POST UTME MADONNA UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Evaluate the definite integral \( int_{0}^{2} \( 2x^3 - 3x^2 + x - 1 \ \) dx ).
A. ( 2 )
B. ( 4 )
C. ( 6 )
D. ( 8 )
Question 2
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x}} ) u\sing the chain rule.
A. ( f'(x) = -\frac{1}{2}x^{-\frac{3}{2}} )
B. ( f'(x) = \frac{1}{2}x^{-\frac{3}{2}} )
C. ( f'(x) = \frac{1}{\sqrt{x}} )
D. ( f'(x) = -\frac{1}{x^{\frac{3}{2}}} )
Question 3
Find the determinant of the matrix \begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{bmatrix}.
A. 0
B. 2
C. 4
D. 6
Question 4
Find the determinant of the matrix \( \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. 0
B. 1
C. 2
D. 3
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
Find the value of ( x ) in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. \( x = 10 \)
B. \( x = 100 \)
C. \( x = 1000 \)
D. \( x = 10000 \)
Question 7
Find the derivative of the function $f(x) = \frac{\log x}{x^2}$ u\sing the chain rule.
A. \frac{1}{x^3} - \frac{2\log x}{x^3}
B. \frac{1}{x^3} + \frac{2\log x}{x^3}
C. \frac{1}{x^3} - \frac{\log x}{x^3}
D. \frac{1}{x^3} + \frac{\log x}{x^3}
Question 8
A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?
A. \frac{1}{4}
B. \frac{1}{2}
C. \frac{3}{8}
D. \frac{3}{5}
Question 9
Solve the system of equations u\sing matrices: \( 2x + 3y = 7 \) and \( x - 2y = -3 \).
A. \begin{bmatrix} 1 \ 2 \end{bmatrix}
B. \begin{bmatrix} 2 \ -1 \end{bmatrix}
C. \begin{bmatrix} -1 \ 1 \end{bmatrix}
D. \begin{bmatrix} 0 \ 0 \end{bmatrix}
Question 10
Find the area under the curve \( y = x^2 + 2x - 3 \) from \( x = 0 \) to \( x = 3 \).
A. 36
B. 45
C. 54
D. 63
Question 11
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 12
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 13
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 14
A histogram has a mean of 25 and a s\tandard deviation of 5. Find the value of the 80th percentile.
A. 30
B. 32
C. 35
D. 40
Question 15
Evaluate the definite integral $\int_0^1 x^2 \log x \, dx$.
A. \frac{1}{9}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{4}{9}

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