On a timed exam like the SAT, when you have barely a minute to solve each math question, there’s nothing worse than getting bogged down in a problem. We’ve all been there: the small square of space in the test booklet becoming crammed with writing, the pile of eraser shavings growing, the clock ticking, and…wait, what was the question even asking again?
I used to dread those moments on the SAT because once I got bogged down in a problem, it was difficult for me to dig myself out—I’d keep frantically writing and re-writing calculations in the hopes that, if I did enough math, I’d get to the right answer.
But doing too much math usually made me lose sight of the original question. It also was a massive waste of time. The tight timing on the SAT math section is indicative: the questions are supposed to be solvable in under two minutes, and the hard questions at the end of each section aren’t necessarily supposed to take longer than the easy ones do.
The key to acing the SAT math sections is to work smarter, not harder. See, SAT math problems are conceptual—the test writers are less interested in your ability to do arithmetic and more interested in how you identify and apply concepts from the math curriculum. This means that what makes a question “easy” or “hard” isn’t the amount of time it takes to complete, or the number of calculations you need to write. It’s all about how advanced the concepts are.
To use a metaphor: every SAT math problem is like door with a conceptual “key” to unlock it, and the hard problems just have fancier keys.
So how do we find the right key, and avoid taking a sledgehammer to the door?
Here are three tips that helped me think like a test writer:
Don’t jump in—take a step back.
It may sound counterintuitive, but rushing into a problem is the easiest way to waste time by missing the forest for the trees. Before you start writing, read and re-read the problem so you know for sure what it’s asking.
What do you know? What do you need to know?
Asking these two questions will guide your setup for the problem and allow you to identify the most relevant information, ignoring any unnecessary bits that the test writers may have thrown in as a distraction.
Identify the conceptual key.
Based on what you’ve read, can you name one or more concepts that the test writers are trying to get at with this problem? Make sure to apply these concepts in your setup.
Once you’ve done these three things, then you can start doing the math.
Let’s try out this approach on a sample problem.
Take a look at the following question:
f(x) = cx2 + 30
For the function f defined above, c is a constant and f(3) = 12. What is the value of f(-3)?A. -12
In this question, we know that f is a function, and that f(3) = 12. We need to know f(-3).
You could solve this problem by plugging (3, 12) into the equation, solving 12 = cx2 + 30 for c, and then plugging -3 back into f(x).
But that’s a lot of math. Is there a quicker conceptual key to this problem? Notice that f(x) is a quadratic function, meaning x is squared. When you square a number, it’s always positive, which means that 3 squared and -3 squared yield the same result: 9.
So, without having to do any math, you can read this problem and know that f(-3) = f(3) = 12.
Notice that when we answered the question, what do we need to know? c wasn’t on the list. Even though c was included in the question as an unknown, solving for c wasn’t necessary to answer the problem. This is the sort of thing that’s easy to miss if you rush into a problem too quickly and assume that you need to solve for every mystery number, attacking the door with a sledgehammer. The conceptual key—recognizing the properties of a quadratic function—is much quicker.
Taking this approach to the SAT math sections helped me realize that if I was filling my test booklet with frantic, messy calculations, I was probably thinking about the problem wrong. In math, elegance and correctness often go hand in hand, and the SAT is no exception.