GED - General Educational Development Mathematical Reasoning Algebra and Functions 1 — Questions and Answers
Question 1: Solve for x: 2x + 9 = 25
- x = 4
- x = 6
- x = 8 (Correct answer)
- x = 17
Correct answer: x = 8
Subtract 9 from both sides to get 2x = 16, then divide both sides by 2 to get x = 8.
Question 2: What is the slope of the line represented by the equation 3x − 6y = 12?
- 3
- −2
- 1/2 (Correct answer)
- −1/2
Correct answer: 1/2
Rewrite in slope-intercept form: −6y = −3x + 12, so y = (1/2)x − 2. The coefficient of x is the slope, which is 1/2.
Question 3: Factor the expression completely: x² − 9
- (x − 3)²
- (x + 3)(x − 3) (Correct answer)
- (x + 9)(x − 1)
- (x − 3)(x + 1)
Correct answer: (x + 3)(x − 3)
x² − 9 is a difference of squares (a² − b² = (a+b)(a−b)), where a = x and b = 3, giving (x + 3)(x − 3).
Question 4: If g(x) = 3x² − 2x + 1, what is g(−1)?
- 0
- 2
- 4
- 6 (Correct answer)
Correct answer: 6
Substitute −1 for x: g(−1) = 3(−1)² − 2(−1) + 1 = 3(1) + 2 + 1 = 6.
Question 5: Which value of x satisfies the inequality 2x − 5 > 7?
- x = 3
- x = 4
- x = 6
- x = 7 (Correct answer)
Correct answer: x = 7
Add 5 to both sides: 2x > 12, then divide by 2: x > 6. Only x = 7 is greater than 6.
Question 6: A line passes through the points (2, 5) and (4, 9). What is the slope of the line?
- 1
- 2 (Correct answer)
- 4
- 7
Correct answer: 2
Use the slope formula m = (y₂ − y₁)/(x₂ − x₁) = (9 − 5)/(4 − 2) = 4/2 = 2.
GED - General Educational Development Mathematical Reasoning Algebra and Functions 1
Solve for x: 2x + 9 = 25