POST UTME ELIZADE UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).
A. \( y = \frac{5-3}{4-2}x + \frac{3\( 4 \ \)-5(2)}{4-2} \)
B. \( y = \frac{5-3}{4-2}x + \frac{3\( 2 \ \)-5(4)}{4-2} \)
C. \( y = \frac{5-3}{4-2}x + \frac{3\( 4 \ \)-5(2)}{4-2} \)
D. \( y = \frac{5-3}{4-2}x + \frac{3\( 2 \ \)-5(4)}{4-2} \)
Question 3
A histogram is shown below. What is the mean of the data represented by the histogram?
A. 10
B. 15
C. 20
D. 25
Question 4
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 5
A sequence is defined by the formula \(a_n = 2n + 1\). Find the sum of the first 10 terms of the sequence.
A. 110
B. 120
C. 130
D. 140
Question 6
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 7
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 8
In a geometric sequence, the first term is 2 and the common ratio is 3. Find the sum of the first 5 terms.
A. 1210
B. 1230
C. 1250
D. 1270
Question 9
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 10
Solve the inequality \( \log_2 \( x^2 + 1 \ \) > 3 ).
A. \( x > -\sqrt{7} \)
B. \( x < \sqrt{7} \)
C. \( x > \sqrt{7} \)
D. \( x < -\sqrt{7} \)
Question 11
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
Question 12
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 13
Find the equation of the circle with center ( (2, 3) ) and radius 4.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16 \)
B. \( x - 3 \)^2 + \( y - 2 \)^2 = 16 \)
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16 \)
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 25 \)
Question 14
Solve the equation \( \sin^2 x + \cos^2 x = 1 \ \) for ( x ) in the interval \( [0, \pi] \).
A. \( x = \frac{\pi}{4} \ \)
B. \( x = \frac{3\pi}{4} \ \)
C. \( x = \frac{\pi}{2} \ \)
D. \( x = \frac{5\pi}{4} \ \)
Question 15
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

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