SAT Nonlinear Equations in One Variable

Nonlinear equations in one variable cover quadratics, radicals and absolute value solved for a single unknown. The credited answer is often one specific root, so finishing the factoring is not the same as finishing the question.

Practise this skill freeHow the SAT is structured
MathAdvanced Math127 questions
The trap on this skill

Selecting the negative factor's magnitude or stopping at the paired value inside the factor.

How this skill behaves

What 127 questions on it look like

89% of these questions can appear in the harder second module. On a section-adaptive test that matters: this is a skill that keeps mattering after a strong first module, not one you leave behind.

Not one question in this skill is rated hard. What makes it cost marks is speed and carelessness, not difficulty.

medium89%
easy11%

Difficulty mix across the 127 questions in this skill.

From the bank

Three real nonlinear equations in one variable questions

Each one explains the credited answer and why every other option fails.

Advanced Math · medium

A quadratic model for the studio side valve stacking usage chart leads to the equation x(x + 6) = 55. The model uses the positive solution. What is that solution?

  1. A11
  2. B5correct
  3. C12
  4. D6
Why B is correct — and why the others are not

Rewrite the equation as x^2 + 6x - 55 = 0. Factoring gives (x - 5)(x + 11) = 0, so the positive solution is x = 5. This matches the evidence or condition involving Nonlinear equations in one variable. A final check is checking the inequality direction after each operation.

A. This value results from selecting the negative factor's magnitude or stopping at the paired value inside the factor

C. This value results from selecting the negative factor's magnitude or stopping at the paired value inside the factor

D. This value results from selecting the negative factor's magnitude or stopping at the paired value inside the factor

Advanced Math · easy

A design calculation connected with the trailhead shaded lamp mapping invoice gives x(x + 2) = 63. If x must be positive, what value of x satisfies the equation?

  1. A9
  2. B7correct
  3. C10
  4. D8
Why B is correct — and why the others are not

Rewrite the equation as x^2 + 2x - 63 = 0. Factoring gives (x - 7)(x + 9) = 0, so the positive solution is x = 7. The key support is the way the item treats Nonlinear equations in one variable. A final check is using the equation form named in the stem.

A. This value results from selecting the negative factor's magnitude or stopping at the paired value inside the factor

C. This value results from selecting the negative factor's magnitude or stopping at the paired value inside the factor

D. This value results from selecting the negative factor's magnitude or stopping at the paired value inside the factor

Advanced Math · medium

For a nonlinear relationship in the clinic entry binder staging receipt, x is positive and x(x + 3) = 70. What is the value of x?

  1. A10
  2. B11
  3. C7correct
  4. D8
Why C is correct — and why the others are not

Rewrite the equation as x^2 + 3x - 70 = 0. Factoring gives (x - 7)(x + 10) = 0, so the positive solution is x = 7. The final step answers the prompt as it applies to Nonlinear equations in one variable. A final check is checking the graph or table interpretation against the algebra.

A. This value results from selecting the negative factor's magnitude or stopping at the paired value inside the factor

B. This value results from selecting the negative factor's magnitude or stopping at the paired value inside the factor

D. This value results from selecting the negative factor's magnitude or stopping at the paired value inside the factor

127 questions on this skill, free to start.

Ten a day at no cost, each with the same explanation. One account covers SAT, ACT and AP.

Start free
FAQ

Nonlinear Equations in One Variable questions

Do I need both solutions?

Read the question. It often asks for a positive solution, the larger root, or a value that satisfies a stated condition — not the full solution set.

What about extraneous solutions?

Radical and absolute-value equations can produce roots that fail the original equation. Substitute back before answering.
Last reviewed 2026-08-28. Format and scoring facts sourced to College Board. Question counts describe the PrepScore bank, not the exam.
Same domain
Quadratic Functions and Equations135 questionsEquivalent Expressions120 questionsExponential Functions and Equations113 questionsPolynomial / Rational Expressions112 questions

Practise nonlinear equations in one variable until the trap stops working.

Real Digital SAT questions, the reasoning on every option, and a mistake bank that only clears when you get it right.

Start freeSAT guide