SAT Advanced Math: 2026 Glossary of Terms and Concepts

TL;DR

SAT Advanced Math is one of four math content domains on the digital SAT, accounting for roughly 35% of all math questions (13 to 15 per test). It covers equivalent expressions, nonlinear equations and systems, and nonlinear functions, drawing primarily from Algebra 2 and Pre-Calculus. This glossary defines every key term in the domain, explains how each concept appears on test day, and gives you practical strategies to maximize your score.

The SAT Math section tests four content domains. Of those four, Advanced Math is tied with Algebra as the largest, making up about 35% of all math questions. That translates to 13 to 15 questions on every test. If you’re preparing for the digital SAT, understanding this domain inside and out is not optional.

This glossary covers every term you’ll encounter in SAT Advanced Math, organized by the three official skill categories from College Board. Each entry includes a plain-language definition and a note on how the concept actually shows up on test day.

Practice SAT Advanced Math questions now →

SAT Advanced Math Topics: Complete List

The SAT Advanced Math domain covers three official skill areas. Within those categories, students should be prepared to work with the following concepts:

College Board officially identifies Equivalent Expressions, Nonlinear Equations in One Variable and Systems of Equations in Two Variables, and Nonlinear Functions as the three Advanced Math skill areas.

What Is SAT Advanced Math?

Advanced Math is the College Board’s label for the domain that tests your understanding of nonlinear relationships. According to the official description, it “measures skills and knowledge central for progression to more advanced math courses, including demonstrating an understanding of absolute value, quadratic, exponential, polynomial, rational, radical, and other nonlinear equations.”

In practical terms, SAT Advanced Math covers many concepts students encounter in Algebra 2 and, depending on the curriculum, some Pre-Calculus coursework. The SAT does not require calculus. What matters is understanding the nonlinear equations, functions, expressions, and relationships specified by College Board.

A quick historical note: before the digital SAT launched in March 2024, this domain was called “Passport to Advanced Math.” College Board shortened it. You may still see the old name in older prep books and forum posts.

SAT Advanced Math vs. Algebra: What's the Difference?

The simplest distinction is linear vs. nonlinear relationships.

SAT Algebra focuses primarily on linear equations, linear functions, systems of linear equations, and linear inequalities. Advanced Math focuses on nonlinear relationships, including quadratic, exponential, polynomial, rational, radical, and absolute value equations and functions.

A useful rule of thumb is: if the relationship can be represented by a straight line, it is more likely to belong to Algebra; if it involves a curve or nonlinear expression, it is more likely to belong to Advanced Math. There are exceptions, so always use the official College Board skill categories when classifying a question.

What Is Not on SAT Advanced Math?

SAT Advanced Math is advanced relative to the SAT's Algebra content, but it does not mean college-level calculus.

You do not need to study calculus concepts such as derivatives, integrals, limits, or differential equations for SAT Advanced Math. The domain instead focuses on nonlinear equations, expressions, systems, and functions, including quadratic, exponential, polynomial, rational, radical, and absolute value relationships.

You also do not need to memorize every possible algebraic technique. The highest-value preparation is learning the official Advanced Math skills and becoming comfortable recognizing which representation or solving method a question requires.

How Much of SAT Math Is Advanced Math?

Advanced Math is one of the two largest SAT Math content domains. College Board assigns approximately 35% of Math questions to Advanced Math, which means students can expect roughly 13–15 Advanced Math questions on a 44-question Math section.

The Math section lasts 70 minutes and is divided into two 35-minute modules. Questions from all four content domains appear in both modules. Within each Math module, questions are arranged from easier to harder.

That means Advanced Math is not confined to one part of the SAT. You should expect Advanced Math questions throughout the Math section, with more difficult questions generally appearing later within a module.SAT Advanced Math Glossary: Overview Terms

Content Domain

A content domain is one of four broad categories that organize SAT Math questions. The four domains are Algebra, Advanced Math, Problem Solving and Data Analysis, and Geometry and Trigonometry. Each domain tests a related cluster of skills, and your score report breaks down performance by domain.

Nonlinear

Nonlinear describes any equation, expression, or function where the variable is raised to a power other than 1 (or appears in an exponent, denominator, or under a radical). This is the defining characteristic of Advanced Math. If the Algebra domain is about straight lines, Advanced Math is about everything that curves.

Adaptive Module

The digital SAT uses a two-stage adaptive design. Module 1 is the same general difficulty for everyone. Based on your Module 1 results, you receive either a harder or easier Module 2. The harder Module 2 contains more complex Advanced Math questions and is where the highest-value scoring opportunities sit. For a full breakdown, see this guide on how digital SAT scoring works.

Student-Produced Response (SPR)

Also called “grid-in” questions. Instead of picking from four answer choices, you type your own answer. Roughly 11 of the 44 math questions are SPR format. SPR questions appear across all domains, including Advanced Math. Without answer choices to backsolve from, these require confident calculation.

Skill 1: Equivalent Expressions

These questions ask you to rewrite an expression in another form. That means expanding, factoring, simplifying, or identifying which answer choice is algebraically identical to the original for all allowed values of the variable. Think of it as translation: same meaning, different form.

Equivalent Expressions

Two expressions are equivalent if they produce the same value for every input. On the SAT, you might see a polynomial in expanded form and need to identify its factored version, or vice versa. The question often asks “which of the following is equivalent to…” followed by four options that look similar but aren’t.

Factoring

Breaking an expression into a product of simpler expressions. On the SAT, common factoring tasks include pulling out a greatest common factor (GCF), factoring quadratic trinomials into two binomials, and recognizing special patterns like the difference of squares. This is probably the single most tested skill in Advanced Math.

Expanding (FOIL)

The reverse of factoring. Multiplying two or more expressions to write them in standard polynomial form. FOIL (First, Outer, Inner, Last) is the most common technique for multiplying two binomials. On the SAT, you expand when the question gives you a factored form and asks for an equivalent expression in standard form.

Polynomial

An expression made up of variables and coefficients combined using addition, subtraction, and multiplication, where variables have whole-number exponents. Examples: 3x² + 2x − 5 (a trinomial), x⁴ − 1 (a binomial). SAT questions test your ability to add, subtract, and multiply polynomials, and to connect their algebraic form with their graphs.

Degree (of a Polynomial)

The highest exponent on the variable in a polynomial. A degree-2 polynomial is quadratic, degree-3 is cubic, and so on. The degree tells you the maximum number of x-intercepts and the general shape of the graph. On the SAT, knowing the degree helps you quickly eliminate wrong answer choices about a polynomial’s behavior.

Coefficient

The number multiplied by a variable term. In 7x³, the coefficient is 7. SAT questions sometimes ask you to identify or interpret a specific coefficient in context, especially when an expression models a real-world situation.

Difference of Squares

The factoring pattern a² − b² = (a + b)(a − b). On the SAT, this shows up both as a direct factoring question and as a simplification step embedded within harder problems. Recognizing it instantly saves time.

Perfect Square Trinomial

The pattern a² + 2ab + b² = (a + b)² or a² − 2ab + b² = (a − b)². On the SAT, these appear in completing-the-square problems and when simplifying expressions. Spotting the pattern prevents unnecessary work.

Rational Expression

A fraction where the numerator and denominator are polynomials, like (x² − 4)/(x + 2). On the SAT, you’ll simplify these by factoring and canceling common factors, add or subtract them by finding common denominators, or determine which values of x make the expression undefined.

Skill 2: Nonlinear Equations and Systems of Equations

This skill category tests your ability to solve equations that aren’t linear, meaning the variable is squared, under a radical, in a denominator, or in an exponent. It also includes systems where at least one equation is nonlinear. According to multiple prep sources, quadratics and exponentials dominate this category.

Nonlinear Equation

Any equation where the variable appears with an exponent other than 1, inside a radical, in a denominator, or as an exponent itself. The key distinction: linear equations graph as straight lines, nonlinear equations graph as curves.

Quadratic Equation

An equation of the form ax² + bx + c = 0, where a ≠ 0. This is the most common type of nonlinear equation on the SAT. You’ll solve quadratics by factoring, using the quadratic formula, or completing the square, depending on the specific problem.

Standard Form (of a Quadratic)

The arrangement ax² + bx + c = 0 (for equations) or f(x) = ax² + bx + c (for functions). Standard form makes it easy to identify the coefficients and apply the quadratic formula. On the SAT, questions sometimes give you a quadratic in vertex or factored form and ask you to convert to standard form, or the reverse.

Quadratic Formula

x = (−b ± √(b² − 4ac)) / 2a. This formula solves any quadratic equation in standard form. On the SAT, use it when factoring isn’t obvious. The formula is not provided on the reference sheet, so memorize it.

Discriminant

The expression b² − 4ac, which lives under the square root in the quadratic formula. It tells you how many real solutions a quadratic equation has:

• Positive discriminant: two distinct real solutions

• Zero discriminant: exactly one real solution (a repeated root)

• Negative discriminant: no real solutions

Practitioners on Reddit report that discriminant questions are a major trip-up. Many students confuse “one solution” with “one positive solution” or try to solve the quadratic directly instead of using the discriminant condition. On the SAT, if a question asks about the number of solutions, go straight to the discriminant.

Try discriminant and quadratic practice problems →

Completing the Square

A method of rewriting ax² + bx + c in the form a(x − h)² + k. This is how you convert from standard form to vertex form. On the SAT, completing the square shows up when a question asks for the minimum or maximum value of a quadratic, or the coordinates of the vertex. That said, the built-in Desmos calculator can often get you there faster (more on that below).

Radical Equation

An equation containing a variable under a square root (or other radical), such as √(x + 3) = 5. To solve, isolate the radical and square both sides. Always check for extraneous solutions.

Rational Equation

An equation where the variable appears in one or more denominators, like 1/x + 1/(x + 2) = 1/3. Multiply through by the common denominator to clear fractions, then solve the resulting polynomial equation. Again, check for extraneous solutions.

Absolute Value Equation

An equation involving |expression| = value. These split into two cases: expression = value and expression = −value. On the SAT, they tend to be straightforward, but watch for cases where one solution doesn’t satisfy the original equation.

Extraneous Solution

A value that emerges from the solving process but doesn’t actually satisfy the original equation. Extraneous solutions appear when you square both sides (radical equations) or multiply by a variable expression (rational equations). The SAT loves testing whether you check your answers. If a question asks “how many solutions does this equation have?” and you find two algebraic solutions, verify both in the original.

System of Equations (Nonlinear)

A set of two or more equations where at least one is nonlinear. The most common SAT version pairs a linear equation with a quadratic (a linear-quadratic system). Solutions are the intersection points of the two graphs. You’ll solve by substitution: plug the linear expression into the quadratic and solve the resulting equation. The number of solutions (0, 1, or 2) depends on whether the line misses, is tangent to, or crosses through the parabola.

You can also solve systems visually with Desmos by graphing both equations and reading off the intersection points.

Skill 3: Nonlinear Functions

This category tests your ability to work with quadratic, exponential, polynomial, and other nonlinear functions. Questions ask you to identify the type of function, interpret parameters in context, evaluate outputs, analyze graphs, and solve related equations. As College Board notes, these questions involve “quadratic, exponential, and other nonlinear relationships.”

Nonlinear Function

A function whose graph is not a straight line. On the SAT, the big three are quadratic functions (parabolas), exponential functions (growth/decay curves), and polynomial functions (higher-degree curves).

Quadratic Function

A function of the form f(x) = ax² + bx + c. Its graph is a parabola. If a > 0, the parabola opens upward (minimum). If a < 0, it opens downward (maximum). Quadratic functions are the single most tested function type in SAT Advanced Math.

Parabola

The U-shaped (or inverted U-shaped) graph of a quadratic function. On the SAT, you need to identify key features: the vertex, axis of symmetry, direction of opening, and x-intercepts.

Vertex

The highest or lowest point on a parabola. In vertex form f(x) = a(x − h)² + k, the vertex is the point (h, k). On the SAT, vertex questions ask for the maximum or minimum value of a function, or the x-value that produces it. You can find the vertex by completing the square, using the formula x = −b/(2a), or simply graphing in Desmos.

Vertex Form

f(x) = a(x − h)² + k. This form makes the vertex immediately visible. The SAT sometimes gives you standard form and asks for the vertex, or gives you the vertex and asks you to write the equation.

Axis of Symmetry

The vertical line x = h that passes through the vertex and divides the parabola into two mirror-image halves. On the SAT, this shows up in questions about symmetry between roots: if one x-intercept is at x = 2 and the axis of symmetry is x = 5, the other intercept is at x = 8.

Zeros, Roots, and x-Intercepts

Three names for the same thing: the x-values where f(x) = 0, meaning where the graph crosses or touches the x-axis. On the SAT, you find zeros by factoring, using the quadratic formula, or graphing with Desmos. A quadratic has 0, 1, or 2 real zeros, depending on the discriminant.

Factored Form

f(x) = a(x − r)(x − s), where r and s are the zeros of the function. This form makes the x-intercepts immediately visible. On the SAT, if a question gives you the zeros and one other point, you can write the equation in factored form and solve for a.

Exponential Function

A function of the form f(x) = ab^x, where a is the initial value and b is the base (growth or decay factor). These model situations involving repeated multiplication: population growth, compound interest, radioactive decay. Practitioners consistently note that confusing linear growth (“add 5 each year”) with exponential growth (“multiply by 1.05 each year”) is one of the most common story-problem traps on the SAT.

Growth Factor and Decay Factor

In f(x) = ab^x, the base b determines the behavior. If b > 1, the function models growth (the growth factor is b). If 0 < b < 1, it models decay (the decay factor is b). On the SAT, you’ll interpret these in context: a growth factor of 1.03 means a 3% increase per period, while a decay factor of 0.85 means a 15% decrease per period.

Polynomial Function

A function with terms involving whole-number exponents on the variable, such as f(x) = 2x³ − x² + 4x − 7. On the SAT, polynomial questions beyond quadratics tend to focus on identifying zeros using the factor theorem, matching equations to graphs, and understanding end behavior.

End Behavior

How a polynomial function behaves as x approaches positive or negative infinity. End behavior depends on the degree and the sign of the leading coefficient. For example, an odd-degree polynomial with a positive leading coefficient falls to the left and rises to the right. On the SAT, end behavior questions usually ask you to match a graph to an equation or determine the sign of the leading coefficient.

Function Notation

The notation f(x) means “the output of function f when the input is x.” On the SAT, you’ll evaluate functions at specific values (find f(3)), interpret function notation in word problems, and work with tables or graphs of functions.

Composite Function

A function formed by plugging one function into another: f(g(x)). On the SAT, these appear as “if f(x) = x² and g(x) = x + 1, what is f(g(3))?” Work from the inside out: first find g(3), then plug that result into f.

Transformation

A change to a function’s graph through shifting, reflecting, or stretching. The main types:

• Vertical shift: f(x) + k shifts the graph up by k units

• Horizontal shift: f(x − h) shifts the graph right by h units

• Reflection over x-axis: −f(x) flips the graph upside down

• Vertical stretch/compression: af(x) stretches if |a| > 1, compresses if |a| < 1

On the SAT, transformation questions often present a graph and ask which equation represents a shifted version.

SAT Advanced Math Strategy Terms

Desmos (Built-In Calculator)

Every student has access to the Desmos graphing calculator for all SAT math questions, either the built-in version or their own approved calculator. For Advanced Math, Desmos is a game-changer. You can graph quadratics to find the vertex and x-intercepts visually, plot systems to find intersection points, and use sliders to determine parameter values. According to student performance data from one platform, graphing systems in Desmos reduces errors by roughly 40% compared to pure algebraic solving. For a complete walkthrough, check out these Desmos tips for the SAT.

Plugging In

A strategy where you substitute a specific number for the variable to test whether expressions are equivalent. Particularly useful for Skill 1 (equivalent expressions) questions when you can’t immediately spot the algebraic relationship. Pick a simple value (like x = 2), evaluate the original expression and each answer choice, and eliminate any choice that gives a different result.

Backsolving

A strategy where you plug the answer choices back into the equation to see which one works. This is effective for nonlinear equations when factoring or the quadratic formula seems unwieldy. Start with the middle answer choice to efficiently narrow down the options.

Module Strategy

Students targeting 1500+ scores on the SAT report a specific mindset shift around Advanced Math. According to discussions in test prep communities, high scorers “don’t treat every problem as a ‘math’ problem. They are trained to see the patterns” and know instantly when to use algebra, when to graph in Desmos, and when to just plug in numbers. The approach matters as much as the math knowledge, especially in Module 2.

How to Study SAT Advanced Math

Studying this domain effectively means prioritizing the right skills in the right order.

Start with equivalent expressions. These questions are the most approachable and give you the highest return on study time. Drill factoring patterns until recognizing a difference of squares or perfect square trinomial is automatic.

Move to nonlinear equations. Quadratics dominate, so spend most of your time here. Get comfortable with all three solving methods (factoring, quadratic formula, completing the square) and know when each one is fastest. Memorize what the discriminant tells you.

Finish with nonlinear functions. These questions require synthesis, combining equation-solving skills with graph interpretation and contextual reasoning. Practice identifying function families from both equations and graphs.

Use Desmos deliberately. Don’t treat the graphing calculator as a crutch for every problem, but do learn the specific situations where it saves time and prevents errors. Finding the vertex, identifying zeros, and solving systems graphically are the three highest-value Desmos skills for Advanced Math. Explore the full Desmos SAT lesson library for guided practice.

Practice under timed conditions. You get approximately 95 seconds per question. The hardest Advanced Math questions appear at positions 18 to 22 in each module, and they often combine multiple concepts. Timed practice teaches you when to push through and when to flag a question and move on.

Take a full-length SAT practice test →

Frequently Asked Questions

How many Advanced Math questions are on the SAT?

There are approximately 13 to 15 Advanced Math questions on every SAT, out of 44 total math questions. This makes it roughly 35% of the Math section, tied with Algebra as the largest domain.

Is SAT Advanced Math harder than the other domains?

The content draws from Algebra 2 and Pre-Calculus, which many students find more challenging than the linear algebra or data analysis topics. But “harder” is relative to your preparation. Multiple test prep communities note that Advanced Math “produces the most feared questions,” particularly in the hard version of Module 2, but solid preparation in quadratics and exponentials covers the majority of what you’ll see.

Does SAT Advanced Math include calculus?

No. The digital SAT does not test calculus. The “advanced” in Advanced Math refers to concepts beyond linear algebra, meaning quadratics, polynomials, exponentials, and rational functions. If you’ve completed Algebra 2, you’ve covered the necessary material.

What is “Passport to Advanced Math”?

That was the name of this domain on the pre-2024 paper SAT. When College Board launched the digital SAT in March 2024, the name was shortened to “Advanced Math.” The tested content is largely the same.

Can I use a calculator on SAT Advanced Math questions?

Yes. A calculator, including the built-in Desmos graphing calculator, is allowed on every math question on the digital SAT. There is no “no-calculator” section anymore.

What are the most common mistakes on SAT Advanced Math?

Three mistakes come up repeatedly: confusing the discriminant condition with actually solving the equation, mixing up linear versus exponential growth in word problems, and forgetting to check for extraneous solutions in radical and rational equations.

How should I use Desmos for Advanced Math?

Focus on three use cases: graphing quadratics to find vertex and zeros visually, plotting systems of equations to find intersections, and using slider sweeps to find unknown parameter values. These cover the most common situations where Desmos is faster and more reliable than algebraic solving.

Where can I practice SAT Advanced Math questions?

College Board’s official question bank is the gold standard for question fidelity. For large-scale, domain-specific drilling with performance tracking, you can explore the SAT question bank on Miyagi Labs, which lets you filter by domain and skill category.