POST UTME AL-HIKMAH UNIVERSITY 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A curve is defined by the equation \( y = \frac{1}{x} \). Find the area under the curve between x = 1 and x = 2.
A. 0.5
B. 1
C. 1.5
D. 2
Question 2
Find the sum of the infinite geometric series \( \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + ldots \).
A. 1
B. 2
C. 3
D. 4
Question 3
Solve the trigonometric equation \( 2 \sin^2 x + 3 \cos x - 1 = 0 \).
A. \frac{\pi}{6}
B. \frac{\pi}{4}
C. \frac{\pi}{3}
D. \frac{\pi}{2}
Question 4
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 50 and 70?
A. 0.68
B. 0.80
C. 0.95
D. 0.99
Question 5
A company produces two products, A and B. The profit from the sale of product A is $10 per unit, and the profit from the sale of product B is $15 per unit. If the company produces 100 units of product A and 50 units of product B, what is the total profit?
A. $1500
B. $2000
C. $2500
D. $3000
Question 6
Find the area of the triangle with vertices ( (0, 0) ), ( (3, 0) ), and ( (0, 2) ).
A. 6
B. 8
C. 10
D. 12
Question 7
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 8
A random variable X has a probability distribution given by the following table. What is the expected value of X?
A. 5
B. 10
C. 15
D. 20
Question 9
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. -2
B. 0
C. 2
D. 4
Question 10
Find the surface area of the sphere with radius 5.
A. 100\pi
B. 200\pi
C. 300\pi
D. 400\pi
Question 11
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find its volume.
A. 30
B. 40
C. 50
D. 60
Question 12
Let X be a random variable with probability density function (pdf) given by f(x) = \( \frac{1}{2}x^2 \) for 0 ≤ x ≤ 2. Find the probability that X is greater than 1.
A. 0.25
B. 0.5
C. 0.75
D. 1
Question 13
Find the equation of the circle with center ( (3, 4) ) and radius ( 5 ).
A. \( x - 3 \ \)^2 + \( y - 4 \)^2 = 25 )
B. \( x - 3 \ \)^2 + \( y - 4 \)^2 = 30 )
C. \( x - 3 \ \)^2 + \( y - 4 \)^2 = 35 )
D. \( x - 3 \ \)^2 + \( y - 4 \)^2 = 40 )
Question 14
Find the area under the curve y = \( \frac{1}{x^2} \) from x = 1 to x = 2.
A. 0.5
B. 1
C. 1.5
D. 2
Question 15
A researcher conducted a study on the relationship between the number of hours spent studying and the final exam scores of students. The data collected is shown in the histogram below. What is the mean number of hours spent studying by the students?
A. 5
B. 10
C. 15
D. 20

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