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POST UTME BELLS UNIVERSITY 2017 Mathematics | Objective

Are you preparing for POST UTME BELLS UNIVERSITY 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 derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.

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

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

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

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

Correct Answer: A

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Question 2

A particle moves along the x-axis with its position given by ( x(t) = 2t^3 - 5t^2 + 3t + 1 ). Find the velocity of the particle at time \( t = 2 \) seconds.

Correct A. \( 12t^2 - 10t + 3 \)

B. \( 6t^2 - 10t + 3 \)

C. \( 12t^2 - 10t - 3 \)

D. \( 6t^2 - 10t - 3 \)

Correct Answer: A

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Question 3

Find the area under the curve \( y = x^2 - 4x + 3 \) from \( x = 1 \) to \( x = 3 \).

A. \( \frac{2}{3} \)

Correct B. \( \frac{4}{3} \)

C. \( \frac{6}{3} \)

D. \( \frac{8}{3} \)

Correct Answer: B

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Question 4

Solve the system of equations \( egin{cases} x + y = 2 \ 2x - y = 3 \end{cases} \).

Correct A. \( x = 1, y = 1 \)

B. \( x = 2, y = 0 \)

C. \( x = 0, y = 2 \)

D. \( x = 1, y = 2 \)

Correct Answer: A

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Question 5

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

Correct A. ( 0 )

B. ( 1 )

C. ( 2 )

D. ( 3 )

Correct Answer: A

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Question 6

Find the determinant of the matrix [ egin{pmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{pmatrix} ].

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 7

A histogram is constructed with 5 classes of equal width. The first class has a frequency of 5, the second class has a frequency of 7, the third class has a frequency of 3, the fourth class has a frequency of 2, and the fifth class has a frequency of 4. What is the mean of the histogram?

A. 4

Correct B. 5

C. 6

D. 7

Correct Answer: B

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Question 8

Find the volume of the solid formed by revolving the region bounded by the parabola y = x^2, the x-axis, and the line x = 2 about the x-axis.

Correct A. 32\pi

B. 64\pi

C. 128\pi

D. 256\pi

Correct Answer: A

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Question 9

A circle with center (0, 0) and radius 4 passes through the point (3, 4). What is the equation of the circle?

Correct A. \( x - 0 \)^2 + \( y - 0 \)^2 = 16

B. \( x - 3 \)^2 + \( y - 4 \)^2 = 16

C. \( x - 0 \)^2 + \( y - 0 \)^2 = 9

D. \( x - 3 \)^2 + \( y - 4 \)^2 = 9

Correct Answer: A

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Question 10

Find the mean deviation of the data set {2, 4, 6, 8, 10} about the mean.

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 11

Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x^2 + 1}} ) u\sing the chain rule.

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

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

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

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

Correct Answer: A

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Question 12

Solve the inequality \( 2^x > 3^x \) for ( x ).

Correct A. x < 0

B. x > 0

C. x < 1

D. x > 1

Correct Answer: A

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Question 13

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

Correct A. \frac{4}{3}\pi

B. \frac{2}{3}\pi

C. \frac{1}{3}\pi

D. \frac{1}{2}\pi

Correct Answer: A

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Question 14

Find the derivative of the function ( f(x) = \sin^2 x ) u\sing the chain rule.

Correct A. f'(x) = 2\\sin x \\cos x

B. f'(x) = \\sin x \\cos x

C. f'(x) = \cos x

D. f'(x) = \sin x

Correct Answer: A

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Question 15

Solve the equation \( x^3 + 2x^2 - 7x + 12 = 0 \) for ( x ).

Correct A. x = -3

B. x = -1

C. x = 3

D. x = 4

Correct Answer: A

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Question 16

Find the area of the region bounded by the curves \( y = x^2 \) and \( y = 2x \) for \( 0 \leq x \leq 2 \).

A. 4

Correct B. 6

C. 8

D. 10

Correct Answer: B

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Question 17

Find the derivative of the function ( f(x) = \frac{1}{x^2} ) u\sing the chain rule.

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

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

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

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

Correct Answer: A

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Question 18

Solve the inequality \( x^2 - 4x + 3 > 0 \) for ( x ).

A. x < 1

Correct B. x > 1

C. x < 3

D. x > 3

Correct Answer: B

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Question 19

Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.

A. x = -2

B. x = -3

Correct C. x = 2

D. x = 3

Correct Answer: C

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Question 20

Find the volume of a cylinder with radius 4 cm and height 6 cm.

A. 48\pi

B. 64\pi

Correct C. 72\pi

D. 96\pi

Correct Answer: C

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Question 21

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

Correct A. x > 4

B. x < 4

C. x > 2

D. x < 2

Correct Answer: A

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Question 22

Find the surface area of a sphere with radius 5 cm.

A. 100\pi

B. 200\pi

Correct C. 300\pi

D. 400\pi

Correct Answer: C

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Question 23

Solve the equation \( x^2 + 2x - 6 = 0 \) by factoring.

Correct A. \( x + 3 \)\( x - 2 \) = 0

B. \( x + 2 \)\( x - 3 \) = 0

C. \( x - 3 \)\( x + 2 \) = 0

D. \( x - 2 \)\( x + 3 \) = 0

Correct Answer: A

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Question 24

Find the area of a triangle with base 6 cm and height 8 cm.

A. 24

B. 30

Correct C. 36

D. 48

Correct Answer: C

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Question 25

Solve the inequality \( x^2 - 4x + 4 > 0 \).

A. x > 2

Correct B. x < 2

C. x > 1

D. x < 1

Correct Answer: B

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