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POST UTME PAN-ATLANTIC UNIVERSITY 2018 Mathematics | Objective

Are you preparing for POST UTME PAN-ATLANTIC 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.

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Question 1

Find the equation of the circle with center at ((2,3)) and pas\sing through the point ((6,5)).

Correct A. $ x-2 \ $^2 + $ y-3 $^2 = 5 )

B. $ x-2 \ $^2 + $ y-3 $^2 = 10 )

C. $ x-2 \ $^2 + $ y-3 $^2 = 15 )

D. $ x-2 \ $^2 + $ y-3 $^2 = 20 )

Correct Answer: A

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Question 2

A random variable X has a probability distribution given by $ P\( X=x \ $ = \frac{1}{2^{x}} ) for $ x = 1, 2, 3, ... $. Find the mean of X.

Correct A. $ \frac{4}{3} $

B. $ \frac{5}{4} $

C. $ \frac{6}{5} $

D. $ \frac{7}{6} $

Correct Answer: A

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Question 3

Solve the inequality $ \frac{x^2 - 4}{x^2 - 9} > 0 $.

Correct A. $ x in \( -infty, -3 \ $ cup (3, infty) )

B. $ x in \( -infty, -3 \ $ cup (3, infty) cup (0, 2) )

C. $ x in \( -infty, -3 \ $ cup (3, infty) cup $ -2, 0 $ )

D. $ x in \( -infty, -3 \ $ cup (3, infty) cup $ -2, 0 $ cup (2, 4) )

Correct Answer: A

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Question 4

Find the area under the curve $ y = \frac{1}{x^2 + 1} $ from $ x = 0 $ to $ x = 1 $.

Correct A. $ \frac{pi}{4} - 1 $

B. $ \frac{pi}{4} - \frac{1}{2} $

C. $ \frac{pi}{4} - \frac{1}{3} $

D. $ \frac{pi}{4} - \frac{1}{4} $

Correct Answer: A

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Question 5

A set A contains the elements ( { 1, 2, 3, 4, 5 } ). Find the number of subsets of A that contain exactly two elements.

A. ( 10 )

Correct B. ( 15 )

C. ( 20 )

D. ( 25 )

Correct Answer: B

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Question 6

A random variable X has a probability distribution given by P(X) = $ 1/2 $^$ X-1 $ for X = 1, 2, 3, ... . Find the probability that X is greater than 2.

A. 1/4

B. 1/2

Correct C. 3/4

D. 1

Correct Answer: C

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Question 7

In the diagram below, a circle with center O and radius 6 cm is inscribed in a square. Find the area of the shaded region.

A. 36π

B. 72π

Correct C. 108π

D. 144π

Correct Answer: C

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Question 8

Solve the equation $ x^2 - 4x - 5 = 0 $ u\sing the quadratic formula.

Correct A. x = 1 ± √6

B. x = 2 ± √3

C. x = 3 ± √2

D. x = 4 ± √1

Correct Answer: A

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Question 9

A vector ( vec{a} ) has a magnitude of 5 units and makes an angle of 30° with the positive x-axis. Find the x and y components of ( vec{a} ).

Correct A. x = 4, y = 4√3

B. x = 3, y = 3√3

C. x = 5, y = 5√3

D. x = 2, y = 2√3

Correct Answer: A

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Question 10

A right circular cone has a height of 10 cm and a base radius of 5 cm. Find the volume of the cone.

A. 250π cm^3

B. 500π cm^3

Correct C. 750π cm^3

D. 1000π cm^3

Correct Answer: C

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Question 11

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 12

A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

Correct A. 1/2

B. 1/3

C. 2/5

D. 3/8

Correct Answer: A

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Question 13

Find the derivative of the function f(x) = $ 2x^2 + 3x - 1 $ / $ x^2 + 1 $ u\sing the quotient rule.

Correct A. $ 4x + 3 $ / $ x^2 + 1 $^2

B. $ 4x^2 + 3x - 1 $ / $ x^2 + 1 $^2

C. $ 2x^2 + 3x - 1 $ / $ x^2 + 1 $^2

D. $ 4x^2 + 3x - 1 $ / $ x^2 + 1 $^3

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 of the sequence.

A. 15

B. 25

Correct C. 35

D. 45

Correct Answer: C

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Question 15

A set of 3 numbers has a mean of 10 and a median of 8. If the largest number is 12, what is the sum of the 3 numbers?

A. 30

B. 40

Correct C. 50

D. 60

Correct Answer: C

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Question 16

Find the value of $\int_0^1 \frac{1}{x^2+4} dx$.

Correct A. \frac{\pi}{4}

B. \frac{\pi}{2}

C. \frac{\pi}{3}

D. \frac{\pi}{5}

Correct Answer: A

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Question 17

A rec\tangular box has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find its volume.

Correct A. 30

B. 40

C. 50

D. 60

Correct Answer: A

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Question 18

Solve the inequality $2x^2-5x-3>0$.

Correct A. $ -\infty, -1 $ \cup $ 3, \infty $

B. $ -\infty, -3 $ \cup $ 1, \infty $

C. $ -\infty, -2 $ \cup $ 2, \infty $

D. $ -\infty, -4 $ \cup $ 4, \infty $

Correct Answer: A

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Question 19

Find the derivative of $f(x)=\frac{1}{x^2+1}$.

A. -\frac{2x}{$ x^2+1 $^2}

Correct B. \frac{2x}{$ x^2+1 $^2}

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

D. \frac{1}{$ x^2+1 $^2}

Correct Answer: B

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Question 20

A circle has a radius of 4 cm. Find its area.

Correct A. 16\pi

B. 32\pi

C. 64\pi

D. 128\pi

Correct Answer: A

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Question 21

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

Correct A. $ \frac{-x}{\( x^2 + 1 \ $^{3/2}} )

B. $ \frac{x}{\( x^2 + 1 \ $^{3/2}} )

C. $ \frac{1}{\( x^2 + 1 \ $^{3/2}} )

D. $ \frac{-1}{\( x^2 + 1 \ $^{3/2}} )

Correct Answer: A

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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 value of $ \log_{10} \( 1000 \ $ ) u\sing the change of base formula.

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 24

A histogram of exam scores has a mean of 70 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 80?

A. 0.68

Correct B. 0.84

C. 0.95

D. 0.99

Correct Answer: B

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Question 25

Find the determinant of the matrix $ egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} $.

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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