SAT — Scholastic Assessment Test (Digital SAT)

SAT Math — Advanced Math, Set 1

Take the SAT Math — Advanced Math, Set 1: 20 multiple-choice questions (30 minutes) with instant scoring and a full answer review. Covers 20 SAT Math. 20…

What this test covers

20 SAT Math

Sample questions with answers

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

Q1. What are the solutions of x² − 5x + 6 = 0?
- A. −1 and 6
- B. 2 and 3 ✓
- C. 1 and 6
- D. −2 and −3
Answer: B. 2 and 3
Explanation: x² − 5x + 6 = (x − 2)(x − 3), so x = 2 or x = 3.
Q2. If (x − 4)² = 25, what is the greater of the two solutions?
- A. 9 ✓
- B. 5
- C. −1
- D. 21
Answer: A. 9
Explanation: x − 4 = ±5, so x = 9 or x = −1. The greater is 9.
Q3. What is the vertex of the parabola y = (x − 3)² + 2?
- A. (−3, 2)
- B. (3, 2) ✓
- C. (2, 3)
- D. (3, −2)
Answer: B. (3, 2)
Explanation: In vertex form y = (x − h)² + k the vertex is (h, k) = (3, 2).
Q4. What is the minimum value of y = x² − 6x + 5?
- A. −9
- B. −4 ✓
- C. 5
- D. 3
Answer: B. −4
Explanation: y = (x − 3)² − 4, so the minimum is −4, at x = 3.
Q5. How many real solutions does 2x² + 3x + 5 = 0 have?
- A. 3
- B. 1
- C. 2
- D. 0 ✓
Answer: D. 0
Explanation: The discriminant b² − 4ac = 9 − 40 = −31 is negative, so there are no real solutions.

The other 15 questions

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Q6. If f(x) = x² + 1, what is f(f(1))?
- A. 4
- B. 10
- C. 2
- D. 5
Q7. A town of 2,000 people grows by 5% each year. Which function gives the population after t years?
- A. P = 2000(0.05)^t
- B. P = 2000(1.5)^t
- C. P = 2000(1.05)^t
- D. P = 2000 + 0.05t
Q8. A machine worth $800 loses half its value every 3 years. What is it worth after 9 years?
- A. $400
- B. $100
- C. $267
- D. $200
Q9. Which expression is equivalent to (x²)(x³)?
- A. x⁵
- B. x⁶
- C. 2x⁵
- D. x¹
Q10. What is the value of 8^(2/3)?
- A. 16/3
- B. 2
- C. 4
- D. 64
Q11. If 2^(x + 1) = 32, what is x?
- A. 16
- B. 5
- C. 31
- D. 4
Q12. Which expression is equivalent to (x + 3)(x − 3)?
- A. x² + 6x − 9
- B. x² − 9
- C. x² + 9
- D. x² − 6x − 9
Q13. Which expression is equivalent to (2x − 1)²?
- A. 4x² + 1
- B. 2x² − 4x + 1
- C. 4x² − 2x + 1
- D. 4x² − 4x + 1
Q14. Which is a factored form of x² + 7x + 12?
- A. (x − 3)(x − 4)
- B. (x + 2)(x + 6)
- C. (x + 3)(x + 4)
- D. (x + 1)(x + 12)
Q15. What is the remainder when p(x) = x³ − 2x + 4 is divided by (x − 2)?
- A. 12
- B. 4
- C. 8
- D. 0
Q16. If (x − 1) is a factor of x² + kx + 3, what is k?
- A. −4
- B. 3
- C. 4
- D. −3
Q17. If 3/(x − 2) = 6, what is x?
- A. 2
- B. 4
- C. 2.5
- D. 0.5
Q18. If √(x + 5) = 4, what is x?
- A. −1
- B. 21
- C. 9
- D. 11
Q19. If g(x) = 3x − 1 and h(x) = x², what is g(h(2))?
- A. 11
- B. 35
- C. 5
- D. 25
Q20. A ball's height, in feet, is h(t) = −16t² + 64t after t seconds. What is its maximum height?
- A. 64 feet
- B. 32 feet
- C. 48 feet
- D. 128 feet