POST UTME RHEMA UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the value of $\sin 75^\circ$ u\sing the angle addition formula.
A. \frac{\sqrt{6} + \sqrt{2}}{4}
B. \frac{\sqrt{6} - \sqrt{2}}{4}
C. \frac{\sqrt{6} + \sqrt{3}}{4}
D. \frac{\sqrt{6} - \sqrt{3}}{4}
Question 2
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 3
Solve the trigonometric equation $\sin^2 x + \cos^2 x = 1$ for $x$.
A. x = \frac{\pi}{4}
B. x = \frac{3\pi}{4}
C. x = \frac{\pi}{2}
D. x = \frac{5\pi}{4}
Question 4
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 5
Solve the matrix equation $\begin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 4 \end{bmatrix}$ for $x$ and $y$.
A. x = 1, y = 2
B. x = 2, y = 1
C. x = 1, y = 1
D. x = 2, y = 2
Question 6
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 7
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 8
Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).
A. \( x = 1 \)
B. \( x = 2 \)
C. \( x = 3 \)
D. \( x = 4 \)
Question 9
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 10
Find the volume of the solid formed by revolving the region bounded by the curves $y = x^2$ 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 11
Solve the equation x^2 + 4x + 4 = 0.
A. x = -2
B. x = -1
C. x = 1
D. x = 2
Question 12
A vector \vec{a} has a magnitude of 5 and makes an angle of 60\circ with the positive x-axis. Find the x and y components of \vec{a}.
A. x = 3, y = 4
B. x = 4, y = 3
C. x = 3, y = -4
D. x = -4, y = 3
Question 13
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 14
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 15
A vector ( mathbf{a} ) has a magnitude of 5 and makes an angle of 30° with the positive x-axis. Find the x-component of ( mathbf{a} ).
A. ( 2.5 )
B. ( 3.5 )
C. ( 4.5 )
D. ( 5.5 )

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