POST UTME UNILORIN 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A circle has a radius of 4 cm. If a chord of the circle subt\ends an angle of 60° at the center, what is the length of the chord?
A. 4 cm
B. 6 cm
C. 8 cm
D. 10 cm
Question 2
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 3
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 2
B. 4
C. 8
D. 16
Question 4
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is less than 60?
A. 0.1587
B. 0.6915
C. 0.8413
D. 0.9772
Question 5
Find the area under the curve y = 2x^2 + 3x - 1 from x = 0 to x = 2.
A. 13
B. 14
C. 15
D. 16
Question 6
A solid is formed by revolving the region bounded by the curves y = x^2 and y = 4 - x^2 about the x-axis. Find the volume of the solid.
A. \frac{16\pi}{3}
B. \frac{32\pi}{3}
C. \frac{64\pi}{3}
D. \frac{128\pi}{3}
Question 7
Find the mean deviation about the median for the data set: 2, 4, 6, 8, 10.
A. 2
B. 4
C. 6
D. 8
Question 8
Find the equation of the line pas\sing through the point ( (1, 2) ) with slope 3.
A. \( y = 3x + 1 \)
B. \( y = 3x - 1 \)
C. \( y = 3x + 2 \)
D. \( y = 3x - 2 \)
Question 9
Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).
A. 12
B. 16
C. 20
D. 24
Question 10
Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).
A. \( y = \frac{1}{2}x + \frac{1}{2} \)
B. \( y = \frac{1}{2}x - \frac{1}{2} \)
C. \( y = 2x - 1 \)
D. \( y = 2x + 1 \)
Question 11
A binary operation ( ast ) is defined as \( a ast b = a^2 + b^2 \). Find the value of ( 2 ast 3 ).
A. 13
B. 25
C. 5
D. 9
Question 12
Solve the inequality: \frac{x}{x-1} > 0.
A. \( -\infty, 0 \) \cup \( 1, \infty \)
B. \( -\infty, 1 \) \cup \( 1, \infty \)
C. \( -\infty, 0 \) \cup (0, 1)
D. (0, 1)
Question 13
Find the equation of the circle with center ( (2, 3) ) and radius 4.
A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 4 )
C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 9 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 25 )
Question 14
Find the surface area of the solid formed by revolving the region bounded by y = x^2, y = 0, and x = 2 about the x-axis.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 15
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \).
A. \( x = -2, x = -3 \)
B. \( x = 2, x = 3 \)
C. \( x = -1, x = -6 \)
D. \( x = 1, x = 6 \)

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