POST UTME UNIPORT 2025 Mathematics | Objective

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Question 1 View Details
Determine the value of x in the equation \(egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 7 \ 11 \end{bmatrix}\).
A. 2
Correct B. 3
C. 4
D. 5

Correct Answer: B

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

Correct Answer: A

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Question 3 View Details
Solve the inequality \(2x^2 + 5x - 3 > 0\) using the quadratic formula.
Correct A. \(x < -1\) or \(x > \frac{3}{2}\)
B. \(x < -\frac{3}{2}\) or \(x > 1\)
C. \(x < -1\) or \(x < \frac{3}{2}\)
D. \(x > -1\) or \(x < \frac{3}{2}\)

Correct Answer: A

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Question 4 View Details
A set A contains the elements {1, 2, 3, 4, 5}. Find the number of subsets of A that contain exactly two elements.
A. 10
Correct B. 15
C. 20
D. 25

Correct Answer: B

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Question 5 View Details
A sequence is defined by the recurrence relation \(a_n = 2a_{n-1} + 1\) with initial term \(a_1 = 3\). Find the value of \(a_{10}\).
Correct A. 1023
B. 1024
C. 1025
D. 1026

Correct Answer: A

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Question 6 View Details
Determine the value of x in the equation \(\sin^2 x \\) + \\(\cos^2(x)\) = 1 ) if \($1x \\) = \(\frac{3}{5}\)\) ).
Correct A. \(\frac{4}{5}\)
B. \(\frac{3}{4}\)
C. \(\frac{5}{4}\)
D. \(\frac{4}{3}\)

Correct Answer: A

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Question 7 View Details
A box contains 5 red balls and 3 blue balls. If two balls are drawn at random, what is the probability that they are of different colors?
Correct A. \(\frac{5}{8}\)
B. \(\frac{3}{8}\)
C. \(\frac{2}{5}\)
D. \(\frac{3}{5}\)

Correct Answer: A

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Question 8 View Details
Solve for x in the equation \(2^x + 2^{x+1} = 100\).
A. ( 4 )
Correct B. ( 5 )
C. ( 6 )
D. ( 7 )

Correct Answer: B

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Question 9 View Details
Find the volume of the solid formed by revolving the region bounded by the curves \(y = x^2\) and \(y = 2x\) about the x-axis.
A. \(\frac{32\pi}{3}\)
Correct B. \(\frac{64\pi}{3}\)
C. \(\frac{128\pi}{3}\)
D. \(\frac{256\pi}{3}\)

Correct Answer: B

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Question 10 View Details
A sequence is defined by the recurrence relation \(a_n = 2a_{n-1} + 1\) with initial term \(a_1 = 3\). Find the value of \(a_{10}\).
A. ( 1023 )
Correct B. ( 1024 )
C. ( 1025 )
D. ( 1026 )

Correct Answer: B

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Question 11 View Details
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 48\pi
B. 64\pi
Correct C. 80\pi
D. 96\pi

Correct Answer: C

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Question 12 View Details
Solve the inequality \(\frac{x}{x-1}\)\\() > 0.\)
Correct A. \(x > 1\)
B. \(x < 1\)
C. \(x > 0\)
D. \(x < 0\)

Correct Answer: A

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Question 13 View Details
Find the equation of the line passing through the points (2, 3) and (4, 5).
Correct A. \(y = 2x - 1\)
B. \(y = 2x + 1\)
C. \(y = x - 1\)
D. \(y = x + 1\)

Correct Answer: A

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Question 14 View Details
Solve the quadratic equation \\((x^2 + 5x + 6\)\(= 0.\)\)
A. \(x = -2\)
Correct B. \(x = -3\)
C. \(x = 2\)
D. \(x = 3\)

Correct Answer: B

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Question 15 View Details
Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).
A. 6
B. 8
Correct C. 10
D. 12

Correct Answer: C

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Question 16 View Details
Find the value of x in the equation \(\log_{10} x^2 \\)\(= 4 ).\)
A. 10
B. 100
C. 1000
Correct D. 10000

Correct Answer: D

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Question 17 View Details
A circle has a radius of 5 units. Find the area of the circle.
Correct A. 25\pi
B. 50\pi
C. 75\pi
D. 100\pi

Correct Answer: A

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Question 18 View Details
A histogram shows the distribution of exam scores. If the mean score is 60 and the standard deviation is 10, find 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 19 View Details
Solve the equation \(\sin^2 x + \cos^2 x = 1\).
A. \(x =\)\(\frac{\pi}{4}\)\)
B. \(x =\)\(\frac{\pi}{2}\)\)
C. \(x =\)\\(\frac{3\pi}{4}\)\)
Correct D. \(x =\)\(\frac{\pi}{2}\)\) \text{ or } \(\frac{3\pi}{4}\)\)

Correct Answer: D

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Question 20 View Details
A random experiment has two independent events, A and B. If the probability of event A is 0.4 and the probability of event B is 0.6, find the probability that both events occur.
Correct A. 0.2
B. 0.4
C. 0.6
D. 0.8

Correct Answer: A

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Question 21 View Details
A circle has a radius of 4 units. Find the length of the arc subtended by a central angle of 60 degrees.
A. 2\pi
Correct B. 4\pi
C. 6\pi
D. 8\pi

Correct Answer: B

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Question 22 View Details
A histogram shows the distribution of exam scores. If the mean score is 70 and the standard deviation is 15, find the probability that a randomly selected score is between 50 and 90.
A. 0.6
B. 0.7
Correct C. 0.8
D. 0.9

Correct Answer: C

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Question 23 View Details
Solve the equation \(\cos^2 x - \sin^2 x = 0\).
A. \(x =\)\(\frac{\pi}{4}\)\)
B. \(x =\)\(\frac{\pi}{2}\)\)
C. \(x =\)\\(\frac{3\pi}{4}\)\)
Correct D. \(x =\)\(\frac{\pi}{2}\)\) \text{ or } \(\frac{3\pi}{4}\)\)

Correct Answer: D

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Question 24 View Details
Determine the value of k in the equation \(egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 2k \ 3k \end{bmatrix}\).
Correct A. 1
B. 2
C. 3
D. 4

Correct Answer: A

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Question 25 View Details
A histogram of exam scores for a class of 100 students is shown. What is the mean score?
A. 60
B. 70
Correct C. 80
D. 90

Correct Answer: C

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