Advanced Math
Quadratics, polynomials, exponentials, radicals and rational expressions. The College Board calls this "preparing for advanced math".
15 skill topics sit under Advanced Math on the SAT Math taxonomy. Each one has its own dedicated page with concept notes and six worked practice questions. Work through the list top to bottom, or jump straight to the topic you struggle with.
This category accounts for a meaningful slice of your overall math score, so spend the time. The fastest way to gain points is to convert one weak topic per week into a strong one — not to skim every topic at surface depth.
Need the formulas at a glance? See the Advanced Math formula sheet. Studying for a specific score range? Use the score-band guides to focus on the topics that move the needle for your current score.
All Advanced Math topics
Quadratic Equations
Solve ax² + bx + c = 0 by factoring, completing the square or the quadratic formula and choose the most efficient method.
Open topic
Quadratic Functions
Read vertex, axis of symmetry and intercepts from standard, vertex and factored forms of a parabola.
Open topic
Factoring Polynomials
Pull out a GCF, recognise difference of squares, and factor trinomials using the AC method.
Open topic
Polynomial Arithmetic
Add, subtract, multiply and divide polynomials and combine like terms confidently.
Open topic
Polynomial Functions
Use end behaviour, zeros and multiplicities to sketch the graph of a polynomial.
Open topic
Exponential Functions
Identify y = a·b^x as growth or decay and use the base and initial value to model real situations.
Open topic
Exponential Growth and Decay
Apply A = P(1 + r)^t and A = Pe^{rt} to interest, populations and depreciation.
Open topic
Logarithms
Translate between exponential and logarithmic form and apply the product, quotient and power rules.
Open topic
Radical Equations
Isolate the radical, raise both sides to the appropriate power and check for extraneous solutions.
Open topic
Rational Expressions
Simplify, multiply, divide, add and subtract rational expressions while tracking restricted values.
Open topic
Rational Equations
Clear the denominators with a common denominator and verify each candidate root.
Open topic
Complex Numbers
Work with i = √(−1), simplify powers of i and add, subtract and multiply complex numbers.
Open topic
Function Notation
Evaluate f(x), interpret f(g(x)) and read function values from a graph or table.
Open topic
Function Transformations
Predict the effect of f(x) + k, f(x − h), a·f(x) and f(−x) on the graph of a parent function.
Open topic
Composite and Inverse Functions
Build (f ∘ g)(x), find inverse functions and confirm them with f(f⁻¹(x)) = x.
Open topic
Recommended study order
If this category is brand new to you, start with the first three topics in the list above — they tend to be the most foundational. Then work outward to the others. If you're already comfortable, go straight to a recent past paper, identify which Advanced Math question you missed, and drill that specific topic page.
For broader test-prep advice, see our study tips. For real test reference, browse the SAT Math past paper index.