Exam Body

Year

Subject

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POST UTME SUMMIT UNIVERSITY 2018 Mathematics | Objective

Are you preparing for POST UTME SUMMIT UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2018 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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

Correct A. \boxed{\( x - 2 \)^2 + \( y - 3 \)^2 = 16}

B. \( x - 2 \)^2 + \( y - 3 \)^2 = 25

C. \( x - 2 \)^2 + \( y - 3 \)^2 = 9

D. \( x - 2 \)^2 + \( y - 3 \)^2 = 36

Correct Answer: A

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Question 2

Solve the inequality \( \frac{x^2 - 4}{x^2 - 9} > 0 \).

Correct A. \boxed{\( -3, -1 \) \cup (1, 3)}

B. \( -3, 1 \)

C. \( -1, 3 \)

D. \( -3, 3 \)

Correct Answer: A

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Question 3

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

Correct A. \boxed{\frac{2x\( x^2 + 1 \) - 2x^3}{\( x^2 + 1 \)^2}}

B. \frac{2x^2 - 2x^3}{\( x^2 + 1 \)^2}

C. \frac{2x^3 - 2x^2}{\( x^2 + 1 \)^2}

D. \frac{2x^2 + 2x^3}{\( x^2 + 1 \)^2}

Correct Answer: A

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Question 4

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

Correct A. \boxed{\frac{1}{3}}

B. \frac{1}{2}

C. \frac{2}{3}

D. \frac{1}{6}

Correct Answer: A

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Question 5

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side.

A. 8 cm

Correct B. 12 cm

C. 6 cm

D. 10 cm

Correct Answer: B

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Question 6

Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x}} ) u\sing the chain rule.

A. f'(x) = -\frac{1}{2x^{3/2}}

Correct B. f'(x) = \frac{1}{2x^{3/2}}

C. f'(x) = \frac{1}{x^{3/2}}

D. f'(x) = -\frac{1}{x^{3/2}}

Correct Answer: B

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Question 7

Solve the inequality \( 2x^2 - 5x - 3 > 0 \) u\sing the quadratic formula.

Correct A. x < -1 or x > \frac{3}{2}

B. x < -1 or x < \frac{3}{2}

C. x > -1 or x > \frac{3}{2}

D. x > -1 or x < \frac{3}{2}

Correct Answer: A

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Question 8

Find the sum of the first 5 terms of the geometric series \( 2x + 3x^2 + 4x^3 + \cdots \).

Correct A. \frac{2x\( 1 - x^5 \)}{1 - x}

B. \frac{2x\( 1 - x^5 \)}{1 + x}

C. \frac{2x\( 1 - x^5 \)}{1 - x^2}

D. \frac{2x\( 1 - x^5 \)}{1 + x^2}

Correct Answer: A

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Question 9

A binary operation \( \ast \) is defined as \( a \ast b = a^2 + b^2 \). Find the value of \( 2 \ast 3 \).

Correct A. 13

B. 14

C. 15

D. 16

Correct Answer: A

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Question 10

A set ( A ) contains the elements \( 1, 2, 3, \ldots, 10 \). Find the number of subsets of ( A ) that contain exactly 3 elements.

Correct A. 120

B. 130

C. 140

D. 150

Correct Answer: A

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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. If two indep\endent random variables X and Y have the same probability distribution, what is the probability that X + Y = 4?

A. 0.1

B. 0.2

Correct C. 0.3

D. 0.4

Correct Answer: C

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Question 12

In a binary operation \ast on a set S, the operation is defined as follows: a \ast b = a + b for all a, b in S. If S = {1, 2, 3, 4, 5}, find the value of 3 \ast \( 2 \ast 4 \).

A. 10

Correct B. 11

C. 12

D. 13

Correct Answer: B

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Question 13

A sequence is defined as follows: a_1 = 2, a_n = 3a_{n-1} for n > 1. Find the value of a_{10}.

A. 2

B. 3

C. 6

Correct D. 9

Correct Answer: D

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Question 14

A set S is defined as follows: S = {x | x is a positive integer and x < 10}. Find the value of \bigcup_{n=1}^{10} S_n, where S_n = {x | x is a positive integer and x < n}.

A. {1, 2, 3, 4, 5, 6, 7, 8, 9}

Correct B. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

C. {1, 2, 3, 4, 5, 6, 7, 8}

D. {1, 2, 3, 4, 5, 6}

Correct Answer: B

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Question 15

A geometric sequence is defined as follows: a_1 = 2, r = 2. Find the value of a_{10}.

Correct A. 1024

B. 512

C. 256

D. 128

Correct Answer: A

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Question 16

A cylindrical \tank with a radius of 7m and a height of 10m is filled with water. If the water level is raised by 2m, what is the increase in the volume of water in the \tank?

A. 140\pi m^3

B. 280\pi m^3

Correct C. 420\pi m^3

D. 560\pi m^3

Correct Answer: C

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Question 17

A triangle has angles A, B, and C, with A = 30°, B = 60°, and C = 90°. What is the value of \sin\( A + B \)?

A. \frac{1}{2}

Correct B. \frac{\sqrt{3}}{2}

C. \frac{\sqrt{2}}{2}

D. \frac{\sqrt{6}}{2}

Correct Answer: B

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Question 18

A random experiment consists of rolling a fair six-sided die. If the outcome is an even number, the experiment is repeated. If the outcome is an odd number, the experiment stops. What is the probability that the experiment stops after exactly two rolls?

Correct A. \frac{1}{8}

B. \frac{1}{4}

C. \frac{1}{2}

D. \frac{3}{4}

Correct Answer: A

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Question 19

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 is between 50 and 70?

A. \frac{1}{4}

Correct B. \frac{1}{2}

C. \frac{3}{4}

D. \frac{7}{8}

Correct Answer: B

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Question 20

A circle has a radius of 5cm. What is the area of the circle?

Correct A. 25\pi cm^2

B. 50\pi cm^2

C. 75\pi cm^2

D. 100\pi cm^2

Correct Answer: A

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Question 21

Find the determinant of the matrix [ egin{array}{ccc} 2 & 3 & 1 \ 4 & 1 & 2 \ 3 & 2 & 4 \end{array} ].

Correct A. -11

B. 11

C. -13

D. 13

Correct Answer: A

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Question 22

Solve the equation [ \frac{\tan x}{1 - \tan x} = \frac{1}{3} \] for [ 0 \leq x \leq \frac{\pi}{2} \].

Correct A. \frac{\pi}{6}

B. \frac{\pi}{3}

C. \frac{\pi}{4}

D. \frac{\pi}{2}

Correct Answer: A

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Question 23

Find the equation of the circle with center [ \( -2, 3 \) \] and radius [ 5 \].

Correct A. \( x + 2 \)^2 + \( y - 3 \)^2 = 25

B. \( x - 2 \)^2 + \( y + 3 \)^2 = 25

C. \( x + 2 \)^2 + \( y + 3 \)^2 = 25

D. \( x - 2 \)^2 + \( y - 3 \)^2 = 25

Correct Answer: A

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Question 24

Evaluate the definite integral [ \int_0^1 x^2 \ln x \, dx \].

Correct A. -\frac{1}{4}

B. \frac{1}{4}

C. -\frac{1}{2}

D. \frac{1}{2}

Correct Answer: A

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Question 25

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 \leq \frac{3}{2}

C. x \geq -1 \text{ or } x \geq \frac{3}{2}

D. x \geq -1 \text{ or } x \leq \frac{3}{2}

Correct Answer: A

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