POST UTME UNILAG 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve for x in the equation 2^x + 3^x = 10.
A. 2
B. 3
C. 4
D. 5
Question 2
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. 0.8413
B. 0.8413 - 0.5
C. 0.5
D. 0.5 - 0.8413
Question 3
The graph of the function \( y = \frac{1}{x} \ \) has a horizontal asymptote at \( y = \boxed{?} \).
A. 0
B. 1
C. ∞
D. -∞
Question 4
Find the derivative of the function ( f(x) = \sin^2 x ).
A. \cos 2x
B. \sin 2x
C. \cos x
D. \sin x
Question 5
Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).
A. \( y = 2x + 1 \)
B. \( y = 2x - 1 \)
C. \( y = -2x + 1 \)
D. \( y = -2x - 1 \)
Question 6
Solve the equation \frac{x^2 - 4x + 4}{x^2 - 4x + 3} = \frac{x + 2}{x - 1}
A. x = 2
B. x = 3
C. x = 4
D. x = 5
Question 7
Determine the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 24\pi
B. 36\pi
C. 48\pi
D. 60\pi
Question 8
Given that \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} \), find the projection of ( mathbf{b} ) onto ( mathbf{a} ).
A. 0.6
B. 0.8
C. 1.2
D. 1.6
Question 9
A random variable ( X ) has a probability density function ( f(x) = \begin{cases} 2x & \text{if } 0 < x < 1 \ 0 & \text{otherwise} \end{cases} ). Find the expected value of ( X ).
A. 0.25
B. 0.5
C. 0.75
D. 1.0
Question 10
Find the area of the triangle with vertices ( (0, 0) ), ( (3, 0) ), and ( (0, 2) ).
A. 6
B. 12
C. 18
D. 24
Question 11
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio \frac{1}{2}.
A. 1.9999
B. 2.0000
C. 2.0001
D. 2.0002
Question 12
A histogram is shown below. What is the mode of the data set?
A. A
B. B
C. C
D. D
Question 13
In a circle with center O and radius 6, what is the length of the arc intercepted by a central angle of 60 degrees?
A. 3π
B. 4π
C. 5π
D. 6π
Question 14
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 2
B. 4
C. 8
D. 16
Question 15
Find the area under the curve y = \sin^2 x from x = 0 to x = \frac{\pi}{2}.
A. \frac{\pi}{4}
B. \frac{\pi}{2}
C. \frac{\pi}{3}
D. \frac{\pi}{6}

Master the Exam!

You've seen a preview, but there are thousands more questions plus AI tutor to break down complex solutions.

Unlock Full Access Available for Android & Windows
Help others prepare! Share this practice hub: