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POST UTME EKSU 2020 Mathematics | Objective

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Question 1 View Details

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 View Details

Find the derivative of the function ( f(x) = \(\frac{1}{x^2 + 1}\)\)\) ) using 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

A histogram of exam scores has a mean of 60 and a standard 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

Determine the value of the infinite series ∑\(n=1\)\(1/2\)^n\(3n+2\) using 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 View Details

A rectangular 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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