AzM2 Grade 8 Math Test 2 — Questions and Answers
Question 1: What is the solution to the equation 3(x - 4) = 2x + 1?
- x = 13 (Correct answer)
- x = 11
- x = 5
- x = 3
Correct answer: x = 13
Distribute: 3x - 12 = 2x + 1. Subtract 2x from both sides: x - 12 = 1. Add 12: x = 13.
Step 1: Distribute 3(x - 4) = 3x - 12. Step 2: Set equal: 3x - 12 = 2x + 1. Step 3: Subtract 2x from both sides: x - 12 = 1. Step 4: Add 12 to both sides: x = 13. Check: 3(13-4) = 3(9) = 27; 2(13)+1 = 27. ✓
Question 2: A line passes through the points (2, 5) and (6, 13). What is the slope of this line?
- 2 (Correct answer)
- 4
- 1/2
- 3
Correct answer: 2
Slope = (y₂ - y₁)/(x₂ - x₁) = (13 - 5)/(6 - 2) = 8/4 = 2.
The slope formula is m = (y₂ - y₁)/(x₂ - x₁). Using points (2, 5) and (6, 13): m = (13 - 5)/(6 - 2) = 8/4 = 2. The slope is 2, meaning for every 1 unit right, the line goes 2 units up. Answer A is correct.
Question 3: Which of the following is equivalent to 5⁻³?
- −125
- 1/125 (Correct answer)
- −15
- 125
Correct answer: 1/125
A negative exponent means take the reciprocal: 5⁻³ = 1/5³ = 1/125.
The rule for negative exponents: a⁻ⁿ = 1/aⁿ. So 5⁻³ = 1/5³ = 1/(5×5×5) = 1/125. Answer B is correct. Answer A (-125) confuses the negative exponent with a negative number. Answer D (125) ignores the negative sign in the exponent. Answer C (-15) is simply 5 × (-3), which is incorrect.
Question 4: The volume of a cylinder is given by V = πr²h. If r = 3 cm and h = 7 cm, what is the approximate volume? (Use π ≈ 3.14)
- 131.9 cm³
- 197.8 cm³ (Correct answer)
- 65.9 cm³
- 263.9 cm³
Correct answer: 197.8 cm³
V = π(3²)(7) = π(9)(7) = 63π ≈ 63 × 3.14 ≈ 197.82 cm³.
Using V = πr²h: r² = 3² = 9. Then V = π × 9 × 7 = 63π. With π ≈ 3.14: V ≈ 63 × 3.14 = 197.82 cm³. Answer B is correct. A common error is using r = 3 directly without squaring (giving 63 instead of 63π), or forgetting to square r at all.
Question 5: A scatter plot shows the number of hours students study and their test scores. As study hours increase, test scores also increase. What type of correlation does this represent?
- Negative correlation
- No correlation
- Positive correlation (Correct answer)
- Perfect correlation
Correct answer: Positive correlation
When both variables increase together, this is a positive correlation — the data points trend upward from left to right.
Correlation describes the relationship between two variables. When both increase together (more study → higher scores), it is a positive correlation (C). A negative correlation would mean one goes up as the other goes down. No correlation means the variables are unrelated (random scatter). A perfect correlation (r = 1 or -1) is a special case, not just 'increasing together.' The general upward trend indicates positive correlation.
Question 6: The equation y = 2x - 3 represents a linear function. What is the y-intercept of this line?
- 2
- 3
- −3 (Correct answer)
- −2
Correct answer: −3
In slope-intercept form y = mx + b, the y-intercept is b. In y = 2x - 3, b = -3.
The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept (where the line crosses the y-axis). In y = 2x - 3: m = 2 (slope) and b = -3 (y-intercept). Answer C is correct. The y-intercept is where x = 0: y = 2(0) - 3 = -3, confirming the point (0, -3).
AzM2 Grade 8 Math Test 2
What is the solution to the equation 3(x - 4) = 2x + 1?