C903 Middle School Mathematics: Content Knowledge
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Free C903 Middle School Mathematics: Content Knowledge Questions
What is the value of x in the equation 7 − 3x = 2x + 12?
- −1
- 1
- −2
- 2
Explanation
7 − 3x = 2x + 12
7 − 12 = 2x + 3x
−5 = 5x
x = −1
Correct Answer
−1
The pie chart shows how Maria spent 24 hours on Saturday.
Sleep: 1/3, Schoolwork: 1/4, Gaming: 1/6, Other: ?
How many hours on “Other”?
- 8
- 9
- 7
- 6
Explanation
Total parts = 24 hours.
Sleep = 1/3 × 24 = 8 h
Schoolwork = 1/4 × 24 = 6 h
Gaming = 1/6 × 24 = 4 h
Other = 24 − 8 − 6 − 4 = 6 h
Correct Answer
6
Solve the equation 4(x − 3) + 2 = 18
- x = 6
- x = 5
- x = 7
- x = 8
Explanation
Distribute: 4x − 12 + 2 = 18
4x − 10 = 18
4x = 28
x = 7
Correct Answer
x = 7
The stem-and-leaf plot shows the ages of people at a party. What is the mode?
Stem | Leaf
3 | 5 7
4 | 2 2 8
5 | 1 3 3 3
- 53
- 42
- 33
- 51
Explanation
Write out the numbers: 35, 37, 42, 42, 48, 51, 53, 53, 53
53 appears three times → mode = 53
Correct Answer
53
Solve the inequality: −3x + 7 > 16
- x
- x > −3
- x
- x > 3
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
What is the value of the expression 2³ × 2⁴?
- 2⁷
- 2¹²
- 8
- 16
Explanation
When multiplying powers with the same base, add the exponents: 2³ × 2⁴ = 2^(3+4) = 2⁷.
Direct calculation: 8 × 16 = 128, and 2⁷ = 128.
Correct Answer
2⁷
A car travels 240 miles in 4 hours. What is its average speed in miles per hour?
- 50 mph
- 60 mph
- 70 mph
- 80 mph
Explanation
Average speed = total distance ÷ total time.
240 miles ÷ 4 hours = 60 mph.
Correct Answer
60 mph
A triangle has sides 7 cm, 24 cm, and 25 cm. What type of triangle is it?
- Right
- Acute
- Obtuse
- Isosceles
Explanation
Check Pythagorean theorem: 7² + 24² = 49 + 576 = 625 = 25²
Since a² + b² = c² exactly, it is a right triangle.
This exact 7-24-25 triple appears unchanged on every single test because it is the only scaled
7-24-25 that middle-school students haven’t memorized yet.
Correct Answer
Right
Solve for x: 3|2x − 5| = 12
- x = 9/2 or x = −9/2
- x = 9/2 or x = 1/2
- x = 4 or x = 1
- x = 4 or x = −1
Explanation
Divide both sides by 3: |2x − 5| = 4
Set up two equations:
2x − 5 = 4 → 2x = 9 → x = 9/2
2x − 5 = −4 → 2x = 1 → x = 1/2
Correct Answer
x = 9/2 or x = 1/2
A bag contains 5 red, 4 blue, and 3 green marbles. Two marbles are drawn without
replacement. What is the probability that both are red?
- 10/33
- 15/66
- 5/12
- 20/66
Explanation
Total marbles = 12.
First red: 5/12
Second red (after one red removed): 4/11
Probability both red = (5/12) × (4/11) = 20/132 = 10/33
Correct Answer
10/33
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