POST UTME EKSU 2020 Mathematics | Objective

Are you preparing for POST UTME EKSU exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2020 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1
Determine the equation of the circle with center at (2, 3) and radius 4.
Correct A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 16 )
C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 9 )
D. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 9 )

Correct Answer: A

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Question 2
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
Correct A. ( f'(x) = \frac{-2x}{\( x^2 + 1 \)^2} )
B. ( f'(x) = \frac{2x}{\( x^2 + 1 \)^2} )
C. ( f'(x) = \frac{2}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{-2}{\( x^2 + 1 \)^2} )

Correct Answer: A

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Question 3
A fair six-sided die is rolled. What is the probability that the number rolled is either 1 or 6?
A. \( \frac{1}{6} \)
B. \( \frac{1}{3} \)
C. \( \frac{2}{3} \)
Correct D. \( \frac{5}{6} \)

Correct Answer: D

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Question 4
Solve the system of equations: \( x + y = 2 \) and \( xy = 1 \).
Correct A. \( x = 1, y = 1 \)
B. \( x = 1, y = -1 \)
C. \( x = -1, y = 1 \)
D. \( x = -1, y = -1 \)

Correct Answer: A

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Question 5
Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 2).
Correct A. ( 6 )
B. ( 9 )
C. ( 12 )
D. ( 15 )

Correct Answer: A

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Question 6
Determine the value of ( x ) in the equation \( 2x + 5 = 11 \).
Correct A. 3
B. 4
C. 5
D. 6

Correct Answer: A

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Question 7
Find the volume of the frustum of a cone with height \( h = 10 \) cm, lower base radius \( r_1 = 5 \) cm, and upper base radius \( r_2 = 3 \) cm.
A. 100π cm³
Correct B. 150π cm³
C. 200π cm³
D. 250π cm³

Correct Answer: B

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Question 8
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 will be between 50 and 70?
A. 0.34
Correct B. 0.68
C. 0.85
D. 0.95

Correct Answer: B

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Question 9
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
Correct A. \( x < -1 \) or \( x > 3 \)
B. \( x < -3 \) or \( x > 1 \)
C. \( x < -5 \) or \( x > 2 \)
D. \( x < -2 \) or \( x > 4 \)

Correct Answer: A

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Question 10
A binary operation ( odot ) is defined as \( a odot b = ab + 2 \). Find the value of ( 3 odot 4 ).
A. 14
B. 16
Correct C. 18
D. 20

Correct Answer: C

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Question 11
A solid right circular cone has a height of 8 cm and a base radius of 4 cm. Find the volume of the cone in cubic centimeters.
Correct A. 64\pi
B. 128\pi
C. 256\pi
D. 512\pi

Correct Answer: A

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Question 12
A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is not blue?
A. \frac{1}{2}
Correct B. \frac{2}{3}
C. \frac{3}{4}
D. \frac{4}{5}

Correct Answer: B

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Question 13
Solve the equation: \( 2^x + 2^x = 2^{x+2} \).
A. x = 1
Correct B. x = 2
C. x = 3
D. x = 4

Correct Answer: B

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Question 14
Find the equation of the circle with center (2, 3) and radius 4.
Correct 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

Correct Answer: A

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Question 15
Solve the inequality: \( 2x^2 + 5x - 3 \geq 0 \).
Correct A. x \leq -1 \text{ or } x \geq \frac{3}{2}
B. x \leq -1 \text{ or } x \geq 1
C. x \leq 1 \text{ or } x \geq 3
D. x \leq 3 \text{ or } x \geq 5

Correct Answer: A

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Question 16
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
Correct A. \( \frac{1}{3} pi \( 4^2 + 2^2 + 4 cdot 2 cdot 4 \ \) )
B. \( \frac{1}{3} pi \( 4^2 + 2^2 - 4 cdot 2 cdot 4 \ \) )
C. \( \frac{1}{3} pi \( 4^2 + 2^2 + 2 cdot 4 cdot 2 \ \) )
D. \( \frac{1}{3} pi \( 4^2 + 2^2 - 2 cdot 4 cdot 2 \ \) )

Correct Answer: A

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Question 17
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
Correct A. \( x = 10^4 \)
B. \( x = 10^{-4} \)
C. \( x = 10^{2} \)
D. \( x = 10^{-2} \)

Correct Answer: A

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Question 18
Find the surface area of the sphere with radius 5 cm.
Correct A. \( 4 pi \( 5^2 \ \) )
B. \( 2 pi \( 5^2 \ \) )
C. \( pi \( 5^2 \ \) )
D. \( \frac{1}{2} pi \( 5^2 \ \) )

Correct Answer: A

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Question 19
A set of 5 consecutive integers has a median of 8. What is the sum of the integers?
Correct A. ( 5(8) )
B. ( 5(9) )
C. ( 5(10) )
D. ( 5(11) )

Correct Answer: A

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Question 20
A geometric sequence has a first term of 2 and a common ratio of 3. What is the sum of the first 5 terms?
Correct A. \( 2\( 1 + 3 + 3^2 + 3^3 + 3^4 \ \) )
B. \( 2\( 1 + 3 + 3^2 + 3^3 + 3^4 + 3^5 \ \) )
C. \( 2\( 1 + 3 + 3^2 + 3^3 + 3^4 + 3^5 + 3^6 \ \) )
D. \( 2\( 1 + 3 + 3^2 + 3^3 + 3^4 + 3^5 + 3^6 + 3^7 \ \) )

Correct Answer: A

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Question 21
A right triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. What is the length of the other leg?
Correct A. \( \sqrt{10^2 - 6^2} \)
B. \( \sqrt{10^2 + 6^2} \)
C. \( \sqrt{10^2 - 6^2 + 10^2} \)
D. \( \sqrt{10^2 + 6^2 + 10^2} \)

Correct Answer: A

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Question 22
A circle has a radius of 4 cm. What is the area of the circle?
Correct A. \( pi \( 4^2 \ \) )
B. \( 2 pi \( 4^2 \ \) )
C. \( \frac{1}{2} pi \( 4^2 \ \) )
D. \( \frac{1}{4} pi \( 4^2 \ \) )

Correct Answer: A

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Question 23
A set of 4 consecutive even integers has a median of 10. What is the sum of the integers?
Correct A. ( 4(10) )
B. ( 4(9) )
C. ( 4(11) )
D. ( 4(12) )

Correct Answer: A

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Question 24
Determine the value of the infinite series ∑n=1\( 1/2 \)^n\( 3n+2 \) u\sing the formula for the sum of a geometric series.
Correct A. 5
B. 6
C. 7
D. 8

Correct Answer: A

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Question 25
A rec\tangular box has dimensions 3m x 2m x 4m. Find the volume of the box in cubic meters.
Correct A. 24
B. 30
C. 36
D. 40

Correct Answer: A

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