POST UTME UNIOSUN 2022 Mathematics | Objective

Are you preparing for POST UTME UNIOSUN exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2022 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1
Determine the value of $x$ in the equation \( \log_{10} \( x^2 \ \) = 4 ).
Correct A. 10
B. 100
C. 1000
D. 10000

Correct Answer: A

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Question 2
A survey of 100 students found that 60 students preferred Mathematics, 30 preferred Science, and 10 preferred both. What is the probability that a randomly selected student prefers either Mathematics or Science?
A. 0.7
Correct B. 0.75
C. 0.8
D. 0.85

Correct Answer: B

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Question 3
The volume of a rec\tangular prism is given by \( V = lwh \). If the length, width, and height of the prism are in the ratio 2:3:4, and the volume is 288 cubic units, find the length of the prism.
A. 6
Correct B. 8
C. 12
D. 16

Correct Answer: B

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Question 4
Solve the inequality \( x^2 - 6x + 8 > 0 \).
Correct A. \( -∞, 2 \) ∪ (4, ∞)
B. \( -∞, 2 \) ∪ (4, ∞)
C. \( -∞, 2 \) ∪ (4, ∞)
D. \( -∞, 2 \) ∪ (4, ∞)

Correct Answer: A

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Question 5
A company produces two products, A and B. The profit from the sale of one unit of product A is ₦100, and the profit from the sale of one unit of product B is ₦120. If the company produces 200 units of product A and 150 units of product B, what is the total profit?
A. ₦35,000
B. ₦40,000
C. ₦45,000
Correct D. ₦50,000

Correct Answer: D

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Question 6
In a set of consecutive integers, the sum of the first 5 terms is 15, and the sum of the next 5 terms is 25. What is the sum of the first 10 terms?
A. 40
B. 50
Correct C. 60
D. 70

Correct Answer: C

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Question 7
A sequence is defined by the recurrence relation $a_n = 2a_{n-1} + 3$, with initial term $a_1 = 2$. Find the sum of the first 5 terms of the sequence.
A. 35
B. 40
C. 45
Correct D. 50

Correct Answer: D

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Question 8
A histogram is constructed with 5 classes, each of width 2. The heights of the bars are 3, 5, 7, 9, and 11. What is the mean of the data?
A. 6
B. 7
Correct C. 8
D. 9

Correct Answer: C

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Question 9
A circle has equation $x^2 + y^2 = 16$. Find the equation of the \tangent line at point $(4, 0)$.
Correct A. y = -x + 4
B. y = x + 4
C. y = -x - 4
D. y = x - 4

Correct Answer: A

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Question 10
Two events are indep\endent if the occurrence of one does not affect the probability of the other. If event A has probability 0.4 and event B has probability 0.6, are events A and B indep\endent?
A. Yes
B. No
C. Maybe
Correct D. Not enough information

Correct Answer: D

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Question 11
In a circle with center $C$ and radius $5$, a chord $AB$ is drawn such that $AC = 3$. Find the length of $AB$.
A. 4
Correct B. 6
C. 8
D. 10

Correct Answer: B

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Question 12
Solve for $x$ in the equation $\log_{2}(x) + \log_{2}\( x+1 \) = 3$.
A. 4
Correct B. 5
C. 6
D. 7

Correct Answer: B

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Question 13
A function $f(x)$ is defined as $f(x) = \frac{x^2 - 4}{x - 2}$. Find the domain of $f(x)$.
Correct A. \( -\infty, 2 \) \cup \( 2, \infty \)
B. \( -\infty, 2 \) \cup (2, 4]
C. \( -\infty, 2 \) \cup \( 4, \infty \)
D. \( -\infty, 4] \cup \( 4, \infty \ \)

Correct Answer: A

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Question 14
In a triangle $ABC$, $AB = 5$, $BC = 6$, and $\angle B = 60^\circ$. Find the length of $AC$.
A. 4
Correct B. 5
C. 6
D. 7

Correct Answer: B

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Question 15
A circle with center $O$ and radius $3$ is inscribed in a square with side length $6$. Find the area of the shaded region.
A. 12
Correct B. 18
C. 24
D. 36

Correct Answer: B

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Question 16
Find the derivative of ( f(x) = \frac{1}{\sqrt{x}} ) u\sing the chain rule.
Correct A. ( f'(x) = -\frac{1}{2}x^{-\frac{3}{2}} )
B. ( f'(x) = \frac{1}{2}x^{-\frac{3}{2}} )
C. ( f'(x) = -\frac{1}{2}x^{-\frac{1}{2}} )
D. ( f'(x) = \frac{1}{2}x^{-\frac{1}{2}} )

Correct Answer: A

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Question 17
Solve for ( x ) in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ).
Correct A. \( x = \frac{pi}{4} \)
B. \( x = \frac{3pi}{4} \)
C. \( x = \frac{pi}{2} \)
D. \( x = \frac{5pi}{4} \)

Correct Answer: A

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Question 18
Find the volume of the solid formed by revolving the region bounded by \( y = x^2 \) and \( y = 4 \) about the x-axis.
Correct A. \( \frac{32pi}{3} \)
B. \( \frac{64pi}{3} \)
C. \( \frac{128pi}{3} \)
D. \( \frac{256pi}{3} \)

Correct Answer: A

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Question 19
Find the equation of the circle with center ( (2,3) ) and radius ( 4 ).
Correct A. \( x-2 \ \)^2 + \( y-3 \)^2 = 16 )
B. \( x-2 \ \)^2 + \( y-3 \)^2 = 4 )
C. \( x-2 \ \)^2 + \( y-3 \)^2 = 9 )
D. \( x-2 \ \)^2 + \( y-3 \)^2 = 25 )

Correct Answer: A

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Question 20
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
Correct A. \( \frac{64}{3} \)
B. \( \frac{128}{3} \)
C. \( \frac{256}{3} \)
D. \( \frac{512}{3} \)

Correct Answer: A

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Question 21
Determine the value of x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) if \( \tan\( x \ \) = 3 ).
Correct A. \( \frac{pi}{3} \)
B. \( \frac{pi}{4} \)
C. \( \frac{pi}{6} \)
D. \( \frac{pi}{2} \)

Correct Answer: A

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Question 22
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
Correct A. ( f'(x) = \frac{-2x}{\( x^2 + 1 \)^2} )
B. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )
C. ( f'(x) = \frac{2}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{-2}{\( x^2 + 1 \)^2} )

Correct Answer: A

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Question 23
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
Correct A. \( x > -1 \) or \( x < 3 \)
B. \( x > 1 \) or \( x < -3 \)
C. \( x > -3 \) or \( x < 1 \)
D. \( x > 3 \) or \( x < -1 \)

Correct Answer: A

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Question 24
Determine the value of x in the equation \( \log_{10}\( x \ \) = 2 ).
Correct A. \( x = 100 \)
B. \( x = 10 \)
C. \( x = 1 \)
D. \( x = 0.1 \)

Correct Answer: A

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Question 25
Find the mean of the data set {2, 4, 6, 8, 10}.
Correct A. \( \frac{30}{5} = 6 \)
B. \( \frac{20}{5} = 4 \)
C. \( \frac{10}{5} = 2 \)
D. \( \frac{40}{5} = 8 \)

Correct Answer: A

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