 03 Mar 2014

## 5 Basic SAT Math Skills You Must Master To Do Well

The SAT Math Section does encompass quite a variety of questions. But here’s the dirty truth – none of the math is actually harder than 9th grade math. You’re never going to do matrixes or derivations. Most problems will involve adding, subtracting, multiplying and just dividing. Heck, you’ll hardly ever even need the Pythagorean Theorem. Yet what the SAT lacks in “stature,” it makes up for in cojones! That’s “balls” for you non-Spanish speakers out there. In short, the SAT math is a tricky S.O.B. So if you want to do well, there’s a basic set of skills you have to master that will be applicable to almost all the math questions.
1) Number The Variables! Above is a hard math problem from the end of a math section. Keep in mind that by the time you get to this question, you probably have about 1 min and 25 sec to solve it. Yes, you theoretically can solve it using algebra. But there’s a couple reasons why you shouldn’t. One, it is time consuming. Two, and more importantly, there is too much room for mistakes. The best way to solve this problem is to number the variable. Make x=3 and y=2 and then solve the problem (46620). THIS is the number you’re going to look for in the answer choices. Now let your calculator do the work and you should find that (C) is the only one that gives you 46620. This is the answer! So when you only have variables and no clue where to start, try putting in your own number.

A restaurant has 19 tables that can seat a total of 84 people. Some of the tables seat 4 people and the others seat 5 people. How many tables seat 5 people?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

Unlike math at school, the SAT is nice in that it gives you the answers (except for the grid-in part, but that’s a small part). So when you see a complicated problem and you’re stuck, try working backwards. The answers are already there, so use them as a starting point.

The problem above isn’t too complicated, but it illustrates this technique well . Traditionally, you can solve this using two equations: x+y = 19 and 4x+5y=84. Here, x represents the 4-person table and y the 5-person table. Solve for y and you solve the problem. But look, you don’t even need algebra. You have the answers there! If you start with (C) and say you have 6 5-person tables, that’s a total of 30 people so far. You now have 13 tables left that are 4-person tables, giving you a total of 52 for those tables. 52+30 = 82, which is not 84 so that can’t be the right answer. You can easily punch these numbers in your calculator and you’ll see that answer choice (E) is it, WITHOUT having to use algebra. Sometimes, using the answer and a common-sense approach can be much quicker on the SAT.
3) Be Smooth With Your Algebra! The problem from tip#2 could’ve been solved with algebra, but in my opinion, it was simpler just using the answers. However, there will be problems where there aren’t any tricks involved. In these cases, you just have to power through. And if you want a top score on the SAT Math section, you’ll have to be able to go through algebraic problems easily. The problem shown isn’t too hard. At first look, you should recognize that using algebra by itself might not help. Remember tip#1 and put it your own number (try 2). From there, cross multiply, solve for x and you would get 5. It doesn’t matter what number you picked for “a” (except you can’t pick 0). You’ll always get 5. The most important thing though is being able to execute this quickly and save time for other problems. There are quite a few geometry problems on the SAT. If you want to do well, you are going to have to know geometric rules. While there are geometry formulas at the beginning of every math section, if you find yourself referring to those, you have not internalize geometric rules enough to do well on the SAT. When faced with a problem like the above example, first draw a picture. You never just solve a geometry problem in your head. Second, label everything.

Here, we see that it is a cylinder with a height of 5 and a base diameter of 4. The hard part is understanding what they’re asking. To help with this, try drawing out the question. It asks for the distance from the center of the base to a point on the circumference of the other base. Yes, there are many options but just pick a point and draw it. I marked the center of the base at the bottom of the cylinder and then I connected it to the far right location at the top. What you now essentially have is a right triangle. The legs are 5 and 2, and it is the hypotenuse that you’re solving for. Now I know that I said in the intro that you will hardly ever use the Pythagorean Theorem and I still stand by that. Unfortunately, this is one of the few cases you do need it. Using Pythagorean (a^2+b^2=c^2), you find that the distance (5^2+2^2=29) is the square root of 29 (Answer C).
5) Functions Are All The Same! Math is universal. Despite what some crazy philosopher might tell you, 2+2 is equal to 4, no matter where you are. However, what is not universal is the way functions are defined. Somewhere along the line, we said that f(x) is our symbol for functions. You can think of f() as the function symbol and x as the variable symbol. All functions will have this. So f(x)=3x+2 tells you that you have to run a set of instructions for whatever number is at the “x” position. Thus, f(2) means that you multiply 2 by 3 and then add 2 to it. We all know this.

Now imagine if an alien arrived on Earth and told you their function for solving the space-time continuum problem is @[email protected]+2. You might go huh at first, but the idea is the same because math is universal! Just like before, there is a function symbol and a variable symbol. The variable symbol is the one that repeats in the equation, so here it is the @ sign. The function symbol is the \$ sign so you should be able to solve 2\$=? (@=2, so the answer is 8).

The above problem is harder than your average function problem, but the idea is the same. First, identify the function and variable symbol. Here, the function symbol is the upside down triangle while the variable symbol is just x. This can be redone as f(x) = x + 1/x. What it’s basically saying is if x is a nonzero integer AND the answer MUST be an integer, what is a possible answer? Like before, use the answers, Luke! Start off with (A). Is there a way to get 1? Well, the smallest positive integer you can use for x is 1. If you put that in, the answer is 2, which is not a possible answer. This might get your brain juice flowing. What if you pick -1? Then the problem becomes -1 + 1/-1 = -1 + (-1). The answer is -2, which just happens to be answer choice (D). Circle that one and move on!
Conclusion
These techniques alone will not be enough to get you a perfect score on the Math SAT section. However, they are the basic skills everyone needs to master to do well on the test. Have these skills down pat and you’ll be well on your way.

Writing math tips is not easy when you don’t explain with a white board. So if anyone is still confused, leave me a comment and I’ll try to clarify. Happy studying!