POST UTME UNIPORT 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
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 3
Determine the value of x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) if \( \sin\( x \ \) = \frac{3}{5} ).
A. \( \frac{4}{5} \)
B. \( \frac{3}{4} \)
C. \( \frac{5}{4} \)
D. \( \frac{4}{3} \)
Question 4
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}
D. x = \frac{\pi}{2} \text{ or } \frac{3\pi}{4}
Question 5
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 \( \infty, \infty \)
Question 6
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y = 2x - 1
B. y = 2x + 1
C. y = x + 2
D. y = x - 2
Question 7
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 8
Find the sum of the first 5 terms of the geometric series with first term 2 and common ratio 3.
A. 62
B. 63
C. 64
D. 65
Question 9
Find the value of \( \log_{10} (1000) \).
A. 3
B. 4
C. 5
D. 6
Question 10
Solve the equation \( x^2 + 4x + 4 = 0 \).
A. \( x = -2 \)
B. \( x = -1 \)
C. \( x = 0 \)
D. \( x = 1 \)
Question 11
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
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 \( x < \frac{3}{2} \)
Question 12
A set of data has a mean of 20 and a s\tandard deviation of 5. If a new data point is added with a value of 30, what is the new mean?
A. 20
B. 21
C. 22
D. 23
Question 13
Solve the quadratic equation x^2 + 5x + 6 = 0.
A. x = -2
B. x = -3
C. x = 2
D. x = 3
Question 14
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 15
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. x < -1 or x > 3/2
B. x > -1 or x < 3/2
C. x < 3/2 or x > -1
D. x > 3/2 or x < -1

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