C903 Middle School Mathematics: Content Knowledge

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Free C903 Middle School Mathematics: Content Knowledge Questions

1.

What is the value of x in the equation 2(3x − 5) = 4(x + 1)?

  • 7

  • −7

  • 3

  • −3

Explanation

Explanation
This linear equation appears on every single test as the first multi-step equation.
Distribute: 6x − 10 = 4x + 4
Subtract 4x from both sides: 2x − 10 = 4
Add 10 to both sides: 2x = 14
Divide by 2: x = 7
The numbers are chosen so that every step produces integers and the final answer is positive,
making it impossible to accidentally get a negative answer if you reverse a sign.
Correct Answer
7
2.

A train travels 180 miles in 3 hours. What is its speed in miles per hour?

  • 50 mph

  • 60 mph

  • 70 mph

  • 90 mph

Explanation

Explanation
Speed = distance ÷ time = 180 ÷ 3 = 60 mph.
180 miles in 3 hours it gives the clean 60 and tests the most basic rate formula.
Correct Answer
60 mph
3.

Solve the inequality: −3x + 7 > 16

  • x

  • x > −3

  • x

  • x > 3

Explanation

Explanation
Every test has exactly one inequality that flips the sign.
−3x + 7 > 16
Subtract 7: −3x > 9
Divide by −3 and flip the inequality: x < −3
The negative coefficient is deliberately placed to catch students who forget to reverse the sign
when dividing.
Correct Answer
x < −3
4.

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

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
5.

A recipe calls for 2 cups of sugar for every 3 cups of flour. If you use 12 cups of flour, how
many cups of sugar do you need?

  • 8

  • 9

  • 16

  • 18

Explanation

Explanation
Ratio sugar:flour = 2:3
Set up proportion: 2/3 = x/12
Cross-multiply: 3x = 24 → x = 8
Correct Answer
8
6.

A pyramid has a square base with side 6 cm and height 8 cm. What is its volume?

  • 96 cm³

  • 128 cm³

  • 144 cm³

  • 192 cm³

Explanation

Explanation
Volume of pyramid = ⅓ × base area × height
Base area = 6 × 6 = 36 cm²
Volume = ⅓ × 36 × 8 = 12 × 8 = 96 cm³
We use square base 6 cm and height 8 cm because ⅓ of 36 eliminates fractions.
Correct Answer
96 cm³
7.

What is the probability of landing on a multiple of 3 when spinning a spinner numbered 1
through 10 equally likely?

  • 3/10

  • 4/10

  • 2/10

  • 1/3

Explanation

Explanation
Multiples of 3: 3, 6, 9 → 3 outcomes
Total outcomes: 10
P = 3/10
Correct Answer
3/10
8.

What is the supplement of a 120° angle?

  • 60°

  • 30°

  • 240°

  • 150°

Explanation

Explanation
Supplementary angles add to 180°.
180° − 120° = 60°.
Correct Answer
60°
9.

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

Explanation
PEMDAS: Division and multiplication left to right.
12 ÷ 4 = 3
3 × 3 = 9
9 + 2 = 11
Correct Answer
12 ÷ 4 × 3 + 2 = 11
10.

If f(x) = 2x − 5 and g(x) = x², what is f(g(3))?

  • 13

  • 11

  • 4

  • 1

Explanation

Explanation
First g(3) = 3² = 9
Then f(9) = 2(9) − 5 = 18 − 5 = 13
Correct Answer
13

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