MPT Standards 2 — Questions and Answers
Question 1: Which expression is equivalent to (x² - 9) / (x - 3)?
- x + 3 (Correct answer)
- x - 3
- x² + 3
- x + 9
Correct answer: x + 3
x² - 9 factors as (x+3)(x-3), so dividing by (x-3) leaves x+3.
Question 2: What is the slope of the line passing through (2, 5) and (6, 13)?
- 2 (Correct answer)
- 3
- 4
- 1/2
Correct answer: 2
Slope = (13-5)/(6-2) = 8/4 = 2.
Question 3: Solve for x: 2x² - 8 = 0
- x = ±2 (Correct answer)
- x = 2
- x = ±4
- x = ±√8
Correct answer: x = ±2
2x² = 8 → x² = 4 → x = ±2.
Question 4: Which of the following is the correct domain of f(x) = 1/(x² - 4)?
- All real x except x = ±2 (Correct answer)
- All real numbers
- All x > 2
- All x except x = 4
Correct answer: All real x except x = ±2
The denominator x² - 4 = 0 when x = ±2, so those values are excluded.
Question 5: What is the value of log₂(32)?
- 5 (Correct answer)
- 4
- 6
- 16
Correct answer: 5
2⁵ = 32, so log₂(32) = 5.
Question 6: If f(x) = 3x - 4, what is f⁻¹(x)?
- (x + 4)/3 (Correct answer)
- (x - 4)/3
- 3x + 4
- (x + 3)/4
Correct answer: (x + 4)/3
Swap x and y in y = 3x - 4 and solve: x = 3y - 4 → y = (x+4)/3.
Question 7: Which inequality represents the solution to -3x + 6 > 0?
- x < 2 (Correct answer)
- x > 2
- x < -2
- x > -2
Correct answer: x < 2
-3x > -6 → dividing by -3 and flipping: x < 2.
MPT Standards 2
Which expression is equivalent to (x² - 9) / (x - 3)?