POST UTME MOUNTAIN TOP UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Determine the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 2
A circle with center ( C ) and radius ( 5 ) has equation \( x - 3 \ \)^2 + \( y - 4 \)^2 = 25 ). Find the equation of the line pas\sing through ( C ) and perp\endicular to the line \( y = x - 2 \).
A. y = -x + 7
B. y = x + 7
C. y = -x - 7
D. y = x - 7
Question 3
A rec\tangular solid has dimensions 5 cm, 8 cm, and 3 cm. Find its surface area.
A. 154 cm^2
B. 156 cm^2
C. 158 cm^2
D. 160 cm^2
Question 4
Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).
A. 12
B. 16
C. 20
D. 24
Question 5
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y = x + 1
B. y = x - 1
C. y = -x + 1
D. y = x - 2
Question 6
Evaluate the definite integral \[ \int_0^1 \( 2x^2 + 3x - 1 \) dx \].
A. 5
B. 6
C. 7
D. 8
Question 7
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \ \) for \( x \ \) in the interval \( [0, 2\pi] \ \).
A. \( x = \frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4} \ \)
B. \( x = \frac{\pi}{2}, \frac{3\pi}{2} \ \)
C. \( x = \frac{\pi}{4}, \frac{3\pi}{4} \ \)
D. \( x = \frac{\pi}{2}, \frac{3\pi}{2}, \frac{5\pi}{2} \ \)
Question 8
The mean of a set of data is 25. If the sum of the data is 150, find the number of data points.
A. 5
B. 6
C. 7
D. 8
Question 9
A box with a square base of side length ( 6 ) and height ( 8 ) has a square hole cut out of one of its sides. The hole has a side length of ( 2 ) and is centered on the side of the box. Find the volume of the box with the hole cut out.
A. 48
B. 50
C. 52
D. 54
Question 10
A vector \( \mathbf{a} \ \) has components \( a_x = 2 \ \) and \( a_y = 3 \ \). A vector \( \mathbf{b} \ \) has components \( b_x = -1 \ \) and \( b_y = 4 \ \). Find the magnitude of the sum of these two vectors.
A. \( \sqrt{\( 2 - 1 \ \)^2 + \( 3 + 4 \)^2} \)
B. \( \sqrt{\( 2 + 1 \ \)^2 + \( 3 - 4 \)^2} \)
C. \( \sqrt{\( 2 - 1 \ \)^2 + \( 3 - 4 \)^2} \)
D. \( \sqrt{\( 2 + 1 \ \)^2 + \( 3 + 4 \)^2} \)
Question 11
The binary operation \( \star \) is defined by \( a \star b = a^2 + b^2 \). Find the result of \( 2 \star 3 \).
A. 13
B. 14
C. 15
D. 16
Question 12
A survey of 100 students found that 60 students preferred coffee, 30 students preferred tea, and 10 students preferred both. What is the probability that a randomly selected student prefers coffee?
A. 0.6
B. 0.7
C. 0.8
D. 0.9
Question 13
Find the equation of the circle with center ( (2, 3) ) and radius 4.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 3 \)^2 + \( y - 2 \)^2 = 16
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 9
D. \( x - 3 \)^2 + \( y - 2 \)^2 = 9
Question 14
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, 1 \) ∪ (3, ∞)
C. \( -∞, -1 \) ∪ (1, ∞)
D. \( -∞, 3 \) ∪ (1, ∞)
Question 15
Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ).
A. 6x + 2
B. 3x^2 + 2
C. 2x^2 + 6
D. x^2 + 2

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