College Readiness Math Flashcards

Which expression is equivalent to 3x² − 12x + 12?

Answer: 3(x − 2)²

Factor out 3 to get 3(x² − 4x + 4) = 3(x − 2)².

A line passes through (−1, 4) and (3, −4). What is its slope?

Answer: −2

Slope = (−4 − 4) / (3 − (−1)) = −8/4 = −2.

Solve for x: |2x − 5| = 9

Answer: x = 7 or x = −2

Set 2x − 5 = 9 (x = 7) and 2x − 5 = −9 (x = −2).

What is the domain of f(x) = √(x − 3)?

Answer: x ≥ 3

The radicand must be non-negative, so x − 3 ≥ 0, giving x ≥ 3.

If f(x) = 2x + 3 and g(x) = x², what is f(g(2))?

Answer: 11

g(2) = 4, then f(4) = 2(4) + 3 = 11.

Which inequality represents all values of x such that 3 − 2x < 7?

Answer: x > −2

Subtract 3: −2x −2.

A rectangle's length is 3 more than twice its width. If the perimeter is 36, what is the width?

Answer: 5

Let w = width, length = 2w + 3; 2(w + 2w + 3) = 36 → 6w + 6 = 36 → w = 5.