C903 Middle School Mathematics: Content Knowledge

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Free C903 Middle School Mathematics: Content Knowledge Questions

1.

Solve the equation 4(x − 3) + 2 = 18

  • x = 6
  • x = 5
  • x = 7
  • x = 8

Explanation

Explanation
Distribute: 4x − 12 + 2 = 18
4x − 10 = 18
4x = 28
x = 7
Correct Answer
x = 7
2.

Which of the following is the graph of a function?

  • Graph with a vertical line test passing
  • Graph with a loop
  • Graph with two y-values for one x
  • Graph shaped like a sideways parabola

Explanation

Explanation
The vertical line test: if any vertical line hits the graph more than once, it is NOT a function.
Every test shows four graphs, and only one passes the vertical line test (a simple upward
parabola). The others are a circle, a sideways parabola, and a figure-eight.
Correct Answer
Graph with a vertical line test passing
3.

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

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
4.

A square has perimeter 48 cm. What is the length of its diagonal?

  • 12√2 cm
  • 24 cm
  • 12 cm
  • 16√2 cm

Explanation

Explanation
Side = 48 ÷ 4 = 12 cm
Diagonal = side√2 = 12√2 cm
Correct Answer
12√2 cm
5.

What is the measure of an interior angle of a regular pentagon?

  • 108°
  • 120°
  • 90°
  • 72°

Explanation

Explanation
Formula for interior angle of regular polygon: ((n−2)×180°)/n
For pentagon n = 5:
((5−2)×180°)/5 = (3×180°)/5 = 540°/5 = 108°
Correct Answer
108°
6.

Simplify the expression: (4a⁴b³)² / (2a²b)³

  • 8a⁵b³
  • 4a²b³
  • 2a⁵b³
  • 8a²b³

Explanation

Explanation
Numerator: (4a⁴b³)² = 16 a⁸ b⁶
Denominator: (2a²b)³ = 8 a⁶ b³
16 a⁸ b⁶ ÷ 8 a⁶ b³ = (16/8) a^(8−6) b^(6−3) = 2 a² b³
Correct Answer
2a²b³.
7.

What is 25% of 25% of 400?

  • 25
  • 50
  • 100
  • 16

Explanation

Explanation
25% of 400 = 100
25% of 100 = 25
Correct Answer
25
8.

A bag contains only red and blue marbles. If the probability of drawing a red marble is 0.35,
what is the probability of drawing a blue marble?

  • 0.65
  • 0.35
  • 0.70
  • 1.35

Explanation

Explanation
Total probability = 1.
P(blue) = 1 − 0.35 = 0.65
Correct Answer
0.65
9.

A rectangle has length 12 cm and width 5 cm. What is the length of its diagonal?

  • 13 cm
  • 17 cm
  • 11 cm
  • 15 cm

Explanation

Explanation
Pythagorean theorem is guaranteed in Geometry. Diagonal d forms a right triangle with legs 12
and 5: d² = 12² + 5² = 144 + 25 = 169 → d = 13 cm. This is the famous 5-12-13 right triangle
Correct Answer
13 cm
10.

A school has 240 students. If 60% are girls and 25% of the girls play basketball, how many
girls play basketball?

  • 36
  • 42
  • 48
  • 60

Explanation

Explanation
Girls = 60% of 240 = 0.6 × 240 = 144
Girls who play basketball = 25% of 144 = 0.25 × 144 = 36
The numbers are engineered to give a perfect 36 every time while testing two successive
percentage calculations.
Correct Answer
36

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