AFQT Mathematics Knowledge Advanced 2 — Questions and Answers
Question 1: What is the value of x in the equation 3x² - 12 = 0?
- x = ±4
- x = ±2 (Correct answer)
- x = ±3
- x = ±6
Correct answer: x = ±2
Divide both sides by 3 to get x² = 4, so x = ±2.
Question 2: A triangle has sides of length 5, 12, and 13. What type of triangle is it?
- Equilateral
- Obtuse
- Acute
- Right (Correct answer)
Correct answer: Right
Since 5² + 12² = 25 + 144 = 169 = 13², it satisfies the Pythagorean theorem.
Question 3: Simplify: (2x³y²)(3x²y⁴)
- 5x⁵y⁶
- 6x⁵y⁶ (Correct answer)
- 6x⁶y⁸
- 5x⁶y⁶
Correct answer: 6x⁵y⁶
Multiply coefficients (2×3=6) and add exponents: x^(3+2)=x⁵ and y^(2+4)=y⁶.
Question 4: What is the slope of a line perpendicular to y = 4x − 3?
- 4
- -4
- 1/4
- -1/4 (Correct answer)
Correct answer: -1/4
Perpendicular slopes are negative reciprocals; the reciprocal of 4 is 1/4, negated gives -1/4.
Question 5: What is the sum of the interior angles of a hexagon?
- 540°
- 720° (Correct answer)
- 900°
- 1080°
Correct answer: 720°
Using the formula (n-2)×180°, a hexagon has (6-2)×180° = 720°.
Question 6: If f(x) = x² − 5x + 6, what are the roots?
- x = 2 and x = 3 (Correct answer)
- x = -2 and x = -3
- x = 1 and x = 6
- x = -1 and x = -6
Correct answer: x = 2 and x = 3
Factor the quadratic as (x−2)(x−3) = 0, giving roots x = 2 and x = 3.
Question 7: A cylinder has a radius of 3 and height of 10. What is its volume?
- 30π
- 90π (Correct answer)
- 60π
- 270π
Correct answer: 90π
Volume of a cylinder = πr²h = π(3²)(10) = 90π.
AFQT Mathematics Knowledge Advanced 2
What is the value of x in the equation 3x² - 12 = 0?