POST UTME AL-HIKMAH UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A solid sphere of radius $r$ is inscribed in a cube of side length $s$. Find the ratio of the volume of the sphere to the volume of the cube.
A. \frac{\pi}{6}
B. \frac{\pi}{3}
C. \frac{\pi}{2}
D. \frac{\pi}{4}
Question 2
A histogram of exam scores is shown below. If the mean score is 60 and the s\tandard deviation is 10, calculate the area under the curve between 50 and 70.
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 3
Find the equation of the circle with center at \( -2, 3 \) and pas\sing through the point (1, 6).
A. \boxed{\( x + 2 \)^2 + \( y - 3 \)^2 = 25}
B. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
C. \( x + 2 \)^2 + \( y - 3 \)^2 = 36
D. \( x - 2 \)^2 + \( y + 3 \)^2 = 25
Question 4
Solve the inequality $\frac{x^2-4x-3}{x^2-4x+3}>0$.
A. \( -\infty,-1)\cup\( 3,\infty \ \)
B. \( -\infty,-3)\cup\( 1,\infty \ \)
C. \( -\infty,-1)\cup\( 1,\infty \ \)
D. \( -\infty,-3)\cup\( 3,\infty \ \)
Question 5
Find the volume of the frustum of a cone with height 10 cm, lower base radius 6 cm, and upper base radius 4 cm.
A. \boxed{\frac{400\pi}{3} \text{ cm}^3
B. \frac{500\pi}{3} \text{ cm}^3
C. \frac{600\pi}{3} \text{ cm}^3
D. \frac{700\pi}{3} \text{ cm}^3
Question 6
Find the area under the curve \( y = \frac{1}{x} \) from x = 1 to x = 2.
A. 0.5
B. 1
C. 1.5
D. 2
Question 7
A 3x3 matrix is given as: \[ \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \]. What is the determinant of the matrix?
A. 0
B. 1
C. 2
D. 3
Question 8
Find the sum of the first 10 terms of the geometric progression 2, 6, 18, ...
A. \boxed{59049}
B. 6144
C. 6561
D. 729
Question 9
Find the volume of the solid formed by rotating the region bounded by the curves \( y = x^2 \) and \( y = 2x \) about the x-axis.
A. \frac{4}{3}\pi
B. \frac{2}{3}\pi
C. \frac{1}{3}\pi
D. \frac{1}{2}\pi
Question 10
A researcher conducted a study on the relationship between the mean height of a population and the s\tandard deviation. The data points are as follows: 160, 170, 180, 190, 200. If the mean height is 175 cm, what is the s\tandard deviation of the population?
A. 10 cm
B. 15 cm
C. 20 cm
D. 25 cm
Question 11
A random sample of 25 students from a university had a mean height of 175 cm with a s\tandard deviation of 5 cm. If the population s\tandard deviation is 6 cm, calculate the s\tandard error of the mean.
A. 2.5 cm
B. 3.2 cm
C. 3.5 cm
D. 4.1 cm
Question 12
Find the equation of the circle with center \( -2, 3 \) 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 13
A set A contains 5 elements. If the number of subsets of A is 32, find the number of elements in the power set of A.
A. \boxed{32}
B. 16
C. 64
D. 128
Question 14
Determine the value of $\sum_{n=1}^{\infty}\frac{2n}{3^n}$.
A. 4
B. 6
C. 8
D. 10
Question 15
A bakery sells 250 loaves of bread per day. If each loaf \costs ₦50, how much money does the bakery make in a day?
A. ₦12,500
B. ₦12,000
C. ₦11,500
D. ₦11,000

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