POST UTME UNIOSUN 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. \left\( -\frac{3}{2}, \frac{3}{4} \right \)
B. \left\( -\frac{3}{4}, \frac{3}{2} \right \)
C. \left\( -\frac{3}{2}, \frac{3}{2} \right \)
D. \left\( -\frac{3}{4}, -\frac{3}{2} \right \)
Question 2
Determine the sum of the first 10 terms of the geometric series \( 2x^2, 4x^3, 8x^4, ldots \) with common ratio \( r = 2x \).
A. 2x^{20} - 1
B. 2x^{20} + 1
C. 2x^{20} - 2
D. 2x^{20} + 2
Question 3
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) )
B. \( \frac{1}{2} left\( \frac{4^2}{2} + 3 cdot 4 - 2 \right \ \) )
C. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 \right \ \) )
D. \( \frac{1}{2} left\( \frac{4^2}{2} + 3 cdot 4 - 2 \right \ \) )
Question 4
Find the value of ( x ) in the equation \( 2^x + 5^x = 7^x \).
A. 1
B. 2
C. 3
D. 4
Question 5
Solve the equation $\sqrt{x^2-4} = 2x-2$.
A. 2
B. 4
C. 6
D. 8
Question 6
Find the probability that at least one of the events ( A ) and ( B ) occurs, given that ( P(A) = 0.4 ) and ( P(B) = 0.3 ).
A. ( 0.5 )
B. ( 0.6 )
C. ( 0.7 )
D. ( 0.8 )
Question 7
A histogram has class boundaries 0, 5, 10, 15, 20 and class marks 2.5, 7.5, 12.5, 17.5. If the frequency of the class 5-10 is 8, find the mean of the histogram.
A. 10
B. 12
C. 14
D. 16
Question 8
A histogram of exam scores is shown below. If the mean score is 70, what is the median score?
A. 65
B. 70
C. 75
D. 80
Question 9
Find the area under the curve $y = \sin x$ from $x = 0$ to $x = \frac{\pi}{2}$.
A. 1
B. 2
C. \frac{1}{2}
D. \frac{1}{4}
Question 10
In a certain number base, the number 1010 is equivalent to 12 in base 10. What is the value of the number base?
A. 4
B. 5
C. 6
D. 7
Question 11
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. ( 0 )
B. ( 1 )
C. ( 2 )
D. ( 3 )
Question 12
A random variable X has a probability distribution given by ( P(X) = egin{cases} 0.2 & \text{if } x = 1 \ 0.3 & \text{if } x = 2 \ 0.5 & \text{if } x = 3 \ \end{cases} ). Find the mean and s\tandard deviation of X.
A. \( \text{Mean} = 2.1, \text{S\tandard Deviation} = 0.8 \)
B. \( \text{Mean} = 2.3, \text{S\tandard Deviation} = 0.9 \)
C. \( \text{Mean} = 2.5, \text{S\tandard Deviation} = 1.0 \)
D. \( \text{Mean} = 2.7, \text{S\tandard Deviation} = 1.1 \)
Question 13
Find the area under the curve \( y = x^2 + 2x - 3 \) from x = 0 to x = 4.
A. 40
B. 60
C. 80
D. 100
Question 14
Find the determinant of the matrix \[ \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \].
A. 0
B. 1
C. 2
D. 3
Question 15
Determine the volume of the frustum of a cone with height 10cm, lower base radius 6cm, and upper base radius 4cm.
A. 60π cm^3
B. 80π cm^3
C. 100π cm^3
D. 120π cm^3

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