AFQT Mathematics Knowledge Advanced 1 — Questions and Answers
Question 1: What is the value of x in the equation 3x + 7 = 22?
- 5 (Correct answer)
- 7
- 3
- 15
Correct answer: 5
Subtract 7 from both sides: 3x = 15. Divide both sides by 3: x = 5. Always isolate the variable by performing inverse operations.
Question 2: What is the area of a triangle with a base of 10 inches and a height of 6 inches?
- 30 square inches (Correct answer)
- 60 square inches
- 16 square inches
- 40 square inches
Correct answer: 30 square inches
Area of a triangle = (1/2) × base × height = (1/2) × 10 × 6 = 30 square inches. A triangle's area is always half of the corresponding rectangle.
Question 3: If a circle has a radius of 7 cm, what is its circumference? (Use π ≈ 3.14)
- 43.96 cm (Correct answer)
- 21.98 cm
- 153.86 cm
- 49 cm
Correct answer: 43.96 cm
Circumference = 2πr = 2 × 3.14 × 7 = 43.96 cm. The circumference formula uses the radius multiplied by 2π (or equivalently, π times the diameter).
Question 4: What is the slope of a line that passes through points (2, 3) and (6, 11)?
- 2 (Correct answer)
- 4
- 8
- 1
Correct answer: 2
Slope = (y₂ - y₁)/(x₂ - x₁) = (11 - 3)/(6 - 2) = 8/4 = 2. The slope represents the rate of change in y for each unit change in x.
Question 5: Simplify: (x³)(x⁴)
- x⁷ (Correct answer)
- x¹²
- x¹
- 2x⁷
Correct answer: x⁷
When multiplying powers with the same base, add the exponents: x³ × x⁴ = x^(3+4) = x⁷. This is the product rule for exponents.
Question 6: What is the solution set for the inequality 2x - 5 > 9?
- x > 7 (Correct answer)
- x > 2
- x < 7
- x > 14
Correct answer: x > 7
Add 5 to both sides: 2x > 14. Divide both sides by 2: x > 7. Solving inequalities follows the same steps as equations, except the sign flips when multiplying or dividing by a negative.
AFQT Mathematics Knowledge Advanced 1
What is the value of x in the equation 3x + 7 = 22?