POST UTME AL-HIKMAH UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the value of $x$ in the equation $\frac{x}{x + 1} = \frac{2}{3}$.
A. -1
B. 2
C. 3
D. 4
Question 2
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 3
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 4
Find the value of $x$ in the equation $2^x + 5^x = 7^x$.
A. -1
B. 0
C. 1
D. 2
Question 5
A particle moves along the x-axis with the equation of motion $x(t)=2t^2-5t+1$. Find the velocity and acceleration at time $t=2$ seconds.
A. (2,6)
B. \( -4,-2 \)
C. (4,6)
D. \( -2,-4 \)
Question 6
Solve the inequality 2x^2 + 3x - 4 > 0.
A. x < -1 or x > 2
B. x < 1 or x > 2
C. x < -2 or x > 1
D. x < 2 or x > 1
Question 7
Solve the equation x^2 + 4x + 4 = 0.
A. x = -2
B. x = -1
C. x = 1
D. x = 2
Question 8
Find the area under the curve y = 2x^2 + 3x - 4 from x = 0 to x = 2.
A. 20
B. 22
C. 24
D. 26
Question 9
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 10
Let X and Y be indep\endent events with P(X) = 0.4 and P(Y) = 0.6. Find the probability that X occurs but Y does not.
A. 0.24
B. 0.36
C. 0.48
D. 0.64
Question 11
A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is red?
A. \frac{1}{2}
B. \frac{2}{3}
C. \frac{5}{8}
D. \frac{3}{4}
Question 12
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. 0
B. 1
C. -1
D. 2
Question 13
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 14
Solve the inequality $|x - 2| > 3$.
A. \( -\infty, -1 \) \cup \( 5, \infty \)
B. \( -\infty, -1 \) \cup (2, 5)
C. \( -\infty, -1 \) \cup \( 2, \infty \)
D. \( -\infty, 5 \) \cup \( 2, \infty \)
Question 15
A company produces two products, A and B. The profit from product A is $10 per unit, and the profit from 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

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