POST UTME UNIBEN 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area of the region bounded by the curves y = x^2 and y = 2x.
A. 4/3
B. 8/3
C. 16/3
D. 32/3
Question 2
Find the area of the triangle with vertices ( (0, 0) ), ( (3, 0) ), and ( (0, 4) ).
A. ( 6 )
B. ( 12 )
C. ( 18 )
D. ( 24 )
Question 3
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 4
Find the volume of the frustum of a cone with height 8cm, lower base radius 4cm, and upper base radius 2cm.
A. 256\pi cm^3
B. 512\pi cm^3
C. 768\pi cm^3
D. 1024\pi cm^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 equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).
A. y = 2x - 1
B. y = 2x + 1
C. y = x - 2
D. y = x + 2
Question 7
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 8
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 9
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. 1/6
B. 1/3
C. 2/3
D. 5/6
Question 10
Find the determinant of the matrix \[ \begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 4 & 2 \end{bmatrix} \].
A. 0
B. 1
C. 2
D. 3
Question 11
Find the sum of the first 5 terms of the geometric series with first term \( a = 2 \) and common ratio \( r = 3 \).
A. \( 2\( 3^5 - 1 \ \) )
B. \( 2\( 3^5 + 1 \ \) )
C. \( 2\( 3^5 - 2 \ \) )
D. \( 2\( 3^5 + 2 \ \) )
Question 12
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
Question 13
Find the area of the circle with radius 4 cm.
A. 50.24 cm^2
B. 25.12 cm^2
C. 50.12 cm^2
D. 25.24 cm^2
Question 14
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 15
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. \( x = 4, y = 1 \ \)

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