POST UTME AL-HIKMAH UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A sphere has a radius of 5 cm. What is the volume of the sphere?
A. \frac{500\pi}{3}
B. \frac{1000\pi}{3}
C. \frac{2000\pi}{3}
D. \frac{5000\pi}{3}
Question 2
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 3
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 4
Find the value of \( \sin^2 \( 60^\circ \ \) + \cos^2 \( 60^\circ \) ).
A. 1
B. 2
C. 3
D. 4
Question 5
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 6
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. \( 1 \times \( 5 \times 9 - 6 \times 8 \ \) - 2 \times \( 4 \times 9 - 6 \times 7 \) + 3 \times \( 4 \times 8 - 5 \times 7 \) )
B. \( 1 \times \( 5 \times 9 - 6 \times 8 \ \) - 2 \times \( 4 \times 9 - 6 \times 7 \) - 3 \times \( 4 \times 8 - 5 \times 7 \) )
C. \( 1 \times \( 5 \times 9 - 6 \times 8 \ \) + 2 \times \( 4 \times 9 - 6 \times 7 \) + 3 \times \( 4 \times 8 - 5 \times 7 \) )
D. \( 1 \times \( 5 \times 9 - 6 \times 8 \ \) + 2 \times \( 4 \times 9 - 6 \times 7 \) - 3 \times \( 4 \times 8 - 5 \times 7 \) )
Question 7
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 8
In a circle of radius 8cm, a chord of length 12cm subt\ends an angle of 60° at the centre. Find the area of the sector formed by the chord and the radii drawn to the \ends of the chord.
A. 48π cm^2
B. 64π cm^2
C. 72π cm^2
D. 80π cm^2
Question 9
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. ( f'(x) = \frac{-2x}{\( x^2 + 1 \)^2} )
B. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )
C. ( f'(x) = \frac{2}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{-2}{\( x^2 + 1 \)^2} )
Question 10
A histogram of exam scores is shown below. What is the mean of the scores?
A. 60
B. 70
C. 80
D. 90
Question 11
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 12
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 13
Solve for ( x ) in the equation \( 2x^2 + 5x - 3 = 0 \).
A. \( x = \frac{-5 pm \sqrt{25 + 24}}{4} \)
B. \( x = \frac{-5 pm \sqrt{25 - 24}}{4} \)
C. \( x = \frac{-5 pm \sqrt{25 + 24}}{2} \)
D. \( x = \frac{-5 pm \sqrt{25 - 24}}{2} \)
Question 14
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 15
Evaluate the definite integral \int_0^1 x^2 dx.
A. 1/3
B. 1/2
C. 2/3
D. 3/4

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