POST UTME UNN 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
In the diagram below, the graph of ( f(x) = \sin^2 x ) is shown. What is the value of \( \theta \) in degrees for which \( f\( \theta \ \) = \frac{1}{2} )?
A. 30
B. 45
C. 60
D. 90
Question 2
Determine the number of solutions to the equation x^2 + 2x + 2 = 0.
A. 0
B. 1
C. 2
D. 3
Question 3
Find the volume of the frustum of a cone with a height of 6 cm, a lower base radius of 4 cm, and an upper base radius of 2 cm.
A. 48\pi
B. 64\pi
C. 72\pi
D. 80\pi
Question 4
Solve for ( x ) in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 5
Determine the mean of the following dataset: {1, 3, 5, 7, 9}.
A. 2
B. 4
C. 6
D. 8
Question 6
A random variable X has a probability distribution given by P(X) = \( 1/2 \)^\( X-1 \) for X = 1, 2, 3, ... . Find the probability that X is greater than 2.
A. 1/4
B. 1/2
C. 3/4
D. 1
Question 7
Find the area under the curve y = 2x^2 + 3x - 4 from x = 0 to x = 2.
A. 14
B. 16
C. 18
D. 20
Question 8
Solve the trigonometric equation \sin(x) = \cos(x) for 0 ≤ x ≤ 2π.
A. \frac{\pi}{4}
B. \frac{3\pi}{4}
C. \frac{5\pi}{4}
D. \frac{7\pi}{4}
Question 9
A bag contains 5 red balls, 4 blue balls, and 3 green balls. If a ball is drawn at random, what is the probability that it is either red or blue?
A. \frac{9}{12}
B. \frac{5}{12}
C. \frac{4}{12}
D. \frac{3}{12}
Question 10
A geometric sequence has a first term of 2 and a common ratio of 3. Find the 5th term of the sequence.
A. 243
B. 243
C. 243
D. 243
Question 11
Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for (x).
A. 0
B. \frac{\pi}{2}
C. \frac{\pi}{4}
D. \frac{3\pi}{4}
Question 12
A vector ( mathbf{a} ) has a magnitude of 6 units and makes an angle of 30° with the positive x-axis. If a vector ( mathbf{b} ) is perp\endicular to ( mathbf{a} ), what is the magnitude of ( mathbf{b} )?
A. 3
B. 6
C. 9
D. 12
Question 13
In a certain number base, the representation of the number 27 is 101. If the base is denoted by 'b', find the value of 'b' u\sing the formula for converting a number from base 'b' to base 10.
A. 3
B. 4
C. 5
D. 6
Question 14
Find the equation of the \tangent line to the curve y = x^2 at the point (1, 1).
A. y = 2x - 1
B. y = 2x + 1
C. y = 3x - 1
D. y = 3x + 1
Question 15
Find the value of y in the equation \( y = 2x + 3 \), given that x = 2.
A. 7
B. 5
C. 3
D. 1

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