POST UTME UNIPORT 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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
C. 80\pi
D. 96\pi
Question 2
Determine the value of k in the equation \( egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 2k \ 3k \end{bmatrix} \).
A. 1
B. 2
C. 3
D. 4
Question 3
Solve the system of equations \( egin{cases} x + y = 4 \ 2x - y = 3 \end{cases} \).
A. x = 1, y = 3
B. x = 2, y = 2
C. x = 3, y = 1
D. x = 4, y = 0
Question 4
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
B. 15
C. 20
D. 25
Question 5
A histogram shows the distribution of exam scores. If the mean score is 70 and the s\tandard deviation is 15, find the probability that a randomly selected score is between 50 and 90.
A. 0.6
B. 0.7
C. 0.8
D. 0.9
Question 6
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}
D. x = \frac{\pi}{2} \text{ or } \frac{3\pi}{4}
Question 7
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?
A. \( \frac{5}{8} \)
B. \( \frac{3}{8} \)
C. \( \frac{2}{5} \)
D. \( \frac{3}{5} \)
Question 8
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
B. 3
C. 4
D. 5
Question 9
Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 10
Find the value of \( \log_{10} (100) \).
A. 2
B. 3
C. 4
D. 5
Question 11
A circle has a radius of 4 units. Find the length of the arc subt\ended by a central angle of 60 degrees.
A. 2\pi
B. 4\pi
C. 6\pi
D. 8\pi
Question 12
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 )
B. ( 1024 )
C. ( 1025 )
D. ( 1026 )
Question 13
Find the value of \( \sqrt{16} \).
A. 4
B. 5
C. 6
D. 7
Question 14
Solve for x in the equation \( 2^x + 2^{x+1} = 100 \).
A. ( 4 )
B. ( 5 )
C. ( 6 )
D. ( 7 )
Question 15
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -\infty, -1 \) \cup \( 3, \infty \)
B. \( -\infty, 1 \) \cup \( 3, \infty \)
C. \( -\infty, -1 \) \cup \( 1, \infty \)
D. \( -\infty, 3 \) \cup \( \infty, \infty \)

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