POST UTME UNIBEN 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
In the diagram below, ( ABC ) is a circle with center ( O ).
A. AB = BC
B. AB > BC
C. AB < BC
D. AB = AC
Question 2
A random variable X has a probability distribution given by P\( X = 1 \) = 0.3, P\( X = 2 \) = 0.4, P\( X = 3 \) = 0.3. If Y is another random variable such that Y = 2X - 1, find the probability that Y is greater than 3.
A. 0.2
B. 0.4
C. 0.6
D. 0.8
Question 3
Solve for x in the equation \frac{x}{x-1} + \frac{x}{x+1} = 2.
A. x = 2
B. x = 1
C. x = -1
D. x = 0
Question 4
Solve the equation \( \frac{1}{x+1} + \frac{1}{x-1} = \frac{1}{2} \) for x.
A. x = 2
B. x = -2
C. x = 1
D. x = -1
Question 5
Find the area of the triangle with vertices ( (0, 0) ), ( (3, 0) ), and ( (0, 4) ).
A. ( 6 )
B. ( 12 )
C. ( 18 )
D. ( 24 )
Question 6
A sequence is defined as follows: a_1 = 2, a_n = 3a_{n-1} + 2 for n > 1. Find the value of a_5.
A. 242
B. 242
C. 242
D. 242
Question 7
Solve the inequality \( \frac{x}{x-2} > 1 \) for \( x > 2 \).
A. \( x > 3 \ \)
B. \( x < 3 \ \)
C. \( x > 2 \ \)
D. \( x < 2 \ \)
Question 8
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 9
Solve the matrix equation \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 7 \ 10 \end{bmatrix} \).
A. \( x = 3, y = 2 \ \)
B. \( x = 2, y = 3 \ \)
C. \( x = 1, y = 4 \ \)
D. \( x = 4, y = 1 \ \)
Question 10
A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 1 \) with initial term \( a_1 = 3 \). Find the sum of the first 5 terms of the sequence.
A. 65
B. 75
C. 85
D. 95
Question 11
Given that \( \sin^2 x + \cos^2 x = 1 \), find \( \tan^2 x \) in terms of \( \sin^2 x \) and \( \cos^2 x \).
A. \( \frac{\sin^2 x}{\cos^2 x} \)
B. \( \sin^2 x + \cos^2 x \)
C. \( \frac{\cos^2 x}{\sin^2 x} \)
D. \( \sin^2 x \cos^2 x \)
Question 12
Find the area of the region bounded by the parabola y = x^2 and the line y = 2x - 3.
A. 9/2
B. 9
C. 18
D. 36
Question 13
Solve the inequality \( |x - 2| > 3 \).
A. \( x < -1 \) or \( x > 5 \)
B. \( x < 1 \) or \( x > 5 \)
C. \( x < -1 \) or \( x > 2 \)
D. \( x < 1 \) or \( x > 2 \)
Question 14
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. \( x = -2 \)
B. \( x = 2 \)
C. \( x = -1 \)
D. \( x = 1 \)
Question 15
Find the equation of the circle with center at (2, 3) and radius 4.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y - 3 \)^2 = 4
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 9
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 25

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