POST UTME AL-HIKMAH UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the mean and s\tandard deviation of the data set: {1, 2, 3, 4, 5}.
A. mean = 3, std dev = 1.414
B. mean = 3, std dev = 1.732
C. mean = 3, std dev = 2.236
D. mean = 3, std dev = 2.828
Question 2
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 3
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 4
In the complex plane, let $z_1 = 2 - 3i$ and $z_2 = 1 + 4i$. Find the value of $|z_1 + z_2|$.
A. 5
B. \sqrt{10}
C. \sqrt{26}
D. \sqrt{50}
Question 5
Solve the inequality \( \frac{x^2 - 4}{x^2 - 9} > 0 \) for \( x in mathbb{R} setminus {3, -3} \).
A. \( -infty, -3 \ \) cup (3, infty) )
B. \( -infty, -3 \ \) cup (3, infty) cup (0, 4) )
C. \( -infty, -3 \ \) cup (3, infty) cup \( -4, 0 \) )
D. \( -infty, -3 \ \) cup (3, infty) cup \( -4, 0 \) cup (0, 4) )
Question 6
A set of 10 numbers has a mean of 20. If 5 is added to each number, what is the new mean?
A. 22.5
B. 25
C. 27.5
D. 30
Question 7
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 8
Solve the inequality $\frac{2x + 1}{x - 1} > 0$.
A. \( -\infty, -\frac{1}{2} \) \cup \( 1, \infty \)
B. \( -\infty, -\frac{1}{2} \) \cup \( 1, \infty \)
C. \( -\infty, -\frac{1}{2} \) \cup \( 1, \infty \)
D. \( -\infty, -\frac{1}{2} \) \cup \( 1, \infty \)
Question 9
Solve the inequality \( 2^x > 3^x \) for ( x ).
A. x < -1
B. x > 1
C. x < 1
D. x > -1
Question 10
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 11
Find the value of $\begin{vmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{vmatrix}$.
A. 0
B. 1
C. -1
D. 2
Question 12
A circle has a radius of 5 cm. Find the area of the circle.
A. ( 25pi )
B. ( 50pi )
C. ( 75pi )
D. ( 100pi )
Question 13
Solve for ( x ) in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 2
B. 4
C. 8
D. 16
Question 14
Find the volume of the solid formed by revolving the region bounded by the curve \( y = \frac{1}{2}x^2 \), the x-axis, and the line \( x = 2 \) about the x-axis.
A. 4π
B. 8π
C. 16π
D. 32π
Question 15
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}

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