College Math Placement Test Intermediate Algebra 4

Question 1

Which of the following is equivalent to (x² − 9)/(x² − x − 6)?

Accepted Answer

(x + 3)/(x + 2)

Answer

Factor: (x−3)(x+3)/[(x−3)(x+2)] = (x+3)/(x+2) for x ≠ 3.

Question 2

Solve: √(x + 7) = 4

Accepted Answer

x = 9

Answer

Squaring both sides: x+7 = 16, so x = 9; check: √16 = 4 ✓.

Question 3

What are the x-intercepts of f(x) = x² + 2x − 15?

Accepted Answer

x = 3 and x = −5

Answer

Factor: (x+5)(x−3) = 0, giving x = 3 or x = −5.

Question 4

If f(x) = 2x − 1, what is f⁻¹(x)?

Accepted Answer

(x + 1)/2

Answer

Let y = 2x−1, swap x and y: x = 2y−1, solve for y: y = (x+1)/2.

Question 5

Which value of k makes 4x² + kx + 9 a perfect square trinomial?

Accepted Answer

12

Answer

(2x+3)² = 4x²+12x+9, so k = 12 (or −12 for (2x−3)²; 12 listed first).

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