POST UTME MOUNTAIN TOP UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 2
Find the value of $x$ in the equation $2^x + 5^x = 7^x$.
A. 1
B. 2
C. 3
D. 4
Question 3
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 50 and 70?
A. ( 0.9544 )
B. ( 0.8413 )
C. ( 0.6915 )
D. ( 0.6827 )
Question 4
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 5
Find the area of the triangle with vertices ( (0, 0) ), ( (3, 0) ), and ( (0, 4) ).
A. ( 6 )
B. ( 8 )
C. ( 10 )
D. ( 12 )
Question 6
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 7
Solve the inequality \( x^2 - 6x + 8 > 0 \).
A. x < 2 or x > 4
B. x < 1 or x > 4
C. x < 2 or x < 4
D. x > 2 or x < 4
Question 8
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 9
Find the equation of the line pas\sing through the points (1,2) and (3,4).
A. \( y = \frac{4}{2} \( x - 1 \ \) + 2 )
B. \( y = \frac{4}{2} \( x - 3 \ \) + 4 )
C. \( y = \frac{4}{2} \( x - 1 \ \) + 4 )
D. \( y = \frac{4}{2} \( x - 3 \ \) + 2 )
Question 10
A histogram of exam scores is shown below. Find the mean of the scores.
A. 60
B. 70
C. 80
D. 90
Question 11
A set of 5 cards numbered 1 to 5 is drawn at random. What is the probability that the sum of the numbers on the cards is 15?
A. \frac{1}{10}
B. \frac{1}{5}
C. \frac{1}{2}
D. \frac{2}{5}
Question 12
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 2 \).
A. \( \frac{1}{2} \)
B. ( 2 )
C. ( 4 )
D. ( 6 )
Question 13
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \left\( - \infty, - \frac{3}{2} \right \) \cup \left\( \frac{1}{2}, \infty \right \)
B. \left\( - \infty, - \frac{1}{2} \right \) \cup \left\( \frac{3}{2}, \infty \right \)
C. \left\( - \infty, - \frac{3}{2} \right \) \cup \left\( - \frac{1}{2}, \infty \right \)
D. \left\( - \infty, - \frac{1}{2} \right \) \cup \left\( \frac{3}{2}, \infty \right \)
Question 14
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 15
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

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