POST UTME PAN-ATLANTIC UNIVERSITY 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the equation \( x^3 - 2x^2 - 5x + 6 = 0 \).
A. 1
B. 2
C. 3
D. 4
Question 2
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 3
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 4
A line passes through the points (1, 2) and (3, 4). Find the equation of the line.
A. y = 2x
B. y = 2x + 1
C. y = 2x - 1
D. y = 2x + 2
Question 5
A circle with center ( (0, 0) ) and radius ( 4 ) has a chord of length ( 6 ). Find the dis\tance from the center to the chord.
A. \( 2 \sqrt{3} \)
B. \( 4 \sqrt{3} \)
C. \( 6 \sqrt{3} \)
D. \( 8 \sqrt{3} \)
Question 6
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 7
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. \( x = \frac{-5 pm \sqrt{25 - 24}}{2} \)
Question 8
A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?
A. 1/2
B. 1/3
C. 2/5
D. 3/8
Question 9
Find the area under the curve y = x^3 - 6x^2 + 9x + 2 from x = 0 to x = 2.
A. 14
B. 28
C. 42
D. 56
Question 10
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 11
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 12
A sequence is defined by \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.
A. 15
B. 20
C. 25
D. 30
Question 13
Let ( X ) be a random variable with a probability density function (PDF) given by ( f(x) = egin{cases} 2x, & 0 < x < 1 \ 0, & \text{otherwise} \end{cases} ). Find the expected value of \( X^2 \).
A. 1/3
B. 1/2
C. 2/3
D. 1
Question 14
Find the area under the curve y = x^2 + 2x - 3 from x = 0 to x = 3.
A. 27
B. 30
C. 33
D. 36
Question 15
A circle passes through the points (2,3) and (4,5). Find the equation of the circle in the form \( x-h \)^2 + \( y-k \)^2 = r^2.
A. \( x-3 \)^2 + \( y-4 \)^2 = 10
B. \( x-2 \)^2 + \( y-3 \)^2 = 10
C. \( x-4 \)^2 + \( y-5 \)^2 = 10
D. \( x-5 \)^2 + \( y-6 \)^2 = 10

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