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POST UTME OSUSTECH 2025 Mathematics | Objective

Are you preparing for POST UTME OSUSTECH exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2025 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Determine the volume of the frustum of a cone with a height of 15 cm, a lower base radius of 4 cm, and an upper base radius of 6 cm.

A. 200\pi\text{ cm}^3

Correct B. 300\pi\text{ cm}^3

C. 400\pi\text{ cm}^3

D. 500\pi\text{ cm}^3

Correct Answer: B

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Question 2

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

A. 1022

B. 1023

Correct C. 1024

D. 1025

Correct Answer: C

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Question 3

Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).

A. 2

B. 4

Correct C. 10

D. 20

Correct Answer: C

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Question 4

A right-angled triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.

A. 4\text{ cm}

B. 6\text{ cm}

Correct C. 8\text{ cm}

D. 10\text{ cm}

Correct Answer: C

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Question 5

A circle has a radius of 4 cm. Find the area of the circle.

A. 16\pi\text{ cm}^2

B. 32\pi\text{ cm}^2

Correct C. 64\pi\text{ cm}^2

D. 128\pi\text{ cm}^2

Correct Answer: C

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Question 6

Determine the value of x in the equation \( \frac{x}{2} + 5 = 11 \).

Correct A. 4

B. 6

C. 8

D. 10

Correct Answer: A

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Question 7

Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \) for x.

Correct A. \frac{\pi}{4}

B. \frac{\pi}{2}

C. \frac{3\pi}{4}

D. \pi

Correct Answer: A

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Question 8

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. What is the probability that a randomly selected score is between 60 and 90?

A. 0.68

Correct B. 0.73

C. 0.83

D. 0.93

Correct Answer: B

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Question 9

A box contains 5 red balls and 3 blue balls. If a ball is randomly selected, what is the probability that it is red?

Correct A. \frac{1}{2}

B. \frac{2}{3}

C. \frac{3}{4}

D. \frac{4}{5}

Correct Answer: A

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Question 10

A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. What is its volume?

A. 30

B. 40

Correct C. 50

D. 60

Correct Answer: C

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Question 11

Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).

A. 10

Correct B. 100

C. 1000

D. 10000

Correct Answer: B

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Question 12

Find the value of y in the equation \( y = \frac{1}{2} \left\( \frac{1}{2} \right \ \)^x ).

A. 0.5

B. 0.25

Correct C. 0.125

D. 0.0625

Correct Answer: C

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Question 13

Solve the inequality \( 2x^2 + 5x - 3 > 0 \).

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, -3 \) ∪ (1, ∞)

C. \( -∞, 1 \) ∪ (3, ∞)

D. \( -∞, -3 \) ∪ (1, ∞)

Correct Answer: A

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Question 14

A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. What is the probability that a randomly selected score is between 50 and 70?

A. 0.5

Correct B. 0.6

C. 0.7

D. 0.8

Correct Answer: B

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Question 15

Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ).

Correct A. 6x + 2

B. 6x - 2

C. 3x + 2

D. 3x - 2

Correct Answer: A

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Question 16

Determine the sum of the first 10 terms of the geometric series with first term 3 and common ratio 2.

A. \( 3 + 6 + 12 + 24 + 48 + 96 + 192 + 384 + 768 + 1536 \)

B. \( 3 + 6 + 12 + 24 + 48 + 96 + 192 + 384 + 768 + 1536 + 3072 \)

C. \( 3 + 6 + 12 + 24 + 48 + 96 + 192 + 384 + 768 + 1536 - 3072 \)

Correct D. \( 3 + 6 + 12 + 24 + 48 + 96 + 192 + 384 + 768 + 1536 \)

Correct Answer: D

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Question 17

Find the equation of the \tangent line to the curve \( y = \frac{1}{x} \) at the point where \( x = 2 \).

Correct A. \( y = -\frac{1}{2}x + 1 \)

B. \( y = \frac{1}{2}x + 1 \)

C. \( y = -\frac{1}{2}x - 1 \)

D. \( y = \frac{1}{2}x - 1 \)

Correct Answer: A

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Question 18

A histogram of exam scores for a class of 50 students is shown below. What is the mean score?

A. 25

Correct B. 30

C. 35

D. 40

Correct Answer: B

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Question 19

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

A. \( \frac{1}{6} \)

B. \( \frac{1}{3} \)

C. \( \frac{2}{3} \)

Correct D. \( \frac{5}{6} \)

Correct Answer: D

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Question 20

Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 2 \).

Correct A. \( \frac{8}{3} \)

B. \( \frac{16}{3} \)

C. \( \frac{32}{3} \)

D. \( \frac{64}{3} \)

Correct Answer: A

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Question 21

A set of 5 numbers has a mean of 10 and a s\tandard deviation of 2. What is the probability that a randomly selected number from this set is greater than 12?

A. \( \frac{1}{4} \)

B. \( \frac{1}{2} \)

Correct C. \( \frac{3}{4} \)

D. \( \frac{3}{2} \)

Correct Answer: C

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Question 22

Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ).

Correct A. ( f'(x) = 6x + 2 )

B. ( f'(x) = 6x - 2 )

C. ( f'(x) = 6x + 4 )

D. ( f'(x) = 6x - 4 )

Correct Answer: A

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Question 23

A population of 1000 bacteria is growing at a rate of 20% per hour. What is the population after 3 hours?

Correct A. ( 1000(1.2)^3 )

B. ( 1000(1.2)^2 )

C. ( 1000(1.2)^4 )

D. ( 1000(1.2)^5 )

Correct Answer: A

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Question 24

In a 3D coordinate system, the equation of a plane in the form \( Ax + By + Cz = D \) is given by \( 2x - 3y + 4z = 7 \). Find the dis\tance of the point \( P\( 1, -1, 2 \ \) ) from the plane.

A. \( \frac{1}{2} \)

B. \( \frac{3}{2} \)

Correct C. \( \frac{5}{2} \)

D. \( \frac{7}{2} \)

Correct Answer: C

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Question 25

A rec\tangular box has dimensions ( x ), ( 2x ), and ( 3x ). If its surface area is 72 square units, find the volume of the box.

A. \( 24x^3 \)

B. \( 36x^3 \)

Correct C. \( 48x^3 \)

D. \( 60x^3 \)

Correct Answer: C

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