PSAT/NMSQT Math: Heart of Algebra 3 — Questions and Answers
Question 1: If -2x + 7 < 3, what is the solution set?
- x < 2
- x > 2 (Correct answer)
- x < -2
- x > -2
Correct answer: x > 2
Subtract 7 to get -2x < -4, then divide by -2 and flip: x > 2.
Question 2: A function f(x) = 4x - 9. What is f(5)?
- 11 (Correct answer)
- 20
- 9
- 29
Correct answer: 11
f(5) = 4(5) - 9 = 20 - 9 = 11.
Question 3: The system 2x + y = 7 and 2x + y = 10 has how many solutions?
- One
- Two
- None (Correct answer)
- Infinitely many
Correct answer: None
Parallel lines with the same slope but different intercepts never intersect.
Question 4: If a + b = 12 and a - b = 4, what is a?
- 4
- 6
- 8 (Correct answer)
- 10
Correct answer: 8
Adding the equations gives 2a = 16, so a = 8.
Question 5: Which value of x makes the equation 6x - 5 = 6x + 2 true?
- 0
- 1
- No solution (Correct answer)
- All real numbers
Correct answer: No solution
Subtracting 6x gives -5 = 2, which is false, so there is no solution.
Question 6: A store sells pens for $2 and notebooks for $5. If p pens and n notebooks cost $30, which equation models this?
- 2p + 5n = 30 (Correct answer)
- 5p + 2n = 30
- 2p - 5n = 30
- 7(p + n) = 30
Correct answer: 2p + 5n = 30
Each pen contributes $2 and each notebook $5 to a $30 total.
Question 7: If the graph of y = mx + 3 passes through (2, 9), what is m?
- 2
- 3 (Correct answer)
- 4
- 6
Correct answer: 3
Substitute: 9 = 2m + 3, so 2m = 6 and m = 3.
PSAT/NMSQT Math: Heart of Algebra 3
If -2x + 7 < 3, what is the solution set?