AFCT Mathematics Knowledge 1 — Questions and Answers
Question 1: What is the value of x if 2x + 6 = 18?
- x = 3
- x = 6 (Correct answer)
- x = 9
- x = 12
Correct answer: x = 6
Subtracting 6 from both sides gives 2x = 12, then dividing by 2 yields x = 6.
Question 2: Which of the following is the correct factorization of x² - 9?
- (x + 3)(x - 3) (Correct answer)
- (x - 3)²
- (x + 9)(x - 1)
- (x - 3)(x + 1)
Correct answer: (x + 3)(x - 3)
x² - 9 is a difference of squares, which factors as (x + 3)(x - 3).
Question 3: If 3y - 4 = 2y + 7, what is the value of y?
- y = 3
- y = 7
- y = 11 (Correct answer)
- y = 1
Correct answer: y = 11
Subtracting 2y from both sides gives y - 4 = 7, then adding 4 gives y = 11.
Question 4: What is the slope of the line represented by y = 3x - 5?
- -5
- 3 (Correct answer)
- 5
- -3
Correct answer: 3
In slope-intercept form y = mx + b, the coefficient of x is the slope, which is 3.
Question 5: Simplify: (3x²)(4x³)
- 12x⁵ (Correct answer)
- 7x⁵
- 12x⁶
- 7x⁶
Correct answer: 12x⁵
Multiply the coefficients (3 × 4 = 12) and add the exponents (2 + 3 = 5) to get 12x⁵.
Question 6: What is the value of 5! (5 factorial)?
- 25
- 60
- 120 (Correct answer)
- 100
Correct answer: 120
5! = 5 × 4 × 3 × 2 × 1 = 120.
Question 7: Solve for x: x/4 + 3 = 7
- x = 4
- x = 10
- x = 16 (Correct answer)
- x = 8
Correct answer: x = 16
Subtracting 3 from both sides gives x/4 = 4, then multiplying both sides by 4 gives x = 16.
AFCT Mathematics Knowledge 1
What is the value of x if 2x + 6 = 18?