POST UTME RHEMA UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the equation \frac{1}{2} \log_{10} \( x^2 \) = 4.
A. 10
B. 100
C. 1000
D. 10000
Question 2
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. \( -1 \)
B. ( 0 )
C. ( 1 )
D. ( 2 )
Question 3
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?
A. ( 0.9544 )
B. ( 0.9772 )
C. ( 0.9987 )
D. ( 0.9999 )
Question 4
A sequence is defined as \( a_n = 2n + 1 \ \). Find the sum of the first 5 terms of the sequence.
A. \( 15 \ \)
B. \( 25 \ \)
C. \( 35 \ \)
D. \( 45 \ \)
Question 5
Determine the value of ( x ) in the equation \( 2x^2 + 5x - 3 = 0 \) u\sing the quadratic formula.
A. \( x = -1 \ \)
B. \( x = 3 \ \)
C. \( x = -3 \ \)
D. \( x = 1 \ \)
Question 6
Solve the system of linear equations u\sing the method of substitution: \begin{align*} x + y &= 4 \ 2x - 3y &= 5 \end{align*}
A. \begin{align*} x &= 3 \ y &= 1 \end{align*}
B. \begin{align*} x &= 1 \ y &= 3 \end{align*}
C. \begin{align*} x &= 2 \ y &= 2 \end{align*}
D. \begin{align*} x &= 4 \ y &= 0 \end{align*}
Question 7
Solve the system of linear equations $\begin{cases} 2x + 3y = 7 \ 4x - 2y = -3 \end{cases}$ u\sing matrices.
A. \left\( \frac{11}{13}, \frac{16}{13} \right \)
B. \left\( \frac{7}{13}, \frac{10}{13} \right \)
C. \left\( \frac{5}{13}, \frac{8}{13} \right \)
D. \left\( \frac{3}{13}, \frac{6}{13} \right \)
Question 8
Find the equation of the circle with center $\( -2, 3 \)$ and radius $4$.
A. \left\( x + 2\right \)^2 + left\( y - 3\right \)^2 = 16
B. \left\( x - 2\right \)^2 + left\( y + 3\right \)^2 = 16
C. \left\( x + 2\right \)^2 + left\( y + 3\right \)^2 = 16
D. \left\( x - 2\right \)^2 + left\( y - 3\right \)^2 = 16
Question 9
Find the equation of the circle with center (2, 3) and radius 4.
A. \( x-2 \)^2 + \( y-3 \)^2 = 16
B. \( x-2 \)^2 + \( y-3 \)^2 = 25
C. \( x-2 \)^2 + \( y-3 \)^2 = 36
D. \( x-2 \)^2 + \( y-3 \)^2 = 49
Question 10
Find the derivative of $f(x) = \frac{1}{1+\sin^2 x}$ u\sing the chain rule.
A. \frac{\cos^2 x}{\( 1+\sin^2 x \)^2}
B. \frac{\sin^2 x}{\( 1+\sin^2 x \)^2}
C. \frac{1}{\( 1+\sin^2 x \)^2}
D. \frac{\cos x}{\( 1+\sin^2 x \)^2}
Question 11
Find the value of $\int_{0}^{\pi} \frac{1}{1+\sin^2 x} dx$.
A. 0
B. \frac{\pi}{2}
C. \frac{\pi}{4}
D. \frac{\pi}{8}
Question 12
Solve the inequality $|x - 2| > 3$.
A. \{x : x < -1 \text{ or } x > 5\}
B. \{x : x < -1 \text{ or } x > 4\}
C. \{x : x < 1 \text{ or } x > 5\}
D. \{x : x < 1 \text{ or } x > 4\}
Question 13
Solve the inequality x^2 - 6x + 8 > 0.
A. \( -\\infty, 2 \) \\cup \( 4, \\infty \)
B. \( -\\infty, 2 \) \\cup \( 4, \\infty \)
C. (2, 4)
D. (2, 4)
Question 14
Solve the system of linear equations u\sing the method of substitution: \begin{align*} x + y &= 3 \ 2x - y &= 5 \end{align*}
A. \begin{align*} x &= 2 \ y &= 1 \end{align*}
B. \begin{align*} x &= 1 \ y &= 2 \end{align*}
C. \begin{align*} x &= 3 \ y &= 0 \end{align*}
D. \begin{align*} x &= 0 \ y &= 3 \end{align*}
Question 15
Find the volume of the frustum of a cone with radii 6 cm and 3 cm and height 8 cm.
A. 120\pi cm^3
B. 240\pi cm^3
C. 360\pi cm^3
D. 480\pi cm^3

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