Study guides
SAT Math study guides
The digital SAT Math section has 44 questions in two 35-minute modules, across four domains: Algebra, Advanced Math, Problem-Solving and Data Analysis, and Geometry and Trigonometry. Each guide below covers one skill: a plain explanation, worked examples from easy to SAT-hard, the mistakes that cost points, honest shortcuts (including Desmos), and five original practice questions. Start at the top and work down, or jump to the skill you keep missing.
Updated
- 1Linear equations in one variable on the SATHow to solve linear equations in one variable on the SAT, plus no solution and infinitely many solutions questions. Worked examples and 5 practice questions.
- 2Linear functions and slope on the SATFind and interpret slope and intercepts on the SAT from points, tables, graphs and word problems. Worked examples, common traps and 5 practice questions.
- 3Systems of linear equations on the SATSolve SAT systems of linear equations by substitution, elimination or Desmos, and spot no solution and infinitely many solutions fast. 5 practice questions.
- 4Linear inequalities on the SATSolve linear inequalities, turn word problems into inequalities, and check points in systems of inequalities on the SAT. Worked examples, 5 practice questions.
- 5Percentages on the SATSolve SAT percent questions with multipliers: percent of, percent change, discounts and tax, reverse percents and repeated changes. Examples and practice.
- 6Ratios, rates, proportions and units on the SATSolve SAT ratio, rate, proportion and unit conversion questions by tracking units, including the area conversion trap. Examples and 5 practice questions.
- 7Equivalent expressions on the SATRewrite SAT expressions by distributing, factoring, using exponent rules and adding fractions, then match coefficients. Examples and 5 questions.
- 8Functions and function notation on the SATEvaluate f(x), read functions from graphs and tables, compose f(g(x)) and shift graphs on the SAT. Worked examples, common traps and 5 practice questions.
- 9Quadratics on the SATSolve SAT quadratics by factoring or the quadratic formula, find the vertex, and count real solutions with the discriminant. Examples and 5 practice questions.
- 10Exponential growth and decay on the SATWrite and read SAT exponential growth and decay models: growth factor, percent rate, doubling time and changing the time unit. Examples and 5 questions.
- 11Nonlinear equations and systems on the SATSolve SAT radical, absolute value and rational equations, and line plus parabola systems, without falling for extraneous solutions. Examples and 5 questions.
- 12Mean, median and spread on the SATFind mean, median and range on the SAT, compare standard deviations, use the total trick, and see how outliers move each measure. Examples and 5 questions.
- 13Probability and two-way tables on the SATAnswer SAT probability questions with two-way tables: find the right total, handle "given that" conditional probability, and combine events. With practice.
- 14Scatterplots, margin of error and study design on the SATRead lines of best fit and residuals, use margin of error, and judge what a sample or experiment can prove on the SAT. Worked examples and 5 practice questions.
- 15Lines, angles and triangles on the SATThe angle and triangle facts the SAT uses again and again: parallel lines, triangle sums, isosceles and similar triangles. Examples and 5 practice questions.
- 16Area and volume on the SATUse the SAT reference sheet for area and volume, work backward to a missing length, and scale shapes correctly. Worked examples and 5 practice questions.
- 17Right triangles and trigonometry on the SATRight triangle trig for the SAT: SOHCAHTOA, special right triangles, sin x = cos(90 - x) and radians. Worked examples, common traps and 5 practice questions.
- 18Circles on the SATSolve SAT circle questions: read the circle equation, complete the square to find center and radius, and find arc length and sector area in degrees or radians.
- 19How to use Desmos on the SATHow to use the built-in Desmos calculator on the digital SAT: systems, parabolas, regressions, statistics and equivalence checks, and when it is slower.
- 20The hardest SAT math question types, and how to beat themThe question types that make SAT math hard: hidden constants, no-solution systems, discriminants, circles, percent chains and tangent lines, with practice.
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