POST UTME UNILAG 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
Find the derivative of the function ( f(x) = \sin^2 x ).
A. \cos 2x
B. \sin 2x
C. \cos x
D. \sin x
Question 3
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 4
Solve the inequality \( x^2 - 4x + 4 > 0 \).
A. x > 2
B. x < 2
C. x > 0
D. x < 0
Question 5
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}
Question 6
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 2
B. 4
C. 8
D. 16
Question 7
Find the area of the triangle with vertices ( (0, 0) ), ( (3, 0) ), and ( (0, 2) ).
A. 6
B. 12
C. 18
D. 24
Question 8
Find the volume of the frustum of a cone with height 6cm, lower base radius 4cm, and upper base radius 2cm.
A. 48\pi cm^3
B. 64\pi cm^3
C. 80\pi cm^3
D. 96\pi cm^3
Question 9
Find the determinant of the matrix \begin{bmatrix} 2 & 1 & 4 \ 3 & 2 & 5 \ 6 & 3 & 7 \end{bmatrix}
A. 0
B. 1
C. 2
D. 3
Question 10
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 11
Determine the mean of the following data set: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?
A. 6
B. 8
C. 10
D. 12
Question 12
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 13
A histogram is shown below. What is the mode of the data set?
A. A
B. B
C. C
D. D
Question 14
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 15
Find the determinant of the matrix \( egin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix} \).
A. 0
B. 1
C. 2
D. 3

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