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POST UTME NILE UNIVERSITY 2022 Mathematics | Objective

Are you preparing for POST UTME NILE UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2022 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Solve the inequality $ \frac{x}{x-1} > 2 $ for $ 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

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

A set of data has a mean of 25 and a s\tandard 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

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

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

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

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

Find the value of $ \tan 2\theta $ given that $ \sin \theta = \frac{3}{5} $ and $ \cos \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

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

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

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

A. -2

Correct B. 1

C. 3

D. 5

Correct Answer: B

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Question 12

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

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

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

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

A. -2

Correct B. -1

C. 1

D. 2

Correct Answer: B

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Question 16

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 \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

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

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

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

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

Find the derivative of the function ( f(x) = \frac{1}{2} \log_{10} $ x^2 + 1 $ ) u\sing 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

Solve the inequality $ 2x^2 - 5x - 3 > 0 $ u\sing 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

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

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

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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