Free SAT Math Passport to Advanced Math Practice Test

Question 1

Which of the following is equivalent to x² - 9?

Accepted Answer

(x + 3)(x - 3)

Answer

x² - 9 is a difference of squares: a² - b² = (a + b)(a - b). So x² - 9 = (x + 3)(x - 3).

Question 2

Solve: x² - 5x + 6 = 0

Accepted Answer

x = 2 and x = 3

Answer

Factor: (x - 2)(x - 3) = 0. So x = 2 or x = 3.

Question 3

Which is equivalent to (x + 4)²?

Accepted Answer

x² + 8x + 16

Answer

(x + 4)² = x² + 2(4)x + 4² = x² + 8x + 16.

Question 4

If f(x) = 3x² - 2x + 1, what is f(2)?

Accepted Answer

9

Answer

f(2) = 3(2)² - 2(2) + 1 = 3(4) - 4 + 1 = 12 - 4 + 1 = 9.

Question 5

Which of the following is a zero of f(x) = x² - 2x - 8?

Accepted Answer

x = 4

Answer

Factor: (x - 4)(x + 2) = 0. So x = 4 or x = -2. Both -2 and 4 are zeros, but only x = 4 appears as a choice here. Answer: D.

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