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POST UTME BELLS UNIVERSITY 2019 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 2019 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

Find the value of x in the equation \( 2x^2 + 5x - 3 = 0 \).

A. 1

Correct B. -1

C. 2

D. -2

Correct Answer: B

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Question 2

A set of exam scores has a mean of 85 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score will be between 70 and 90?

A. 0.135

B. 0.25

Correct C. 0.5

D. 0.75

Correct Answer: C

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Question 3

Solve the system of equations u\sing matrices: \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).

Correct A. x = 1, y = 2

B. x = 2, y = 1

C. x = 3, y = 4

D. x = 4, y = 3

Correct Answer: A

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Question 4

Find the sum of the first 10 terms of the geometric series: \( 2 + 6 + 18 + ... \).

A. 123

B. 124

Correct C. 125

D. 126

Correct Answer: C

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Question 5

In the diagram below, \( \sin \theta = \frac{3}{5} \). Find the value of \( \cos \theta \).

A. 0.6

Correct B. 0.8

C. 0.4

D. 0.2

Correct Answer: B

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Question 6

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

Correct A. 14

B. -14

C. 16

D. -16

Correct Answer: A

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Question 7

The equation of a circle is given by \( x - h \ \)^2 + \( y - k \)^2 = r^2 ). If the center of the circle is at ( (3, 4) ) and the radius is 5, find the equation of the circle.

Correct A. \( x - 3 \)^2 + \( y - 4 \)^2 = 25

B. \( x - 3 \)^2 + \( y - 4 \)^2 = 30

C. \( x - 3 \)^2 + \( y - 4 \)^2 = 20

D. \( x - 3 \)^2 + \( y - 4 \)^2 = 35

Correct Answer: A

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Question 8

If ( f(x) = \frac{1}{x^2 + 1} ), find ( f'(x) ).

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

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

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

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

Correct Answer: A

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Question 9

Solve the inequality \( 2x^2 + 3x - 1 > 0 \).

Correct A. \( -\infty, -\frac{1}{2} \) \cup \( \frac{1}{3}, \infty \)

B. \( -\infty, -\frac{1}{2} \) \cup \( \frac{1}{3}, 0 \)

C. \( -\infty, 0 \) \cup \( \frac{1}{3}, \infty \)

D. \( -\infty, -\frac{1}{2} \) \cup \( 0, \infty \)

Correct Answer: A

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Question 10

Find the value of ( x ) in the equation \( 2^x + 3^x = 5^x \).

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 11

Find the equation of the circle pas\sing through the points ( (2,3) ), ( (4,5) ), and ( (6,7) ).

Correct A. \( x^2 + y^2 - 10x - 2y + 23 = 0 \)

B. \( x^2 + y^2 - 12x - 4y + 35 = 0 \)

C. \( x^2 + y^2 - 14x - 6y + 47 = 0 \)

D. \( x^2 + y^2 - 16x - 8y + 59 = 0 \)

Correct Answer: A

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Question 12

Evaluate the definite integral \( int_{0}^{2} \( 2x^3 - 5x^2 + 3x - 1 \ \) dx ).

A. ( 2 )

B. ( 4 )

Correct C. ( 6 )

D. ( 8 )

Correct Answer: C

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Question 13

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

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

Correct 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: B

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Question 14

Solve the vector equation \( mathbf{a} \times \( mathbf{b} + mathbf{c} \ \) = mathbf{0} ) for ( mathbf{a} ), given that \( mathbf{b} = egin{pmatrix} 2 \ 3 \ 4 \end{pmatrix} \) and \( mathbf{c} = egin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} \).

Correct A. \( mathbf{a} = egin{pmatrix} 0 \ 0 \ 0 \end{pmatrix} \)

B. \( mathbf{a} = egin{pmatrix} 3 \ 4 \ 5 \end{pmatrix} \)

C. \( mathbf{a} = egin{pmatrix} 4 \ 5 \ 6 \end{pmatrix} \)

D. \( mathbf{a} = egin{pmatrix} 5 \ 6 \ 7 \end{pmatrix} \)

Correct Answer: A

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Question 15

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

Correct A. \( x = \frac{pi}{6} \)

B. \( x = \frac{pi}{4} \)

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

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

Correct Answer: A

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Question 16

Find the area under the curve y = x^2 + 2x + 1 from x = 0 to x = 3.

Correct A. 27

B. 30

C. 36

D. 45

Correct Answer: A

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Question 17

A fair six-sided die is rolled. What is the probability that the number obtained is a multiple of 3?

A. 1/2

B. 1/3

C. 2/3

Correct D. 1/6

Correct Answer: D

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Question 18

Find the volume of the solid formed by rotating the region bounded by y = x^2, y = 0, and x = 2 about the x-axis.

A. 32\pi/5

B. 64\pi/5

Correct C. 128\pi/5

D. 256\pi/5

Correct Answer: C

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Question 19

A vector \vec{a} = 2\hat{i} + 3\hat{j} and a vector \vec{b} = -4\hat{i} + 5\hat{j}. Find the magnitude of the cross product of \vec{a} and \vec{b}.

A. 13

Correct B. 15

C. 17

D. 19

Correct Answer: B

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Question 20

Solve the equation x^2 + 4x + 4 = 0.

Correct A. -2

B. 0

C. 2

D. 4

Correct Answer: A

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Question 21

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

Correct A. \( \frac{29}{3} \)

B. \( \frac{31}{3} \)

C. \( \frac{32}{3} \)

D. \( \frac{33}{3} \)

Correct Answer: A

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Question 22

Solve the inequality \( \frac{2x + 1}{x - 1} > 0 \).

Correct A. \( x < -1 \) or \( x > 1 \)

B. \( x < 1 \) or \( x > -1 \)

C. \( x < -1 \) or \( x = 1 \)

D. \( x < 1 \) or \( x = -1 \)

Correct Answer: A

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Question 23

Find the value of ( x ) in the equation \( x^3 - 6x^2 + 11x - 6 = 0 \).

A. \( x = 1 \)

B. \( x = 2 \)

Correct C. \( x = 3 \)

D. \( x = 4 \)

Correct Answer: C

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Question 24

Find the area of the triangle with vertices ( A(1, 2) ), ( B(3, 4) ), and ( C(2, 1) ).

Correct A. ( 5 )

B. ( 6 )

C. ( 7 )

D. ( 8 )

Correct Answer: A

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Question 25

Solve the system of equations \( x + y = 4 \) and \( xy = 5 \).

Correct A. \( x = 2, y = 2 \)

B. \( x = 3, y = 1 \)

C. \( x = 1, y = 3 \)

D. \( x = 4, y = 0 \)

Correct Answer: A

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