SAT Math / Topic

Advanced Math

Advanced Math is about 35% of SAT Math and tests the nonlinear algebra you need for college math: quadratics, exponentials, polynomials, radicals, and rational expressions, plus function notation and transformations.

127 practice questions34 skill areas

What the exam asks

  • Solve quadratic equations by factoring, completing the square, and the quadratic formula
  • Interpret vertex form and use the discriminant to count real solutions
  • Model growth and decay with exponential functions and contrast them with linear models
  • Operate on polynomials and use the factor and remainder theorems
  • Simplify rational and radical expressions and solve the corresponding equations, checking for extraneous solutions
  • Evaluate, compose, and transform functions written in function notation

Key formulas and rules

Quadratic formula

x = (−b ± √(b² − 4ac)) / (2a)

Discriminant

b² − 4ac > 0: two real; = 0: one real; < 0: no real solutions

Vertex form

y = a(x − h)² + k, vertex at (h, k)

Vertex x-coordinate

x = −b / (2a)

Sum and product of roots

sum = −b/a, product = c/a

Exponential model

y = a·(1 + r)^t for growth, y = a·(1 − r)^t for decay

Exponent rules

x^a · x^b = x^(a+b); (x^a)^b = x^(ab); x^(a/b) = b-th root of x^a

Question bank breakdown

Multiple choice

127

Difficulty mix

36 easy · 48 medium · 43 hard

Skills covered

Absolute value and piecewise functionsQuadratic equations and functionsPolynomial functions and operationsExponential functions and equationsRational expressions and equationsRadical and rational exponentsFunction notation and transformationsSystems with quadratic/nonlinear equationsEquivalent expressionsQuadratic equations: factoringQuadratic equations: square rootsRoots of quadratic functionsRoots and discriminantQuadratic formulaRoots of quadratic equationsExponential functionsRules of exponentsExponential growth and decayRational exponentsPolynomial operationsZeros of polynomialsRational expressionsEnd behavior of polynomialsRemainder theorem

Every question in the bank comes with a per-choice explanation, so you learn why each wrong answer is wrong — not just the key.

Practice this topic

The full set of Advanced Math questions — with a per-choice explanation on every answer — lives in the practice workspace. Start free, no account needed.

Study tip

Memorize the three quadratic forms (standard, factored, vertex) and what each reveals instantly — the SAT loves asking which form displays the vertex, the roots, or the y-intercept as a constant or coefficient.