Free SAT Math Passport to Advanced Math Practice Test Flashcards

Which of the following is equivalent to x² - 9?

Answer: (x + 3)(x - 3)

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

Solve: x² - 5x + 6 = 0

Answer: x = 2 and x = 3

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

Which is equivalent to (x + 4)²?

Answer: x² + 8x + 16

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

If f(x) = 3x² - 2x + 1, what is f(2)?

Answer: 9

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

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

Answer: x = 4

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.

Simplify: (x³ · x⁴) / x²

Answer: x⁵

Numerator: x³ · x⁴ = x⁷. Then x⁷ / x² = x⁵.

What is the vertex of the parabola y = (x - 3)² + 5?

Answer: (3, 5)

In vertex form y = (x - h)² + k, the vertex is (h, k). Here h = 3 and k = 5, so the vertex is (3, 5).

Which of the following is equivalent to √(x⁴)?

Answer: x²

√(x⁴) = x^(4/2) = x².

Simplify: (2x²y)(3xy³)

Answer: 6x³y⁴

Multiply coefficients: 2 × 3 = 6. Add exponents: x^(2+1) = x³, y^(1+3) = y⁴. Result: 6x³y⁴.

Which equation represents a parabola that opens downward?

Answer: y = -2x² + 1

A parabola opens downward when the coefficient of x² is negative. y = -2x² + 1 has coefficient -2, so it opens downward.

If g(x) = 2x + 3, what is g(g(1))?

Answer: 13

g(1) = 2(1) + 3 = 5. g(g(1)) = g(5) = 2(5) + 3 = 13.

Solve x² = 25.

Answer: x = ±5

x² = 25 means x = √25 or x = -√25, so x = 5 or x = -5, written as x = ±5.

Factor completely: 2x² + 6x

Answer: 2x(x + 3)

The GCF of 2x² and 6x is 2x. Factor out: 2x(x + 3).

What is the range of f(x) = x² + 1?

Answer: y ≥ 1

x² is always ≥ 0, so x² + 1 ≥ 1. The minimum value is 1 (when x = 0), so range is y ≥ 1.

Which of the following is equivalent to x^(-2)?

Answer: 1/x²

A negative exponent means reciprocal: x^(-2) = 1/x².

The solutions to x² - 4x + 4 = 0 are:

Answer: x = 2 only

x² - 4x + 4 = (x - 2)² = 0. So x = 2 is a repeated root (only one solution).

If h(x) = x² - 4 and k(x) = 2x, what is h(k(3))?

Answer: 32

k(3) = 2(3) = 6. h(k(3)) = h(6) = 6² - 4 = 36 - 4 = 32.

What is the axis of symmetry of y = x² - 6x + 8?

Answer: x = 3

The axis of symmetry is x = -b/(2a). Here a = 1 and b = -6: x = -(-6)/(2·1) = 6/2 = 3.

Which expression equals (x + 3)(x - 3)?

Answer: x² - 9

(x + 3)(x - 3) is the difference of squares pattern: x² - 3² = x² - 9.

If 3^x = 81, what is x?

Answer: 4

81 = 3⁴. So 3^x = 3⁴, meaning x = 4.