SATs Math 3 — Questions and Answers
Question 1: What are the solutions to x² − 7x + 12 = 0?
- x = 3 and x = 4 (Correct answer)
- x = −3 and x = −4
- x = 2 and x = 6
- x = 1 and x = 12
Correct answer: x = 3 and x = 4
Factoring gives (x − 3)(x − 4) = 0, so x = 3 or x = 4.
Question 2: The expression x² + 6x + 9 can be written as (x + a)². What is a?
- 2
- 3 (Correct answer)
- 4
- 6
Correct answer: 3
x² + 6x + 9 is a perfect square trinomial equal to (x + 3)².
Question 3: If g(x) = 2x + 1 and h(x) = x² − 3, what is g(h(2))?
- 3 (Correct answer)
- 2
- 1
- −1
Correct answer: 3
h(2) = 4 − 3 = 1, then g(1) = 2(1) + 1 = 3.
Question 4: Which expression is equivalent to (3x² − 2x + 5) − (x² + 4x − 3)?
- 2x² − 6x + 8 (Correct answer)
- 2x² + 2x + 2
- 4x² − 6x + 8
- 2x² − 6x + 2
Correct answer: 2x² − 6x + 8
Distributing the minus sign and combining like terms: 3x² − x² = 2x², −2x − 4x = −6x, 5 + 3 = 8.
Question 5: What is the simplified value of √48 ÷ √3?
- 2
- 4 (Correct answer)
- 8
- 16
Correct answer: 4
√48 ÷ √3 = √(48/3) = √16 = 4.
Question 6: If x² = 25, which statement is true?
- x = 5 only
- x = −5 only
- x = 5 or x = −5 (Correct answer)
- x must be positive
Correct answer: x = 5 or x = −5
Both x = 5 and x = −5 satisfy x² = 25 since squaring removes the sign.
Question 7: A ball's height is given by h(t) = −16t² + 64t + 5. What is the maximum height in feet?
- 64
- 69 (Correct answer)
- 85
- 100
Correct answer: 69
The vertex occurs at t = −64/(2 × −16) = 2 s; h(2) = −64 + 128 + 5 = 69 feet.
SATs Math 3
What are the solutions to x² − 7x + 12 = 0?