# SAT Advanced Math: quadratics, systems and nonlinear functions

Advanced Math is about 35% of the Digital SAT Math section, 13 to 15 questions. What equivalent expressions and nonlinear functions actually ask for, with three worked items and the traps around them.

## The short answer

Advanced Math matches Algebra as the largest Math domain, about 35% of the section and 13 to 15 of the 40 operational questions. It covers three things: equivalent expressions, nonlinear equations and systems, and nonlinear functions. Quadratics carry most of it, in factored form and in standard form. Exponential growth models and rational expressions belong here too, and so does anything with a variable in an exponent.

## Key facts

- **Section:** Math
- **Domain:** Advanced Math
- **Domain share:** ~=35% of the section, 13-15 questions
- **Question format:** Multiple choice and student-produced response
- **Skill points in this domain:** 3, all of them nonlinear
- **Math section:** 44 questions, 40 operational, 70 minutes

Question counts, timings and domain shares come from College Board's test pages and the Digital SAT Suite Specifications Overview, checked 28 September 2026.

## How it's scored

One mark per question, the same as every other Math item. Advanced Math and Algebra are each about 35% of the section, so between them they decide most of your Math score. The two domains split on one line: linear goes to Algebra, everything else comes here.

College Board names three skill and knowledge testing points in this domain:

- Equivalent expressions
- Nonlinear equations in one variable and systems of equations in two variables
- Nonlinear functions

Equivalent expressions is the quiet one. It asks you to rewrite rather than to solve, so the answer is another expression instead of a number.

> Factor first, then read the question again. A quadratic usually has two solutions, and the item often wants only one of them, or their sum, or the value of an expression built from them.

## Advanced Math examples

Worked examples written for this page. Answer each one before you open the model response: memorizing a response is scored as an irrelevant answer in the real test.

**Example 1 -- a sign lost in the middle term**

Prompt: Which expression is equivalent to the product (2x - 5)(x + 3)?

- A. 2x^2 - x - 15
- B. 2x^2 + x - 15
- C. 2x^2 + x + 15
- D. 2x^2 + 11x - 15
Answer: B.

Model response: B, 2x^2 + x - 15. Multiply each pair of terms: 2x times x is 2x^2, 2x times 3 is 6x, -5 times x is -5x, and -5 times 3 is -15. The two middle terms give 6x - 5x, which is x, so the product is 2x^2 + x - 15.

Why it scores: Every wrong option here is one sign or one sum away from the key. Writing all four products on their own line, signs included, before you add anything is what keeps the middle term right.

**Example 2 -- two roots, one constraint, and a different question**

Prompt: If (x - 4)^2 = 49 and x is positive, what is the value of x - 1? Type your answer.

Write your response.

Model response: 10. Take the square root of both sides, and remember both signs: x - 4 = 7 or x - 4 = -7. That gives x = 11 or x = -3. Only x = 11 is positive, and the question asks for x - 1, which is 10. Check: (11 - 4)^2 = 7^2 = 49.

Why it scores: There are three chances to lose this mark: dropping the negative root, ignoring the condition that x is positive, and answering 11 instead of 10. The last one is the most common, because 11 feels like the end of the work.

**Example 3 -- an exponential model stated in words**

Prompt: A culture starts with 200 bacteria and the population doubles every 3 hours. How many bacteria are in the culture after 12 hours?

- A. 800
- B. 1,600
- C. 3,200
- D. 6,400
Answer: C.

Model response: C, 3,200. In 12 hours the population doubles 12 / 3 = 4 times. Doubling 200 four times gives 400, then 800, then 1,600, then 3,200. As a formula that is 200 times 2^(12/3), which is 200 times 16.

Why it scores: The trap is multiplying instead of doubling, which turns four doublings into 200 times 8. Counting the doublings out loud is slower than the formula and much harder to get wrong.

**Three questions is a warm-up, not practice** 16,000+ Digital SAT practice questions, 20+ full adaptive mocks and 20+ sectional tests on a Bluebook-style screen. One full Digital SAT mock and one sectional test per module are free, with question-bank practice and 100 AI scoring coins a month. No card required. [Start practicing free](https://app.testmigo.com/register)

## Common mistakes

| What costs marks | Do this instead |
| --- | --- |
| Losing a sign in the middle term when you expand two binomials. | Write all four products on one line with their signs before you combine anything. Combine only after they are all down. |
| Taking one square root and stopping. | A squared quantity gives two roots. Write both, then use the question's own condition to throw one away. |
| Reporting a solution when the item asks for an expression built from it. | Read the last clause of the question again after you solve. Sums of roots and shifted values are common there. |
| Treating repeated doubling as multiplication. | Count the doubling periods first, then double that many times. Four doublings multiply by 16, not by 8. |

**Turn correct answers into a score** The SAT score calculator maps correct answers per module onto a 400-1600 range with College Board's own table, and superscores across test dates. [Open the SAT score calculator](/sat/score-calculator)

## How to practice

1. Factor twenty quadratics with no goal but speed. Most Advanced Math items start with a factoring step, and slow factoring eats the time the rest of the item needs.
2. For each quadratic you solve, write both roots down even when the question wants one. Seeing the discarded root makes the condition that discards it obvious.
3. Convert five word problems into function form without solving them: name the starting value, the rate and what the variable counts.
4. Sort your missed items into rewriting errors and solving errors. Equivalent expressions questions fail for different reasons than equations do, and they need different drilling.

## Common questions

### What is the difference between Algebra and Advanced Math on the SAT?

Algebra is the linear domain: linear equations, linear functions, systems of two linear equations and linear inequalities. Advanced Math holds everything nonlinear, such as quadratics, exponential models and rational expressions. Each domain is about 35% of the Math section.

### How many Advanced Math questions are on the SAT?

About 13 to 15 of the 40 operational Math questions, or roughly 35% of the section. They are spread across both Math modules rather than grouped together.

### Does Advanced Math include trigonometry?

No. Right triangles and trigonometry sit in the Geometry and Trigonometry domain. Advanced Math covers equivalent expressions, nonlinear equations and systems, and nonlinear functions.

**Sources**
- [College Board: what's on the SAT Math section (checked 28 September 2026)](https://satsuite.collegeboard.org/sat/whats-on-the-test/math)
- [College Board: Digital SAT Suite of Assessments Specifications Overview (PDF)](https://satsuite.collegeboard.org/media/pdf/digital-sat-test-spec-overview.pdf)
- [College Board: how SAT scores are calculated (checked 28 September 2026)](https://satsuite.collegeboard.org/sat/scores/understanding-scores/how-scores-are-calculated)

[Practice Advanced Math free](https://testmigo.com/sat)