What Is on SAT Math? The Four Content Domains

The Digital SAT Math section tests four content domains defined by College Board: Algebra, Advanced Math, Problem-Solving and Data Analysis, and Geometry and Trigonometry. Algebra and Advanced Math each make up about 35% of the scored questions (13–15 each), and the other two about 15% each (5–7 each). Every skill you can be tested on sits inside one of those four domains, and College Board publishes the full list of domains and skills.

This guide goes through the domains one at a time, using College Board's own skill names, and answers three common questions: whether piecewise functions come up, which geometry is tested, and how percentages and ratios appear.

The Math section at a glance

Math is the second section of the Digital SAT, taken in the Bluebook app after Reading and Writing. It has 44 questions in two modules of 22, and each module is timed separately at 35 minutes, so the section lasts 70 minutes. In each module, 20 questions count towards your score and 2 are unscored pretest questions that look exactly like the rest.

• Adaptive by module. The first module gives everyone a broad mix of easy, medium and hard questions. How you do on it decides whether your second module is, on average, harder or easier.
• All four domains in every module. Questions from each domain appear in both modules, and within a module they run from easiest to hardest.
• Two answer formats. About 75% of the questions are four-option multiple choice. The rest are student-produced responses, where you type in your own answer.
• A calculator throughout. A graphing calculator is built into Bluebook for the whole section, and you may use your own approved calculator as well. A reference sheet of common formulas is available too.
• Questions in context. About 30% of Math questions are set in a science, social studies or real-world context, and College Board has made these word problems shorter on average than on the paper test.

The split matters when you plan. Algebra and Advanced Math together account for roughly 70% of the scored Math questions, so a gap there costs far more than a gap in circles or probability. College Board makes the same point about practice score reports: if your level is similar across several domains, work first on the ones that appear most often on the test.

Algebra: linear equations, functions and systems

Everything in Algebra is linear. College Board describes the domain as analysing, solving and creating linear equations and inequalities, and solving equations and systems of equations with more than one technique. Its detailed testing points break the five skills down like this:

• Linear equations in one variable: solving them, writing one from a situation, explaining what a constant or the solution means, and deciding when an equation has no solution, exactly one, or infinitely many.
• Linear functions: modelling a relationship, reading the meaning of the rate of change and the starting value in context, moving between a table, an equation and a graph, and writing the rule from two input–output pairs.
• Linear equations in two variables: constraints such as a budget spent on two items, the graph of Ax + By = C, and the equation of a line through two points, or through one point parallel or perpendicular to another line.
• Systems of two linear equations in two variables: solving them, modelling two conditions at once, and deciding when a system has no solution, one solution or infinitely many.
• Linear inequalities in one or two variables: modelling limits and deciding whether a point in the xy-plane belongs to the solution set.

The difficulty in Algebra is rarely the algebra itself. It is turning a paragraph into the right equation and knowing what a number means once you have it. A question may hand you a cost model and ask what the 15 in it represents, rather than asking you to solve for x.

Advanced Math: quadratics, exponentials and other nonlinear work

Advanced Math is the domain College Board describes as central to progressing to more advanced courses. It names the function families involved: absolute value, quadratic, exponential, polynomial, rational and radical. The four skills cover:

• Equivalent expressions: factorising (common factors, a difference of two squares, a trinomial as two binomials), adding, subtracting and multiplying polynomials, rewriting simple rational expressions, and rewriting rational exponents in radical form.
• Nonlinear equations in one variable: quadratics written in many different forms, linear absolute value equations, simple rational and radical equations, and polynomial equations already in factored form; also deciding whether a quadratic has no real solution, one or two.
• Systems of equations in two variables: a linear equation paired with a nonlinear one, solved algebraically or by linking the solutions to the points where the two graphs meet.
• Nonlinear functions: building quadratic and exponential models, interpreting intercepts and points on a graph in context, connecting tables, equations and graphs (including transformed graphs), and choosing the form of an expression that shows a particular feature, such as a minimum value.

Quadratics run through three of those four skills, which is why they feel so frequent. You may need factored form to read the zeros, vertex form to read a minimum or maximum, or the discriminant to count real solutions without solving at all. Exponential functions are the other big family: building exponential models and explaining what the initial value and the growth factor mean in context.

Are piecewise functions on the SAT?

College Board does not list piecewise functions among its Math skills, either on its Math section pages or in the detailed testing points of its assessment framework. The nonlinear families it does name are absolute value, quadratic, exponential, polynomial, rational and radical. The nearest relative you will meet is the absolute value function, whose graph is two straight pieces joined at a corner; reading |x − 3| as "the distance between x and 3" makes most absolute value questions straightforward. Put your time into the named families first.

Problem-Solving and Data Analysis: percentages, ratios and data

This is the quantitative-literacy domain: ratios, rates and proportional relationships, unit rates, and reading one- and two-variable data. It has seven skills, more than any other domain, yet only about 15% of the scored questions, so any single test samples just a few of them.

How percentages and ratios are tested

College Board's testing points are specific here. Percentage questions cover discounts, interest, taxes and tips, percentage increases and decreases, and the link between a percentage change and a growth factor: a 5% increase is multiplication by 1.05, and percentages of 100% or more are included. Ratio and rate questions cover proportional relationships, scale drawings, one-step and multistep unit conversions, and derived units such as kilowatt-hours or population per square kilometre. One idea from the list is worth learning outright: when two quantities are proportional and one changes by a scale factor, the other changes by the same factor.

The usual trap is the base of a percentage. If a price rises by 20% and then falls by 20%, it ends at 1.2 × 0.8 = 0.96 of the original, a 4% fall overall, because the second percentage is taken of a larger number.

Data, probability and statistical claims

• One-variable data: frequency tables, histograms, dot plots and box plots; mean, median and range; comparing distributions with different means or different standard deviations; and the effect of an outlier on the mean and the median.
• Two-variable data: scatterplots, fitting linear, quadratic and exponential models, making predictions from a model, and comparing linear with exponential growth.
• Probability and conditional probability: worked out from two-way tables, frequency displays, area models or a description of a situation.
• Inference from sample statistics and margin of error: estimating a population mean or proportion from a sample, and knowing that a larger sample generally gives a smaller margin of error.
• Evaluating statistical claims: results from a random sample extend only to the population it was drawn from, and a cause-and-effect conclusion needs an experiment with random assignment.

Geometry and Trigonometry: what is actually tested

Geometry and Trigonometry has four skills and about 15% of the scored questions. In detail:

• Area and volume: area, perimeter, surface area and volume of figures and of objects modelled by them, plus scale factors: multiplying every length by k multiplies areas by k² and volumes by k³.
• Lines, angles, and triangles: congruent and similar triangles, the angle sum of a triangle, vertically opposite angles, and the angles formed when a transversal crosses parallel lines.
• Right triangles and trigonometry: Pythagoras' theorem, special right triangles, sine, cosine and tangent, and the fact that the sine of an angle equals the cosine of its complement.
• Circles: radii, diameters, tangents, arc length and sector area; radians and the unit circle; and the equation of a circle, (x − h)² + (y − k)² = r², including completing the square to find its centre and radius.

Two things are worth knowing. The reference sheet supplies common formulas, so the skill being tested is picking the right one and applying it correctly, not reciting it. And circles are where geometry meets algebra: completing the square on a circle's equation is the same technique Advanced Math uses on quadratics, so practice in one domain pays off in the other.

What is not on SAT Math

The lists also tell you what to leave alone. No calculus appears in any domain. There is no separate no-calculator section either: the old paper SAT's no-calculator portion was replaced by a single Math section with a calculator allowed throughout. The trigonometry listed is right-triangle trigonometry, radians and trigonometric ratios on the unit circle, nothing beyond.

How to turn the domain list into a practice plan

1. Find your weakest domain with a full-length test. A domain-level report tells you more than a total score. Our full-length SAT practice tests use the two-module format and report accuracy by topic and skill along with the time spent on each question.
2. Weight the gaps by frequency. A weakness in Advanced Math (13–15 questions) deserves more of your week than one in Geometry and Trigonometry (5–7 questions), unless the geometry gap is quick to close.
3. Drill one skill at a time. The SAT question bank is organised by College Board's domains and skills, so you can pick, say, Nonlinear functions at hard difficulty and work through a set with a worked explanation for every answer. Its Math questions are almost all multiple choice, so get your practice at typing in your own answers from the full-length tests.
4. Retest in exam conditions. Sit the next full test in one go, with module timing, and compare the domain results with the last one. If you want a refresher on how the modules and timing fit together first, read our guide to the Digital SAT format, or see how our practice mirrors the test on the Digital SAT practice page.

Knowing exactly which skills each domain contains lets you stop revising "SAT Math" in general and start fixing named weaknesses, which is a much shorter list.

Frequently asked questions