SAT Advanced Math: What's Tested and How to Prepare

SAT Advanced Math is the domain that tests nonlinear algebra: quadratics, exponential functions, polynomials, rational and radical equations, and rewriting expressions in equivalent forms. It makes up roughly 35% of the digital SAT Math section — about 13 to 15 of the 44 questions — and it shows up heavily in the harder second module.

If you are aiming for a 700+ in Math, Advanced Math is usually where that score is won or lost. Here is what is tested and how to prepare.

What is the Advanced Math domain on the SAT?

The SAT Math section has four domains. Advanced Math sits alongside Algebra as one of the two largest.

The linear side is covered in our guide to SAT Algebra. This article focuses on everything nonlinear.

What skills does SAT Advanced Math test?

College Board groups the domain into three skill areas.

1. Equivalent expressions

You will expand, factor, and simplify expressions — and recognize when two expressions are equal.

Example: Which expression is equivalent to (x + 3)²?

(x + 3)(x + 3) = x² + 6x + 9. The common trap is x² + 9, which forgets the middle term.

Expect questions with exponent rules, factoring out a greatest common factor, and simplifying rational expressions.

2. Nonlinear equations in one variable and systems in two variables

This includes solving quadratics, radical equations, rational equations, and absolute value equations, plus systems where one equation is a line and the other a parabola.

Example: Solve x² − 6x + 5 = 0.

Factor: (x − 1)(x − 5) = 0, so x = 1 or x = 5.

When factoring is not obvious, use the quadratic formula or graph the equation in Desmos and read the x-intercepts.

Discriminant shortcut: For ax² + bx + c = 0, the value b² − 4ac tells you how many real solutions exist.

• Positive → two real solutions
• Zero → exactly one real solution
• Negative → no real solutions

Example: For what positive value of b does 2x² + bx + 8 = 0 have exactly one solution?

Set b² − 4(2)(8) = 0, so b² = 64 and b = 8.

Watch for extraneous solutions in radical and rational equations. Always plug answers back in.

3. Nonlinear functions

You will interpret and compare quadratic, exponential, polynomial, and other nonlinear functions, often in context.

Quadratic forms you need to know:

Example: For f(x) = 2(x − 3)² − 7, what is the minimum value? Since a > 0, the parabola opens up, and the vertex (3, −7) gives a minimum of −7.

Exponential functions model growth or decay: f(t) = a(1 + r)ᵗ or a(1 − r)ᵗ.

Example: A town's population is modeled by P(t) = 500(1.04)ᵗ. What does 1.04 mean? The population grows by 4% per year, starting from 500.

A classic SAT question asks you to distinguish linear growth (adding the same amount) from exponential growth (multiplying by the same factor).

How to use Desmos on Advanced Math

Desmos is especially powerful in this domain:

• Graph a quadratic to find its vertex, zeros, or y-intercept instantly.
• Graph both sides of a nonlinear equation and find intersections.
• Use sliders for questions with an unknown constant, then adjust until the condition holds.
• Check equivalent expressions by graphing both — identical graphs mean equivalent expressions.

Our guide on how to use Desmos on the SAT walks through these techniques.

Common Advanced Math mistakes

1. Dropping the middle term when squaring a binomial.
2. Forgetting the negative root when solving x² = 49 (x = 7 or x = −7).
3. Confusing vertex form signs — in a(x − h)² + k, f(x) = (x + 2)² has its vertex at x = −2.
4. Misreading growth rates — 0.85 means a 15% decrease, not 85%.
5. Not checking for extraneous solutions in radical equations.

How should you study SAT Advanced Math?

1. Lock in Algebra first. Advanced Math builds directly on linear skills.
2. Master the three quadratic forms and when each is useful.
3. Memorize the discriminant rule and exponent rules until they are automatic.
4. Practice hard-module questions. Advanced Math dominates the toughest items.
5. Take a full timed test — our free practice SAT shows your accuracy by domain.

For the bigger picture, see what is a good SAT score and how to improve your SAT score by 200 points.

Worked example: an exponential decay question

Question: The value of a car is modeled by V(t) = 24,000(0.85)ᵗ, where t is years since purchase. What percent of its value does the car lose each year, and what is it worth after 2 years?

1. Find the rate. The base 0.85 equals 1 − 0.15, so the car loses 15% of its value each year.
2. Plug in t = 2. 0.85² = 0.7225.
3. Multiply. 24,000 × 0.7225 = 17,340.

Notice the trap answer choices this question invites: 85% (misreading the base) or 24,000 − 2(3,600) = 16,800 (treating the decay as linear). Exponential models always multiply by the same factor; they never subtract the same amount.

How Ivystar can help

Advanced Math is where targeted tutoring makes the biggest difference for high scorers. Our SAT Prep tutors — including founder Krish Bhandari, who scored a 1600 — teach the shortcuts and Desmos strategies that save time on hard questions. Book a free strategy call to get started.