Exam Body

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POST UTME UNIPORT 2017 Mathematics | Objective

Are you preparing for POST UTME UNIPORT 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

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 24π cm^3

Correct B. 48π cm^3

C. 96π cm^3

D. 192π cm^3

Correct Answer: B

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Question 2

A box 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. 1/2

Correct B. 2/3

C. 3/5

D. 4/7

Correct Answer: B

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Question 3

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

Correct A. x = -2

B. x = 2

C. x = -1

D. x = 1

Correct Answer: A

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Question 4

Find the mean of the data set: 2, 4, 6, 8, 10.

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 5

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 = 16

C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16

D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16

Correct Answer: A

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Question 6

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 50\pi cm^3

B. 75\pi cm^3

Correct C. 100\pi cm^3

D. 125\pi cm^3

Correct Answer: C

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Question 7

Solve the inequality \frac{x^2 - 4x - 5}{x^2 - 4x + 4} > 0.

Correct A. \left\( -\infty, -1\right \) \cup \left\( 1, \infty\right \)

B. \left\( -\infty, -1\right \) \cup \left\( 1, 2\right \)

C. \left\( -\infty, -1\right \) \cup \left\( 2, \infty\right \)

D. \left\( -\infty, 1\right \) \cup \left\( 2, \infty\right \)

Correct Answer: A

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Question 8

Find the equation of the circle pas\sing through the points (2, 3), (4, 1), and \( -1, -2 \).

Correct A. \( x - 1 \)^2 + \( y + 2 \)^2 = 10

B. \( x + 1 \)^2 + \( y - 2 \)^2 = 10

C. \( x - 2 \)^2 + \( y + 1 \)^2 = 10

D. \( x + 2 \)^2 + \( y - 1 \)^2 = 10

Correct Answer: A

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Question 9

Evaluate the definite integral \int_0^1 x^2 \sin x dx.

Correct A. -\frac{1}{2} + \frac{1}{3}

B. -\frac{1}{2} - \frac{1}{3}

C. \frac{1}{2} - \frac{1}{3}

D. \frac{1}{2} + \frac{1}{3}

Correct Answer: A

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Question 10

Find the derivative of the function f(x) = \frac{x^2 + 2x - 3}{x^2 - 4x + 3} u\sing the quotient rule.

Correct A. \frac{2x + 2}{\( x^2 - 4x + 3 \)^2}

B. \frac{2x - 2}{\( x^2 - 4x + 3 \)^2}

C. \frac{2x + 4}{\( x^2 - 4x + 3 \)^2}

D. \frac{2x - 4}{\( x^2 - 4x + 3 \)^2}

Correct Answer: A

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Question 11

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

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

B. \( x+2 \ \)^2 + \( y-3 \)^2 = 16 )

C. \( x-2 \ \)^2 + \( y+3 \)^2 = 32 )

D. \( x+2 \ \)^2 + \( y-3 \)^2 = 32 )

Correct Answer: A

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Question 12

Solve the system of equations u\sing matrices:

Correct A. \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \)

B. \( egin{bmatrix} 2 & 1 \ 4 & 3 \end{bmatrix} \)

C. \( egin{bmatrix} 1 & 3 \ 2 & 4 \end{bmatrix} \)

D. \( egin{bmatrix} 3 & 1 \ 2 & 4 \end{bmatrix} \)

Correct Answer: A

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Question 13

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 14

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

Correct A. \( x = -2 \)

B. \( x = 2 \)

C. \( x = -1 \)

D. \( x = 1 \)

Correct Answer: A

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Question 15

Find the area of the triangle with vertices at ((0,0)), ((3,0)), and ((0,4)).

Correct A. ( 6 )

B. ( 8 )

C. ( 10 )

D. ( 12 )

Correct Answer: A

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Question 16

Determine the volume of the frustum of a cone with a height of 10 cm, a lower base radius of 4 cm, and an upper base radius of 6 cm.

A. 20π cm³

Correct B. 30π cm³

C. 40π cm³

D. 50π cm³

Correct Answer: B

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Question 17

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 probability that X is greater than 2.

A. 0.3

B. 0.4

Correct C. 0.5

D. 0.6

Correct Answer: C

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Question 18

Solve the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) for x in the interval ( [0, 2pi] ).

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

B. \( x = \frac{\pi}{2} \ \)

C. \( x = \frac{3\pi}{4} \ \)

D. \( x = \frac{5\pi}{4} \ \)

Correct Answer: A

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Question 19

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{-x}{\( x^2 + 1 \)^2} \)

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

Correct Answer: A

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Question 20

A circle with a radius of 5 cm is inscribed in a square. Find the area of the square.

A. 25 cm²

B. 50 cm²

C. 75 cm²

Correct D. 100 cm²

Correct Answer: D

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Question 21

Find the volume of the frustum of a cone with height 8cm, lower base radius 4cm, and upper base radius 2cm.

A. 256\pi cm^3

B. 512\pi cm^3

Correct C. 768\pi cm^3

D. 1024\pi cm^3

Correct Answer: C

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Question 22

A histogram of exam scores is shown below. What is the mean score?

A. 50

B. 60

Correct C. 70

D. 80

Correct Answer: C

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Question 23

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 = 16

C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16

D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16

Correct Answer: A

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Question 24

Solve for x in the equation \frac{1}{2}x^2 + 3x - 2 = 0.

A. x = -4

Correct B. x = -2

C. x = 1

D. x = 4

Correct Answer: B

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Question 25

Find the determinant of the matrix \begin{bmatrix} 2 & 1 \ 4 & 3 \end{bmatrix}.

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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