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POST UTME CHRISTOPHER UNIVERSITY 2018 Mathematics | Objective

Are you preparing for POST UTME CHRISTOPHER 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.

Practice these randomly selected questions to test your readiness.

Question 1

Find the mean of the data set: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?

A. 12

Correct B. 14

C. 16

D. 18

Correct Answer: B

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Question 2

In the set of numbers {1, 2, 3, 4, 5}, what is the value of x if the set is modified to {1, 2, x, 4, 5} such that the mean of the set is 3?

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 3

Solve for x in the equation: \( 2x^2 + 5x - 3 = 0 \).

A. -1

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 4

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 5

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

A. -2

Correct B. 2

C. 4

D. 6

Correct Answer: B

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Question 6

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

A. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 7

Solve the matrix equation \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 9 \end{bmatrix}.

Correct A. \begin{bmatrix} 1 \\ 3 \end{bmatrix}

B. \begin{bmatrix} 2 \\ 4 \end{bmatrix}

C. \begin{bmatrix} 3 \\ 9 \end{bmatrix}

D. \begin{bmatrix} 4 \\ 12 \end{bmatrix}

Correct Answer: A

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Question 8

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

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 \frac{x^2 - 4}{x^2 - 9} > 0.

Correct A. \( -3, -1 \) \cup (1, 3)

B. \( -3, -1 \) \cup (1, 3) \cup (4, 6)

C. \( -3, -1 \) \cup (1, 3) \cup \( -6, -4 \)

D. \( -3, -1 \) \cup (1, 3) \cup (6, 8)

Correct Answer: A

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Question 10

Find the surface area of the solid formed by revolving the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.

A. 32\pi

Correct B. 64\pi

C. 128\pi

D. 256\pi

Correct Answer: B

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Question 11

Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} \). Find the vector ( mathbf{a} cdot mathbf{b} ) u\sing the dot product formula.

A. 4

Correct B. -1

C. 5

D. 7

Correct Answer: B

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Question 12

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 13

Let \( A = { 1, 2, 3, 4, 5 } \) and \( B = { 2, 4, 6, 8, 10 } \). Find ( A cap B ).

A. { 1, 2, 3, 4, 5 }

B. { 2, 4, 6, 8, 10 }

C. { 1, 2, 3, 4, 5, 6, 8, 10 }

Correct D. { 2, 4 }

Correct Answer: D

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Question 14

Find the sum of the first 5 terms of the geometric series \( 2x + 4x^2 + 8x^3 + ldots \).

Correct A. 126x^5

B. 126x^4

C. 126x^3

D. 126x^2

Correct Answer: A

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Question 15

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

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 16

Let ( X ) be a random variable with a normal distribution with mean \( mu = 5 \) and s\tandard deviation \( sigma = 2 \). Find the probability that ( X ) takes a value between 3 and 7.

A. \( P\( 3 < X < 7 \ \) = 0.5 )

Correct B. \( P\( 3 < X < 7 \ \) = 0.75 )

C. \( P\( 3 < X < 7 \ \) = 0.25 )

D. \( P\( 3 < X < 7 \ \) = 0.875 )

Correct Answer: B

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Question 17

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 18

Solve the matrix equation \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).

Correct A. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 4 \end{bmatrix} \)

B. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 4 \ 3 \end{bmatrix} \)

C. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 2 \ 1 \end{bmatrix} \)

D. \( egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 1 \ 2 \end{bmatrix} \)

Correct Answer: A

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Question 19

Find the sum of the first 5 terms of the geometric series \( 2x^2 + 3x + 1 \).

Correct A. \( 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 = 10x^2 + 15x + 5 \)

B. \( 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 = 10x^2 + 15x + 5 \)

C. \( 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 = 10x^2 + 15x + 5 \)

D. \( 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 + 2x^2 + 3x + 1 = 10x^2 + 15x + 5 \)

Correct Answer: A

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Question 20

Find the mean and s\tandard deviation of the data set ( { 2, 4, 6, 8, 10 } ).

Correct A. \( \text{mean} = 6, \text{s\tandard deviation} = 2 \)

B. \( \text{mean} = 4, \text{s\tandard deviation} = 2 \)

C. \( \text{mean} = 8, \text{s\tandard deviation} = 2 \)

D. \( \text{mean} = 10, \text{s\tandard deviation} = 2 \)

Correct Answer: A

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Question 21

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 = 20

C. \( x - 2 \)^2 + \( y - 3 \)^2 = 12

D. \( x - 2 \)^2 + \( y - 3 \)^2 = 8

Correct Answer: A

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Question 22

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

Correct A. \boxed{x < -2 \text{ or } x > 1}

B. x < -2 \text{ or } x < 1

C. x > -2 \text{ or } x < 1

D. x > -2 \text{ or } x > 1

Correct Answer: A

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Question 23

Find the value of \log_{10} (1000).

Correct A. \boxed{3}

B. 2

C. 4

D. 5

Correct Answer: A

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Question 24

Solve the equation \sqrt{x + 2} = 3.

Correct A. \boxed{x = 7}

B. x = 5

C. x = 9

D. x = 11

Correct Answer: A

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Question 25

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

Correct A. \boxed{y = 1x + 1}

B. y = 2x + 2

C. y = 3x + 3

D. y = 4x + 4

Correct Answer: A

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