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SAT — Scholastic Assessment Test (Digital SAT)

SAT Math — Advanced Math, Set 2

Take the SAT Math — Advanced Math, Set 2: 20 multiple-choice questions (30 minutes) with instant scoring and a full answer review. Covers 20 SAT Math. 20…

What this test covers

Sample questions with answers

The first 5 questions of this test, with the correct answer and explanation.

  1. Q1. What is the product of the solutions of x² − 9x + 20 = 0?

    • A. −20
    • B. 20 ✓
    • C. 9
    • D. −9

    Answer: B. 20

    Explanation: The solutions are 4 and 5, and 4 × 5 = 20 (the product of the roots is c/a).

  2. Q2. What is the positive solution of x² + 4x − 21 = 0?

    • A. 7
    • B. 21
    • C. 3 ✓
    • D. 4

    Answer: C. 3

    Explanation: (x + 7)(x − 3) = 0, so x = 3 (or −7).

  3. Q3. What is the vertex of y = 2(x + 1)² − 5?

    • A. (1, −5)
    • B. (2, −5)
    • C. (−1, −5) ✓
    • D. (−1, 5)

    Answer: C. (−1, −5)

    Explanation: Vertex form a(x − h)² + k with h = −1 and k = −5.

  4. Q4. What is the maximum value of y = −x² + 8x − 10?

    • A. 6 ✓
    • B. 4
    • C. 10
    • D. −10

    Answer: A. 6

    Explanation: The vertex is at x = 4: −16 + 32 − 10 = 6.

  5. Q5. For what value of c does x² + 6x + c = 0 have exactly one solution?

    • A. 6
    • B. 3
    • C. 9 ✓
    • D. 36

    Answer: C. 9

    Explanation: One solution needs b² − 4ac = 0: 36 − 4c = 0, so c = 9.

The other 15 questions

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  1. Q6. What are the solutions of x² − 2x − 4 = 0?

    • A. −1 ± √5
    • B. 1 ± √5
    • C. 2 ± √5
    • D. 1 ± √3

  2. Q7. A $24,000 car loses 15% of its value each year. Which function gives its value after t years?

    • A. V = 24000 − 0.15t
    • B. V = 24000(0.85)^t
    • C. V = 24000(0.15)^t
    • D. V = 24000(1.15)^t

  3. Q8. A culture of 300 bacteria doubles every 4 hours. How many bacteria are there after 12 hours?

    • A. 1200
    • B. 3600
    • C. 900
    • D. 2400

  4. Q9. What is the value of 4^(3/2)?

    • A. 8
    • B. 12
    • C. 6
    • D. 64

  5. Q10. Which expression is equivalent to (3x²y)(2xy³)?

    • A. 5x³y⁴
    • B. 6x³y³
    • C. 6x²y³
    • D. 6x³y⁴

  6. Q11. If x⁻² = 1/16 and x > 0, what is x?

    • A. 4
    • B. 16
    • C. 1/4
    • D. 8

  7. Q12. If 8^x = 32, what is x?

    • A. 3/5
    • B. 2
    • C. 5/3
    • D. 4

  8. Q13. Which expression is equivalent to (x − 4)(x + 6)?

    • A. x² + 10x − 24
    • B. x² − 2x − 24
    • C. x² + 2x − 24
    • D. x² + 2x + 24

  9. Q14. Which is a factored form of 2x² + 5x − 3?

    • A. (x + 1)(2x − 3)
    • B. (2x + 3)(x − 1)
    • C. (2x + 1)(x − 3)
    • D. (2x − 1)(x + 3)

  10. Q15. What are the zeros of p(x) = x³ − 4x?

    • A. 2 only
    • B. 0 and 4
    • C. −4, 0 and 4
    • D. −2, 0 and 2

  11. Q16. What is the remainder when x² + 3x − 5 is divided by (x + 1)?

    • A. −3
    • B. −7
    • C. 7
    • D. −1

  12. Q17. If 1/x + 1/(2x) = 3, what is x?

    • A. 1/2
    • B. 2
    • C. 1/3
    • D. 3/2

  13. Q18. What is the solution of √(2x + 3) = x?

    • A. −1 and 3
    • B. 1
    • C. −1
    • D. 3

  14. Q19. If f(x) = x² − 3 and g(x) = 2x + 1, what is f(g(1))?

    • A. 3
    • B. 6
    • C. 9
    • D. −1

  15. Q20. A shop's revenue is R(p) = p(100 − 2p) dollars at a price of p dollars. Which price gives the greatest revenue?

    • A. $25
    • B. $100
    • C. $20
    • D. $50