POST UTME MADONNA UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality |x - 2| > 3.
A. x > 5 or x < -1
B. x > 5 and x < -1
C. x < 5 or x > -1
D. x < 5 and x > -1
Question 2
A line passes through the points ( (2, 3) ) and ( (4, 5) ). Find the equation of the line.
A. \( y = x + 1 \)
B. \( y = x - 1 \)
C. \( y = -x + 1 \)
D. \( y = x + 2 \)
Question 3
Find the volume of the solid formed by revolving the region bounded by the curve y = x^2 and the line 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 4
Solve the matrix equation AX = B, where A = \begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix}, X = \begin{bmatrix} x \\ y \end{bmatrix}, and B = \begin{bmatrix} 3 \\ 4 \end{bmatrix}.
A. \begin{bmatrix} \frac{5}{3} \\ \frac{1}{3} \end{bmatrix}
B. \begin{bmatrix} \frac{1}{3} \\ \frac{5}{3} \end{bmatrix}
C. \begin{bmatrix} \frac{2}{3} \\ \frac{4}{3} \end{bmatrix}
D. \begin{bmatrix} \frac{4}{3} \\ \frac{2}{3} \end{bmatrix}
Question 5
Let $X$ and $Y$ be indep\endent random variables with probability density functions $f_X(x) = 2x$ and $f_Y(y) = 3y^2$, respectively, for $0 < x < 1$ and $0 < y < 1$. Find the probability that $X + Y < 1$.
A. \frac{1}{2}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{3}{4}
Question 6
Solve the inequality \( \frac{x}{x-2} > 1 \) for \( x > 2 \).
A. 2 < x < 3
B. x > 3
C. x < 2
D. x = 3
Question 7
Evaluate the definite integral \( int_{0}^{2} \( 2x^3 - 3x^2 + x - 1 \ \) dx ).
A. ( 2 )
B. ( 4 )
C. ( 6 )
D. ( 8 )
Question 8
Solve the inequality x^2 - 4x - 5 > 0.
A. x < -1 or x > 5
B. x < 1 or x > 5
C. x < -1 or x < 5
D. x > 1 or x > 5
Question 9
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
A. 32
B. 64
C. 128
D. 256
Question 10
A bag contains 5 red marbles, 4 blue marbles, and 3 green marbles. If a marble is drawn at random, what is the probability that it is blue?
A. 1/3
B. 1/4
C. 1/5
D. 2/5
Question 11
Find the vector \overrightarrow{AB} if A = (2, 3) and B = (4, 5).
A. \begin{pmatrix} -2 \ -2 \end{pmatrix}
B. \begin{pmatrix} 2 \ 2 \end{pmatrix}
C. \begin{pmatrix} -2 \ 2 \end{pmatrix}
D. \begin{pmatrix} 2 \ -2 \end{pmatrix}
Question 12
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. \( -2, 0 \)
B. \( -1, 1 \)
C. \( -2, 2 \)
D. \( -1, -1 \)
Question 13
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 50
C. 60
D. 70
Question 14
Solve the system of linear equations $\begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix}$ u\sing matrices.
A. \begin{bmatrix} 1 \ 2 \end{bmatrix}
B. \begin{bmatrix} 2 \ 1 \end{bmatrix}
C. \begin{bmatrix} -1 \ 2 \end{bmatrix}
D. \begin{bmatrix} 1 \ -2 \end{bmatrix}
Question 15
Solve the system of linear equations u\sing the method of substitution: \( 2x + 3y = 7 \) and \( x - 2y = -3 \).
A. \( x = 2, y = 1 \)
B. \( x = 1, y = 2 \)
C. \( x = 2, y = -1 \)
D. \( x = 1, y = -2 \)

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