POST UTME AL-HIKMAH UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Simplify the expression [ \sqrt{16x^2} \cdot \sqrt{9x^2} \]
A. 12x^2
B. 4x^2
C. 6x^2
D. 24x^2
Question 2
A surveyor measures the dis\tance between two points on a straight line as 100 meters. If the angle between the line of sight and the horizontal is 60°, find the height of the point above the horizontal.
A. 50
B. 75
C. 100
D. 150
Question 3
A histogram of exam scores has a mean of 80 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 70 and 90?
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 4
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. 2/5
C. 3/8
D. 1/4
Question 5
Find the equation of the circle with center at $\( -2, 3 \)$ and radius $4$.
A. \( x + 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
Question 6
Solve for ( x ) in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 2
B. 4
C. 8
D. 16
Question 7
Find the value of $\int_0^1 \frac{1}{x^2 + 1} dx$.
A. \frac{\pi}{2}
B. \frac{\pi}{4}
C. \frac{\pi}{6}
D. \frac{\pi}{8}
Question 8
The mean of a set of numbers is 25. If the set contains 5 numbers, what is the sum of the numbers?
A. 100
B. 125
C. 150
D. 175
Question 9
Find the area of the triangle with vertices ( A(0, 0) ), ( B(3, 0) ), and ( C(0, 4) ).
A. 6
B. 12
C. 18
D. 24
Question 10
A sequence is defined by \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.
A. 15
B. 25
C. 35
D. 45
Question 11
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{1}{\( x^2 + 1 \)^2}
D. \frac{1}{\( x^2 + 1 \)^2}
Question 12
A random experiment consists of rolling a fair six-sided die. If the number rolled is even, the die is rolled again. If the number rolled is odd, the die is rolled three more times. What is the probability that the number rolled is greater than 4?
A. 1/3
B. 1/2
C. 2/3
D. 5/6
Question 13
A set A contains 5 elements. If B is a subset of A, and |B| = 3, what is the number of possible subsets of A?
A. 10
B. 15
C. 20
D. 25
Question 14
A set of numbers is defined as \( S = \{ 1, 2, 3, 4, 5 \} \). Find the mean of the set.
A. 3
B. 4
C. 5
D. 6
Question 15
A circle has a radius of 5 cm. Find the area of the circle.
A. ( 25pi )
B. ( 50pi )
C. ( 75pi )
D. ( 100pi )

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