POST UTME RSU 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the trigonometric equation \( 2 \sin^2 x + 3 \cos x - 1 = 0 \) u\sing the identity \( \sin^2 x + \cos^2 x = 1 \).
A. \sin x = \frac{1}{2}
B. \cos x = \frac{1}{2}
C. \sin x = \frac{1}{3}
D. \cos x = \frac{1}{3}
Question 2
Solve the system of linear equations $\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 7 \end{bmatrix}$.
A. \begin{bmatrix} 1 \\ -1 \end{bmatrix}
B. \begin{bmatrix} 2 \\ 3 \end{bmatrix}
C. \begin{bmatrix} 3 \\ 4 \end{bmatrix}
D. \begin{bmatrix} 4 \\ 5 \end{bmatrix}
Question 3
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \ 4 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \ 1 \end{pmatrix} \). Find the cross product \( mathbf{a} \times mathbf{b} \).
A. \begin{pmatrix} -7 \ 7 \ -1 \end{pmatrix}
B. \begin{pmatrix} 7 \ -7 \ 1 \end{pmatrix}
C. \begin{pmatrix} 1 \ -1 \ 2 \end{pmatrix}
D. \begin{pmatrix} -1 \ 1 \ -2 \end{pmatrix}
Question 4
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{1}{\( x^2 + 1 \)^2}
D. \frac{1}{\( x^2 + 1 \)^2}
Question 5
Solve the equation \( x^2 + 4x - 5 = 0 \).
A. x = -5, x = 1
B. x = -1, x = 5
C. x = 1, x = -5
D. x = -1, x = -5
Question 6
Find the mean deviation of the data set ( 2, 4, 6, 8, 10 ).
A. \( \frac{1}{5} left\( 2 + 4 + 6 + 8 + 10 \right \ \) )
B. \( \frac{1}{5} left\( 2 + 4 + 6 + 8 + 10 \right \ \) - 6 )
C. \( \frac{1}{5} left\( 2 + 4 + 6 + 8 + 10 \right \ \) + 6 )
D. \( \frac{1}{5} left\( 2 + 4 + 6 + 8 + 10 \right \ \) - 10 )
Question 7
Solve the matrix equation \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).
A. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 2 \ 3 \end{bmatrix} \)
B. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 2 \end{bmatrix} \)
C. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 4 \ 5 \end{bmatrix} \)
D. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 4 \end{bmatrix} \)
Question 8
A histogram has a mean of 25 and a s\tandard deviation of 5. Find the z-score of a value that is 35.
A. 0
B. 1
C. 2
D. 3
Question 9
Let $X$ and $Y$ be indep\endent random variables with probability density functions $f_X(x) = \frac{1}{2}e^{-|x|}$ and $f_Y(y) = \frac{1}{3}e^{-|y|}$, respectively. Find $P\( X+Y<0 \)$.
A. \frac{1}{6}
B. \frac{1}{3}
C. \frac{1}{2}
D. \frac{2}{3}
Question 10
Solve the equation \( 2x + 5 = 11 \).
A. 3
B. 4
C. 5
D. 6
Question 11
In the complex plane, the points $z_1 = 2 + 3i$ and $z_2 = 4 - 5i$ are represented by vectors $mathbf{v}_1$ and $mathbf{v}_2$ respectively. If the vector $mathbf{v}_3$ is the sum of $mathbf{v}_1$ and $mathbf{v}_2$, find the magnitude of $mathbf{v}_3$.
A. \( \sqrt{185} \)
B. \( \sqrt{193} \)
C. \( \sqrt{205} \)
D. \( \sqrt{217} \)
Question 12
Find the equation of the circle pas\sing through the points $\( -2, 3 \)$ and $\( 4, -1 \)$.
A. \( x^2 + y^2 + 6x - 10y + 13 = 0 \)
B. \( x^2 + y^2 - 6x + 10y + 13 = 0 \)
C. \( x^2 + y^2 + 6x + 10y + 13 = 0 \)
D. \( x^2 + y^2 - 6x - 10y + 13 = 0 \)
Question 13
A bakery sells a total of 480 loaves of bread per day. They sell a combination of whole wheat and white bread. If the ratio of whole wheat to white bread is 5:4, how many loaves of whole wheat bread are sold per day?
A. ( 200 )
B. ( 220 )
C. ( 240 )
D. ( 260 )
Question 14
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
A. 64
B. 32
C. 16
D. 8
Question 15
A histogram of exam scores is shown below. If the mean score is 60, find the value of the upper limit of the interval.
A. 65
B. 70
C. 75
D. 80

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