POST UTME PAN-ATLANTIC UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the equation of the circle with center [ (2, 3) \] and radius [ 4 \].
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 3 \)^2 + \( y - 2 \)^2 = 16
C. \( x + 2 \)^2 + \( y - 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
Question 2
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. \frac{-2x}{\( x^2 + 1 \)^2}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. \frac{-2}{\( x^2 + 1 \)^2}
D. \frac{2}{\( x^2 + 1 \)^2}
Question 3
Solve the inequality $2x^2-5x-3>0$.
A. \( -\infty, -1 \) \cup \( 3, \infty \)
B. \( -\infty, -3 \) \cup \( 1, \infty \)
C. \( -\infty, -2 \) \cup \( 2, \infty \)
D. \( -\infty, -4 \) \cup \( 4, \infty \)
Question 4
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. 0.68
B. 0.84
C. 0.95
D. 0.99
Question 5
Find the equation of the circle with center at ((2,3)) and pas\sing through the point ((6,5)).
A. \( x-2 \ \)^2 + \( y-3 \)^2 = 5 )
B. \( x-2 \ \)^2 + \( y-3 \)^2 = 10 )
C. \( x-2 \ \)^2 + \( y-3 \)^2 = 15 )
D. \( x-2 \ \)^2 + \( y-3 \)^2 = 20 )
Question 6
Find the value of $\int_0^1 \frac{1}{x^2+4} dx$.
A. \frac{\pi}{4}
B. \frac{\pi}{2}
C. \frac{\pi}{3}
D. \frac{\pi}{5}
Question 7
Solve the equation \frac{dx}{dt} + 2x = e^{-2t} u\sing an integrating factor.
A. x = \frac{1}{2}e^{-t} + \frac{1}{4}e^{-2t}
B. x = \frac{1}{2}e^{-t} - \frac{1}{4}e^{-2t}
C. x = \frac{1}{4}e^{-t} + \frac{1}{2}e^{-2t}
D. x = \frac{1}{4}e^{-t} - \frac{1}{2}e^{-2t}
Question 8
In the diagram below, a circle with center O and radius 6 cm is inscribed in a square. Find the area of the shaded region.
A. 36π
B. 72π
C. 108π
D. 144π
Question 9
A circle has a radius of 4 cm. Find its area.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 10
A sequence is defined by the formula a_n = 2n + 1. Find the sum of the first 5 terms of the sequence.
A. 15
B. 25
C. 35
D. 45
Question 11
A right circular cone has a height of 10 cm and a base radius of 5 cm. Find the volume of the cone.
A. 250π cm^3
B. 500π cm^3
C. 750π cm^3
D. 1000π cm^3
Question 12
Solve the inequality \( 2x^2 - 5x - 3 > 0 \) u\sing the quadratic formula.
A. \( x < -1 \) or \( x > \frac{3}{2} \)
B. \( x < -1 \) or \( x < \frac{3}{2} \)
C. \( x > -1 \) or \( x > \frac{3}{2} \)
D. \( x < -1 \) or \( x < \frac{3}{2} \)
Question 13
A vector ( vec{a} ) has a magnitude of 5 units and makes an angle of 30° with the positive x-axis. Find the x and y components of ( vec{a} ).
A. x = 4, y = 4√3
B. x = 3, y = 3√3
C. x = 5, y = 5√3
D. x = 2, y = 2√3
Question 14
If [ S = \{ 1, 2, 3, 4, 5 \} \], find the sum of the first five terms of the arithmetic progression [ 2n - 1 \].
A. 25
B. 26
C. 27
D. 28
Question 15
Solve the inequality \( |x - 2| > 3 \).
A. x < -1 or x > 5
B. x > -1 or x < 5
C. x < 1 or x > 5
D. x > 1 or x < 5

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