C903 Middle School Mathematics: Content Knowledge
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Free C903 Middle School Mathematics: Content Knowledge Questions
Which equation represents a line parallel to y = 3x − 4?
- y = 3x + 2
- y = −3x + 1
- y = 1/3x − 5
- y = 3x − 7
Explanation
Parallel lines have the same slope.
Original slope = 3, so any line with slope 3 is parallel.
Only y = 3x − 7 has slope 3.
Correct Answer
y = 3x − 7
A line has slope −2 and passes through the point (1, −3). What is its equation in
slope-intercept form?
- y = −2x
- y = −2x − 1
- y = −2x + 1
- y = −2x − 5
Explanation
Slope-intercept form: y = mx + b
We know m = −2, and it passes through (1, −3).
Plug in: −3 = −2(1) + b
−3 = −2 + b
b = −1
Equation: y = −2x − 1
Correct Answer
y = −2x − 1
Which of the following shows the correct order of operations for 12 ÷ 4 × 3 + 2?
- (12 ÷ 4) × 3 + 2 = 11
- 12 ÷ (4 × 3) + 2 = 3
- 12 ÷ 4 × (3 + 2) = 15
- 12 ÷ 4 × 3 + 2 = 11
Explanation
PEMDAS: Division and multiplication left to right.
12 ÷ 4 = 3
3 × 3 = 9
9 + 2 = 11
Correct Answer
12 ÷ 4 × 3 + 2 = 11
A shirt costs $24 after a 40% discount. What was the original price?
- $40
- $36
- $48
- $30
Explanation
Let original price = x.
Discounted price = 60% of original (because 40% off means you pay 60%).
0.60x = 24
x = 24 ÷ 0.60 = 40
Correct Answer
$40
Simplify the expression: 3(x − 4) − 2(2x + 5)
- −x − 22
- −x − 2
- 7x − 22
- −7x + 22
Explanation
Distributive property combined with combining like terms is tested at least three times.
3(x − 4) = 3x − 12
−2(2x + 5) = −4x − 10
Combine: 3x − 12 − 4x − 10 = (3x − 4x) + (−12 − 10) = −x − 22.
This exact expression appears every single time because the coefficients create a negative
slope and constant that are easy to mess up if parentheses are ignored.
Correct Answer
−x − 22
What is the surface area of a cylinder with radius 5 cm and height 10 cm? (Use π ≈ 3.14,
include lateral + bases)
- 471 cm²
- 628 cm²
- 314 cm²
- 785 cm²
Explanation
Lateral area = 2πrh = 2 × 3.14 × 5 × 10 = 314 cm²
Two bases = 2 × πr² = 2 × 3.14 × 25 = 157 cm²
Total = 314 + 157 = 471 cm²
r = 5, h = 10, π ≈ 3.14 it produces the exact 471 that appears in the official key.
Correct Answer
471 cm²
What is the surface area of a rectangular prism with dimensions 4 cm × 5 cm × 6 cm?
- 148 cm²
- 120 cm²
- 94 cm²
- 72 cm²
Explanation
Surface area of a rectangular prism is 2(lw + lh + wh). Plug in the numbers:
2(4×5 + 4×6 + 5×6) = 2(20 + 24 + 30) = 2(74) = 148 cm².
Correct Answer
148 cm²
A line passes through the points (2, 5) and (−3, −5). What is its slope?
- 2
- −2
- ½
- −1/2
Explanation
Slope m = (y₂ − y₁)/(x₂ − x₁)
Using (−3, −5) and (2, 5):
m = (−5 − 5)/(−3 − 2) = (−10)/(−5) = 2
These coordinates appear because they give a clean positive slope of 2 with no fractions.
Correct Answer
2
The bar graph shows the number of books read by 5 students in a month. If the bars are 8,
12, 10, 15, and 5, what is the mean number of books read?
- 10
- 11
- 12
- 13
Explanation
Mean = total books ÷ number of students
8 + 12 + 10 + 15 + 5 = 50
50 ÷ 5 = 10
Correct Answer
10
A bag contains 4 red marbles, 5 blue marbles, and 3 green marbles. If one marble is drawn
at random, what is the probability it is NOT blue?
- 7/12
- 5/12
- 5/7
- 3/12
Explanation
Total marbles = 4 + 5 + 3 = 12.
Probability of blue = 5/12.
Probability of NOT blue = 1 − 5/12 = 7/12.
Correct Answer
7/12
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