Tricks NO ONE told you for ACING math - Math champion + perfect scorer (ACT/SAT tips)

not a single one of my students knew or heard about in school any of the things I'm about to teach you right now if you're struggling on the math section wondering why it's the easiest section for others well it's not your fault school math just hasn't prepared you I've got perfect scores on the ACT and sat math sections with 10 minutes to spare on the sections for both tests if you want proof and study motivation now I'm a private tutor and my three most recent students got a 33 a 35 and a 33 on the ACT and said that math became their easiest section so proud so today you'll learn how to solve problems like a mathlete I'll walk through three problems with the solutions that I would use but it's not just three problems you're learning how to solve these techniques can apply to many more other questions let's go these are common problems you'll see on both the act and sat greatest common factor and least common multiple come up all the time what is the greatest common factor of 42 126 and 210 so what I do is write out the three numbers in a row leaving some space between them then I draw this L-shaped line and what I'm going to do next is look for small common factors between them here I can see everything's divisible by two so I write the two on the left side and then 42 divided by 2 is 21 126 divided by 2 is 63 210 divided by 2 is 105. next I'm going to look for another small common factor 3 is a common factor and actually how I know that is because the sum of the digits of 21 is divisible by 3 and the sum of the digits of 63 is 9 and is divisible by 3. and finally the sum of the digits of 105 is 6 which is also divisible by 3. whenever the digits of a number added together is divisible by 3 then the original whole number is divisible by 3. that's why now I write a 3 on the left side and I divide so we get 7 21 and then 35. now it's easy to see that we actually have another common factor which is seven so I repeat the same process write a 7 on the left 7 divided by 7 is 1 21 divided by 7 is 3 35 divided by 7 is 5. and finally we can't divide anymore because we already have a 1 here and guess what the greatest common factor is everything on the left side multiplied together so 2 times 3 times 7 so that is 42 and that is your answer super easy but not only that if the question was least common multiple instead it's literally the same thing but it's the product of all of these numbers outside of the Big L so 2 times 3 times 7 times 3 times 5 and whatever that is you can use a calculator for this then that will be your least common multiple easy and you don't have to use guess and check a lot of the official Solutions I've seen are using guess and check like oh try all of the answer options to see if they're the greatest common factor but that wastes time and then it's very easy to make mistakes because you you might not try a number correctly and it's just not a complete solution where you're actually getting to the answer in the direct rigorous way if you found tip one helpful quick reminder to please give me a like because it really helps me know that the effort and time I put into these videos for you is worth it and I should keep doing it if you don't watch through this whole video it means that one you didn't actually want to get a good score on that section or two that you can't stay focused throughout the whole video focus is one of the most important skills to do well on this test and any test so watch to the end I promise you will regret it Sam and John both start at the same point Sam walks 30 feet North while John walks 40 feet West how far apart are they at their new locations this seems straightforward enough first we want to draw a diagram to keep track of information and this also prevents mistakes from happening first we have Sam here 30 and then John here at 40. the distance between them is whoa this line and it looks like the hypotenuse so just like like the answer explanation here we can just do the Pythagorean theorem where we have 30 squared plus 40 squared equals c squared okay sure maybe you can solve this in 60 seconds but I'm going to show you how to do it in five seconds whenever we see right triangles we want to look for special right triangles because of my practice and knowing special right triangles which will review any bit I can already see that this is going to be a 3 4 5 triangle how did I see that that brings me to my second tip which is to simplify because we can divide both sides by 10 to see that the similar triangle has side lengths of three and four this is why I know it's a three four five triangle so right away I know that the hypotenuse is 5 times 10 because of the factor of 10 we took away previously so the answer is 5 times 10 which is 50. special right triangles are huge for saving time on the test because the ACT and sat he uses special right triangles all the time I'll teach you common special right triangles so there's a three four five there's five 12 13 7 24 25 and 9 40 41. now before you freak out and think oh my gosh I have to memorize more stuff this is how you know these without memorizing them so notice that for the shortest side length here's three we can square it and that becomes nine nine if we split it in half it's 4.5 but we choose integers on either side so that's four and five four plus five equals nine so we have three four five triangle we can see this holds true for all of these other ones where the shortest side length is an odd number 5 squared is 25 split in half is 12.5 but we choose the numbers on either side so we get 12 and 13 your 5 12 13 triangle 7 squared is 4 nine and we split that in two we get our 24 and 25 and naturally you know that 9 squared 81 becomes 40 and 41. that's how in the Sam and John problem you can solve it so much more quicker than the official Solution on whatever website or whatever book you use once you use this mathlete mindset like I'm teaching you now the point you can get to is where I read the problem and I Circle the answer right away without writing anything because I see in my head that North is 30 then West 40 and the hypotenuse will be 50 because of the special right triangle the hardest problem of them all because oh my gosh we have to get I to the 117th power for I equals square root of negative 1 which of the following is equal to I to the 117 Power Man how do we get this it's very important to remember that none of the problems on the act or sat are supposed to be really hard and take you a long time you should realize that if you see an absurd number like this there's no way they would make you multiply I 117 times that'll lead you to know that there's going to be a pattern even if you don't know the pattern you can usually quickly get it just by writing out a few numbers in the sequence so if we have a table like this n the power in the top row and then I to the n in the bottom and we write it this way so 0 1 2 3 4 5 6. however many you need to confirm the pattern so I to the zero power is one I to the one power just I I squared is you tell me minus 1 then to the third power you just do negative 1 times I which is negative i i to the fourth power be careful on this one that's negative I times I so you get negative I squared which is just going to be negative negative one so it's positive one then to the fifth power if we multiply by I again it's just I I to the sixth power negative one and you see a pattern here because essentially every four you have the same result for I to whatever power that's your pattern your pattern of four for example if we have I to the eighth power then a divided by four has remainder of zero so we can go into our table 0 because we know that I to the 8th is the same as I to the zero I to the eighth equals one and for a larger number like I to the 15th power hour 15 divided by 4 gives you a remainder of 3. under I to the third power it's negative I so I to the 15th equals negative I so yes exactly for I to the 117 power we have 117 divided by four so if I write it on this side here 117 divide by 4 remainder one here we get a remainder one which means that I to the 117 equals I 2 1 which equals I and there you have it if you know the pattern it's super easy and on the spot if you forget it you can derive it to so that's basically how you can guarantee to get every problem right because even if you forget something you can get the pattern yourself huge huge bonus tip I asked my students what their favorite tip for me was and this was the top one I'll demonstrate this tip in two problems simplify as much as you can and leave calculations to the end in this problem a rectangular prism is 21 feet tall and has a square base with a width of eight feet what is one-fourth of the volume of a figure in cubic feet the volume is going to be 21 times 8 times 8 because the bottoms is square right so instead of already multiplying this out to get whatever it is you already know that you want to get 1 4 of this whole thing so you simplify and leave the calculations to the end I would cancel and simplify such that then I only put this in my calculator this may seem like it only saves you a few clicks but all those clicks add up not only time wise but the fewer clicks on the calculator you do than the fewer mistakes you could possibly make same thing for this problem we have this triangle where we're looking for ankle X and we know this is 125 degrees and 20 degrees right typically students would want to find this angle because by finding this angle we can get angle X by doing 180 subtracted by this angle so we can write an equation this is y then we have 180 minus 20 minus 125 equals y and then we want x x is our goal and x equals 180 minus y less directly substitute this whole thing in for y so we get x equals 180 minus quantity 180 minus 20 minus 125 and that's the beauty of simplification because look 180 and 180 cancel so then your answer will just be 2 20 plus 125 and that you can do in your head which is going to be 145 and that's so much easier and quicker than if you had gotten y first by doing 180 minus 20 minus 125 also because subtraction is harder than addition this is a lot harder to do than just adding 20 and 125 by simplifying and waiting to do all calculations at the end you save a lot of time and fewer steps which reduces your room for error the key to solving problems in a smart way and quickly is not relying on memorization is to use the problem solving that we learned today so that the three problems you saw today will actually help you in so much more than just those exact problems wow the light keeps changing so much but anyway you can use those skills on new problems to dramatically improve your score like when I took this math section I demonstrated live all the work that I actually wrote down to solve each problem and what things that I don't use the calculator for and this all save me a ton of time then when I'm not in that time crunch I can actually solve problems and get them right you saw three problems today but you can follow along this video and see how I solved all 60 questions on the time crunch and it's probably the best study motivation you'll actually see so we're grinding through this together guys comment below would you like to see next thanks peace so proud

Channel: Amy Wang

Views: 66,137

Keywords: act, sat, math, college admissions, college prep, college, college applications, math tricks, mathlete, math competitions

Id: jkkDGG6FOPg

Length: 13min 3sec (783 seconds)

Published: Sat Aug 19 2023