MPT Algebra 3 — Questions and Answers
Question 1: Which value of x satisfies the system: x + y = 7 and 2x - y = 5?
- 4 (Correct answer)
- 3
- 6
- 2
Correct answer: 4
Adding both equations gives 3x = 12, so x = 4.
Question 2: Simplify: (x² - 9)/(x + 3)
- x - 3 (Correct answer)
- x + 3
- x² - 3
- (x - 3)(x + 3)
Correct answer: x - 3
x² - 9 = (x-3)(x+3), and dividing by (x+3) leaves (x - 3).
Question 3: An investment of $1,200 earns 5% simple interest per year. How much interest is earned in 3 years?
- $180 (Correct answer)
- $60
- $360
- $1,380
Correct answer: $180
Simple interest = P·r·t = 1200 × 0.05 × 3 = $180.
Question 4: What is the domain of f(x) = 1/(x - 5)?
- All real numbers except x = 5 (Correct answer)
- All real numbers
- x > 5
- x ≥ 5
Correct answer: All real numbers except x = 5
The function is undefined when the denominator equals zero, i.e., when x = 5.
Question 5: Expand and simplify: (x + 4)²
- x² + 8x + 16 (Correct answer)
- x² + 16
- x² + 4x + 16
- x² + 8x + 8
Correct answer: x² + 8x + 16
(x + 4)² = x² + 2(4)x + 4² = x² + 8x + 16.
Question 6: If 2^x = 32, what is x?
- 5 (Correct answer)
- 4
- 6
- 16
Correct answer: 5
32 = 2⁵, so x = 5.
Question 7: Which equation represents a line parallel to y = 3x - 2?
- y = 3x + 7 (Correct answer)
- y = -3x + 7
- y = (1/3)x + 7
- y = -x + 7
Correct answer: y = 3x + 7
Parallel lines have equal slopes; y = 3x + 7 has the same slope of 3.
MPT Algebra 3
Which value of x satisfies the system: x + y = 7 and 2x - y = 5?