POST UTME AL-HIKMAH UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. What is the volume of the prism?
A. 72
B. 96
C. 120
D. 144
Question 2
A bag contains 5 red marbles, 8 white marbles, and 4 blue marbles. If a marble is drawn at random, what is the probability that it is either red or blue?
A. \frac{9}{17}
B. \frac{5}{17}
C. \frac{3}{17}
D. \frac{1}{17}
Question 3
Find the derivative of the function f(x) = 3x^2 + 2x - 5 u\sing the chain rule.
A. 6x + 2
B. 3x + 1
C. 2x - 5
D. x^2 + 2x - 5
Question 4
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)
B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)
C. \( \frac{1}{2} \times 4^2 + 3 \times 4^2 - 2 \times 4 \)
D. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \)
Question 5
The surface area of a cube with side length 4 cm is 96 cm^2. What is the volume of the cube?
A. 64
B. 96
C. 128
D. 256
Question 6
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. 1/4
B. 1/3
C. 3/8
D. 5/8
Question 7
Find the value of \( \sin^2 \( 60^\circ \ \) + \cos^2 \( 60^\circ \) ).
A. 1
B. 2
C. 3
D. 4
Question 8
A set of 5 numbers has a mean of 12. Find the sum of the numbers.
A. 60
B. 61
C. 62
D. 63
Question 9
Find the equation of the line pas\sing through the points (2,3) and (4,5).
A. y - 3 = \frac{1}{2} \( x - 2 \)
B. y - 3 = \frac{2}{2} \( x - 2 \)
C. y - 3 = \frac{3}{2} \( x - 2 \)
D. y - 3 = \frac{4}{2} \( x - 2 \)
Question 10
Determine the sum of the first 10 terms of the geometric series with first term 3 and common ratio 2.
A. 3 + 6 + 12 + 24 + 48 + 96 + 192 + 384 + 768 + 1536
B. 3 + 6 + 12 + 24 + 48 + 96 + 192 + 384 + 768 + 1537
C. 3 + 6 + 12 + 24 + 48 + 96 + 192 + 384 + 768 + 1538
D. 3 + 6 + 12 + 24 + 48 + 96 + 192 + 384 + 768 + 1539
Question 11
Find the volume of the frustum of a cone with height 10cm, radius of the larger base 8cm, and radius of the smaller base 4cm.
A. 800π cm^3
B. 1000π cm^3
C. 1200π cm^3
D. 1400π cm^3
Question 12
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. What is the probability that a randomly selected score is between 50 and 70?
A. \( \frac{1}{2} \)
B. \( \frac{1}{4} \)
C. \( \frac{3}{4} \)
D. \( \frac{1}{4} \)
Question 13
A circle has a radius of 4 cm. What is the area of the circle?
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 14
Solve the matrix equation \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix}.
A. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 1 \ 2 \end{bmatrix}
B. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 2 \ 3 \end{bmatrix}
C. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 4 \end{bmatrix}
D. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 4 \ 5 \end{bmatrix}
Question 15
Solve for x in the equation: 2^x + 5^x = 7^x.
A. x = 2
B. x = 3
C. x = 4
D. x = 5

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