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SAT Math Tips

3,914 views
Teacher/Instructor Eva Holtz
Eva Holtz

Harvard University
Perfect scores on the SAT and 4 SATIIs

Eva is a certified admissions counselor and the founder of PrepPoint, a premier test prep company in the San Francisco Bay Area.

In this episode I'm going to share with you some quick tips for the math section, some of them are strategies that really only take a few seconds to describe and others are things you could just keep in mind or know about how the SAT math works. Let's have a look; we're going to talk about how you should read carefully, use you calculator wisely, use all the information given, not worry about formulas or about symbols and know how to tackle 'always', 'never' and 'must' problems as well as 'could' and 'can' problems. Let's go into details now.
So first of all it is so important to read carefully on the math section, I'm not saying that this is a strategy for rocket scientists but I do want you to keep in mind that so many points are lost by students reading the question wrong or not answering the right question. So keep in mind any restrictions, if you're told that you're dealing with a prime number make sure you're dealing with a prime number or if a, b and c have to be distinct integers, don't make them the same as each other just basically pay attention to what you're being told to do and of course answer the question being asked so if you've solved for X make sure that you're supposed to turn in your answer for X rather than say Y.
Next up, use your calculator wisely. Calculators are allowed on the SAT basically as long as you don't have a calculator with a QWERTY keyboard that beeps and prints out tape which I think would be pretty hard to find, you'll be fine. That said, you want to know that SAT problems are designed so you can solve them without calculators. So what that means is, if you are using your calculator and you find yourself doing some really not so elaborate calculations, you might want to stop and think; am I doing something wrong or did I miss a shortcut? You might be doing a brute forced approach to your math problem that could really be solved more easily by just stepping back and reading and thinking.
Also you definitely want to use all the information given; if you solved a problem without using all the information given to you, there's something wrong. I kind of think of it like a toaster, if you take a toaster apart and you put it back together and you have a piece left over, there's a problem. Definitely think of math problems the same way, if you have a piece left over you didn't use, you have a faulty toaster/math problem and it's so rare that an SAT problem can be solved without using all the information given that you should really question yourself if you think you pulled it off. That's going to be maybe less than once per test that you can get away with that so be suspicious.
Now don't worry about formulas, the SAT is there to test your logic, your math skills generally but it's not there to test your knowledge of formulas so for instance here are two formulas that might look familiar, I hope they do and it might be the case that you could use them but it will never be the case that you have to use them and the formulas that are used on the SAT are pretty straight forward and they'll be given to you at the front of the section. So for instance Pythagorean Theorem you probably know but it's also given to you, area of a circle you probably know but it's also given to you; that will be at the very start of every math section. That said, even though the formulas are given to you, you might want to consider studying them anyway, that way you can move faster through the test and spend time problem solving instead of trying to remember or look up formulas from the front of the test.
Another thing besides formulas you don't have to worry about is symbols; a lot of people see things like these and they freak out. So you might see on the SAT something that looks like let a... let's call it box, 'let a box b be defined as blah, blah, blah.' Very simple, you just need to know that if you seen an unfamiliar symbol chances are it's made up. A lot of people immediately shut down figuring, "Oh my God, I didn't learn that, I don't know how to do it, I better not even try" but in fact you just are being tested on your ability to follow instructions so whatever definition they give you for the symbol, follow those instructions and you'll be fine.
Here's an example, let me show you what I mean; the problem says 'let X box Y be defined for all X and Y as X squared minus Y, what is the value of 3 box 2?' Now, when they say let X box Y be defined for all X and Y as X squared minus Y what they're really saying is that X box Y equals, is defined as means equals X squared minus Y so that's basically a formula they're giving us and we just have to plug in. So if they're saying, "hey what's 3 box 2?" you say "well, 3 box 2 is, well follow the formula," the first guy squared minus the second guy is the formula so we're going to do the first guy squared minus the second guy. So 3 squared minus 2 is 9 minus 2 and that's seven and just by following the directions we got the answer. It's actually quite simple once we get over the hump of being freaked out by an unfamiliar symbol.
Next up you should know how to tackle the 'always', 'never' and 'must' problems. When you see an 'always', 'never' or 'must' problem, you shouldn't respond by looking for an example that does work rather you should look for any counter example you can find and when you're looking for the counter example, you want to try a variety of numbers; zero, negative numbers, positive numbers, large numbers and small numbers. If you want to find the counter example, you're often going to have to try 'unexpected numbers' so trying two and then three and then four might not provide a counter example but one half might or a zero might or negative five might so experiment and then if you find a counter example then you should eliminate that answer choice. These rules apply to 'always', 'never' and 'must', when you see those words, look for a counter example and if you find one, eliminate the answer choice.
Now on the flip side we have this other type of question; 'could' and 'can', for those you have to follow different rules. You look for an example that does work and yet again you are going to use those funky numbers sometimes, try zeros, negatives and positives, large and small numbers and then if you do actually find an example that works instead of eliminating the answer, you're going to select that answer. So those are opposites of each other so keep an eye out. Let's see what this looks like on a sample SAT problem.
So here's a math question you might see on the SAT that relates to the last topic we talked about, the word must. Let's start by reading this problem over and I'm talking about how must is relevant here. If X is an integer other than zero, which of the following must be true? Now remember with must we're not looking to prove an answer choice right by finding a single example that works, on the contrary we're looking for any counter example we can find and as soon as we can succeed in finding a counter example, we triumphantly eliminate that answer choice. Now the thing with 'must' is that you are again looking for a counter example and that sometimes means you have to choose funky numbers. Let me show you what happens if you choose a very normal number, you will not get very helpful results. Let's try the number X equals 2 and plug this in for A through E. Here we get 2 squared is 4, 4 is greater than 2, that's true. 2 cubed is 8, 8 is greater than 2, also true. 2 cubed is 8, 8 is greater than 2 squared which is 4, true. 2 is greater than negative 2, true and 2 squared is 4 is greater than negative 2 squared which is negative 4.
Okay that was really uninspiring, all the answer choices we came up with are true that's because we chose what you might call a normal number; we need to look for weirder numbers. Weirder numbers provide exceptions, exceptions or counter examples will let us eliminate the answer choices so here's one to try. How about negative 1 because negatives are some numbers that can often break rules that are generally true by providing examples when they are not always true, let's see what negative 1 looks like. Negative 1 squared is 1, 1 is greater than negative 1 that's true, negative 1 cubed is negative 1 is greater than negative 1 close but not true, now see negative 1 cubed that's negative 1 is greater than negative 1 squared that's one; not true, D negative 1 is greater than negative negative 1 that's one.
Now I want to point out a lot of people look at D they see the negatives and assume that this value's negative, that's actually not necessarily the case, the negative means switch the sign so in the case of negative 1, when we plug it in, this negative actually makes it positive so keep that in mind. So this is false and the last example negative 1 squared that's 1 is greater than negative negative 1 squared which is negative 1, alright that's also true. So we've made some progress, we're down to A and E which are both right. At this point we want to find a counter example that actually proves one of these wrong but not the other because one of them is always going to be true, it must be true. Let's try 1; A is going to be 1 squared is 1 is greater than 1 and that's not true because they're equal but let's check E make sure it still stays true, 1 squared is 1 is greater than negative 1 squared, so this is true in all three cases so that makes E the right answer. So remember must means look for counter examples, if you find a counter example, cross the answer choice out. Now let's recap everything we've covered in this episode.
So in this episode to recap we've gone over some quick tips and they may not be strategies you need to have explained to a great length or math that you've learned in school but just things you need to know about how the SAT math section works and things to keep in mind as you're testing. So they are first of all read carefully, one of the most common ways to lose points is by answering the question wrong or slightly misunderstanding it especially because the language of the SAT is really complicated needlessly so, some might say. Use your calculator wisely, remember that the SAT doesn't technically require a calculator so if you're doing something really involved and elaborate you might be over thinking it and maybe you should step back and think through the problem a little more.
Use all the information given, it's super rare that you'll be given a problem in the math section of the SAT that doesn't require to use every single piece of information in the problem and don't worry about the formulas, the big fancy ones won't come up and the easier ones you'll either have memorized or be able to look up at the beginning of the section. Similarly don't worry about crazy symbols that seem unfamiliar. Whenever you see a symbol that's unfamiliar, chances are really really good it's just an operation, it's just some instructions that are being defined for you and if you follow the instruction as they're laid out you'll be fine. And then the last two; tackle always, never and must problems appropriately. When you see always, never and must try to find counter examples, whenever you find a counter example, cross out the answer choice you found a counter example too. Meanwhile with 'could' and 'can' you just have to find a single example that works, whenever you do find that example, you've also found the answer choice that's the right answer.
So those are some quick tips to keep in mind as you go through the math section of the SAT.