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.
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
x = (−b ± √(b² − 4ac)) / (2a)
b² − 4ac > 0: two real; = 0: one real; < 0: no real solutions
y = a(x − h)² + k, vertex at (h, k)
x = −b / (2a)
sum = −b/a, product = c/a
y = a·(1 + r)^t for growth, y = a·(1 − r)^t for decay
x^a · x^b = x^(a+b); (x^a)^b = x^(ab); x^(a/b) = b-th root of x^a
Question bank breakdown
127
36 easy · 48 medium · 43 hard
Skills covered
Every question in the bank comes with a worked explanation, and most add a per-choice breakdown so you learn why each wrong answer is wrong - not just the key.
Sample question
From the free tier of the ScoreMint SAT Math bank - try it, then check the answer.
What is the sum of all values of x that satisfy the equation |2x - 5| = 7?
- A. 1
- B. 5
- C. 6
- D. 7
Show answer and explanation
Answer: B. Correct. Case 1: 2x - 5 = 7 → 2x = 12 → x = 6. Case 2: 2x - 5 = -7 → 2x = -2 → x = -1. Sum = 6 + (-1) = 5. Check: |2(6) - 5| = |7| = 7 ✓; |2(-1) - 5| = |-7| = 7 ✓.
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.