POST UTME RSU 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 2
B. 4
C. 10
D. 20
Question 2
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 3
A histogram represents the distribution of exam scores. The histogram has a mean of 60 and a s\tandard deviation of 10. If the highest score is 90, what is the lowest score?
A. 30
B. 40
C. 50
D. 60
Question 4
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 5
Find the sum of the first 10 terms of the geometric progression ( 2, 6, 18, ldots ).
A. \( 2 left\( \frac{3^{10} - 1}{3 - 1} \right \ \) )
B. \( 2 left\( \frac{3^{10} + 1}{3 + 1} \right \ \) )
C. \( 2 left\( \frac{3^{10} - 1}{3 + 1} \right \ \) )
D. \( 2 left\( \frac{3^{10} + 1}{3 - 1} \right \ \) )
Question 6
Find the equation of the line pas\sing through the points $(2, 3)$ and $\( 4, -1 \)$.
A. \( y = -\frac{4}{3}x + \frac{17}{3} \)
B. \( y = \frac{4}{3}x - \frac{17}{3} \)
C. \( y = -\frac{4}{3}x - \frac{17}{3} \)
D. \( y = \frac{4}{3}x + \frac{17}{3} \)
Question 7
Find the determinant of the matrix \( egin{pmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 1 & 3 & 2 \end{pmatrix} \).
A. -1
B. 1
C. -2
D. 2
Question 8
Determine the value of \( int_{0}^{1} \frac{1}{x^2 + 1} dx \) u\sing the method of substitution.
A. \frac{\pi}{2}
B. \frac{\pi}{4}
C. \frac{\pi}{6}
D. \frac{\pi}{8}
Question 9
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 10
Solve the equation \( 2x + 5 = 11 \).
A. 3
B. 4
C. 5
D. 6
Question 11
Solve the system of equations u\sing matrices: \( \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix} \).
A. \begin{bmatrix} 1 \ 2 \end{bmatrix}
B. \begin{bmatrix} 2 \ 3 \end{bmatrix}
C. \begin{bmatrix} 3 \ 4 \end{bmatrix}
D. \begin{bmatrix} 4 \ 5 \end{bmatrix}
Question 12
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
A. 64
B. 32
C. 16
D. 8
Question 13
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 14
Find the value of x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) if \( \tan\( x \ \) = 3 ).
A. π/3
B. π/4
C. π/6
D. π/2
Question 15
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 = 16
C. \( x + 3 \)^2 + \( y - 2 \)^2 = 16
D. \( x - 3 \)^2 + \( y + 2 \)^2 = 16

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