POST UTME MOUNTAIN TOP UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -1 \) or \( x > \frac{3}{2} \)
B. \( x < -1 \) or \( x < \frac{3}{2} \)
C. \( x > -1 \) or \( x > \frac{3}{2} \)
D. \( x > -1 \) or \( x < \frac{3}{2} \)
Question 2
Solve the equation \( x^2 + 4x + 4 = 0 \).
A. \( x = -2 \)
B. \( x = -1 \)
C. \( x = 1 \)
D. \( x = 2 \)
Question 3
A binary operation \(*\) on the set \{1, 2, 3, 4\} is defined as follows: \(a \ast b = a^2 + b^2\). Find the value of \(2 \ast 3\).
A. 13
B. 17
C. 19
D. 21
Question 4
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -1 \) or \( x > \frac{3}{2} \)
B. \( x < -1 \) or \( x < \frac{3}{2} \)
C. \( x > -1 \) or \( x > \frac{3}{2} \)
D. \( x > -1 \) or \( x < \frac{3}{2} \)
Question 5
In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side u\sing the Pythagorean theorem.
A. 8 cm
B. 12 cm
C. 16 cm
D. 20 cm
Question 6
Find the volume of the solid formed by rotating the area bounded by the curve \( y = x^2 \) and the line \( x = 2 \) about the x-axis.
A. 16π/3
B. 32π/3
C. 64π/3
D. 128π/3
Question 7
Find the value of $x$ in the equation $2^x + 5^x = 7^x$.
A. 1
B. 2
C. 3
D. 4
Question 8
Let ( f(x) = \frac{1}{x^2 + 1} ). Find the derivative of ( f(x) ) u\sing the chain rule.
A. \frac{-2x}{\( x^2 + 1 \)^2}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. \frac{-2}{\( x^2 + 1 \)^2}
D. \frac{2}{\( x^2 + 1 \)^2}
Question 9
The equation of a circle is given by \(x^2 + y^2 + 4x + 6y = 0\). Find the center and radius of the circle.
A. \( -2, -3 \) and 5
B. ( 2, 3 ) and 5
C. \( -2, 3 \) and 5
D. \( 2, -3 \) and 5
Question 10
A set of 5 numbers has a mean of 10. If 2 is added to each number, what is the new mean?
A. 8
B. 10
C. 12
D. 14
Question 11
A histogram of exam scores is shown below. Find the mean of the scores.
A. 60
B. 70
C. 80
D. 90
Question 12
A histogram of exam scores is shown below. Find the mean score.
A. \( \frac{1}{4} \( 10 + 20 + 30 + 40 \ \) = 25 )
B. \( \frac{1}{4} \( 10 + 20 + 30 + 40 \ \) = 25 )
C. \( \frac{1}{4} \( 10 + 20 + 30 + 40 \ \) = 25 )
D. \( \frac{1}{4} \( 10 + 20 + 30 + 40 \ \) = 25 )
Question 13
The mean of five numbers is 15. If one of the numbers is 10, find the sum of the other four numbers.
A. 50
B. 60
C. 70
D. 80
Question 14
In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.
A. 5 cm
B. 7.07 cm
C. 10 cm
D. 14.14 cm
Question 15
A sequence is defined as \(a_n = 2n + 1\). Find the sum of the first five terms of the sequence.
A. 15
B. 25
C. 35
D. 45

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