Mathematics (School)

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

Q. If a quadrilateral is a rectangle, what can be said about its diagonals?

A. They are equal and bisect each other
B. They are unequal
C. They are perpendicular
D. They are parallel

Solution

In a rectangle, the diagonals are equal in length and bisect each other.

Correct Answer: A — They are equal and bisect each other

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Q. If a quadrilateral is a rectangle, which of the following statements is true?

A. All sides are equal
B. Opposite sides are equal
C. All angles are acute
D. Diagonals are perpendicular

Solution

In a rectangle, opposite sides are equal in length.

Correct Answer: B — Opposite sides are equal

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Q. If a recipe calls for 2 cups of flour and you want to make half the recipe, how much flour do you need?

A. 1 cup
B. 2 cups
C. 3 cups
D. 4 cups

Solution

2 cups ÷ 2 = 1 cup

Correct Answer: A — 1 cup

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Q. If a recipe calls for 2 cups of flour and you want to make half the recipe, how many cups do you need?

A. 1
B. 2
C. 3
D. 4

Solution

2 cups ÷ 2 = 1 cup

Correct Answer: A — 1

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Q. If a recipe needs 2 cups of flour and you want to make half the recipe, how many cups do you need?

A. 1
B. 2
C. 3
D. 4

Solution

2 cups ÷ 2 = 1 cup

Correct Answer: A — 1

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Q. If a recipe needs 2 cups of flour for every 3 cups of sugar, how many cups of flour are needed for 6 cups of sugar?

A. 2
B. 3
C. 4
D. 5

Solution

For 6 cups of sugar, you need (2/3) * 6 = 4 cups of flour.

Correct Answer: C — 4

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Q. If a rectangle has a length of (x + 2) and a width of (x - 3), what is the area?

A. x^2 - x - 6
B. x^2 + x - 6
C. x^2 - 6
D. x^2 + 6

Solution

Area = Length × Width = (x + 2)(x - 3) = x^2 - 3x + 2x - 6 = x^2 - x - 6.

Correct Answer: A — x^2 - x - 6

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Q. If a rectangle has a length of 10 cm and a width of 2 cm, what is its area?

A. 20 cm²
B. 12 cm²
C. 15 cm²
D. 25 cm²

Solution

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

Correct Answer: A — 20 cm²

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Q. If a rectangle has a length of 10 cm and a width of 4 cm, what is its area?

A. 40 cm²
B. 44 cm²
C. 50 cm²
D. 60 cm²

Solution

Area of a rectangle is calculated as length × width, so 10 cm × 4 cm = 40 cm².

Correct Answer: A — 40 cm²

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Q. If a rectangle has a length of 3x and a width of 2x, what is its area?

A. 5x^2
B. 6x^2
C. 7x^2
D. 8x^2

Solution

Area = Length × Width = 3x × 2x = 6x^2.

Correct Answer: B — 6x^2

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Q. If 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. 20 cm

Solution

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

Correct Answer: C — 16 cm

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Q. If a rectangle has a length of 7 cm and a width of 5 cm, what is its area?

A. 30 cm²
B. 32 cm²
C. 35 cm²
D. 40 cm²

Solution

Area = length × width = 7 cm × 5 cm = 35 cm².

Correct Answer: C — 35 cm²

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Q. If a rectangle has a length of 7 cm and an area of 28 cm², what is its width?

A. 3 cm
B. 4 cm
C. 5 cm
D. 6 cm

Solution

Width = Area ÷ length = 28 cm² ÷ 7 cm = 4 cm.

Correct Answer: B — 4 cm

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Q. If a rectangle has a perimeter of 24 cm and a length of 10 cm, what is its width?

A. 2 cm
B. 4 cm
C. 6 cm
D. 8 cm

Solution

Perimeter = 2(length + width) => 24 cm = 2(10 cm + width) => width = 4 cm.

Correct Answer: B — 4 cm

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Q. If a rectangle has a perimeter of 30 cm and a length of 10 cm, what is its width?

A. 5 cm
B. 7.5 cm
C. 10 cm
D. 12.5 cm

Solution

Perimeter = 2(length + width), so 30 cm = 2(10 cm + width). Width = (30 cm/2) - 10 cm = 5 cm.

Correct Answer: B — 7.5 cm

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Q. If a rectangle has an area of 24 cm² and a width of 4 cm, what is its length?

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

Solution

Length = Area ÷ width = 24 cm² ÷ 4 cm = 6 cm.

Correct Answer: B — 6 cm

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Q. If a rectangle has vertices at (1, 1), (1, 4), (5, 1), and (5, 4), what is its area?

A. 12
B. 16
C. 20
D. 24

Solution

The area of a rectangle is given by the formula: Area = length * width. The length is 5 - 1 = 4 and the width is 4 - 1 = 3. Thus, Area = 4 * 3 = 12.

Correct Answer: B — 16

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Q. If a rectangle's length is doubled and its width is halved, what happens to its area?

A. It remains the same
B. It doubles
C. It halves
D. It quadruples

Solution

New area = (2 * length) * (width/2) = length * width = original area, so it doubles.

Correct Answer: B — It doubles

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Q. If a regular hexagon has a side length of 3 cm, what is the perimeter of the hexagon?

A. 9 cm
B. 12 cm
C. 15 cm
D. 18 cm

Solution

The perimeter of a regular hexagon is calculated as 6 times the side length. Therefore, perimeter = 6 × 3 cm = 18 cm.

Correct Answer: D — 18 cm

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Q. If a regular hexagon has a side length of 6 cm, what is its perimeter?

A. 24 cm
B. 30 cm
C. 36 cm
D. 42 cm

Solution

The perimeter of a regular hexagon is calculated as P = 6 * side length. Here, P = 6 * 6 cm = 36 cm.

Correct Answer: C — 36 cm

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Q. If a regular hexagon has a side length of 6 cm, what is the perimeter of the hexagon?

A. 24 cm
B. 30 cm
C. 36 cm
D. 42 cm

Solution

The perimeter of a regular hexagon is calculated as 6 times the side length. Therefore, perimeter = 6 × 6 cm = 36 cm.

Correct Answer: C — 36 cm

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Q. If a rhombus has diagonals of lengths 10 and 24, what is its area?

A. 120
B. 140
C. 160
D. 180

Solution

Area = (d1 * d2) / 2 = (10 * 24) / 2 = 120.

Correct Answer: A — 120

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Q. If a shirt costs $20 and is on sale for 10% off, how much is the discount?

A. $1
B. $2
C. $3
D. $4

Solution

10% of $20 = $2

Correct Answer: D — $4

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Q. If a shirt costs $40 and is on sale for 25% off, how much is the discount?

A. $5
B. $10
C. $15
D. $20

Solution

25% of $40 = $10

Correct Answer: B — $10

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Q. If a square has a perimeter of 32 cm, what is the area of the square?

A. 64 cm²
B. 128 cm²
C. 16 cm²
D. 32 cm²

Solution

Side length = perimeter/4 = 32/4 = 8 cm. Area = side² = 8² = 64 cm².

Correct Answer: A — 64 cm²

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Q. If a square has a perimeter of 40 cm, what is the area of the square?

A. 100 cm²
B. 160 cm²
C. 200 cm²
D. 250 cm²

Solution

Side length = perimeter/4 = 40/4 = 10 cm. Area = side² = 10² = 100 cm².

Correct Answer: A — 100 cm²

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Q. If a square has a perimeter of 40 cm, what is the length of one side?

A. 5 cm
B. 10 cm
C. 15 cm
D. 20 cm

Solution

The perimeter of a square is calculated as 4 times the side length. Therefore, if the perimeter is 40 cm, then side length = 40 cm / 4 = 10 cm.

Correct Answer: B — 10 cm

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Q. If a square has a side length of 4 cm, what is its area?

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

Solution

The area of a square is given by the formula: Area = side². Here, side = 4 cm. Area = 4² = 16 cm².

Correct Answer: A — 16 cm²

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Q. If a square has a side length of 4 cm, what is its perimeter?

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

Solution

Perimeter = 4 × side = 4 × 4 cm = 16 cm.

Correct Answer: B — 16 cm

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Q. If a square has a side length of 5 cm, what is its area?

A. 20 cm²
B. 25 cm²
C. 30 cm²
D. 15 cm²

Solution

The area of a square is given by the formula: Area = side². Here, Area = 5² = 25 cm².

Correct Answer: B — 25 cm²

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