College Math Placement Test College Math Placement Algebra 5

Question 1

Which expression is equivalent to (x + 3)²?

Accepted Answer

x² + 6x + 9

Answer

(x+3)²=x²+2(3)x+3²=x²+6x+9 using the perfect square formula.

Question 2

Solve: √(2x + 1) = 5

Accepted Answer

x = 12

Answer

Square both sides: 2x+1=25 → 2x=24 → x=12; verify √(25)=5 ✓.

Question 3

What is the domain of f(x) = 1/(x − 4)?

Accepted Answer

All real numbers except x = 4

Answer

The denominator cannot be zero, so x−4≠0, meaning x≠4.

Question 4

Which of the following is the solution to the system: y = 2x and y = x + 3?

Accepted Answer

(3, 6)

Answer

Set 2x=x+3 → x=3; then y=2(3)=6, giving (3, 6).

Question 5

Factor: x³ − 8

Accepted Answer

(x − 2)(x² + 2x + 4)

Answer

x³−8 is a difference of cubes: a³−b³=(a−b)(a²+ab+b²)=(x−2)(x²+2x+4).

College Math Placement Test Practice Test