so I have to do 9 divided by 4. and I have to set this equal to 0 here all right so without simplifying this we don&amp;#39;t have to do any math here because we can look at the answer choices and see that they&amp;#39;ve left their answers as fractions so there&amp;#39;s no need to plug this into your calculator or anything like that what you can do now is let me try to bring this up a little bit that&amp;#39;s going to bring the whole problem up okay let me clear some room out so basically what I want to do is I need to get the X by itself so I need to subtract nine over four from both sides of my equation here okay so when I rewrite this I would get X equals negative nine over four all right and so the answer is going to be a because my Solutions are x equals negative 9 over 4 which is right here and x equals 1 which I found down here okay the next question says what is 70 of 350 is it a 230 B 75 C 245 or D 390 and let&amp;#39;s have you pause the video give this one a try and then when you&amp;#39;re ready we&amp;#39;ll go over it okay so there are different ways to solve percent questions and I&amp;#39;m going to show you one method here I think this method is pretty easy um at the end of the day you have to do what works with you what works best for you it says 70 here in the question so that tells me that I&amp;#39;m going to go into this formula and I&amp;#39;m going to replace the percent sign with the number 70. it says of 350. so I&amp;#39;m going to take 350 and I&amp;#39;m going to plug it into the formula here in place of of so what&amp;#39;s going to go into the formula for is well that&amp;#39;s actually what I&amp;#39;m trying to find because it&amp;#39;s asking me what is so I don&amp;#39;t know what goes in is so I&amp;#39;m just going to put an X in here and now we&amp;#39;re going to basically plug the numbers in and we want to rearrange this so that we&amp;#39;ve got X by itself on one side of the equation and that&amp;#39;s going to tell us what number is is so since it&amp;#39;s x divided by 350 and I want to get the X I want to multiply by 350. now why would I do that well watch this if I have 350 divided by 350 that&amp;#39;s going to equal 1 1 times x is just X so I&amp;#39;ve effectively got the X by itself on the left hand side but whatever I do to one side I also have to do it to the other side all right so I have 70 divided by 100 times 350 now okay so now what I want to do is you can just put this in your calculator if that&amp;#39;s easiest for you and if I do that the answer is going to be C 245. what is the equation of a line that passes through the points 1 negative 10 and 2 8 is it a y equals 12x plus 28 b y equals 18x minus 28 c y equals 8X minus 2 or d y equals 9x plus 74. let&amp;#39;s have you pause the video and give this one a try and as always if you get stuck don&amp;#39;t worry about it we don&amp;#39;t care for right now whether you get this right or wrong it&amp;#39;s all about the knowledge so let&amp;#39;s have you pause the video and try it out okay so there&amp;#39;s two formulas that we want to use to figure out this question the first is the slope formula m equals Y2 minus y1 all over X2 minus X1 so when we put a 1 here to indicate that you want to start with this formula here and you want to calculate the slope and then once we know the slope we&amp;#39;re going to use that and plug it into the point-slope equation which we&amp;#39;ll use second all right so if you&amp;#39;re completely lost don&amp;#39;t worry let me show you the first step here so the first step is to calculate the slope so what I have to do is I&amp;#39;ve got to look at my pairs here I have 1 and negative 10. now the first number in a pair is always an x coordinate so this one I&amp;#39;m going to call this X1 and this negative 10 I&amp;#39;m going to call that y1 because the second number is always y now let me look at this pair right here so this too what do you think I&amp;#39;m going to call that well I&amp;#39;m going to call that two X2 and this a I&amp;#39;m going to call the eight Y2 so simply put all I&amp;#39;m going to do is I&amp;#39;m going to take my Y2 which is 8 and I&amp;#39;m going to plug it into the formula here where it says Y2 and I&amp;#39;m going to take my y1 which is negative 10 and I&amp;#39;m going to plug that into the formula here for y1 what do you think I&amp;#39;m going to do after that well I&amp;#39;m going to take my two which I labeled as X2 plug it into the formula for X2 and lastly I&amp;#39;m going to take my X1 which I labeled the one right here and I&amp;#39;m going to plug that into the formula for X1 okay so let me show you how I would do this so m equals Y2 minus y1 so what do I put in for Y2 well remember I&amp;#39;m going to put 8 in for Y2 so it&amp;#39;s 8 minus my negative 10. so here&amp;#39;s a little trick here minus a minus is the same as plus so instead of doing 8 minus negative 10 I can just write it as 8 plus 10. all right and I&amp;#39;m going to divide that by X2 minus X1 so X2 is 2. and X1 is 1. so it&amp;#39;s 2 minus 1. 8 plus 10 is what 8 plus 10 is 18. two minus 1 is just 1 18 divided by 1 is just 18. so what did I figure out well I just figured out that my slope is equal to 18. now what I&amp;#39;m going to do is I&amp;#39;m going to take this m this 18 and I&amp;#39;m going to substitute it into the formula here in place of M so let me now use the second equation so it&amp;#39;s y minus y1 so what do you think I&amp;#39;m going to plug in for my y1 well since I labeled negative 10 as y1 I&amp;#39;m going to plug that in so it would be y minus negative 10. now remember I said minus a minus is the same as plus so really I&amp;#39;m just going to write that as y plus 10. so this is equal to my slope which I just calculated was 18. times x minus X1 and my X1 is 1. so I have x minus 1. so there&amp;#39;s two ways to do this now you could start by handling the 10 over here or you could start by Distributing the 18. so I&amp;#39;m going to start by Distributing the 18 just personal preference so I would do 18 times x which is going to be 18x then 18 times negative 1 which is going to be negative 18. so I have y plus 10 equals 18 X minus 18. now you could have also dealt with the plus 10 first I decided to deal with that last but what I&amp;#39;m trying to do here I need to get y by itself on the left hand side of the equation so I have y plus 10 the opposite of plus is minus so I do 10 minus 10. whatever you do to one side you also have to do to the other so I&amp;#39;m going to subtract 10 over here from the 18. all right we&amp;#39;ve got to work with like terms here so I can&amp;#39;t do 18x minus 10 because the 10 doesn&amp;#39;t have an X but I can do minus 18 minus 10. okay and so now what I&amp;#39;m going to get if I rewrite this I am going to get y equals 18 x minus 20 eight So my answer is going to be B determine the mean median mode and range for the following data set 8938 into so let&amp;#39;s hope you pause the video trying to figure this one out and then when you&amp;#39;re ready we&amp;#39;ll go over it okay so let&amp;#39;s go over how to do this and to start we&amp;#39;re going to first figure out the mean so the mean simply means the average so to find the average I want to add up all the numbers in the number set and then I&amp;#39;m going to count up how many numbers there are in the number set total and I&amp;#39;m going to divide by that number and if it sounds like I&amp;#39;m speaking uh a different language like from another planet or something don&amp;#39;t worry because I&amp;#39;m going to show you how to do this mean median mode and range questions are fair game for science for Math and for social studies so you&amp;#39;re probably going to get something like this at some point on your test all I&amp;#39;m doing here to calculate the mean is I want to take each number as you can see I&amp;#39;ve got my eight I&amp;#39;ve got my nine all right I&amp;#39;ve got my three I&amp;#39;ve got my eight and my two I&amp;#39;m just adding up all the numbers and then I&amp;#39;m gonna count up how many numbers there are there&amp;#39;s one two three four five that&amp;#39;s where I put the five downstairs here so you add up all the numbers in the data set and you divide by five and if we do this if we put it in our calculator we&amp;#39;re gonna find out that the mean is equal to six okay so to start off we know that the mean is six so now let&amp;#39;s go to the median so what a lot of people do sometimes I&amp;#39;ve seen when I did a lot of in-person tutoring I saw a lot of students do this and a lot of people will look at three and they&amp;#39;ll say okay well three is the middle number so it must be the median and they&amp;#39;ll think D is the right answer and there&amp;#39;s first of all let me say that if you made this mistake you know don&amp;#39;t worry about it right now I&amp;#39;m not picking on you by any means I just want to make sure that you know how to do this so that way on your test you can get as many points as possible and you can move on faster but just know that it&amp;#39;s I like the thought process I like that you probably remembered that the median had something to do with the middle number and so you looked for three and you saw that hey three is right in the middle here so I like the thought process but we have to take that take it another step further and what you have to do first is you have to put the numbers in order from smallest to largest all right so 8 is actually the median here so let&amp;#39;s talk about the mode next the mode is the most occurring number in the data set get it mode most the mode is the most occurring number in the data set so we see that 8 shows up twice all the other numbers only show up one time so 8 is going to be our mode the biggest number is nine the smallest number is two so if I subtract them 9 minus two is seven here so the range is seven so the answer that&amp;#39;s going to be correct here the mean should be 6 the median should be eight the mode should be eight and the range should be seven so answer Choice a is the correct answer please answer the following question without using a calculator so what I&amp;#39;m going to do is order of operations and so we have please excuse my dear Aunt Sally so the please the p is parentheses e exponents multiplication and division those guys are buddies addition and subtraction those guys are also Buddies first thing I&amp;#39;m going to do is what is in the parentheses so here I have 20 minus 10 is just 10 squared and I like to rewrite everything 10 minus 8 is 2. next exponent so we have our 10 squared so really that&amp;#39;s just 10 times 10. which is 100 and again rewrite all of it multiplication and division so I have 4 times 2 which is 8. addition and subtraction go from left to right and just go on through so I have 100 plus 18 is 118 minus 8 118 minus 8 is 110 and look here&amp;#39;s our answer B 110. okay the next question says which table represents a function is it A B C or D let&amp;#39;s hope you pause the video give this one a shot you never know and then we&amp;#39;ll go over it okay let&amp;#39;s talk about functions now so a function relates in input to an output and to teach this I&amp;#39;m going to show you in imaginary soda machine here that functions very unlike a soda machine would in real life so with this imaginary soda machine let&amp;#39;s say that every time you put one dollar into the machine you always get out of sprite all right and let&amp;#39;s say every time you put two dollars into the machine you&amp;#39;re always going to get out a Diet Coke now let&amp;#39;s say every single time you put in three dollars you get a vitamin water and the point here with this imaginary soda machine is that one dollar will only ever get you a Sprite so every time you put one dollar into the machine you&amp;#39;re always going to get a Sprite same with the two dollars two dollars will always get you a Diet Coke you&amp;#39;re not going to put in two dollars and get a monster you&amp;#39;re not gonna put in two dollars and get a water you&amp;#39;re not gonna put two dollars and get a vitamin water two dollars will only ever give you a Diet Coke okay so this is parallel to or this is a metaphor for what happens with a function in math I Think metaphor is the word I want to use here I don&amp;#39;t know but the point is that this example here with the soda machine is very similar to how a uh to what we&amp;#39;re trying to do here with understanding which table represents a function so in other words with a function in math each input has exactly one output you&amp;#39;re never going to put you know the same input into the machine and get two different outputs all right just like you&amp;#39;re not not going to put in three dollars and get out a monster and a Coke and a Sprite you&amp;#39;re only going to get one output every time so if we look at a here the x&amp;#39;s and well the X is not just an A in every case the X&amp;#39;s represent the inputs what you&amp;#39;re putting into the function and the Y&amp;#39;s represent the output okay so here this is telling us that if we put in negative 2 as an input we get 3 as an output but also if we put negative 2 in as an input we get 18 as an output so you could put negative 2 in and there&amp;#39;s two different outputs well this is not going to be a function because remember that would be like putting three dollars into the machine and getting a Sprite or a monster or a vitamin water so what about two here we see that if we or what about B we see that if we put in 2 as an input we get three but it also shows us that if you put 2 in 8 is also an output so this is not going to work all right again that&amp;#39;s like trying to put a dollar in and getting a spray to Coke a monster or this or that no it doesn&amp;#39;t work that way the function machine function soda machine every time you put that dollar in you only ever get that Sprite so what about C here well it looks like for C we put in two we get three as an output we put in negative five we get three as an output we put in negative one we get 8 is an output we put a negative two we get 18 as an output so for each input there&amp;#39;s exactly one output now I know what you might be thinking you might be thinking well how come we have two output three negative five output three well the outputs can be the same we don&amp;#39;t care if the outputs are the same we just don&amp;#39;t want we just want for every input there has to be one output all right it&amp;#39;s okay to get the same output for different inputs so in other words it&amp;#39;d be okay let&amp;#39;s say maybe you put in three dollars you get a vitamin water you put in five dollars you can also get out of Vitamin Water there&amp;#39;s two different inputs five and three are both different inputs but it&amp;#39;s okay if they have the same output so it&amp;#39;s okay if two and negative 5 have the same output but it wouldn&amp;#39;t be okay if for example over here 12 and 12 have different outputs that wouldn&amp;#39;t match all right that would not work so C is the correct answer okay the next question says multiply 3x minus y times four X plus seven Y and we&amp;#39;ve got answer choices a b c and d so so let&amp;#39;s have you pause the video give this one a try and then when you&amp;#39;re ready unpause the video and we&amp;#39;ll go over how to do it so to get a question like this right we&amp;#39;re going to use What&amp;#39;s called the foil method and it stands for first outer inner and last so let me break down how to do this in case you haven&amp;#39;t studied this or in case it&amp;#39;s been a while so I want to look at each set of parentheses and I want to look at the first number in the first set of parentheses and then in the second set of parentheses I want to look at the first number there too so I&amp;#39;ve got three and I&amp;#39;ve got four so I want to start by multiplying the first number inside each of the parentheses so what is 4X times 3x well that is going to give me 12x squared so don&amp;#39;t forget that instead of just doing 3 times 4 we also have to do x times x x times x is going to be 12x squared so that takes care of the first so now we want to do the outer so for the outer I want to start with this 3x here and I&amp;#39;m going to go over here and I&amp;#39;m going to do 3x times 7y so what is 3 times 7 well 3 times 7 is 21. and what is x times y well x times Y is best left as just x times y so that takes care of my outer so now I want to look at the inner two numbers here in this case I&amp;#39;ve got negative 1y or just negative Y and I&amp;#39;ve got 4X so what is negative 1 times 4 negative 1 times 4 is just negative 4. what is x times y x times Y is just simply x y all right so since we&amp;#39;ve got 21xy and we&amp;#39;ve got minus 4xy I&amp;#39;m going to Blind them up on top of each other here and this will become 17 because 21 minus 4 is 17. so I can really rewrite this as 12 x squared minus 17 X y so I&amp;#39;ve done my inners now the L stands for last so the last two numbers that I haven&amp;#39;t multiplied yet that&amp;#39;s what I&amp;#39;m going to do last which would be negative Y and 7y so negative 1 times 7 is negative seven and Y times Y is y squared so I&amp;#39;ve got negative 7 y squared and this whole thing is going to match up with C so C is the correct answer to this question what is the slope of a line that is perpendicular to 7x plus 4y equals twelve is it A B C or D let&amp;#39;s have you pause the video try this out and then when you&amp;#39;re ready we&amp;#39;ll go over it okay so again we want to start since this is a slope question we want to start with this formula y equals m x plus b and the first thing that we&amp;#39;re going to do here is we&amp;#39;re going to figure out what the slope of that line is so we&amp;#39;re going to take this formula and we&amp;#39;re going to rearrange it into the form y equals MX plus b and we&amp;#39;re going to find the slope but we&amp;#39;re not done yet there&amp;#39;s another step we have to do since we want to know about perpendicular for this question so what I&amp;#39;m going to do here is I want to start by getting the Y by itself so let me just right off the bat get rid of this 7x so since it&amp;#39;s positive 7x If I subtract 7x I&amp;#39;m going to cancel this out but whatever I do to one side I also have to do it to the other so I&amp;#39;m going to have to subtract minus 7x from the other side as well and I still have that positive 12 there so I rewrite this as 4y equals negative 7x plus 12. now I want to deal with this 4. so if I want to get rid of the force it&amp;#39;s 4 times y 4 divided by 4 is just 1 1 times Y is just y but now what I have to do is divide both numbers here by 4. since whatever I do to one side I also have to do it to the other so I could rewrite this as y equals negative 7 over 4 X plus 12 over 4. now 12 divided by 4 is the same as 3 but we don&amp;#39;t have to do anything with this 12 divided by 4 so I&amp;#39;m just going to leave it like this what we really care about is this number right here which is our slope the negative 7 over 4 is the slope but since we need to figure out what is the slope of the line that&amp;#39;s perpendicular we have to flip this upside down and change the sign so whenever you find the slope and you need to know what is the slope of a line that&amp;#39;s perpendicular to that equation you have to take the opposite reciprocal so that&amp;#39;s a fancy word for flip it upside down so instead of 7 over 4 I make it 4 over 7 and since it was negative 7 over 4 I make this positive so you take the opposite reciprocal the opposite this is negative it becomes positive and you flip it upside down so it becomes four over seven so the correct answer here is a Nick is shipping one package that weighs 10 pounds in eight boxes that all weigh the same in total the shipment is 118 pounds what is the weight in pounds of each box is it A B C or D you know the drill by now let&amp;#39;s have you pause the video give this a shot and then we&amp;#39;ll go over how to do it all right thank you for sticking with me so far into the video so basically here what we need to do is we want to write an equation here so it tells us that he&amp;#39;s got one package that weighs 10 pounds and 8 boxes but we don&amp;#39;t know how much each box weighs right that&amp;#39;s what we need to find but we know that there&amp;#39;s eight of them so let&amp;#39;s say eight times B where B represents the weight of just one box right so since all boxes weigh the same if we find what that weight is it multiplied by 8 it tells us the weight of eight boxes we add that to the weight of the package and that will add up to be 118 right because it tells us in total the shipment is 118 pounds so we have this equation here and all we have to do now is we have to solve this equation for B all right so what&amp;#39;s and when I say solve the equation by B all I mean is we have to get B by itself on one side of the equation so first I would subtract 10 from both sides of the equation 10 minus 10 is 0 118 minus 10 is 108. so I can rewrite this now as a b equals 108. and again the name of the game here is to get B by itself so it&amp;#39;s 8 times B what do I need to do here well I need to divide by 8 because if we&amp;#39;ve got 8 times B the opposite of times is division 8 divided by eight is one one times B is B so the eights are really canceling out here but whatever I do to one side I have to do it to the other so I have to do 108 divided by 8. and if we throw that in our calculator we&amp;#39;ll see that b equals 13.5 pounds and so we know that c is the correct answer here the next question says what is the value of f of x equals 9x cubed minus 2 when x equals negative three is it a negative 9 38 B negative 2 45 C 241 or D 928 so that&amp;#39;s up for you that&amp;#39;s up to you to decide I&amp;#39;ll let you pause the video give this one a shot and then as always we&amp;#39;ll go over how to do it okay hopefully you had a chance to try this so whenever you see a question like this I know this can seem kind of confusing but all you&amp;#39;re really being asked to do here is to substitute negative 3 into the equation for x so if I were to rewrite this I would rewrite it as 9 times negative 3 raised to the third power minus 2. and negative 3 so what is negative 3 cubed well that&amp;#39;s the same as negative 3 times negative three times another negative 3. so negative 3 times negative 3 would be positive nine but then when I multiply Pi multiply positive 9 by negative 3 what I get is negative 27 so I would rewrite this again now as 9 times negative 27 . minus 2. and if you plug this in your calculator here 9 times negative 27 minus 2 the answer is going to be B negative 245. simplify 15x plus 13 times x minus 1 in parentheses please put your answer in the box below now I know you obviously can&amp;#39;t literally write your answer in this box below but just imagine you could and let&amp;#39;s have you pause the video give this one a try and then as always we&amp;#39;ll go over it okay so the trick here is you have to distribute this 13 so you would distribute it to the X and then you distribute it to the minus 1 and yes you do have to take this minus sign into consideration so rewriting this I would have 15 x plus 13 X because 13 times x is 13x then I have 13 minus 1 which would be minus 13. so now what I want to do is I want to add up the like terms so 15x and 13x since they both have X&amp;#39;s I can add them up and that would be 28 X minus 13 and since the 13 doesn&amp;#39;t have an X there I can&amp;#39;t subtract 28x minus 13 so I just leave it here and this is all I can do I can&amp;#39;t simplify any further than this so this would be the correct answer the next question says what is the area of the following triangle now this side says 7 this side says 50 and this is a question mark I didn&amp;#39;t give you the side for the question here I&amp;#39;m reading this to you in case you&amp;#39;re on a phone or a small screen device so in case it&amp;#39;s hard to see these numbers and I&amp;#39;ve given you answers a b c and d now let me warn you this is a hard question so if you get stuck on this one don&amp;#39;t worry about it okay don&amp;#39;t beat yourself up because this is in my opinion the hardest one on this test so far so let&amp;#39;s have you pause the video give it a try and then it like I said don&amp;#39;t worry if you don&amp;#39;t get this right you&amp;#39;re you&amp;#39;re going to learn from it we&amp;#39;re going to go over it okay so to get this question right uh there&amp;#39;s actually a few things that you have to be aware of here and the first is that this is a triangle question and we have this little 90 degree angle this little box down here which represents a 90 degree angle which means that this is a right triangle so we may be able to use the formula for the Pythagorean theorem which is a squared plus b squared equals c squared now this formula is not directly going to give us the area so why am i showing you this formula here well we we don&amp;#39;t know what this side is equal to right this side is one big question mark and we know that side a is 7 and we know that side C the biggest side of the triangle is 50. um but we don&amp;#39;t know what this side is however we can figure it out all right so the other formula that is going to be relevant to this question though is the formula for the area of a triangle so I&amp;#39;m going to put an a to represent area I&amp;#39;m going to put a little T here to represent triangle so this stands for the area of the triangle that&amp;#39;s equal to the base times the height of the triangle all divided by 2. another way to write this would be half times the base times the height okay that is another way of writing the exact same thing so however you want to look at it base times height divided by two or half times base times height is two ways of saying the same exact thing so these are the two formulas that are going to be relevant here and this formula up here this a squared plus b squared equals c squared we&amp;#39;re going to use this formula to figure out what the unknown side of the triangle is then once we know what both sides of the triangle both sides down here of the triangle are we can do base times height divided by 2 and get the answer all right so if if it seems like this is really complicated this is really confusing let me break it down and put some real numbers to this and hopefully it&amp;#39;ll make more sense so we&amp;#39;re going to start with this formula right here like I said now 7 we can conveniently plug into the formula for a and 50 we can plug into the formula for side C which would look like this 7 squared plus b squared and I&amp;#39;m leaving this as B squared because we don&amp;#39;t know what this side is down here so let&amp;#39;s say that this side is B we don&amp;#39;t know what B is so I&amp;#39;m just going to leave it right here all right and that is equal to 50 squared okay so what is 7 squared 7 squared is 49 so I&amp;#39;m just regretting this as 49 plus b squared and what is 50 squared 50 squared is 2500. all right so now what I&amp;#39;m doing and what I&amp;#39;m going to do is I&amp;#39;m going to take this 49 and I want to get rid of it so I want to subtract by 49 from both sides or in other words I want to take 49 subtract from both sides all right now why am I doing this all right why am I doing this I&amp;#39;m doing this because I want to find B squared by itself and if I figure out what B squared is I can take the square root of both sides and if I do that I&amp;#39;m going to be able to figure out what the missing side of the triangle is why do I want to figure out what this missing side of the triangle is because then I can go up here and use the second formula and that&amp;#39;s going to give me the answer so now we figured out what B squared is B squared equals 2451. so what I want to do is take the square root of both sides of our equation here so the square root of B squared just gives me B the square root of 2451 is 49 point five so we now know that the missing side of our triangle is equal to 49 .5 so why is this information helpful what&amp;#39;s my next step well what I&amp;#39;m going to do now is I&amp;#39;m going to take the base and substitute it into the formula for B and I&amp;#39;m going to take this 7 plug it into the formula for the height so let me rewrite this now so we know that the base is equal to 49.5 and the height is equal to seven and if I divide by 2 what does this tell me well it tells us the area of the triangle because formula two is the formula for the area of the triangle so that&amp;#39;s going to give me a if I put this in my calculator so basically just a quick recap because this is kind of hard what I had to do here is I had to take a Formula 1 the Pythagorean theorem a squared plus b squared equals c squared I had to take the 7 in the 50 and I had to use them by putting them into this formula here and I had to solve for b once I found b b told me what this side of the triangle was equal to in other words B was the base of the triangle once I had both the height of the triangle and the base of the triangle I plugged them both into the formula for the area of the triangle I did the base times the height divided up by 2 and a is the correct answer for which value or values of X is the function f of x undefined if f of x equals 72 plus x divided by X plus 12 is it a x equals 0 b x equals negative 12 let&amp;#39;s see x equals 19 or d x equals negative 20. so now would be a good time to have you pause the video give this one a shot and then we&amp;#39;ll go over how to do it okay so these questions do come up on the test and this is an important topic to understand um but this can be a little confusing for some people so let me break it down like this when we see this notation F parenthesis X all that means we just read this as f of x and the f is the name of the function now it could be G it could be H typically it&amp;#39;s just going to be F but just know that it could be G of X2 that does happen but this out here this letters just will be called the name of the function now what about the x or whatever&amp;#39;s in the parentheses that is what we call the input so we already kind of talked about this concept a little bit if you remember when we did the function soda machine question where I went off on a big spiel about uh putting inputs into the machine and getting out an output well here the x is just the input all right we&amp;#39;ve got f is the name of the function the x is our input and all of this stuff out here this is our output okay and the idea with this question is that we need to figure out which value of x is going to make the function undefined now there are two cases when a function is undefined okay the first is when you have to divide by zero so I&amp;#39;m going to abbreviate this I&amp;#39;m just going to put div for division divide by zero okay you can never divide by zero and if you don&amp;#39;t believe me just take out your calculator and just pick any random number let&amp;#39;s just do 10 put 10 divided by 0 in your calculator and your calculator is going to give you an error message because you can never divide something by zero now you can go the other way you could do 0 divided by 10 and the answer would just be zero okay but you can never do you can never have uh anything that you&amp;#39;re actually dividing by zero that&amp;#39;s going to give you an error all right the other case is when you have a negative under a square root all right so let me just put this like I&amp;#39;m going to abbreviate this negative number under a square root all right so if you&amp;#39;re you&amp;#39;re taking notes this would be a good thing to add so the two cases that are going to make a function undefined if you have a zero in the denominator in other words if you&amp;#39;re trying to divide by zero or if you have a negative number underneath the square root okay and so I should also mention that whenever you have a fraction like this the top part of the fraction is what we call the numerator and the bottom part is what we call the denominator so here what I&amp;#39;m going to do is I&amp;#39;m going to take the denominator and I&amp;#39;m going to set it equal to 0. so I have X plus 12 and I&amp;#39;m just going to set this equal to 0 and I want to solve this equation for x again when I say solve the equation for x that&amp;#39;s just you know a fancy way of saying I want to get X by itself on one side of the equation so I have X plus 12. I want to do the opposite of addition here which is subtraction and that&amp;#39;s going to get the X by itself on the left hand side but in math whatever you do to one side you always have to do it to the other so I have to subtract 0 I could do 0 minus 12. so subtract 12 to the other side too so I I end up with x equals negative 12. now what does this tell me Well if you go back to the original question 72 plus x divided by X plus 12. if you put in negative 12 for X here it&amp;#39;s going to make the bottom number zero all right so watch this if I do 72 and then instead of X here I write negative 12 and then down here on the bottom I do instead of writing X here I write negative 12 plus 12 all right negative 12 plus 12 is going to be 0. all right and so we have 72 minus 12 divided by 0 and this is an error because we can&amp;#39;t divide by zero if x is negative 12 the function is going to be undefined because if x is negative 12 e would have a situation here where you&amp;#39;re trying to divide by zero and that is an illegal move in math you&amp;#39;re not allowed to do this in math it won&amp;#39;t work so basically B is the correct answer here so to Simply put if you get a question like this you just take the denominator here take the bottom take everything from the bottom and just set it equal to zero and solve for x and the majority of time that is going to give you the right answer which answer Choice represents the inequality graphed on the number line a x is less than negative 2 b x is less than or equal to negative 2 c x is greater than or equal to negative two or D X is greater than two let&amp;#39;s have you pause the video try to figure this out and then when you&amp;#39;re ready we&amp;#39;ll go over how to do it and again no worries no pressure let&amp;#39;s just see how it goes all right let&amp;#39;s talk about this one so note here that the arrow starts at negative two and it goes to 5 and it just kind of keeps going and also note here that at negative 2 we have a closed Circle the closed Circle tells us that negative two is going to be included in the range of values here so if I were to draw a little stick figure person right here above negative two note here that if the person were to Walk This Way to the right what happens to the numbers well they go from negative one to zero to one to two and so on and so forth so we see here that the numbers get bigger as we go to the right as we Follow the arrow from negative two to five the numbers are getting bigger so let&amp;#39;s look at a a is telling us that X is less than negative two well if that were the case then the arrow would be pointing this way to the left the arrow would be going through the smaller numbers the numbers that are decreasing which is now what we see and that&amp;#39;s the same with b b tells us X is less than or equal to negative two that is also not the case so A and B are out here now D tells us X is greater than two and this is also not the right answer because the arrow doesn&amp;#39;t start here at 2 or it says X is greater than positive two the arrow doesn&amp;#39;t start here at 2 and keep going it starts back here at negative two all right so note here that the right answer is X is greater than or equal to negative two and this answer includes the negative 2 and the range of values here that&amp;#39;s why it&amp;#39;s not just X is greater than negative 2. it&amp;#39;s X is greater than or equal to negative 2 because the closed Circle tells us that negative 2 is included in the range of values so this question let&amp;#39;s have you try this without a calculator it says between which pair of decimals should 5 8 be placed on a number line is it a 0.4 and 0.5 is it B 0.5 and 0.6 is it C 0.6 and 0.7 or D 0.7 and 0.8 so again let&amp;#39;s have you try this without a calculator you could pause the video give it a shot and then when you&amp;#39;re ready we&amp;#39;ll go over how to do it okay so to answer a question like this what the first step I would recommend is to look at the fraction and just figure out is this greater than or less than half okay that&amp;#39;s always a good first step here now to do that you look at the bottom number in the fraction the bottom number is eight and so what is half of eight well half of eight would be four so I have the fraction 4 over 8 here and I want to compare four over eight to five over eight now really the key to getting this question right is to understand the skill that when two fractions have the same denominator you can figure out which one is the bigger fraction by which one has the bigger numerator so in other words here these fractions both have an 8 downstairs in the denominator so I look up top here and I see we&amp;#39;ve got 5 8 and we&amp;#39;ve got 4 8 well 5 is bigger than four so 5 8 is bigger than 4 8 and since 4 8 is equal to half we know that 5 8 is greater than half so 5 8 is greater than half and why does this matter well it matters because half as a fraction is equal to 0.5 as a decimal all right so again all I did here is I looked at 5 over 8 and I I thought about the fact that if it was 4 over 8 it would be equal to half but it&amp;#39;s 5 over 8 so I know that this fraction is going to be greater than 0.5 all right 5 over 8 is greater than half half is equal to 0.5 so this lets me take answer Choice a out of the question here so if you don&amp;#39;t if you&amp;#39;re having a little trouble following what I just did it might be a good idea to just rewind the video watch it maybe slowly just just think about it here because this is an important skill and if you got that then great job the next thing I would do is we want to figure out we know that 5 over 8 is bigger than 0.5 but we next want to see is it greater than or or less than 0.6 if 5 over 8 as a 5 over 8 converted to a decimal is bigger than 0.6 then we would know that b is the wrong answer here so how do we do that well let&amp;#39;s compare five over eight let&amp;#39;s compare that to 0.6 and then if we need to we&amp;#39;ll compare it to 0.7 so how do I write 0.6 that&amp;#39;s a decimal how do I write that as a fraction 0.6 is equal to 6 over 10. all right so now what I want to do is I want to get a common denominator so we&amp;#39;ve got 5 over 8 and 6 over 10. so what I&amp;#39;m going to do is I&amp;#39;m going to say hey 6 over 10 has the 10 in the denominator so I&amp;#39;m going to multiply both the top number and the bottom number of 5 over 8 by 10. and if I do that I get 50. over 80 now down here I have 6 over 10. I look up at the the five over eight fraction I see that there&amp;#39;s an 8 in the denominator so I multiply the top and the bottom number of this fraction by 8. and again all we&amp;#39;re trying to do is we we need to compare five over eight and six over ten and I need to get a common denominator and then we&amp;#39;re going to see which fraction is bigger so 6 times 8 is 48 and 10 times 8 is 80. so now we can compare the two fractions 50 over 80 is bigger than 48 over 80 because 50 is bigger than 48. so which fraction is bigger is 5 is it 5 over 10 or 6 over 10 or I&amp;#39;m sorry is it 5 over 8 or 6 over 10 which one is bigger well we know that once we got a common denominator we saw that 50 over 80 was bigger than 48 over 80. so this tells us that 5 over 8 is greater than 6 over 10. so let&amp;#39;s rule B out here because we know that when we take 5 over 8 and compare it to 6 over 10 5 over 8 ends up being the bigger number so we know that 5 8 cannot be between 0.5 and 0.6 so now let&amp;#39;s look at 0.7 so 0.7 how can I write that as a fraction well I can write that as a fraction because point seven is equal to 7 over 10. so now what I want to do is I want to compare 5 over 8 to 7 over 10. so I want to get a common denominator all right so how am I going to get a common denominator here all right what what I want to do is I want to multiply the top and the bottom number of 7 over 10. both by eight now seven times eight is what 56. 8 times 10 is 80. all right so what is a bigger number 56 or 50. well hopefully you see that 56 is a bigger number so basically you know we can see here that 48 over 80 is smaller than 50 over 80. but 56 over 80 is bigger than 50 over 80. so again if we go back to our original fractions here we see that 5 8 is bigger than 6 over 10 but it&amp;#39;s smaller than 7 over 10. so therefore we know that c is the right answer because we know that 5 8 is smaller than 0.7 but it&amp;#39;s bigger than 0.6 all right so this question is a little tricky maybe watch this one again if you had trouble with it because this is an important skill to understand the next question which of the following is true A B C or D let&amp;#39;s have you pause the video think about this one and then when you&amp;#39;re ready we&amp;#39;ll go over how to do this question okay so this question is just testing you on how well you understand basic math signs and symbols and their translations so let me put this big table up on screen here and if you had trouble with this question it would be it wouldn&amp;#39;t hurt to pause the video and put these down in your notes basically this if I read a out loud if I translate the symbols to math words this would say 88 is greater than 109 which is false that is not true um C would read as 109 is less than 88 and 109 is bigger than 88 so C is wrong now B would read as 88 does not equal 109 which is true so B is the right answer here and like I said if you had trouble with this don&amp;#39;t worry about it for right now we&amp;#39;re just practicing definitely study this table that I have on the screen and then when you&amp;#39;re ready we&amp;#39;ll go on to the next question if the area of a circle is 200 what is the diameter please rate your answer in the box below now you obviously can&amp;#39;t write your answer in the box below through the screen but imagine if you could and I want you to pause the video try to figure this one out this is a tough one uh whenever you&amp;#39;re ready we&amp;#39;ll go over it and like always don&amp;#39;t worry uh if this question&amp;#39;s hard uh we&amp;#39;re just going to learn how to do it okay so let&amp;#39;s learn how to do this question now um so the formula is of a circle it&amp;#39;s area of a circle equals pi r squared so we need to use this formula to get the right answer now R is the radius of a circle so the radius of a circle and this is a pretty bad drawing of a circle it actually looks more like an orange but hopefully my bad drawing skills help help make this more memorable for you but if I were to measure half of the circle that&amp;#39;s what we call the radius and if I were to measure the entire circle and this actually is an even worse Circle but just pretend this is a circle you have to be really open-minded to watch my videos because some of my examples are just very out there but imagine this was a circle if I measured across the entire circle that would be the diameter so we can say that the radius is half of the diameter and the diameter is double the radius all right so the point here is what we&amp;#39;re going to do is we&amp;#39;re going to use the formula for the area we&amp;#39;re going to figure out what the radius is and we&amp;#39;re going to double it that simply tells us what the diameter is so fortunately we already know the area of the circle it&amp;#39;s 200 so I can say let me write it over here 200 equals pi are r squared so we can divide by pi on both sides and why would I want to divide by pi on both sides well the reason is because I want to get the radius by itself so I want to kind of clear the Pi&amp;#39;s out of the row here now another thing that you should know is that Pi is uh you can think of it as being equal to 3.14 it&amp;#39;s actually not it&amp;#39;s equal to 3.14 and then a ton of other numbers but you could just think of it roughly as being equal to 3.14 although technically it&amp;#39;s not uh but that&amp;#39;s beside the point here coming back to question here you know we can cancel the pies out here over here we have 200 Pi all right now you could take this pie out and replace it with 3.14 all right uh if you want to but I&amp;#39;m just going to leave it as the pi symbol for right now and when I rewrite this so that we can see it more clearly here I rewrite it we&amp;#39;ve got 200 divided by pi equals r squared so even if you&amp;#39;re completely lost or have been up until this point in the video I want you to ask yourself right now 200 divided by pi equals r squared how would I solve this for R and we&amp;#39;ve talked about this in the example with triangles I think it was earlier in the video and now we have a it&amp;#39;s a different scenario but it&amp;#39;s a very similar idea so the answer is that if we want to get just R we have to take the square root of both sides all right the square root of r squared is just equal to R so we now have the square root of 200 over pi is equal to the radius and we don&amp;#39;t want to find so we need to find the radius but the final answer we need to know what the diameter is for the final answer here so fortunately we already know that the radius is equal to half of the diameter and that the diameter is equal to twice the radius so if I double this number here the square root of 200 over Pi if I double that it&amp;#39;s going to give me the diameter so I would say that the diameter is a 2 times the square root of 200 divided by pi so if I put this in my calculator and I do uh the square root of 200 divided by pi multiplied by 2. the answer you should have would be 15.96 maybe you rounded it a little bit different I don&amp;#39;t really care for now I just want you to have either gotten this 2 times the square root of 200 divided by pi or 15.96 or an answer very close to this if you round it a little bit differently and you might be wondering on the test how will the answer choices be are the answer choice is going to have the pi symbol and the answer or are they going to be a numerical value like this the answer is that it depends on how they do the test it might be a number they might also leave Pi on the answer choices it could be either way so be ready for for both and and really either way you just have to remember Pi is 3.14 again that&amp;#39;s not technically mathematically correct there&amp;#39;s a bunch of other numbers on it too but all you really need to remember is it is 3.14 for the purposes of the GED test and I know this is a hard question so you know give yourself on the a pad on the back just for trying this if you got it right fantastic work if not fantastic job for trying Mr Burns wants to take his wife and children to the movies both children are under 13 years old each child will bring one friend along of the same age the ticket prices are shown in the table below children under 13 years old five dollars each for a day show seven dollars each for a night show then we have over here adults and teens 13 years old and up twelve dollars each for a day show and 15 each for a night show now if Mr Burns is buying the tickets how much money will they save on the cost of the tickets if they attend a day show instead of a night show please disregard sales tax in your answer a 44 dollars B 58 C 14 or d 16 let that be pause the video try to figure this out and then when you&amp;#39;re ready we&amp;#39;ll go over it okay so basically here let&amp;#39;s take stock of how many people we have here so a represents adults so we have two adults here we&amp;#39;ve got Mr Burns and his wife and as far as the children go we know that he has two children and because it tells us that both are under 13 and each child is going to bring one friend of the same age so as far as children that are under 13 we know that we&amp;#39;re going to have four here so what we have to do here is we have to calculate the cost in total that he&amp;#39;s going to pay for a night show and the cost for a day show and we&amp;#39;re going to subtract them all right so let&amp;#39;s start with night here so to calculate the cost at night we would have to say well there are two adults going and at night the cost for an adult is 15 bucks so I would want to do 2 times 15. now I&amp;#39;m going to add that to the cost of the children so how much does he have to pay for the children well think about it there are four kids that he&amp;#39;s going to be taking to the movies and the cost for one kid would be seven dollars all right so we would do seven times four here and if you just plug this all into your calculator you&amp;#39;ll see that the cost for a night show is gonna be 58 dollars so that&amp;#39;s how you would do night now the process for day is basically the same thing here except it&amp;#39;s going to be different numbers so again we have to add up the cost of the adults and the cost of the children but this time we&amp;#39;re looking at the prices from the day so there&amp;#39;s again there&amp;#39;s two adults there&amp;#39;s him and his wife and the cost for one adult for a day show would be twelve dollars and we&amp;#39;re gonna now add the cost that he&amp;#39;s going to pay for the children so again we have four children still and the cost for one child child would be five dollars all right so again we can plug this in the calculator do two times twelve plus four times five and we&amp;#39;ll get forty four dollars so now what we have to do is we have to take the cost of a Night Show in total which is 58 and the cost in total of the day show which is 44 and we have to subtract them and if we subtract them we get C as our answer Kate&amp;#39;s parents let her start her own lemonade stand to sell lemonade to the neighbors during which period did our earnings increase the most a April through may be June through July C May through June or D March through April and we have a graph over here it says Kate&amp;#39;s Lemonade Stand profits from January through July now on our vertical axis we see the monthly earnings on the horizontal axis we see the months and so I&amp;#39;ll turn it over to you to pause the video give this one a shot and then we&amp;#39;ll go over how to do it okay so one of the key words in this question is the word increase and we want to look on the graph meaning the blue line here and we want to look at each period here and find the one that had the biggest increase so let me first identify the period April through May so I find April down here and I find May right here so to determine what&amp;#39;s happening what happened between April and May the only thing that I need to look at is what&amp;#39;s happening on the line in between the months through April and May now if you were to imagine a little stick figure person starting at the leftmost part of the line and imagine this blue line here is a hill if the person were to follow the line which direction would they be going well hopefully you can see that if they just ran on this line they&amp;#39;d be going downhill that means that there is a decrease between April and May and so we can take April and May answer Choice a out right away because we&amp;#39;re trying to find the period that had the biggest increase so what about June through July so to do that let me start by finding June and obviously you&amp;#39;re not going to be able to write lines like this on your test but I&amp;#39;m just kind of showing you how to check the period through June and July all you have to do is check what&amp;#39;s happening on the graph in between June and July so detection in July I don&amp;#39;t care about what&amp;#39;s happening with the graph over here I just need to look between this two period this this period right here now again if we imagine that we had a little stick figure person and the person was going to start at the leftmost part of the graph and follow the line they would be running downhill which means a decrease so from June to July we know that there was a decrease so we can take B out as well here so let&amp;#39;s check answer Choice C May through June so again find you want to First identify the part of the graph that is going to be relevant to answering the question so here&amp;#39;s May and June looks kind of like right here okay so now here&amp;#39;s the point that we want to get at here so from May through June if we start over here at the leftmost part of the line which would be May and now what if our stick figure person were to just follow this line right here which direction would they be going well now we can see the person would have an uphill battle right here they&amp;#39;d have an uphill climb so we do see that there would be an increase from May to June but let&amp;#39;s look at March and April 2. so if we look here&amp;#39;s March here&amp;#39;s April so if we just focus on what&amp;#39;s happening with this part of the blue line right here between March and April and we give it the stick figure test if the stick figure starts right here at March and just follows the line towards April they would also be going uphill so we know that there was an increase in March and April but the question is which had the the biggest increase well one other way to think about this is which Hill would be harder to climb this little Hill right here or this big hill right here well just by the eyeball test it looks like the hill for me to June would be harder to climb all right and we can verify this with numbers too so let me get the stick figures out of the road here and I&amp;#39;ll show you what I mean so let&amp;#39;s look at May here so may is about here all right so what&amp;#39;s the numerical value for May so if I start at May and I kind of draw a line all the way over here I see that I would land somewhere in between ten and five but closer to 10. so let&amp;#39;s say that it was maybe eight dollars in May all right and again I can&amp;#39;t tell the exact number but I&amp;#39;m just guessing it&amp;#39;s about eight so let&amp;#39;s look at June so right here was June that looks like it&amp;#39;s exactly at 25. so here&amp;#39;s 25 right here let me just Mark that down all right and so if we look at March and April March right here if I look over here on the left I see that that is maybe two dollars maybe something like that so let&amp;#39;s say in March she made two dollars and from April which is right here if I trace April over here I see that it&amp;#39;s almost it&amp;#39;s not quite 10. so let me just call that nine now I can subtract the values here so I can do what is 25 minus eight so 25 minus 8 is 17 so I see that there was a 17 dollar increase from the start of the month that may till June she had a 17 increase and if I look at where she was at in March and look at where she was at in April and I do 9 minus two nine minus two is seven so it looks like she had a seven dollar increase from March to April so clearly the biggest increase was C so what I want to want you to take away from this is that you know you can do a question like this in two ways you can actually put numbers to it or you can just kind of use the eyeball test and the eyeball test of just thinking you know hey this is going downhill so I don&amp;#39;t have to look at that this is going uphill this is going uphill this hill is bigger so the biggest increase was May through June two different ways to do it up to you to decide which way makes the most sense to you Ryan invested twelve hundred dollars for two months at a 10 interest rate how much interest did he earn on his money Parker must know me well because I love questions dealing with money and interest as my students know this is the way to make you really really rich so compound interest a beautiful thing but we&amp;#39;re actually doing simple interest here so what we&amp;#39;re going to do is we&amp;#39;re going to take 1200 and we&amp;#39;re going to divide that by 10 percent okay so let&amp;#39;s just think if I take 12 and I just move the decimal point over that&amp;#39;s dividing it so that gives us a hundred twenty dollars which is actually not per month it&amp;#39;s per year it&amp;#39;s called annual percentage rate maybe you&amp;#39;ve heard that that means that the 120 is actually broken down into 12 months so we&amp;#39;re going to divide the 120 by 12 and we get a nice easy 10. so he&amp;#39;s making ten dollars per month how many months is he doing it two right so we&amp;#39;re going to say ten dollars times two equals twenty dollars so he is making twenty dollars in simple interest G wrestled in eight matches he scored two one eight zero twelve four one and twelve points during each match respectively what was Jay&amp;#39;s average number of points scored in these eight matches rounded to the nearest whole number a 9 e 5 C 2 or is it D12 let&amp;#39;s have you pause the video give this one a shot and then when you&amp;#39;re ready we&amp;#39;ll go over how to do it okay so we&amp;#39;re trying to find the average here and we&amp;#39;ve talked about mean earlier in the video and we said that mean means the average and so mean and average are two words for the same thing but that&amp;#39;s all we&amp;#39;re doing here is we&amp;#39;re finding the average and the way that we do that is we want to add all the numbers up and then what we&amp;#39;re going to do is we&amp;#39;re going to divide by the total number of numbers in the set okay so all I&amp;#39;m doing here is again I took all of these numbers here gonna add them all up which I&amp;#39;m doing up here and I&amp;#39;ll throw a parentheses around all of this and so I&amp;#39;d add all these numbers up and then down here I&amp;#39;m going to divide by the total number of numbers and so we know that he wrestled in eight matches and we have eight numbers here right one two three four five six seven eight so all you do is you put this add these all up in your calculator you can divide by eight and the answer you should get is five so hopefully that makes sense

Transcript for:GED Math Power Rules and Problem-Solving Strategies

Transcript for:
GED Math Power Rules and Problem-Solving Strategies