POST UTME EKSU 2018 Mathematics | Objective

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Question 1
A circle with center (0, 0) and radius 5 passes through the point (3, 4). Find the equation of the circle.
A. \( x - 0 \)^2 + \( y - 0 \)^2 = 25
B. \( x - 3 \)^2 + \( y - 4 \)^2 = 25
C. \( x - 0 \)^2 + \( y - 0 \)^2 = 16
D. \( x - 3 \)^2 + \( y - 4 \)^2 = 16
Question 2
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If 80% of the scores are above 50, what is the median score?
A. 55
B. 60
C. 65
D. 70
Question 3
Solve the inequality x^2 - 4x - 5 > 0.
A. \( -\\infty, -1 \) \\cup \( 5, \\infty \)
B. \( -\\infty, 1 \) \\cup \( 5, \\infty \)
C. \( -\\infty, -1 \) \\cup \( 1, \\infty \)
D. \( -\\infty, 1 \) \\cup \( 5, \\infty \)
Question 4
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
A. (16)
B. (32)
C. (64)
D. (128)
Question 5
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 = 16
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
Question 6
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. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 16 )
D. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 4 )
Question 7
Find the equation of the circle with center at ((2,3)) and radius (5).
A. \( x-2 \ \)^2 + \( y-3 \)^2 = 25 )
B. \( x-3 \ \)^2 + \( y-2 \)^2 = 25 )
C. \( x+2 \ \)^2 + \( y-3 \)^2 = 25 )
D. \( x-2 \ \)^2 + \( y+3 \)^2 = 25 )
Question 8
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the prism.
A. 30
B. 50
C. 60
D. 70
Question 9
A curve is defined by the equation \( y = \frac{1}{x^2 + 1} \). Find the area under the curve between x = 0 and x = 1.
A. 0.5
B. 0.75
C. 1
D. 1.5
Question 10
A set of 5 consecutive integers has a median of 10. Find the sum of the integers.
A. 250
B. 300
C. 350
D. 400
Question 11
A random variable X has a probability distribution given by \( P\( X = 1 \ \) = 0.3 ), \( P\( X = 2 \ \) = 0.4 ), and \( P\( X = 3 \ \) = 0.3 ). Find the expected value of X.
A. 1.4
B. 1.6
C. 1.8
D. 2.0
Question 12
In a circle of radius 5 cm, a chord of length 8 cm subt\ends an angle of 60° at the centre. Find the area of the sector formed by the chord and the radii.
A. \( \frac{5}{3} pi \)
B. \( \frac{10}{3} pi \)
C. \( \frac{15}{3} pi \)
D. \( \frac{20}{3} pi \)
Question 13
A sequence is defined by the formula \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.
A. 15
B. 20
C. 25
D. 30
Question 14
Find the derivative of the function (f(x) = 3x^2 + 2x - 5) u\sing the chain rule.
A. (f'(x) = 6x + 2)
B. (f'(x) = 6x + 2x - 5)
C. (f'(x) = 6x^2 + 2x - 5)
D. (f'(x) = 6x + 2x^2 - 5)
Question 15
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)
B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)
C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2 \)
D. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^3 \)

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