POST UTME PAN-ATLANTIC UNIVERSITY 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the system of linear equations u\sing matrices: \begin{align*} x + 2y - z &= 3 \ 2x - 3y + 4z &= 5 \ -x + y - 2z &= -2 \end{align*}
A. \begin{pmatrix} 1 \ 2 \ -1 \end{pmatrix}
B. \begin{pmatrix} 2 \ -1 \ 3 \end{pmatrix}
C. \begin{pmatrix} 3 \ 4 \ -2 \end{pmatrix}
D. \begin{pmatrix} 5 \ 6 \ -3 \end{pmatrix}
Question 2
Find the volume of the solid formed by revolving the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.
A. 64\pi
B. 128\pi
C. 256\pi
D. 512\pi
Question 3
Find the value of x in the equation 2^x + 3^x = 5^x.
A. 1
B. 2
C. 3
D. 4
Question 4
Find the sum of the infinite geometric series \( sum_{n=1}^{infty} \frac{1}{2^n} \) u\sing the formula \( S = \frac{a}{1 - r} \), where (a) is the first term and (r) is the common ratio.
A. 1
B. 2
C. 3
D. 4
Question 5
A histogram of exam scores has a mean of 70 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 80?
A. 0.135
B. 0.341
C. 0.674
D. 0.954
Question 6
Let X and Y be indep\endent random variables with probability density functions f_X(x) = 2x, 0 < x < 1, and f_Y(y) = 3y^2, 0 < y < 1. Find the probability that X + Y < 1.
A. 1/4
B. 1/2
C. 3/4
D. 1
Question 7
A sequence is defined by the recurrence relation a_n = 2a_{n-1} + 3, with a_1 = 2. Find the sum of the first 5 terms of the sequence.
A. 122
B. 142
C. 162
D. 182
Question 8
A histogram is constructed from the following data: \( \begin{array}{|c|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 & 4 \hline f\( x \ \) & 2 & 3 & 4 & 2 & 1 \hline \end{array} \). Find the mean of the data.
A. 2.2
B. 2.5
C. 2.8
D. 3.1
Question 9
Find the volume of the sphere with radius 4 cm.
A. 268.08 cm^3
B. 268.08 cm^3
C. 268.08 cm^3
D. 268.08 cm^3
Question 10
Find the volume of the solid formed by rotating the region bounded by the curves y = x^2 and y = 4 - x^2 about the x-axis.
A. 32\pi
B. 64\pi
C. 128\pi
D. 256\pi
Question 11
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. 24\pi cm^3
B. 48\pi cm^3
C. 96\pi cm^3
D. 192\pi cm^3
Question 12
Find the volume of the frustum of a cone with height 8cm, lower base radius 4cm, and upper base radius 2cm.
A. 64\pi cm^3
B. 128\pi cm^3
C. 256\pi cm^3
D. 512\pi cm^3
Question 13
Find the area under the curve \( y = x^2 + 2x - 3 \) from \( x = 0 \) to \( x = 2 \).
A. 5/3
B. 7/3
C. 9/3
D. 11/3
Question 14
Find the area under the curve \[ y = \frac{1}{x^2 + 1} \] from x = 0 to x = 1.
A. \frac{\pi}{4}
B. \frac{\pi}{2}
C. \frac{\pi}{3}
D. \frac{\pi}{6}
Question 15
Solve for ( x ) in the equation \( 2x^2 + 5x - 3 = 0 \).
A. \( x = \frac{-5 pm \sqrt{25 + 24}}{4} \)
B. \( x = \frac{-5 pm \sqrt{25 - 24}}{4} \)
C. \( x = \frac{-5 pm \sqrt{25 + 24}}{2} \)
D. \( x = \frac{-5 pm \sqrt{25 - 24}}{2} \)

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