SAT Math: Nonlinear Equations (Drill 2)

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 x^2/3 = 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 = 4^3/2 = (√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.