SAT Math Study Guide

The math you need is mostly first- and second-year algebra plus a slice of geometry and data. The section leans on a few skills you will use over and over: solving linear equations and systems, manipulating quadratics and exponentials, interpreting tables, graphs, and percentages, and applying basic geometry and right-triangle trigonometry.

A calculator (built into the testing app, or your own) is allowed on every question, and a reference sheet with common formulas is always on screen — so the exam is not testing whether you memorized the area of a circle. It is testing whether you can set up the right equation from a sentence, keep your arithmetic honest, and recognize which tool fits. Many problems are word problems: the hard part is translating English into math, not the calculation that follows. Some questions are multiple choice; others are "student-produced response" where you type the answer yourself, so you cannot back-solve from options.

The College Board groups the questions into four content areas with roughly these shares of the section:

• Algebra — ~35%
• Advanced Math — ~35%
• Problem-Solving and Data Analysis — ~15%
• Geometry and Trigonometry — ~15%

The headline is that Algebra and Advanced Math together are about 70% of your score. Algebra is linear thinking — equations, inequalities, and systems. Advanced Math is the nonlinear cousin: quadratics, polynomials, exponential models, and working with functions. If your time is limited, pour it here first. Problem-Solving and Data Analysis (ratios, percentages, units, reading charts) and Geometry and Trigonometry (angles, area, volume, the Pythagorean theorem, basic trig) are smaller but high-value because the questions are often quick once you know the setup.

SAT Math is a setup exam, not a recall exam. A routine that works:

1. Master linear algebra cold. Solving and interpreting $y=mx+b$, systems, and inequalities is the backbone of a third of the test and shows up disguised inside other questions. Slope as a rate of change is one of the most reused ideas on the exam.
2. Translate words to equations on paper. Before touching the calculator, write what each quantity is and what the question actually asks. Most missed points are setup errors, not arithmetic errors.
3. Use the calculator deliberately. The built-in graphing tool can solve equations and find intersections instantly — but typing a misread expression fast just gets you a wrong answer faster. Know when graphing beats algebra.
4. Practice for the adaptive front-loading. Because the first module steers the second, drill the easy and medium questions until they are automatic. Banking those early points unlocks the harder, higher-ceiling second module.
5. Review with full solutions. Reading why you missed a problem — and why a tempting wrong answer was wrong — is worth more than three new problems you already know how to do.

• Answering a different question than the one asked — solving for $x$ when the question wants $x+3$, or finding the part when it wants the whole.
• Mishandling percent change, especially successive increases/decreases, where percentages do not simply add.
• Sign and distribution slips when expanding or moving terms across an equals sign.
• Trusting the calculator over the setup — a fast computation of the wrong expression is still wrong.
• Guessing blind on student-produced response questions instead of estimating, since there are no choices to eliminate — and forgetting that there is no penalty for a wrong answer, so every blank should at least get a guess.
• Spending too long on one hard question early and running short on quick points you could have banked.

Every content area below has a focused practice set with full written explanations and a rationale for every wrong choice, plus a worked-solutions page you can read straight through. Start with Algebra or Advanced Math since they carry the most weight, then take a mixed set across the whole section to rehearse picking the right tool under time pressure. It is free and needs no account.