SAT Math · 35% of section

Advanced MathSAT Math Prep

Master Advanced Math with 337+ adaptive practice questions. This domain makes up 35% of the SAT Math section (13–15 questions on test day).

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Skills Covered

Equivalent ExpressionsRewriting algebraic expressions — factoring, expanding, combining rational expressions, and applying exponent rules to show two forms are equivalent.Nonlinear Equations & SystemsSolving quadratic, radical, rational, and exponential equations, plus systems that mix a line with a curve — including discriminant reasoning.Nonlinear FunctionsQuadratic, exponential, and polynomial functions: vertex form, growth and decay, end behavior, and interpreting key features in context.Function NotationEvaluating and composing functions written as f(x), interpreting what f(a) = b means, and translating between notation, tables, and graphs.

At a Glance

337+

Questions

35%

of Math

13–15

Qs on test day

Difficulty levels

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Study Strategies for Advanced Math

Factor before you expand

Many Advanced Math questions involve quadratics or higher-degree polynomials. Resist the urge to expand everything—instead, look for factoring opportunities first. Factoring reveals roots, simplifies expressions, and often leads directly to the answer. Practice recognizing difference of squares, perfect square trinomials, and sum/difference of cubes so these patterns become automatic.

Know your function transformations

The SAT tests function notation and transformations heavily. Memorize how f(x − h) shifts right by h, f(x) + k shifts up by k, and −f(x) reflects over the x-axis. When a question describes a transformation in words, translate it into the algebraic form immediately. These questions are fast points once the rules are internalized.

Connect equivalent expressions to context

Equivalent expression questions often ask which form of an equation reveals a specific property (vertex, roots, y-intercept). Learn which form shows what: standard form reveals the y-intercept, vertex form reveals the maximum/minimum, and factored form reveals the zeros. Recognizing this connection lets you answer without any calculation.

Practice nonlinear systems

The Digital SAT includes questions where a line intersects a parabola or circle. Set the two equations equal and solve the resulting quadratic. The discriminant (b² − 4ac) tells you how many intersection points exist: positive means two, zero means one (tangent), negative means none. This single technique covers multiple question types.

Common Mistakes to Avoid

Forgetting to check for extraneous solutions

When you square both sides of an equation or work with rational expressions, you may introduce solutions that do not satisfy the original equation. Always plug your answers back in to verify.

Mixing up vertex form and standard form

Students often confuse which form reveals the vertex versus the y-intercept. Vertex form is a(x − h)² + k (vertex at (h, k)); standard form is ax² + bx + c (y-intercept at c).

Errors with negative exponents and fractional exponents

Remember that x⁻² = 1/x² and x^(1/2) = √x. Many students misapply these rules, especially when combined. Practice converting between radical and exponential notation until it is automatic.

Ignoring domain restrictions

Rational and radical expressions have domain restrictions (denominators cannot be zero, radicands must be non-negative). The SAT tests these restrictions directly. Always check what values of x are excluded.

Frequently Asked Questions

What topics fall under Advanced Math on the Digital SAT?+

Advanced Math covers nonlinear equations (quadratics, exponentials, and other polynomial equations), nonlinear functions and their graphs, equivalent expressions (factoring, expanding, simplifying), and function notation including transformations. This domain makes up about 35% of the Math section and tends to include the most difficult questions on the test.

How important is factoring for the Digital SAT?+

Factoring is one of the most important skills in the Advanced Math domain. You should be able to factor quadratic trinomials, recognize difference of squares and perfect square trinomials, and factor by grouping. Many questions that look complex become straightforward once you factor the expression. It is also essential for finding the zeros of quadratic functions and simplifying rational expressions.

What should I know about function notation?+

You should understand how to evaluate functions (find f(3)), compose functions (find f(g(x))), and interpret function notation in context (if f(t) represents height at time t, what does f(5) = 20 mean?). You also need to know how transformations affect the graph: horizontal shifts, vertical shifts, reflections, and stretches. These questions are very predictable once you learn the patterns.

Explore Other SAT Domains

Information and Ideas26%Craft and Structure28%Expression of Ideas20%Standard English Conventions26%Algebra35%Problem-Solving & Data Analysis15%Geometry and Trigonometry15%

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Advanced MathQuestion 1 of 1,804

If x² = 64, what is the value of x² + 10?

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