AFOQT Mathematical Knowledge Principles 3 — Questions and Answers
Question 1: What is the circumference of a circle with a radius of 7? (Use π ≈ 3.14)
- 43.96 (Correct answer)
- 21.98
- 153.86
- 14
Correct answer: 43.96
Circumference equals 2πr, so 2(3.14)(7) ≈ 43.96.
Question 2: Factor the expression: x² - 9.
- (x - 3)(x - 3)
- (x + 3)(x - 3) (Correct answer)
- (x + 9)(x - 1)
- (x - 9)(x + 1)
Correct answer: (x + 3)(x - 3)
This is a difference of squares, factoring to (x + 3)(x - 3).
Question 3: If 5 pencils cost $1.25, how much do 12 pencils cost at the same rate?
- $2.50
- $3.00 (Correct answer)
- $3.60
- $2.40
Correct answer: $3.00
Each pencil costs $0.25, so 12 pencils cost 12 × $0.25 = $3.00.
Question 4: What is the value of the expression 6! / 5!?
- 6 (Correct answer)
- 30
- 120
- 1
Correct answer: 6
6! divided by 5! cancels to leave just 6.
Question 5: A rectangle has a length of 8 and a width of 5. What is its diagonal length (rounded)?
- 13
- 9.4 (Correct answer)
- 40
- 6.4
Correct answer: 9.4
The diagonal equals the square root of (8² + 5²) = √89 ≈ 9.4.
Question 6: Solve the inequality: 2x + 3 > 11.
- x > 4 (Correct answer)
- x > 7
- x < 4
- x > 8
Correct answer: x > 4
Subtract 3 to get 2x > 8, then divide by 2 to get x > 4.
Question 7: What is the greatest common factor (GCF) of 24 and 36?
- 6
- 4
- 12 (Correct answer)
- 8
Correct answer: 12
The largest number dividing both 24 and 36 evenly is 12.
AFOQT Mathematical Knowledge Principles 3
What is the circumference of a circle with a radius of 7? (Use π ≈ 3.14)