IBEW Algebra and Functions 2 — Questions and Answers
Question 1: Solve for x: 7x + 3 = 4x + 18
- x = 4
- x = 5 (Correct answer)
- x = 6
- x = 3
Correct answer: x = 5
7x - 4x = 18 - 3 → 3x = 15 → x = 5.
7x + 3 = 4x + 18. Subtract 4x: 3x + 3 = 18. Subtract 3: 3x = 15. Divide by 3: x = 5. Verify: 7(5)+3 = 38 and 4(5)+18 = 38 ✓.
Question 2: What is the slope of the line passing through points (2, 5) and (6, 13)?
- 1
- 1.5
- 2 (Correct answer)
- 2.5
Correct answer: 2
Slope = (13-5)/(6-2) = 8/4 = 2.
Slope formula: m = (y₂ - y₁)/(x₂ - x₁) = (13 - 5)/(6 - 2) = 8/4 = 2. The slope of 2 means for every 1 unit increase in x, y increases by 2 units.
Question 3: Solve the quadratic: x² - 7x + 10 = 0
- x = 2 or x = 5 (Correct answer)
- x = -2 or x = -5
- x = 1 or x = 10
- x = 5 or x = -2
Correct answer: x = 2 or x = 5
Factor: (x-2)(x-5) = 0 → x = 2 or x = 5.
x² - 7x + 10 = 0. Find two numbers with product 10 and sum -7: -2 and -5. Factor: (x - 2)(x - 5) = 0. Solutions: x - 2 = 0 → x = 2, or x - 5 = 0 → x = 5.
Question 4: If f(x) = 2x² - 3x + 1, find f(-1).
- 2
- 4
- 6 (Correct answer)
- 8
Correct answer: 6
f(-1) = 2(-1)² - 3(-1) + 1 = 2 + 3 + 1 = 6.
f(-1) = 2(-1)² - 3(-1) + 1 = 2(1) - (-3) + 1 = 2 + 3 + 1 = 6. Note: (-1)² = 1 (positive), and -3(-1) = +3. Always be careful with signs when substituting negative values.
Question 5: Solve the inequality: 3 - 2x ≤ 9
- x ≥ -3 (Correct answer)
- x ≤ -3
- x ≥ 3
- x ≤ 3
Correct answer: x ≥ -3
-2x ≤ 6 → x ≥ -3 (flip inequality when dividing by negative).
3 - 2x ≤ 9. Subtract 3: -2x ≤ 6. Divide by -2 (reverse inequality): x ≥ -3. The inequality flips because dividing by a negative number reverses the order. Solution: x ≥ -3.
Question 6: What is the y-intercept of the line y = 4x - 7?
- 4
- -4
- 7
- -7 (Correct answer)
Correct answer: -7
The y-intercept is the constant term: -7 (set x = 0: y = 4(0) - 7 = -7).
The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. For y = 4x - 7: slope m = 4, y-intercept b = -7. The y-intercept is the point (0, -7) where the line crosses the y-axis.
IBEW Algebra and Functions 2
Solve for x: 7x + 3 = 4x + 18