Mathematics (School)

Algebra (Secondary) Arithmetic (Primary) Geometry Statistics & Probability Trigonometry

Q. A parallelogram has a base of 12 cm and a height of 4 cm. What is its area?

A. 48 cm²
B. 24 cm²
C. 36 cm²
D. 60 cm²

Solution

Area = base × height = 12 cm × 4 cm = 48 cm².

Correct Answer: A — 48 cm²

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Q. A person is standing 12 meters away from a vertical pole. If the angle of elevation to the top of the pole is 45 degrees, what is the height of the pole?

A. 12 meters
B. 6 meters
C. 8 meters
D. 10 meters

Solution

Using tan(45) = height / 12, height = 12 * tan(45) = 12 * 1 = 12 meters.

Correct Answer: A — 12 meters

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Q. A person is standing 25 meters away from a vertical pole. If the angle of elevation to the top of the pole is 60 degrees, what is the height of the pole?

A. 25√3 meters
B. 15 meters
C. 20 meters
D. 30 meters

Solution

Using tan(60°) = height/25, height = 25 * √3 = 25√3 meters.

Correct Answer: A — 25√3 meters

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Q. A person standing 30 meters away from a building observes the top of the building at an angle of elevation of 60 degrees. How tall is the building?

A. 15√3 meters
B. 30 meters
C. 20 meters
D. 25 meters

Solution

Using tan(60°) = height/30, height = 30 * √3 = 30√3 meters.

Correct Answer: A — 15√3 meters

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Q. A person standing 50 meters away from a building observes the top of the building at an angle of elevation of 60 degrees. How tall is the building?

A. 25√3 meters
B. 50 meters
C. 30 meters
D. 40 meters

Solution

Using tan(60) = height / 50, height = 50 * tan(60) = 50 * √3 = 25√3 meters.

Correct Answer: A — 25√3 meters

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Q. A point Q divides the segment joining P(1, 1) and R(7, 5) in the ratio 2:1. What are the coordinates of Q?

A. (5, 3)
B. (4, 2)
C. (6, 4)
D. (3, 2)

Solution

Using the section formula: Q = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) where m=2, n=1. Q = ((2*7 + 1*1)/(2+1), (2*5 + 1*1)/(2+1)) = (5, 3).

Correct Answer: A — (5, 3)

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Q. A rectangle has a length of 10 cm and a width of 2 cm. What is its area?

A. 20 cm²
B. 22 cm²
C. 24 cm²
D. 26 cm²

Solution

Area = length × width = 10 cm × 2 cm = 20 cm².

Correct Answer: A — 20 cm²

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Q. A rectangle has a length of 10 m and a width of 2 m. What is its area?

A. 12 m²
B. 20 m²
C. 22 m²
D. 24 m²

Solution

Area = length × width = 10 m × 2 m = 20 m².

Correct Answer: B — 20 m²

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Q. A rectangle has a length of 5 cm and a width of 3 cm. What is its perimeter?

A. 8 cm
B. 10 cm
C. 16 cm
D. 18 cm

Solution

Perimeter = 2(length + width) = 2(5 + 3) = 16 cm

Correct Answer: C — 16 cm

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Q. A rectangle has a length of 8 cm and a width of 2 cm. What is its area?

A. 16 cm²
B. 20 cm²
C. 10 cm²
D. 12 cm²

Solution

Area = length × width = 8 cm × 2 cm = 16 cm².

Correct Answer: A — 16 cm²

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Q. A rectangle has a length of 8 cm and a width of 3 cm. What is its area?

A. 24 cm²
B. 26 cm²
C. 30 cm²
D. 32 cm²

Solution

Area = length × width = 8 cm × 3 cm = 24 cm².

Correct Answer: A — 24 cm²

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Q. A rectangle has a length of 8 cm and a width of 3 cm. What is its perimeter?

A. 22 cm
B. 24 cm
C. 20 cm
D. 26 cm

Solution

Perimeter = 2(length + width) = 2(8 + 3) = 22 cm.

Correct Answer: A — 22 cm

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Q. A rectangle has a length of 8 cm and a width of 5 cm. What is its area?

A. 40 cm²
B. 30 cm²
C. 50 cm²
D. 20 cm²

Solution

Area = length × width = 8 cm × 5 cm = 40 cm².

Correct Answer: A — 40 cm²

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Q. A rectangle has a length of 8 m and a width of 3 m. What is its perimeter?

A. 22 m
B. 24 m
C. 20 m
D. 26 m

Solution

Perimeter = 2 * (length + width) = 2 * (8 + 3) = 22 m.

Correct Answer: A — 22 m

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Q. A rectangle has a length that is 3 times its width. If the perimeter of the rectangle is 48 cm, what is the width?

A. 4 cm
B. 6 cm
C. 8 cm
D. 10 cm

Solution

Let the width be w cm. Then the length is 3w cm. The perimeter is given by: 2(length + width) = 48. Thus, 2(3w + w) = 48. Simplifying gives 8w = 48, so w = 6 cm.

Correct Answer: B — 6 cm

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Q. A rectangle has a length that is twice its width. If the width is w, what is the area of the rectangle?

A. 2w^2
B. w^2
C. 2w
D. w

Solution

Area = Length × Width. Length = 2w, so Area = 2w × w = 2w^2.

Correct Answer: A — 2w^2

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Q. A rectangle has an area of 24 cm² and a width of 4 cm. What is its length?

A. 6 cm
B. 8 cm
C. 4 cm
D. 5 cm

Solution

Area = length × width, so length = Area ÷ width = 24 cm² ÷ 4 cm = 6 cm.

Correct Answer: A — 6 cm

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Q. A rectangle has an area of 30 cm² and a width of 5 cm. What is its length?

A. 6 cm
B. 5 cm
C. 7 cm
D. 8 cm

Solution

Area = length × width, so length = Area ÷ width = 30 cm² ÷ 5 cm = 6 cm.

Correct Answer: A — 6 cm

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Q. A rectangle's length is 3 times its width. If the perimeter is 48 cm, what is the width?

A. 4 cm
B. 6 cm
C. 8 cm
D. 10 cm

Solution

Let the width be x. Then, length = 3x. The perimeter is 2(length + width) = 48. So, 2(3x + x) = 48. Simplifying gives 8x = 48, thus x = 6 cm.

Correct Answer: C — 8 cm

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Q. A rectangle's length is 3 times its width. If the perimeter is 48, what is the width?

A. 4
B. 6
C. 8
D. 10

Solution

Let the width be w. Then the length is 3w. The perimeter is 2(w + 3w) = 48. Simplifying gives 8w = 48. Dividing by 8 gives w = 6.

Correct Answer: B — 6

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Q. A right triangle has legs of lengths 6 cm and 8 cm. What is the area of the triangle?

A. 24 cm²
B. 30 cm²
C. 48 cm²
D. 36 cm²

Solution

Area = 1/2 * base * height = 1/2 * 6 * 8 = 24 cm².

Correct Answer: A — 24 cm²

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Q. A right triangle has legs of lengths 6 cm and 8 cm. What is the length of the hypotenuse?

A. 10 cm
B. 12 cm
C. 14 cm
D. 16 cm

Solution

Using the Pythagorean theorem, hypotenuse = √(6² + 8²) = √(36 + 64) = √100 = 10 cm.

Correct Answer: A — 10 cm

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Q. A school has 120 students. If the number of boys is twice the number of girls, how many boys are there?

A. 30
B. 40
C. 80
D. 60

Solution

Let the number of girls be x. Then the number of boys is 2x. The equation is x + 2x = 120. Solving gives 3x = 120, so x = 40. Therefore, boys = 2x = 80.

Correct Answer: D — 60

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Q. A school has a total of 300 students. If the ratio of boys to girls is 3:2, how many girls are there?

A. 120
B. 150
C. 180
D. 200

Solution

Let the number of boys be 3x and the number of girls be 2x. Then, 3x + 2x = 300. This gives 5x = 300, so x = 60. Therefore, the number of girls is 2x = 120.

Correct Answer: B — 150

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Q. A school has boys and girls in the ratio of 5:3. If there are 64 students in total, how many girls are there?

A. 24
B. 32
C. 40
D. 16

Solution

Let the number of girls be 3x and boys be 5x. The equation is 3x + 5x = 64. Solving gives 8x = 64, so x = 8. Therefore, girls = 3x = 24.

Correct Answer: A — 24

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Q. A sector of a circle has a radius of 5 cm and a central angle of 60 degrees. What is the area of the sector?

A. 13.09 cm²
B. 25 cm²
C. 15.71 cm²
D. 20.94 cm²

Solution

Area of sector = (θ/360) * πr² = (60/360) * π(5)² = (1/6) * 25π ≈ 13.09 cm².

Correct Answer: A — 13.09 cm²

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Q. A sector of a circle has a radius of 6 cm and a central angle of 60 degrees. What is the area of the sector?

A. 12π cm²
B. 6π cm²
C. 3π cm²
D. 9π cm²

Solution

Area of sector = (θ/360) * πr² = (60/360) * π(6)² = (1/6) * 36π = 6π cm².

Correct Answer: B — 6π cm²

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Q. A square has a side length of 4 cm. What is its area?

A. 8 cm²
B. 12 cm²
C. 16 cm²
D. 20 cm²

Solution

Area = side x side = 4 x 4 = 16 cm²

Correct Answer: C — 16 cm²

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Q. A square has a side length of 4 cm. What is its perimeter?

A. 16 cm
B. 12 cm
C. 8 cm
D. 20 cm

Solution

Perimeter = 4 sides × 4 cm = 16 cm.

Correct Answer: A — 16 cm

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Q. A square has a side length of 4 m. What is its area?

A. 8 m²
B. 12 m²
C. 16 m²
D. 20 m²

Solution

Area = side² = 4² = 16 m².

Correct Answer: C — 16 m²

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