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POST UTME NILE UNIVERSITY 2022 Mathematics | Objective

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Question 1 View Details

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

A. \(x > 3\)

B. \(x < 3\)

Correct C. \(x > 1\) and \(x < 3\)

D. \(x > 3\) and \(x < 5\)

Correct Answer: C

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Question 2 View Details

Find the area under the curve \(y = x^2\) from \(x = 0\) to \(x = 4\).

Correct A. \(\frac{64}{3}\)

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

C. \(\frac{16}{3}\)

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

Correct Answer: A

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Question 3 View Details

A set of data has a mean of 25 and a standard deviation of 5. If the data is normally distributed, find the probability that a randomly selected value is between 20 and 30.

Correct A. ( 0.9772 )

B. ( 0.6827 )

C. ( 0.3413 )

D. ( 0.1587 )

Correct Answer: A

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Question 4 View Details

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

Correct A. \(x = -2\)

B. \(x = -1\)

C. \(x = 0\)

D. \(x = 1\)

Correct Answer: A

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Question 5 View Details

A sequence is defined by the formula \(a_n = 2n + 1\). Find the sum of the first 5 terms of the sequence.

A. ( 15 )

B. ( 25 )

C. ( 35 )

Correct D. ( 45 )

Correct Answer: D

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Question 6 View Details

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

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

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

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

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

Correct Answer: A

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Question 7 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 8 View Details

Find the value of (\(12\theta\) given that \\((\)12theta\(\(1\theta = \frac{3}{5}\) and 1\\(theta =\)\(\frac{4}{5}\)\).

Correct A. \(\frac{24}{25}\)

B. \(\frac{25}{24}\)

C. \(\frac{24}{25}\)

D. \(\frac{25}{24}\)

Correct Answer: A

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Question 9 View Details

A histogram of the scores of 20 students in a mathematics test is shown below. If the mean score is 60, find the value of ( sigma ).

Correct A. ( 10 )

B. ( 20 )

C. ( 30 )

D. ( 40 )

Correct Answer: A

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Question 10 View Details

Solve the equation \(x^3 - 6x^2 + 11x - 6 = 0\).

Correct A. \(x = 1\)

B. \(x = 2\)

C. \(x = 3\)

D. \(x = 4\)

Correct Answer: A

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Question 11 View Details

Determine the value of (x\) in the equation \(x^2 + 4x - 5 = 0\\((x) in the equation\).

A. -2

Correct B. 1

C. 3

D. 5

Correct Answer: B

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Question 12 View Details

A histogram of exam scores is shown below. If the mean score is 70, what is the median score?

A. 65

Correct B. 70

C. 75

D. 80

Correct Answer: B

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Question 13 View Details

Solve the inequality \(\frac{x}{2} + 3 > 7\).

Correct A. \(x > 4\)

B. \(x < 4\)

C. \(x > 2\)

D. \(x < 2\)

Correct Answer: A

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Question 14 View Details

A sequence is defined by the formula \(a_n = 2n + 1\). Find the sum of the first 5 terms.

A. 15

B. 20

Correct C. 25

D. 30

Correct Answer: C

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Question 15 View Details

A quadratic equation is given by \((x^2 + 4x + 4\) = 0\). Solve for \(x\\((x^2 + 4x + 4 = 0). Solve for\).

A. -2

Correct B. -1

C. 1

D. 2

Correct Answer: B

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Question 16 View Details

In the diagram below, the equation of the circle is \(x - 2 \\)^2 + \(y - 3)^\(2 = 4\) ). If the point P(6, 7) lies on the circle, what is the equation of the \\\\((()^(2\) = 4\)\tangent at point P?

Correct A. \(y = -x + 13\)

B. \(y = x + 5\)

C. \(y = -x - 5\)

D. \(y = x - 5\)

Correct Answer: A

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Question 17 View Details

A sequence is defined by the recurrence relation \(a_n = 2a_{n - 1} + 3\), with initial term \(a_1 = 2\). Find the sum of the first 5 terms of the sequence.

Correct A. 63

B. 65

C. 67

D. 69

Correct Answer: A

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Question 18 View Details

A set A contains 5 elements, and a set B contains 3 elements. If the intersection of sets A and B contains 2 elements, what is the number of elements in the union of sets A and B?

A. 8

B. 9

Correct C. 10

D. 11

Correct Answer: C

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Question 19 View Details

A circle with center C(2, 3) and radius 4 passes through the point P(6, 7). Find the equation of the \tangent at point P.

Correct A. \(y = -x + 13\)

B. \(y = x + 5\)

C. \(y = -x - 5\)

D. \(y = x - 5\)

Correct Answer: A

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Question 20 View Details

A geometric sequence has first term 2 and common ratio 3. Find the sum of the first 5 terms of the sequence.

Correct A. 325

B. 327

C. 329

D. 331

Correct Answer: A

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Question 21 View Details

Find the derivative of the function ( f(x) = \(\frac{1}{2}\)\) \log_{10} \(x^2 + 1\) ) using the chain rule.

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

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

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

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

Correct Answer: B

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Question 22 View Details

Solve the inequality \(2x^2 - 5x - 3 > 0\) using the quadratic formula.

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 23 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 + \(y - 3\)^\(2 = 4\) )

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

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

Correct Answer: A

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Question 24 View Details

A histogram of exam scores is shown. Find the mean score.

A. ( 60 )

B. ( 70 )

Correct C. ( 80 )

D. ( 90 )

Correct Answer: C

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Question 25 View Details

Find the vector ( mathbf{a} ) such that \(\mathbf{a} \cdot \mathbf{b} = 10\) and \(\mathbf{a} \cdot \mathbf{c} = 5\), where \(\mathbf{b} = egin{pmatrix} 2 \ 3 \end{pmatrix}\) and \(\mathbf{c} = egin{pmatrix} 1 \ 2 \end{pmatrix}\).

Correct A. \(egin{pmatrix} 5 \ 5 \end{pmatrix}\)

B. \(egin{pmatrix} 3 \ 5 \end{pmatrix}\)

C. \(egin{pmatrix} 5 \ 3 \end{pmatrix}\)

D. \(egin{pmatrix} 3 \ 3 \end{pmatrix}\)

Correct Answer: A

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