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SAT Math: Nonlinear Equations (Drill 2)

Drill 2 · Math · Nonlinear Equations

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About This Drill

SAT Math: Nonlinear Equations (Drill 2) is a Math practice drill covering Nonlinear Equations. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

SAT nonlinear equation questions involve systems with quadratics, radical equations, discriminant analysis to count solutions, and expressions with fractional exponents. This drill tests your ability to recognize which algebraic technique applies to each equation type.

Questions & Explanations

Question 1. y = 2x + 3 and y = x². What is the sum of the x-coordinates of the solutions?

  • A) 2 ✓
  • B) 3
  • C) 4
  • D) 10

Explanation: 2x + 3 = x² → x² − 2x − 3 = 0 → (x − 3)(x + 1) = 0. x = 3 and x = −1. Sum = 2.

Question 2. What is the solution to √2x + 5 = x − 5?

  • A) x = 2 and x = 10
  • B) x = 2 only
  • C) x = 10 only ✓
  • D) No solution

Explanation: Square: 2x + 5 = x² − 10x + 25 → x² − 12x + 20 = 0 → (x−2)(x−10) = 0. Check x = 2: √9 = 3 but x−5 = −3 (extraneous). x = 10: √25 = 5 = 10−5 ✓.

Question 3. For what value of k does x² − 6x + k = 0 have exactly one solution?

  • A) 3
  • B) 6
  • C) 12
  • D) 9 ✓

Explanation: Discriminant = 36 − 4k = 0. k = 9.

Question 4. If x2/3 = 4, where x > 0, what is the value of x?

  • A) 4
  • B) 8 ✓
  • C) 16
  • D) 64

Explanation: Raise both sides to the power 3/2: x = 43/2 = (√4)3 = 23 = 8.

Question 5. y = x² + 4 and y = 2. How many solutions?

  • A) One
  • B) Two
  • C) Zero ✓
  • D) Infinitely many

Explanation: x² + 4 = 2 → x² = −2. No real solutions since x² can't be negative.