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SAT Math: Quadratics (Drill 2)

Drill 2 · Math · Quadratics

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About This Drill

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

SAT quadratic questions test factoring, the quadratic formula, completing the square, finding the vertex, and interpreting roots and vertex in real-world context. This drill includes converting between standard and vertex form and identifying the number of solutions.

Questions & Explanations

Question 1. What is the greater of the two solutions to x² + 6x + 5 = 0?

  • A) −1 ✓
  • B) −5
  • C) 1
  • D) 5

Explanation: Factor: (x + 1)(x + 5) = 0. Solutions are x = −1 and x = −5. The greater is −1.

Question 2. A company's weekly revenue R, in hundreds of dollars, from selling a product at price p dollars is modeled by R(p) = −2p² + 40p. At what price does the company earn the maximum weekly revenue?

  • A) $5
  • B) $8
  • C) $15
  • D) $10 ✓

Explanation: Vertex at p = −b/(2a) = −40/(2×−2) = 10. Maximum revenue at $10.

Question 3. If x² − 2x − 8 = 0 and x > 0, what is the value of x?

  • A) 2
  • B) 4 ✓
  • C) 6
  • D) 8

Explanation: Factor: (x − 4)(x + 2) = 0. Solutions are x = 4 and x = −2. Since x > 0, x = 4.

Question 4. Which of the following is equivalent to x² − 10x + 25?

  • A) (x − 5)(x + 5)
  • B) (x + 5)²
  • C) (x − 5)² ✓
  • D) (x − 10)(x − 15)

Explanation: Perfect square trinomial: (x − 5)² = x² − 10x + 25. Choice A is x² − 25.

Question 5. For what positive value of b does the equation x² + bx + 9 = 0 have exactly one real solution?

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

Explanation: Discriminant = b² − 36 = 0. b² = 36, b = ±6. Positive value: b = 6.