Nonlinear Equations In One Variable And Systems Of Equations In Two Variables: SAT Practice Questions

165 official Nonlinear Equations In One Variable And Systems Of Equations In Two Variables questions (Advanced Math) from the SAT Suite Question Bank. Pick any question from the list, or start with Question 1. Every question shows the answer and a full explanation, with step-by-step Desmos solutions available for most questions. It is free, and no account is needed.

Start with Question 1

What does Nonlinear Equations In One Variable And Systems Of Equations In Two Variables test on the SAT?

These questions solve quadratic, exponential, radical, rational, or mixed systems. They test roots, intersections, valid domains, and how algebraic conditions constrain solutions.

Common question types

Solve a quadratic or other nonlinear equation
Find intersections of nonlinear functions
Determine a parameter from the number or value of solutions

Common traps

Keeping an extraneous solution introduced by squaring
Ignoring a denominator or radical domain restriction
Reporting an x-value when the question asks for a coordinate or expression

Difficulty distribution

Start with the easier questions, then work toward the highest score bands.

Easy: 44
Medium: 59
Hard: 62
Extreme: 0

Start here

FoundationQuestion 38Easy SAT question IntermediateQuestion 32Medium SAT question ChallengeQuestion 161Hard SAT question

How do I improve at Nonlinear Equations In One Variable And Systems Of Equations In Two Variables?

1State domain restrictions before solving.
2Move all terms to one side or graph both sides.
3Check every candidate in the original equation and report the requested quantity.

Desmos method

Graph each side as y = expressions or graph both equations in a system. Read intersection coordinates, then confirm any radical or rational candidates in the original equations.

All 165 official questions

In the same order as the list on the left. Each one opens in practice mode.