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POST UTME PAN-ATLANTIC UNIVERSITY 2022 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 2022 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Find the area under the curve of ( f(x) = \frac{1}{x^2} ) from \( x = 1 \) to \( x = 2 \).

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 2

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

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, 1 \) ∪ (3, ∞)

C. \( -∞, -1 \) ∪ (1, 3)

D. \( -∞, 1 \) ∪ (3, ∞)

Correct Answer: A

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Question 3

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

Correct A. 3x^2 - 4x + 3

B. 3x^2 - 2x + 1

C. 2x^2 - 4x + 3

D. x^2 - 2x + 1

Correct Answer: A

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Question 4

A sequence is defined by \( a_n = 2n + 1 \). 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 5

A set of numbers is defined as \( S = \{ x | x^2 - 4x + 3 = 0 \} \ \). Find the elements of S.

Correct A. \{1, 3\}

B. \{-1, 3\}

C. \{1, -3\}

D. \{-1, -3\}

Correct Answer: A

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Question 6

Find the value of k such that the equation \( x^2 + kx + 16 = 0 \) has equal roots.

A. 8

Correct B. -8

C. 4

D. -4

Correct Answer: B

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Question 7

A histogram is constructed from the following data: 2, 4, 5, 7, 8, 9, 10. What is the class width of the histogram?

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 8

Find the equation of the circle with center \( -2, 3 \) and radius 4.

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

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

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

D. \left\( x - 2 \right \)^2 + \left\( y - 3 \right \)^2 = 16

Correct Answer: A

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Question 9

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

Correct A. \left\( -\infty, -1 \right \) \cup \left\( 3, \infty \right \)

B. \left\( -\infty, 1 \right \) \cup \left\( 3, \infty \right \)

C. \left\( -\infty, -1 \right \) \cup \left\( 1, \infty \right \)

D. \left\( -\infty, 1 \right \) \cup \left\( -3, \infty \right \)

Correct Answer: A

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Question 10

Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ).

Correct A. 6x + 2

B. 6x - 2

C. 3x + 2

D. 3x - 2

Correct Answer: A

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Question 11

A set of 10 numbers has a mean of 20 and a s\tandard deviation of 5. If a new number is added to the set, the mean increases by 2. What is the value of the new number?

A. 42

B. 45

Correct C. 48

D. 50

Correct Answer: C

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Question 12

Solve the equation \[ \frac{\sqrt{3}}{2} \sin \left\( \frac{\pi}{6} \right \) + \frac{1}{2} \cos \left\( \frac{\pi}{6} \right \) = \frac{1}{2} \]

Correct A. \frac{\pi}{6}

B. \frac{\pi}{3}

C. \frac{\pi}{4}

D. \frac{\pi}{2}

Correct Answer: A

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Question 13

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

A. \frac{\pi}{4}

Correct B. \frac{\pi}{2}

C. \frac{\pi}{3}

D. \frac{\pi}{6}

Correct Answer: B

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Question 14

A sequence is defined by \[ a_n = \frac{1}{n^2} \] for \[ n = 1, 2, 3, \ldots \]. Find the sum of the first 10 terms of the sequence.

A. \frac{1}{90}

B. \frac{1}{80}

C. \frac{1}{70}

Correct D. \frac{1}{60}

Correct Answer: D

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Question 15

A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 50 and 70?

Correct A. 0.3413

B. 0.3415

C. 0.3417

D. 0.3419

Correct Answer: A

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Question 16

Find the area under the curve of ( f(x) = 2x^2 + 3x - 1 ) from \( x = 0 \) to \( x = 2 \).

A. 10

B. 12

Correct C. 15

D. 18

Correct Answer: C

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Question 17

Solve the system of equations u\sing matrices: \( \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 6 \end{bmatrix} \).

Correct A. \begin{bmatrix} 1 \ 2 \end{bmatrix}

B. \begin{bmatrix} 2 \ 3 \end{bmatrix}

C. \begin{bmatrix} 3 \ 4 \end{bmatrix}

D. \begin{bmatrix} 4 \ 5 \end{bmatrix}

Correct Answer: A

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Question 18

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} = 5, \text{S\tandard Deviation} = 1

C. \text{Mean} = 4, \text{S\tandard Deviation} = 3

D. \text{Mean} = 3, \text{S\tandard Deviation} = 4

Correct Answer: A

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Question 19

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

Correct A. \begin{bmatrix} -2 \ 2 \end{bmatrix}

B. \begin{bmatrix} -1 \ 1 \end{bmatrix}

C. \begin{bmatrix} 1 \ -1 \end{bmatrix}

D. \begin{bmatrix} 2 \ -2 \end{bmatrix}

Correct Answer: A

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Question 20

Find the area of the triangle with vertices (0, 0), (2, 0), and (0, 3).

A. 3

B. 6

Correct C. 9

D. 12

Correct Answer: C

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Question 21

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.

A. 5 cm

Correct B. 7.5 cm

C. 10 cm

D. 12.5 cm

Correct Answer: B

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Question 22

A set of 10 consecutive integers has a median of 12. Find the sum of the integers.

A. 120

B. 150

Correct C. 180

D. 210

Correct Answer: C

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Question 23

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

A. 50.24 cm^2

B. 100.48 cm^2

C. 200.96 cm^2

Correct D. 314.16 cm^2

Correct Answer: D

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Question 24

A sequence is defined as: 1, 2, 4, 8, ... . Find the next term in the sequence.

A. 16

B. 32

C. 64

Correct D. 128

Correct Answer: D

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Question 25

A histogram shows the distribution of exam scores for a class of 20 students. The histogram has 5 bars, each representing a different score range. The heights of the bars are 2, 4, 5, 6, and 3, respectively. Find the mean score of the class.

A. 5.5

B. 6.5

Correct C. 7.5

D. 8.5

Correct Answer: C

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