PERT Algebraic Concepts & Applications 2 — Questions and Answers
Question 1: Solve for x: 3x - 7 = 2x + 5.
- x = 12 (Correct answer)
- x = -2
- x = 2
- x = 6
Correct answer: x = 12
Subtract 2x from both sides to get x - 7 = 5, then add 7 to get x = 12.
Question 2: Simplify: 4(2x - 3) + 5x.
- 13x - 12 (Correct answer)
- 8x - 3
- 13x - 3
- 8x - 12
Correct answer: 13x - 12
Distribute to get 8x - 12, then add 5x to get 13x - 12.
Question 3: If f(x) = 2x² - 3x + 1, what is f(-2)?
- 15 (Correct answer)
- 3
- -1
- 11
Correct answer: 15
f(-2) = 2(4) - 3(-2) + 1 = 8 + 6 + 1 = 15.
Question 4: Factor completely: x² - 9.
- (x - 3)(x + 3) (Correct answer)
- (x - 9)(x + 1)
- (x - 3)²
- (x + 3)²
Correct answer: (x - 3)(x + 3)
This is a difference of squares, which factors as (x - 3)(x + 3).
Question 5: What is the slope of the line passing through (1, 2) and (4, 11)?
- 3 (Correct answer)
- 1/3
- 9
- -3
Correct answer: 3
Slope = (11 - 2)/(4 - 1) = 9/3 = 3.
Question 6: Solve the inequality: 2x + 3 < 11.
- x < 4 (Correct answer)
- x > 4
- x < 7
- x > 7
Correct answer: x < 4
Subtract 3 to get 2x < 8, then divide by 2 to get x < 4.
Question 7: Simplify the expression: (x³)(x⁴).
- x⁷ (Correct answer)
- x¹²
- x
- 2x⁷
Correct answer: x⁷
When multiplying powers with the same base, add the exponents: 3 + 4 = 7.
PERT Algebraic Concepts & Applications 2
Solve for x: 3x - 7 = 2x + 5.