POST UTME OSUSTECH 2025 Mathematics | Objective

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Question 1 View Details
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\pitext{ cm}^3
Correct B. 300\pitext{ cm}^3
C. 400\pitext{ cm}^3
D. 500\pitext{ cm}^3

Correct Answer: B

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Question 2 View Details
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 View Details
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 View Details
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 View Details
A circle has a radius of 4 cm. Find the area of the circle.
A. 16\pitext{ cm}^2
B. 32\pitext{ cm}^2
Correct C. 64\pitext{ cm}^2
D. 128\pitext{ cm}^2

Correct Answer: C

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Question 6 View Details
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 View Details
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 View Details
A histogram of exam scores has a mean of 75 and a standard 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 View Details
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 View Details
A rectangular 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 View Details
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 View Details
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 View Details
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 View Details
A histogram of exam scores has a mean of 60 and a standard 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 View Details
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 View Details
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 View Details
Find the equation of the tangent line to the curve \(y = \frac{1}{x}\\(tangent line to the curve (y =\) 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 View Details
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 View Details
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 View Details
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 View Details
A set of 5 numbers has a mean of 10 and a standard 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 View Details
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 View Details
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 View Details
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 distance of the point \(P 1, -1, 2 \\((2x - 3y + 4z = 7). Find the distance of the point \\) ) 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 View Details
A rectangular 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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