Mathematics (School)

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

Q. What is the area of a triangle with vertices at (0, 0), (6, 0), and (3, 4)?

A. 12
B. 14
C. 16
D. 18

Solution

Area = 1/2 * base * height = 1/2 * 6 * 4 = 12.

Correct Answer: A — 12

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Q. What is the area of a triangle with vertices at (0, 0), (b, 0), and (0, h)?

A. bh/2
B. bh
C. b+h
D. b*h/2

Solution

Area = 1/2 * base * height = 1/2 * b * h = bh/2.

Correct Answer: A — bh/2

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Q. What is the area of a triangle with vertices at (0, 0), (b, 0), and (b/2, h)?

A. (bh)/2
B. (b^2h)/2
C. (b^2)/2
D. (bh)/4

Solution

Area = 1/2 * base * height = 1/2 * b * h = (bh)/2.

Correct Answer: A — (bh)/2

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Q. What is the area of a triangle with vertices at (1, 1), (4, 1), and (1, 5)?

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

Solution

Area = 1/2 * base * height = 1/2 * (4 - 1) * (5 - 1) = 1/2 * 3 * 4 = 6.

Correct Answer: A — 6

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Q. What is the area of a triangle with vertices at (1, 1), (4, 5), and (7, 2)?

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

Solution

Area = 0.5 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)| = 0.5 * |1(5 - 2) + 4(2 - 1) + 7(1 - 5)| = 0.5 * |3 + 4 - 28| = 0.5 * 21 = 10.5.

Correct Answer: B — 12

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Q. What is the area of an equilateral triangle with a side length of 4 cm?

A. 4√3 cm²
B. 8 cm²
C. 4 cm²
D. 16 cm²

Solution

Area = (√3/4)s² = (√3/4)(4)² = (√3/4)(16) = 4√3 cm².

Correct Answer: A — 4√3 cm²

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Q. What is the area of an isosceles triangle with a base of 10 cm and equal sides of 13 cm?

A. 60 cm²
B. 65 cm²
C. 70 cm²
D. 75 cm²

Solution

Using Heron's formula, s = (10 + 13 + 13) / 2 = 18. Area = √(s(s-a)(s-b)(s-c)) = √(18(18-10)(18-13)(18-13)) = √(18*8*5*5) = 60 cm².

Correct Answer: B — 65 cm²

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Q. What is the area of triangle formed by points A(0, 0), B(4, 0), and C(0, 3)?

A. 6.0
B. 12.0
C. 8.0
D. 10.0

Solution

Area = 1/2 * base * height = 1/2 * 4 * 3 = 6.0.

Correct Answer: A — 6.0

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Q. What is the area of triangle formed by points A(0, 0), B(4, 0), and C(4, 3)?

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

Solution

Area = 0.5 * base * height = 0.5 * 4 * 3 = 6.

Correct Answer: A — 6

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Q. What is the area of triangle formed by the points (0, 0), (4, 0), and (0, 3)?

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

Solution

Area = 1/2 * base * height = 1/2 * 4 * 3 = 6.

Correct Answer: A — 6

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Q. What is the area of triangle PQR with a base of 10 cm and a height of 5 cm?

A. 25 cm²
B. 30 cm²
C. 50 cm²
D. 15 cm²

Solution

Area = 1/2 * base * height = 1/2 * 10 * 5 = 25 cm².

Correct Answer: A — 25 cm²

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Q. What is the circumference of a circle with a diameter of 10 cm?

A. 31.4 cm
B. 20 cm
C. 15.7 cm
D. 25 cm

Solution

The circumference of a circle is calculated using the formula C = πd. For d = 10 cm, C = π(10) ≈ 31.4 cm.

Correct Answer: A — 31.4 cm

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Q. What is the circumference of a circle with a diameter of 10 units?

A. 10π
B. 20π
C. 5π
D. 15π

Solution

The circumference of a circle is given by C = πd. For d = 10, C = π(10) = 10π.

Correct Answer: B — 20π

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Q. What is the circumference of a circle with a diameter of 10?

A. 10π
B. 20π
C. 30π
D. 40π

Solution

Circumference = πd = π(10) = 10π.

Correct Answer: B — 20π

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Q. What is the circumference of a circle with a diameter of 12 cm? (Use π = 3.14)

A. 37.68 cm
B. 24 cm
C. 12 cm
D. 18.84 cm

Solution

Circumference = π * diameter = 3.14 * 12 cm = 37.68 cm.

Correct Answer: A — 37.68 cm

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Q. What is the circumference of a circle with a diameter of 12 units?

A. 12π units
B. 24π units
C. 6π units
D. 36π units

Solution

The circumference of a circle is given by C = πd. For a diameter of 12 units, C = π * 12 = 12π units.

Correct Answer: B — 24π units

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Q. What is the circumference of a circle with a radius of 3 cm?

A. 6π cm
B. 9π cm
C. 12π cm
D. 15π cm

Solution

Circumference = 2πr = 2π(3) = 6π cm.

Correct Answer: A — 6π cm

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Q. What is the circumference of a circle with a radius of 4 cm?

A. 12.56 cm
B. 25.12 cm
C. 16 cm
D. 50.24 cm

Solution

Circumference = 2πr = 2π(4) = 8π ≈ 25.12 cm.

Correct Answer: A — 12.56 cm

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Q. What is the circumference of a circle with a radius of 5 cm?

A. 10π cm
B. 15π cm
C. 20π cm
D. 25π cm

Solution

Circumference = 2πr = 2π(5) = 10π cm.

Correct Answer: A — 10π cm

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Q. What is the circumference of a circle with a radius of 5 units?

A. 10π
B. 15π
C. 20π
D. 25π

Solution

The circumference of a circle is given by the formula: C = 2πr. Here, r = 5, so C = 2π * 5 = 10π.

Correct Answer: A — 10π

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Q. What is the circumference of a circle with a radius of 5?

A. 10π
B. 15π
C. 20π
D. 25π

Solution

Circumference = 2πr = 2π(5) = 10π.

Correct Answer: A — 10π

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Q. What is the circumference of a circle with a radius of 7 cm? (Use π ≈ 3.14)

A. 43.96 cm
B. 44.00 cm
C. 42.00 cm
D. 45.00 cm

Solution

Circumference = 2 * π * radius = 2 * 3.14 * 7 = 43.96 cm.

Correct Answer: A — 43.96 cm

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Q. What is the circumference of a circle with a radius of 7 units?

A. 14π
B. 21π
C. 28π
D. 7π

Solution

The circumference of a circle is given by the formula C = 2πr. Therefore, C = 2π * 7 = 14π.

Correct Answer: A — 14π

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Q. What is the circumference of a circle with a radius of 7?

A. 14π
B. 21π
C. 28π
D. 35π

Solution

Circumference = 2πr = 2π(7) = 14π.

Correct Answer: B — 21π

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Q. What is the circumradius of a triangle with sides 5 cm, 12 cm, and 13 cm?

A. 6.5 cm
B. 7 cm
C. 8 cm
D. 5 cm

Solution

For a right triangle, circumradius R = hypotenuse / 2 = 13 / 2 = 6.5 cm.

Correct Answer: B — 7 cm

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Q. What is the common difference in the arithmetic progression 7, 10, 13, ...?

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

Solution

The common difference d is found by subtracting the first term from the second term: d = 10 - 7 = 3.

Correct Answer: B — 3

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Q. What is the common difference in the sequence 3, 7, 11, 15, ...?

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

Solution

The common difference is found by subtracting the first term from the second: 7 - 3 = 4.

Correct Answer: B — 3

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Q. What is the common ratio of the geometric sequence 3, 6, 12, ...?

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

Solution

The common ratio is found by dividing the second term by the first: 6/3 = 2.

Correct Answer: A — 2

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Q. What is the coordinates of the midpoint of the line segment joining (3, 7) and (9, 1)?

A. (6, 4)
B. (5, 5)
C. (7, 4)
D. (8, 3)

Solution

Using the midpoint formula: M = ((3 + 9)/2, (7 + 1)/2) = (6, 4).

Correct Answer: A — (6, 4)

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Q. What is the coordinates of the point that divides the line segment joining (0, 0) and (6, 8) in the ratio 3:1?

A. (4.5, 6)
B. (3, 4)
C. (4, 5)
D. (3.5, 4)

Solution

Using the section formula: P = ((3*6 + 1*0)/(3+1), (3*8 + 1*0)/(3+1)) = (4.5, 6).

Correct Answer: A — (4.5, 6)

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