POST UTME ELIZADE UNIVERSITY 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the value of $k$ such that the lines $2x + 3y = 7$ and $kx - 2y = 5$ are parallel.
A. -\frac{14}{5}
B. -\frac{7}{5}
C. \frac{7}{5}
D. \frac{14}{5}
Question 2
Solve the system of equations u\sing matrices: \begin{align*} 2x + 3y &= 7 \ x - 2y &= -3 \ \end{align*}
A. \begin{bmatrix} 1 \ 2 \end{bmatrix}
B. \begin{bmatrix} 1 \ -2 \end{bmatrix}
C. \begin{bmatrix} 1 \ 2 \end{bmatrix}
D. \begin{bmatrix} 1 \ -2 \end{bmatrix}
Question 3
Solve the inequality \( x^2 - 4x + 4 > 0 \).
A. x < 2
B. x > 2
C. x < 1
D. x > 1
Question 4
Solve for x in the equation \( 2x^2 + 5x - 3 = 0 \).
A. \( x = -3 \)
B. \( x = 1 \)
C. \( x = -1 \)
D. \( x = 3 \)
Question 5
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 = 25
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 36
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 49
Question 6
Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.
A. \frac{2x\( x^2 - 4 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
B. \frac{2x\( x^2 - 4 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
C. \frac{2x\( x^2 - 4 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
D. \frac{2x\( x^2 - 4 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
Question 7
Two events $A$ and $B$ are indep\endent. If $P(A) = \frac{1}{4}$ and $P(B) = \frac{1}{3}$, find $P\( A \cap B \)$.
A. \frac{1}{12}
B. \frac{1}{6}
C. \frac{1}{4}
D. \frac{1}{3}
Question 8
Solve the inequality \( 2x - 5 > 3 \).
A. \( x > 4 \)
B. \( x < 4 \)
C. \( x > 2 \)
D. \( x < 2 \)
Question 9
Find the probability of drawing two aces from a s\tandard deck of 52 cards.
A. \( \frac{1}{52} \)
B. \( \frac{1}{26} \)
C. \( \frac{1}{4} \)
D. \( \frac{1}{2} \)
Question 10
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \) for x.
A. \( x = -2 \)
B. \( x = -1 \)
C. \( x = 1 \)
D. \( x = 2 \)
Question 11
Find the area under the curve \( y = x^2 + 1 \) from \( x = 0 \) to \( x = 2 \).
A. \frac{7}{3}
B. \frac{11}{3}
C. \frac{13}{3}
D. \frac{17}{3}
Question 12
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
A. f'(x) = \frac{-x}{\( x^2 + 1 \)^{3/2}}
B. f'(x) = \frac{x}{\( x^2 + 1 \)^{3/2}}
C. f'(x) = \frac{1}{\( x^2 + 1 \)^{3/2}}
D. f'(x) = \frac{-1}{\( x^2 + 1 \)^{3/2}}
Question 13
Solve the system of equations u\sing matrices: \begin{align*} x + y + z &= 6 \ 2x - 2y + 3z &= 7 \ x - 3y + 2z &= -2 \end{align*}
A. \begin{bmatrix} 1 \ 2 \ -1 \end{bmatrix}
B. \begin{bmatrix} 1 \ -2 \ 3 \end{bmatrix}
C. \begin{bmatrix} 1 \ 2 \ -1 \end{bmatrix}
D. \begin{bmatrix} 1 \ -2 \ 3 \end{bmatrix}
Question 14
Find the area of the triangle with vertices ( (0, 0) ), ( (3, 0) ), and ( (0, 2) ).
A. 3
B. 4
C. 5
D. 6
Question 15
Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. \( x = 10 \)
B. \( x = 100 \)
C. \( x = 1000 \)
D. \( x = 10000 \)

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