SAT Topics: Math

The second half of the SAT consists of a pair of modules on mathematics, 35 minutes each. The content ranges widely over algebra and geometry, and unlike the Reading & Writing modules, there is no regular order to the problems. The College Board groups all of their math problems into four major categories, as they do for the Reading & Writing, but the different problem types could occur in any order.

Topics NOT Covered on the SAT — The SAT contains problems involving exponential functions and basic trigonometric ratios, but those are the most advanced topics. There are no logarithms on the SAT, and there are no problems involving vectors or matrices. There are also no imaginary numbers on the SAT. Whenever you are asked about solutions to quadratic equations, they will always be real solutions. There are rare problems involving polynomials or rational functions, but there are usually tricks to make them simpler. You might occasionally need to solve a polynomial equation, but it will be given in factored form, so the zeros are easy to see. You might rarely need to solve a rational equation, but you can always do so by multiplying both sides of the equation by the denominator of the rational function, thus turning the rational equation into a linear or quadratic equation. There is some trigonometry on the SAT, but it deals mostly with basic ratios, i.e. SOHCAHTOA. There are no reciprocal trigonometric functions, no inverse trigonometric functions, and there are no problems involving the law of sines or the law of cosines. Questions involving the equation of a circle in the coordinate plane are not uncommon, but there are never any questions involving ellipses or hyperbolas (which is a shame, because conic sections are fascinating). So, to summarize, you do not need to worry about...

Major Categories or Domains

Algebra — This covers all algebra topics that don't involve squares, roots, or transcendental functions. In other words, it covers linear algebra. Slopes, intercepts, and interpretation problems are common, as well as solving simple equations. Systems of linear equations also fall into this category. Many of the problems in this category can be solved quickly and easily using Desmos.

Advanced Math — Advanced Math could mean almost anything. In this case, it means nonlinear algebra. Here you'll find questions involving quadratic functions and equations, exponential functions, radicals, and fractional exponents.

Problem Solving and Data Analysis — About half of this category is composed of problems that involve basic arithmetic (solving proportion problems, converting units, dealing with percents), and the rest all have to do with statistics or probability.

Geometry and Trigonometry — Unsuprisingly, this category contains problems involving geometry and trigonometry. Area and volume formulas, solving proportion problems with similar figures, and deducing unknown angles are all common. There are also problems involving the Pythagorean Theorem and the equation of a circle in the coordinate plane. This is also naturally where the basic trig ratio problems occur.

General Strategies

Use Desmos! — With many of the easy questions, even if you know how to do them with pencil and paper, they are long and tedious and have many steps, and every step is another opportunity for you to make a mistake. Desmos is a great way to save time and mental energy. Use Desmos to automate all of your basic, tedious calculations and equation-solving.

Look for Simple Tests to Rule Out Wrong Answers — With many problems, you don't need to go to the trouble of calculating the exact answer, because you can rule out all of the wrong answers with simple tests. Sign checks are a great place to start. Do you need a negative number or a positive number? Do you need a big number or a small number? Should the inequality be pointing to the left or the right? If the answer choices are numbers that are not close together, you can often just estimate the answer, and rule out the choices that aren't in the ballpark.

Allow Yourself Throw-Away Problems — Near the end of the math modules there will probably be a few messy, tangled, obnoxiously twisted problems. These are the weird, unfamiliar, backwards, tangled, painful problems that make you want to pull your hair out. Sometimes they aren't as bad as they seem once you start thinking about them. Sometimes there is a shortcut or a trick, if you can recognize it. But often, they are as bad as they seem. Even if you can solve them, they will probably take a long time, and there will be many opportunities for making mistakes along the way. Depending on your desires and your skill levels, you may want to just ignore these problems. Take the time that you save and use it to proofread your other work. This can work especially well if you are the sort of person who makes lots of simple calculation errors or who is susceptible to hasty oversights. Even with simple problems, it can be easy to overlook important pieces of information or make hasty mistakes. So if you lose a point or two because you guessed on the extremely risky and time-consuming problems, but you catch three or four hasty mistakes on the simpler problems, you're still ahead a couple of points. So allowing yourself a couple of "throw-away" problems can actually be part of a healthy strategy.

Take it One Step at a Time. — If you do want to attempt the weird, obnoxious problems, you might not have any idea how to go from what you are given to what they ask for. The route you need to take might be long and twisted. But it's often not as bad as you fear if you take it one step at a time. Just look for anything remarkable or noteworthy in the problem setup. Ask yourself, what's something easy and straightforward I can do with what I'm given?. Then after you have a new piece of information, repeat the question and take another step. Often after jumping around a little, you'll discover that you've arrived at the answer.