POST UTME CHRISTOPHER UNIVERSITY 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( x^2 - 4x - 5 > 0 \) u\sing factoring.
A. x < -1, x > 5
B. x < -5, x > 1
C. x < 1, x > 5
D. x < 5, x > 1
Question 2
Find the value of \( \sin 2\theta \) given that \( \cos \theta = \frac{3}{5} \) and \( \sin \theta = \frac{4}{5} \).
A. 0.8
B. 0.9
C. 1.2
D. 1.5
Question 3
Solve the system of equations \( egin{cases} x + y = 4 \ x - y = 2 \end{cases} \) u\sing substitution.
A. x = 3, y = 1
B. x = 1, y = 3
C. x = 2, y = 2
D. x = 4, y = 0
Question 4
Solve for ( x ) in the equation \( 2^x + 5^x = 7^x \).
A. 1
B. 2
C. 3
D. 4
Question 5
Solve the inequality \( \frac{x - 2}{x + 1} > 0 \) u\sing a sign table.
A. x < -1, x > 2
B. x < -1, x < 2
C. x > -1, x > 2
D. x > -1, x < 2
Question 6
A histogram of exam scores is shown below. What is the mean score?
A. 40
B. 50
C. 60
D. 70
Question 7
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 64
B. 80
C. 96
D. 128
Question 8
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \)
A. 0
B. 1
C. 2
D. 3
Question 9
A binary operation ( oplus ) is defined as \( a oplus b = a + b - ab \). Find the value of ( 2 oplus 3 )
A. 1
B. 2
C. 3
D. 4
Question 10
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the quotient rule.
A. f'(x) = \frac{-2x}{\( x^2 + 1 \)^2}
B. f'(x) = \frac{2x}{\( x^2 + 1 \)^2}
C. f'(x) = \frac{2}{\( x^2 + 1 \)^2}
D. f'(x) = \frac{-2}{\( x^2 + 1 \)^2}
Question 11
Determine the value of x in the matrix equation \( egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} egin{bmatrix} x \ 2 \end{bmatrix} = egin{bmatrix} 14 \ 26 \end{bmatrix} \)
A. 3
B. 4
C. 5
D. 6
Question 12
A random experiment consists of rolling a fair six-sided die. If the outcome is an even number, the experimenter wins a prize. Find the probability that the experimenter wins the prize
A. 1/2
B. 1/3
C. 2/3
D. 3/4
Question 13
Solve for x in the equation \( \tan^2 x + \tan x - 6 = 0 \) u\sing the quadratic formula.
A. x = 0.5, x = -2
B. x = 1, x = -6
C. x = 2, x = -3
D. x = 3, x = -2
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 = 16
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
Question 15
Two events ( A ) and ( B ) are indep\endent. If ( P(A) = 0.3 ) and ( P(B) = 0.4 ), find the probability that both events occur.
A. 0.12
B. 0.24
C. 0.36
D. 0.48

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