SAT Math Topics: Every Skill on the Digital SAT

SAT math topics fall into four domains: Algebra (13–15 questions), Advanced Math (13–15), Problem-Solving and Data Analysis (5–7), and Geometry and Trigonometry (5–7), for 44 questions total. Algebra and Advanced Math together make up most of the section, so linear equations, systems, functions, quadratics, and exponentials deserve the bulk of your study time. Below is every skill College Board lists, what each looks like on the test, and which formulas you need to know because they are not on the reference sheet.

SAT math topics at a glance

The Math section has two 35-minute modules of 22 questions each. Questions from all four domains appear in each module, generally arranged from easiest to hardest, and a calculator is allowed throughout.

Algebra: the largest share of points

Algebra questions are about linear relationships. Expect both pure equations and word problems where you must build or interpret a linear model.

What to master:

• Solving linear equations, including ones with fractions and variables on both sides.
• Slope-intercept form (y = mx + b), point-slope form, and standard form (Ax + By = C).
• Interpreting slope and y-intercept in context. If a phone plan costs C = 15m + 40, then 15 is the cost per month and 40 is the starting fee.
• Systems of two linear equations: solving by substitution, elimination, or graphing, and knowing when a system has no solution (parallel lines) or infinitely many (the same line).
• Linear inequalities, including which points satisfy a system of inequalities.

Example. If 3(x − 2) = 2x + 5, what is x? Distribute to get 3x − 6 = 2x + 5, so x = 11.

Advanced Math: functions, quadratics, and exponentials

Advanced Math is where many high-scoring students gain or lose their last points.

What to master:

• Quadratics in standard form (ax² + bx + c), vertex form (a(x − h)² + k), and factored form (a(x − r)(x − s)), and what each form reveals: the vertex, the zeros, the y-intercept.
• The discriminant b² − 4ac: positive means two real solutions, zero means one, negative means none.
• Exponential functions (y = a·bˣ): growth when b > 1, decay when 0 < b < 1, and translating "increases by 6% per year" into b = 1.06.
• Function notation and composition, such as finding f(g(2)).
• Equivalent expressions: factoring, expanding, combining rational expressions, and rewriting exponents and radicals.
• Nonlinear systems, such as a line and a parabola, including how many intersection points exist.

Example. The function f(x) = (x − 4)² + 7 has its minimum at what point? Vertex form shows the vertex directly: (4, 7), so the minimum value is 7.

Problem-Solving and Data Analysis

These questions reward careful reading more than advanced math.

What to master:

• Ratios, rates, and unit conversions, such as converting miles per hour to feet per second.
• Percentages, including percent increase and decrease. A price that rises 20% and then falls 20% ends at 96% of the original, not 100%.
• One-variable data: mean, median, range, and standard deviation as a measure of spread. Know how adding an outlier affects mean versus median.
• Two-variable data: scatterplots, lines of best fit, and interpreting the slope of a model.
• Probability and conditional probability, often from a two-way table. Read the denominator carefully: "of the students who chose biology" restricts the group.
• Margin of error and inference: a sample estimate with a margin of error gives a plausible range for the population value.
• Evaluating statistical claims: random sampling allows generalizing to a population; random assignment allows cause-and-effect conclusions.

Geometry and Trigonometry

What to master:

• Area and volume of common shapes (most formulas are on the reference sheet).
• Lines and angles: vertical angles, angles formed by parallel lines and a transversal, and the triangle angle sum.
• Similar triangles: corresponding sides are proportional.
• Right triangles: the Pythagorean theorem, 30-60-90 and 45-45-90 triangles, and SOH CAH TOA.
• Trigonometry: the relationship sin x = cos(90° − x), and radian measure and the unit circle.
• Circles: arc length, sector area, central and inscribed angles, and the equation of a circle, (x − h)² + (y − k)² = r², including completing the square to find the center and radius.

Example. A circle has equation x² + y² − 6x + 4y − 12 = 0. What is its radius? Complete the square: (x − 3)² + (y + 2)² = 12 + 9 + 4 = 25, so the radius is 5.

Formulas on the reference sheet (and those that are not)

The reference sheet in Bluebook gives you area formulas (circle, rectangle, triangle), circumference, the Pythagorean theorem, special right triangle ratios, volumes of a rectangular prism, cylinder, sphere, cone, and pyramid, the number of degrees and radians in a circle, and the sum of a triangle's angles.

You must memorize these, which are not on the sheet:

How to prioritize your SAT math study

1. Start with Algebra. It is the largest domain and the foundation for everything else.
2. Move to Advanced Math, especially quadratics and exponentials, which dominate the hardest questions.
3. Treat data questions as reading questions. Most misses come from misreading the table or the question.
4. Learn the small set of geometry facts above; the domain is only 5–7 questions, but those points are very learnable.
5. Learn Desmos for systems, quadratics, and regressions; our Desmos SAT guide shows how.

Use the official SAT Suite Question Bank to filter practice by domain, skill, and difficulty, and log every miss by skill. For the full test structure, see the Digital SAT format explained, and for a week-by-week plan, see how to improve your SAT score by 200 points.

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