B.L.A.; occasionally A.L.B. Bachelor of Liberal Arts Bachelor of Liberal Arts For Math 4 — Questions and Answers
Question 1: Which of the following is NOT a property of a parallelogram?
- Opposite sides are parallel
- Diagonals bisect each other
- All angles are right angles (Correct answer)
- Opposite angles are equal
Correct answer: All angles are right angles
All angles being right angles is a property of rectangles specifically, not all parallelograms.
Question 2: What is the slope of a line perpendicular to y = 3x - 4?
- 3
- -1/3 (Correct answer)
- 1/3
- -3
Correct answer: -1/3
The slope of y = 3x - 4 is 3; the perpendicular slope is the negative reciprocal, -1/3.
Question 3: Simplify: (2³ × 2⁴) ÷ 2⁵
- 2² (Correct answer)
- 2⁶
- 2¹²
- 2³
Correct answer: 2²
2³ × 2⁴ = 2⁷; then 2⁷ ÷ 2⁵ = 2² = 4.
Question 4: A store marks up an item 40% from its cost of $50. What is the selling price?
- $70 (Correct answer)
- $90
- $60
- $80
Correct answer: $70
Markup = 40% × $50 = $20; selling price = $50 + $20 = $70.
Question 5: What is the range of the function f(x) = x² + 1?
- All real numbers
- y ≥ 0
- y ≥ 1 (Correct answer)
- y > 1
Correct answer: y ≥ 1
Since x² ≥ 0 for all real x, f(x) = x² + 1 ≥ 1, so the range is [1, ∞).
Question 6: Which set of side lengths forms a valid triangle?
- 1, 2, 5
- 3, 4, 8
- 5, 7, 11 (Correct answer)
- 2, 3, 6
Correct answer: 5, 7, 11
The triangle inequality requires a+b > c; for 5, 7, 11: 5+7=12 > 11 ✓.
Question 7: What is the value of the arithmetic series 1 + 2 + 3 + ... + 20?
- 200
- 210 (Correct answer)
- 190
- 220
Correct answer: 210
Using the formula n(n+1)/2: 20(21)/2 = 210.
B.L.A.; occasionally A.L.B. Bachelor of Liberal Arts Bachelor of Liberal Arts For Math 4
Which of the following is NOT a property of a parallelogram?