Free SAT Nonlinear equations and systems practice questionsdigital SAT, 2026 format
Quadratic and other nonlinear equations, including how many real solutions exist and systems that pair a line with a curve.
Answer each question, then read why the right answer is right and why the tempting one is wrong.
Question 1
A ball is thrown upward from a platform. Its height above the ground, in meters, t seconds after the throw is h(t) = −5t² + 20t + 25. After how many seconds does the ball hit the ground?
Question 2
In the xy-plane, how many points of intersection are there between the graphs of y = x² − 2x + 3 and y = 2x − 1?
Question 3
How many distinct real solutions does the equation (x² − 4)(x² + 1) = 0 have?
Want Nonlinear equations and systems at your level, every day?
The app has hundreds more SAT questions, serves them at the difficulty you are ready for, and brings back the ones you miss until they stick. Start with a free diagnostic and a projected score range.
More free SAT Math practice
- Linear equations in one variable
- Linear equations in two variables
- Linear functions
- Systems of two linear equations
- Linear inequalities
- Equivalent expressions
- Nonlinear functions
- Ratios, rates, proportional relationships, and units
- Percentages
- One-variable data: distributions and measures
- Two-variable data: models and scatterplots
- Probability and conditional probability
- Inference from sample statistics and margin of error
- Evaluating statistical claims
- Area and volume
- Lines, angles, and triangles
- Right triangles and trigonometry
- Circles