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POST UTME CHRISTOPHER UNIVERSITY 2018 Mathematics | Objective

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Question 1 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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

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 View Details

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 View Details

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} ) using the dot product formula.

A. 4

Correct B. -1

C. 5

D. 7

Correct Answer: B

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Question 12 View Details

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 View Details

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 View Details

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 View Details

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 View Details

Let ( X ) be a random variable with a normal distribution with mean \(\mu = 5\) and standard 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 View Details

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

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 View Details

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 View Details

Find the mean and standard 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

Find the equation of the line passing 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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