Exam Body

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Subject

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POST UTME UNN 2017 Mathematics | Objective

Are you preparing for POST UTME UNN exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2017 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Let ( f(x) = \frac{x^2 - 4}{x^2 - 9} ). Find the value of \( f\( -3 \ \) ).

Correct A. \( \frac{5}{-18} \)

B. \( \frac{-5}{18} \)

C. \( \frac{5}{18} \)

D. \( \frac{-5}{-18} \)

Correct Answer: A

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Question 2

A set ( A ) contains the elements \( \{ 1, 2, 3, 4, 5 \} \). Find the number of subsets of ( A ) that contain exactly two elements.

A. 10

Correct B. 15

C. 20

D. 25

Correct Answer: B

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Question 3

In the diagram below, ( ABC ) is a right-angled triangle with \( AB = 6 \) cm and \( BC = 8 \) cm. Find the length of the hypotenuse ( AC ).

A. 10

B. 12

C. 14

Correct D. 16

Correct Answer: D

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Question 4

A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 3 \) with initial term \( a_1 = 2 \). Find the value of \( a_5 \).

A. 37

B. 41

C. 45

Correct D. 49

Correct Answer: D

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Question 5

A random experiment consists of rolling a fair six-sided die. Find the probability that the sum of the numbers on the two dice is greater than 9.

A. \( \frac{1}{6} \)

B. \( \frac{1}{3} \)

C. \( \frac{1}{2} \)

Correct D. \( \frac{2}{3} \)

Correct Answer: D

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Question 6

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 7

Solve for x in the equation \( \log_{10} \( x^2 \) = 4 \).

Correct A. \boxed{x = 10^2}

B. x = 10^4

C. x = 10^8

D. x = 10^16

Correct Answer: A

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Question 8

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

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

B. f'(x) = \frac{2x}{\( x^2 + 1 \)^2}

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

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

Correct Answer: A

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Question 9

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{5}{6}

Correct Answer: A

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Question 10

Solve the inequality \( 2x^2 + 5x - 3 > 0 \).

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

B. \( -\infty, 1 \) \cup \( 3, \infty \)

C. \( -\infty, -1 \) \cup \( 1, \infty \)

D. \( -\infty, 1 \) \cup \( -3, \infty \)

Correct Answer: A

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Question 11

Solve for x in the equation \( \sin^2 x + \cos^2 x = 1 \) u\sing the identity \( \sin^2 x + \cos^2 x = 1 \).

Correct A. x = \frac{\pi}{4}

B. x = \frac{3\pi}{4}

C. x = \frac{5\pi}{4}

D. x = \frac{7\pi}{4}

Correct Answer: A

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Question 12

Find the volume of the solid formed by revolving the region bounded by the curve \( y = x^2 \) and the line \( x = 2 \) about the x-axis.

A. \frac{32}{3}\pi

Correct B. \frac{64}{3}\pi

C. \frac{128}{3}\pi

D. \frac{256}{3}\pi

Correct Answer: B

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Question 13

Solve the equation \( 2^x + 2^{-x} = 10 \) for x.

Correct A. x = \log_2 5

B. x = \log_2 2

C. x = \log_2 4

D. x = \log_2 8

Correct Answer: A

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Question 14

Find the surface area of the solid formed by revolving the region bounded by the curve \( y = x^3 \) and the line \( x = 1 \) about the x-axis.

A. 6\sqrt{2}

B. 12\sqrt{2}

Correct C. 24\sqrt{2}

D. 48\sqrt{2}

Correct Answer: C

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Question 15

Solve the inequality \( \log_2 x > 2 \) for x.

A. x > 4

B. x > 8

C. x > 16

Correct D. x > 32

Correct Answer: D

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Question 16

Find the mean of the set of numbers: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.

A. 10

Correct B. 12

C. 14

D. 16

Correct Answer: B

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Question 17

Solve the inequality: \( 2x^2 + 5x - 3 \geq 0 \).

Correct A. \( x \leq -3 \) or \( x \geq \frac{3}{2} \)

B. \( x \leq -3 \) or \( x \geq 1 \)

C. \( x \leq 1 \) or \( x \geq -3 \)

D. \( x \leq -1 \) or \( x \geq 3 \)

Correct Answer: A

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Question 18

Find the derivative of the function: \( f(x) = 3x^2 + 2x - 5 \).

Correct A. \( f'(x) = 6x + 2 \)

B. \( f'(x) = 6x - 2 \)

C. \( f'(x) = 3x^2 + 2 \)

D. \( f'(x) = 3x^2 - 2 \)

Correct Answer: A

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Question 19

A set of numbers has a mean of 10 and a s\tandard deviation of 2. Find the probability that a randomly selected number from the set is greater than 12.

A. \( P\( X > 12 \) = 0.25 \)

B. \( P\( X > 12 \) = 0.5 \)

Correct C. \( P\( X > 12 \) = 0.75 \)

D. \( P\( X > 12 \) = 0.9 \)

Correct Answer: C

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Question 20

Solve the quadratic equation: \( x^2 + 4x + 4 = 0 \).

Correct A. \( x = -2 \)

B. \( x = -1 \)

C. \( x = 0 \)

D. \( x = 2 \)

Correct Answer: A

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Question 21

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. 15

C. 17

D. 19

Correct Answer: A

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Question 22

Find the value of \( x \) in the equation: \( 2x + 5 = 11 \).

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 23

A sequence is defined as: \( a_n = 2n + 1 \). Find the value of \( a_5 \).

A. 9

Correct B. 11

C. 13

D. 15

Correct Answer: B

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Question 24

Find the value of \( x \) in the equation: \( x^2 - 4x - 3 = 0 \).

A. 3

B. -1

C. 5

D. -3

Correct Answer: VIEW ANSWER

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Question 25

Find the determinant of the matrix [ egin{array}{ccc} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{array} ] u\sing the expansion by minors method.

Correct A. -120

B. 120

C. -60

D. 60

Correct Answer: A

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