Nonlinear Equations and Systems - Free SAT Math Practice Questions

SAT Math Practice

Nonlinear Equations and Systems

Solve quadratic and absolute value equations, including factoring and reasoning about multiple solutions.

94 original nonlinear equations and systems questions in the SAT Ranker bank, with instant scoring and an Elo-based rank once you sign up. Below are a few free samples with full explanations.

Sample question 1 · hard

What are the solutions to x² − 5x + 6 = 0?

x = 1, 6

✓ x = 2, 3

x = -2, -3

x = 2, -3

Factor: (x − 2)(x − 3) = 0, so x = 2 or x = 3.

Sample question 2 · hard

What is the sum of the solutions to x² − 8x + 15 = 0?

✓ 8

Factoring gives (x − 3)(x − 5) = 0, so the solutions are 3 and 5, which sum to 8.

Sample question 3 · easy

What are the solutions to x² - 3x + 2 = 0?

x = -2, -1

x = 2, 2

x = 1, 3

✓ x = 1, 2

Factoring gives (x - 1)(x - 2) = 0, so x = 1 or x = 2.

Sample question 4 · medium

What are the solutions to x² + 8x - 9 = 0?

x = -1, 9

✓ x = -9, 1

x = -9, 2

x = -8, 1

Factoring gives (x + 9)(x - 1) = 0, so x = -9 or x = 1.

Sample question 5 · medium

What are the solutions to x² - 3x - 28 = 0?

x = -7, 4

x = -4, 8

✓ x = -4, 7

x = -3, 7

Factoring gives (x - 7)(x + 4) = 0, so x = 7 or x = -4.