POST UTME BABCOCK UNIVERSITY 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Determine the value of $\int_{0}^{\pi} \frac{1}{1+\sin^2x} dx$.
A. \frac{\pi}{2}
B. \frac{\pi}{4}
C. \frac{\pi}{3}
D. \frac{\pi}{6}
Question 2
Convert the decimal number 0.000123 to a binary number.
A. 0.000123
B. 0.00011011
C. 0.00010101
D. 0.00011101
Question 3
Find the value of \( \sin 2\theta \) given that \( \sin \theta = \frac{3}{5} \) and \( \cos \theta = \frac{4}{5} \).
A. 24/25
B. 16/25
C. 20/25
D. 12/25
Question 4
Find the area under the curve y = x^2 from x = 0 to x = 2.
A. 4
B. 6
C. 8
D. 10
Question 5
Find the value of ( x ) in the equation \( x^2 - 4x - 5 = 0 \).
A. 5
B. -1
C. 2
D. 3
Question 6
A set of 5 numbers has a mean of 10. If 2 is added to each number, what is the new mean?
A. 12
B. 13
C. 14
D. 15
Question 7
Find the sum of the first 5 terms of the geometric series ( 2, 6, 18, ... ).
A. ( 62 )
B. ( 64 )
C. ( 66 )
D. ( 68 )
Question 8
A histogram of exam scores is shown below. If the mean score is 75, what is the median score?
A. 70
B. 75
C. 80
D. 85
Question 9
A histogram of the heights of 100 students is shown below. If the mean height of the students is 175 cm, what is the s\tandard deviation?
A. 5 cm
B. 10 cm
C. 15 cm
D. 20 cm
Question 10
Solve the equation $\tan^2x+\tan x-6=0$ for $x$ in the interval $[0, 2\pi)$.
A. x=\frac{\pi}{3}
B. x=\frac{\pi}{4}
C. x=\frac{\pi}{6}
D. x=\frac{\pi}{2}
Question 11
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -3 \) ∪ (1, ∞)
B. \( -∞, -1 \) ∪ (3, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ \( -1, ∞ \)
Question 12
Find the volume of the solid formed by rotating the region bounded by $y=x^2$ and $y=4-x^2$ about the x-axis.
A. \frac{16\pi}{3}
B. \frac{32\pi}{3}
C. \frac{64\pi}{3}
D. \frac{128\pi}{3}
Question 13
Solve the matrix equation $\begin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 3 \end{bmatrix}$.
A. \begin{bmatrix} 1 \ 1 \end{bmatrix}
B. \begin{bmatrix} 1 \ 2 \end{bmatrix}
C. \begin{bmatrix} 2 \ 1 \end{bmatrix}
D. \begin{bmatrix} 2 \ 2 \end{bmatrix}
Question 14
A company produces two products, A and B. The profit from the sale of product A is ₦200 per unit, while the profit from the sale of product B is ₦150 per unit. If the company produces 100 units of product A and 50 units of product B, what is the total profit?
A. ₦25000
B. ₦30000
C. ₦35000
D. ₦40000
Question 15
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. \( \frac{-2x}{\( x^2 + 1 \ \)^2} )
B. \( \frac{2x}{\( x^2 + 1 \ \)^2} )
C. \( \frac{-2}{\( x^2 + 1 \ \)^2} )
D. \( \frac{2}{\( x^2 + 1 \ \)^2} )

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