POST UTME ELIZADE UNIVERSITY 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
Find the area of the triangle with vertices ( (0, 0) ), ( (3, 0) ), and ( (0, 2) ).
A. 3
B. 4
C. 5
D. 6
Question 3
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 4
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 5
Solve the system of equations \( egin{cases} x + y = 4 \ 2x - 3y = -1 \end{cases} \).
A. x = 1, y = 3
B. x = 2, y = 2
C. x = 3, y = 1
D. x = 4, y = 0
Question 6
Find the value of x in the equation \( \tan x = \frac{1}{2} \).
A. \( x = \frac{pi}{6} \)
B. \( x = \frac{pi}{4} \)
C. \( x = \frac{pi}{3} \)
D. \( x = \frac{pi}{2} \)
Question 7
Find the area of the triangle with vertices ( (0, 0), (3, 0), (0, 4) ).
A. ( 6 )
B. ( 8 )
C. ( 10 )
D. ( 12 )
Question 8
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 9
Solve for x in the equation \( 2x^2 + 5x - 3 = 0 \).
A. \( x = -3 \)
B. \( x = 1 \)
C. \( x = -1 \)
D. \( x = 3 \)
Question 10
Solve the inequality \( x^2 - 4x + 4 > 0 \).
A. x < 2
B. x > 2
C. x < 1
D. x > 1
Question 11
Solve for $x$: [ \sin^2 x + \cos^2 x = 1 ] and [ \tan^2 x + 1 = sec^2 x ].
A. \frac{\pi}{4}
B. \frac{\pi}{2}
C. \frac{3\pi}{4}
D. \frac{\pi}{6}
Question 12
Find the value of ( x ) in the equation \( 2^x = 32 \).
A. 5
B. 6
C. 7
D. 8
Question 13
Solve the equation $\sin^2 x + \cos^2 x = 1$.
A. $x = \frac{\pi}{4}$
B. $x = \frac{\pi}{2}$
C. $x = \frac{3\pi}{4}$
D. $x = \frac{5\pi}{4}$
Question 14
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 15
A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 3 \) with initial term \( a_1 = 2 \). Find the value of \( a_{10} \).
A. 1023
B. 1024
C. 1025
D. 1026

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