One of the biggest mistakes students make in preparing for the SAT is that they treat the math section like just another school math test, like an Algebra II final with some Geometry mixed in and just a dash of Pre-calc and Stats. It’s a natural approach — for most students, that’s the only kind of math test they’ve ever taken. But whereas school math is focused on content mastery, the SAT math is focused on problem solving, and understanding what that means can make or break a student’s score.
Taking control of the problem-solving process
School math often trains students to approach questions robotically. Students complete entire worksheets on the basis of a single word of instruction — factor, solve, simplify — without being asked to spend time thinking about when or why to use the technique they’re engraving into their muscle memory.
When these students get to the SAT math, they tend to find themselves stumped. The problems aren’t simple enough that they can just react immediately to the kind of equation or shape that’s given, and even when they can, many questions have a final twist in their ask that students forget by the time they’re finished solving.
On the SAT math, it’s imperative that students build in designated periods for problem solving both before and after “doing the math.” Students should plan to take at least two reads of every question: one to get the gist, and then a second where they think about what information is being given (including the answer choices), what’s being asked for, and how best to solve. And after solving, students should reread the question sentence to make sure they haven’t been hoodwinked by a tricky ask.
Hacking multiple-choice questions
Unlike school math tests, which are generally free response, the SAT math is composed primarily of multiple-choice questions. Many students approach multiple-choice questions like free-response questions with an extra step at the end, and while that’s not necessarily wrong, it is missing an opportunity to make difficult problems significantly more concrete by either plugging in the answers or making examples.
Plugging in the answers — or “plug and chug” — is intuitive for most students. If a question is asking for the value of something, its often easier to try each answer choice one-by-one than it is to solve. And even if the answer choices can’t be plugged in directly, like in longer word problems, using a concrete number instead of a variable can still make things much more manageable.
The second way students can use multiple-choice answers is by making examples on problems where the answer choices are all variable expressions. For instance, if a problem asks you which of four factored polynomials is equivalent to an expanded polynomial, students can pick a value for x and plug it into both the expanded polynomial and the answer choices. Whichever answer choice gives the same output as the expanded polynomial has to be correct — after all, if something’s true for x generally, it will also be true for any specific value of x.
Maximizing the built-in graphing calculator
With the SAT’s move to a digital format, students have access to an adapted version of Desmos’s graphing calculator for the entire math section. This is a significant upgrade from the TI-83s and 84s students may be used to using in class. On handheld graphing calculators, the process for solving equations via graphs is often too finnicky to be worth the effort. On the SAT’s built-in graphing calculator, on the other hand, solving equations is as simple as typing in both sides of the equation on separate lines and then zooming out until the intersection is visible.
Anytime a question involves some kind of function, it’s generally a good idea to start off by graphing it. Even if a student feels confident about doing a question the “normal” way, it’s often significantly faster and more straightforward to identify things like x-intercepts, maxes, and mins via a graph.
Students should also make it a point to practice with the built-in calculator. For practice tests they take on Bluebook, College Board’s official app for taking the SAT, the calculator will be right there. But for third-party tests or isolated problems, students should have Desmos pulled up on either a laptop or via the Desmos app on a phone or tablet.
In summary, here are three problem-solving strategies for the SAT math:
- Make it a habit to take two passes through each question before deciding how to solve, then make sure you’ve answered the question before finalizing an answer
- Use the answers to make abstract problems more concrete
- Consider using the built-in graphing calculator for any question that involves an equation
