POST UTME ELIZADE UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
In a certain number base, the value of the digit 5 is represented as \( overline{101}_b \). If the base is denoted as ( b ), and the value of the digit 5 is equal to 6 in base 10, find the value of ( b ).
A. 2
B. 3
C. 4
D. 5
Question 2
A vector ( mathbf{a} ) has a magnitude of 5 units and makes an angle of 60° with the positive x-axis. Find the x and y components of ( mathbf{a} ).
A. \( x = 2.5, y = 4.33 \)
B. \( x = 4.33, y = 2.5 \)
C. \( x = 2.5, y = 2.5 \)
D. \( x = 4.33, y = 4.33 \)
Question 3
Solve for x in the equation \(\log_{10} \( x^2 \) = 4\).
A. 10
B. 100
C. 1000
D. 10000
Question 4
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \) u\sing integration.
A. 64
B. 32
C. 16
D. 8
Question 5
A geometric shape is shown below. What is the volume of the shape?
A. 8
B. 10
C. 12
D. 15
Question 6
A circle has an equation of \( x^2 + y^2 - 6x + 4y + 4 = 0 \). Find the center and radius of the circle.
A. \( 3, -2 \), 1
B. (3, 2), 1
C. (2, 3), 1
D. (1, 1), 1
Question 7
A set A contains 5 elements, and a set B contains 3 elements. If the intersection of sets A and B contains 2 elements, what is the number of elements in the union of sets A and B?
A. 6
B. 7
C. 8
D. 9
Question 8
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x}} ) u\sing the chain rule.
A. \( -\frac{1}{2} x^{-\frac{3}{2}} \)
B. \( \frac{1}{2} x^{-\frac{3}{2}} \)
C. \( -\frac{1}{2} x^{-\frac{1}{2}} \)
D. \( \frac{1}{2} x^{-\frac{1}{2}} \)
Question 9
Solve the matrix equation \( egin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix} \).
A. \( x = 1, y = 2 \)
B. \( x = 2, y = 1 \)
C. \( x = 1, y = 1 \)
D. \( x = 2, y = 2 \)
Question 10
A rec\tangular prism has a length of 10 cm, a width of 5 cm, and a height of 8 cm. Calculate its surface area.
A. 240 cm^2
B. 200 cm^2
C. 220 cm^2
D. 260 cm^2
Question 11
A histogram of exam scores is given below. If the mean score is 75 and the s\tandard deviation is 10, what is the probability that a randomly selected student scored above 85?
A. 0.2
B. 0.3
C. 0.4
D. 0.5
Question 12
Determine the value of \( \sin^2 30^circ + \cos^2 30^circ \) u\sing the Pythagorean identity.
A. 1
B. 0
C. 2
D. 3
Question 13
A set of 10 numbers has a mean of 20. If 5 is added to each number, what is the new mean?
A. 15
B. 20
C. 25
D. 30
Question 14
Find the derivative of the function ( f(x) = \frac{1}{x^2} \) with respect to ( x ).
A. ( f'(x) = -\frac{2}{x^3} \)
B. ( f'(x) = \frac{2}{x^3} \)
C. ( f'(x) = -\frac{1}{x^2} \)
D. ( f'(x) = \frac{1}{x^2} \)
Question 15
Find the determinant of the matrix [ egin{array}{ccc} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{array} ].
A. -120
B. 120
C. 0
D. -60

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