POST UTME OAU 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( \frac{x}{x-2} > 2 \) for \( x > 2 \).
A. x > 4
B. x > 6
C. x < 4
D. x < 6
Question 2
A matrix ( A ) is given by \( A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \). Find the determinant of ( A ).
A. 1
B. 2
C. 3
D. 4
Question 3
Solve for x in the equation \( 2^x = 12 \).
A. 3
B. 4
C. 5
D. 6
Question 4
A circle has a radius of 4 cm. Find the area of the circle.
A. 50.24
B. 100.48
C. 200.96
D. 251.2
Question 5
A histogram is given below. Find the mean of the data.
A. 10
B. 20
C. 30
D. 40
Question 6
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x}} ) u\sing the chain rule.
A. \frac{-1}{2x^{3/2}}
B. \frac{1}{2x^{3/2}}
C. \frac{-1}{x^{3/2}}
D. \frac{1}{x^{3/2}}
Question 7
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. \frac{1}{6}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{5}{6}
Question 8
A binary operation ( ast ) on the set of integers is defined as \( a ast b = a^2 + b^2 \). Find the value of ( 2 ast 3 ).
A. 11
B. 13
C. 17
D. 19
Question 9
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -3/2 \) or \( x > 1/2 \)
B. \( x < -3/2 \) or \( x < 1/2 \)
C. \( x > -3/2 \) or \( x > 1/2 \)
D. \( x < -3/2 \) or \( x < 1/2 \)
Question 10
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.
A. \frac{-x}{\( x^2 + 1 \)^{3/2}}
B. \frac{x}{\( x^2 + 1 \)^{3/2}}
C. \frac{1}{\( x^2 + 1 \)^{3/2}}
D. \frac{-1}{\( x^2 + 1 \)^{3/2}}
Question 11
Find the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \) and the line \( y = 4 \) about the x-axis.
A. \( 64/3 \)
B. \( 64/5 \)
C. \( 64/7 \)
D. \( 64/9 \)
Question 12
A set A contains the elements {1, 2, 3, 4, 5}. Find the number of subsets of A that contain exactly three elements.
A. 10
B. 15
C. 20
D. 25
Question 13
Solve the system of linear equations \( \begin{cases} x + y = 2 \ x - 2y = -3 \end{cases} \).
A. \begin{pmatrix} 1 \ 1 \end{pmatrix}
B. \begin{pmatrix} 1 \ -1 \end{pmatrix}
C. \begin{pmatrix} -1 \ 1 \end{pmatrix}
D. \begin{pmatrix} -1 \ -1 \end{pmatrix}
Question 14
Find the area under the curve \( y = \sin^2 x \) from \( x = 0 \) to \( x = \frac{pi}{2} \).
A. 0
B. 1
C. 2
D. 3
Question 15
A box contains 5 red balls and 3 blue balls. Two balls are drawn at random without replacement. What is the probability that the first ball drawn is red and the second ball drawn is blue?
A. \( \frac{5}{8} \times \frac{3}{7} \ \)
B. \( \frac{5}{8} \times \frac{4}{7} \ \)
C. \( \frac{5}{8} \times \frac{3}{6} \ \)
D. \( \frac{5}{8} \times \frac{4}{6} \ \)

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