Advanced Math is one of the four SAT Math domains and about 35% of the scored Math questions, roughly 14 of 40, tied with Algebra as the largest. It covers nonlinear math in three skills: equivalent expressions, nonlinear equations and systems, and nonlinear functions. That means quadratics, exponentials, polynomials, and rational, radical and absolute value equations.
Below are 12 free practice questions, four for each skill, including four student-produced response questions where you type the answer. Each comes with a worked solution. Finish the set to see which skill to study first, then use the guide for the formulas, Desmos moves and traps behind every question. Domain share and skills are from College Board, checked October 31, 2026.
Four questions for each Advanced Math skill. Check each answer to see why it's right. Aim for 19:05, real-test pace; the clock starts with your first answer.
College Board lists three skills in Advanced Math: equivalent expressions, nonlinear equations in one variable and systems of equations in two variables, and nonlinear functions. The domain covers "absolute value, quadratic, exponential, polynomial, rational, radical, and other nonlinear equations," and the connections between their equations and graphs.
| Skill | What you'll see | Key fact |
|---|---|---|
| Equivalent expressions | Expand, factor or simplify polynomials, rational expressions, radicals and exponents | Plugging in a number like x = 2 checks any choice |
| Nonlinear equations and systems | Solve quadratics, radical and absolute value equations; a line meeting a parabola; how many solutions | Discriminant b² − 4ac: positive = 2, zero = 1, negative = 0 real solutions |
| Nonlinear functions | Interpret exponential and quadratic models, vertex, zeros, graphs and transformations | In a(b)^t, a is the start and b is the factor per period |
About 14 of the 40 scored Math questions, roughly 35%, split across both Math modules. Each module has 22 questions in 35 minutes, including 2 unscored pretest questions, so you have about 95 seconds per question (College Board test structure).
| Domain | Share | About this many scored questions |
|---|---|---|
| Algebra | ≈35% | 14 |
| Advanced Math | ≈35% | 14 |
| Problem-Solving and Data Analysis | ≈15% | 6 |
| Geometry and Trigonometry | ≈15% | 6 |
Algebra and Advanced Math together are about 70% of the Math section, so they decide most of your Math score. The second module adapts to your first-module performance. The hardest Advanced Math questions are usually multi-step, such as systems with a parameter and functions defined by a graph or table. For the hardest versions, see the hardest SAT Math questions.
About ten facts cover nearly every Advanced Math question. Learn them well enough to use without thinking.
| Fact | Formula | Use it when |
|---|---|---|
| Difference of squares | a² − b² = (a + b)(a − b) | You see x² − 9 or 4x² − 25 (questions 2 and 3) |
| Perfect square | (a ± b)² = a² ± 2ab + b² | Expanding (x − 5)², or recognizing x² − 10x + 25 |
| Quadratic formula | x = (−b ± √(b² − 4ac)) / 2a | A quadratic won't factor nicely |
| Discriminant | b² − 4ac | "How many real solutions" (question 6) |
| Sum and product of roots | For x² + bx + c: sum = −b, product = c | Finding the other zero fast (question 11) |
| Vertex form | y = a(x − h)² + k, vertex (h, k) | Maximum or minimum value (question 10) |
| Factor and zero | If f(r) = 0, then (x − r) is a factor | Linking zeros, factors and x-intercepts |
| Exponent rules | xᵃ · xᵇ = xᵃ⁺ᵇ, (xᵃ)ᵇ = xᵃᵇ, x^(m/n) = ⁿ√(xᵐ) | Rewriting powers and radicals (question 4) |
| Exponential model | a(1 + r)^t growth, a(1 − r)^t decay | Percent change per period (question 9) |
| Repeated doubling | a(2)^(t/k) doubles every k units | "Doubles every 3 hours" (question 12) |
Expand or factor carefully, and when the algebra is long, plug a simple number into the original and into each choice. The choices that give a different value are out.
Get everything to one side and factor, use the quadratic formula, or graph both sides in Desmos. Then check your answers in the original equation and make sure you answer the value asked for.
Know what each number in a function's form means: in a(b)^t, a is the start and b the factor per period; in a(x − h)² + k, the vertex is (h, k); and each zero r gives a factor (x − r). Most function questions are interpretation, not calculation.
Desmos is built into the Bluebook app for every Math question, and graphing is often faster than algebra for equations and systems (College Board calculator policy, checked October 31, 2026). Useful moves:
y = √(x + 7) and y = x − 5, and tap the intersection. Only real solutions show, so extraneous answers disappear on their own.y = x² + bx + 12, add the slider for b, and move it until the graph passes through the given point.Our SAT Desmos calculator guide has step-by-step examples with practice questions. Algebra is still faster for questions like 3 and 4, where there's nothing to graph.
Most Advanced Math misses come from five traps, and every one of them is a listed answer choice.
| Trap | Example | Fix |
|---|---|---|
| Answering the wrong value | Giving x when the question asks for y (question 7), or the vertex's x when it asks for the maximum (question 10) | Underline what's asked before solving |
| Extraneous solutions | Keeping x = 2 in √(x + 7) = x − 5 (question 8) | Plug every answer back into the original |
| Kept vs. lost | Reading 0.85 as an 85% decrease (question 9) | 1 − b is the decay rate; b − 1 is the growth rate |
| Dropped terms and signs | (2x + 3)(x − 4) = 2x² − 12 (question 1) | Write all four products, or plug in a number |
| Wrong exponent rule | x^(1/2) · x^(1/3) = x^(1/6) (question 4) | Multiply powers: add exponents |
Two weeks of 30 minutes a day, one skill at a time, fixes most Advanced Math gaps, because the domain repeats a small set of patterns. Start with the weakest skill from your drill result.
| Days | Focus | What to do |
|---|---|---|
| 1–2 | Formulas | Copy the formula table from memory each day until you can write it in 3 minutes. |
| 3–5 | Equivalent expressions | 15 questions a day: expanding, factoring, exponent rules. Check each with a plugged-in number. |
| 6–8 | Nonlinear equations and systems | 15 questions a day. Solve each by algebra, then confirm in Desmos. |
| 9–11 | Nonlinear functions | 15 questions a day on exponential models, vertex form and zeros. Say what each number means. |
| 12–13 | Timed mixed sets | 14 Advanced Math questions in about 22 minutes, the share of a real section at real pace. |
| 14 | Full section | Take a full Math section in a practice test and compare your domain results. |
For more questions across all four Math domains, use our SAT Math practice or the mixed 16-question set on SAT practice questions. When you're ready for a score, take a free full-length digital SAT practice test. If you've already taken the SAT, the Knowledge and Skills section of your score report shows your Advanced Math performance; how to read your SAT score report explains it.
Checked October 31, 2026:
The practice questions on this page are written by Test Ninjas in the style of the digital SAT. They aren't official SAT questions; for those, use the practice tests in College Board's Bluebook app.