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POST UTME PAN-ATLANTIC UNIVERSITY 2023 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 2023 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Solve the inequality \( \frac{x}{x+1} > \frac{1}{x+1} \) for \( x in mathbb{R} setminus { -1 } \).

Correct A. \( -1, 0 \) ∪ (1, ∞)

B. \( -1, 0 \) ∪ (0, ∞)

C. \( -1, 0 \) ∪ \( -∞, -1 \)

D. \( -1, 0 \) ∪ (0, 1)

Correct Answer: A

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Question 2

Find the sum of the first 10 terms of the geometric series \( 2x^2 + 4x^3 + 8x^4 + ldots \).

Correct A. 2x^2 \( 1 - x^2 \)^{-1} \( 1 - x^{10} \)

B. 2x^2 \( 1 - x^2 \)^{-1}

C. 2x^2 \( 1 - x^{10} \)

D. 2x^2 \( 1 - x^2 \)^{-1} \( 1 - x^{10} \)^{-1}

Correct Answer: A

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Question 3

Solve the system of linear equations \( egin{cases} 2x + 3y = 7 \ 4x - 2y = -3 \end{cases} \).

Correct A. x = 1, y = 1

B. x = 2, y = 1

C. x = 1, y = 2

D. x = 2, y = 2

Correct Answer: A

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Question 4

Find the determinant of the matrix \( egin{pmatrix} 2 & 1 & 1 \ 4 & 3 & 2 \ 1 & 2 & 3 \end{pmatrix} \).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 5

Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \) for ( x in [0, 2pi] ).

Correct A. [0, \frac{pi}{2}] cup [\frac{3pi}{2}, 2pi]

B. [0, \frac{pi}{2}] cup [\frac{pi}{2}, pi]

C. [0, \frac{pi}{2}] cup [pi, \frac{3pi}{2}]

D. [0, \frac{pi}{2}] cup [\frac{3pi}{2}, 2pi]

Correct Answer: A

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Question 6

Find the area under the curve \( y = \frac{1}{2}x^2 + 2x - 3 \) from \( x = 0 \) to \( x = 4 \).

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 7

A random variable ( X ) has a probability density function ( f(x) = \begin{cases} 2x & 0 < x < 1 \ 0 & \text{otherwise} \end{cases} ). Find \( P\( 0.2 < X < 0.8 \ \) ).

A. 0.3

B. 0.4

Correct C. 0.5

D. 0.6

Correct Answer: C

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Question 8

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

A. 0.2

B. 0.3

C. 0.4

Correct D. 0.5

Correct Answer: D

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Question 9

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

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

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

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

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

Correct Answer: B

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Question 10

A vector \( \vec{a} \) has components \( a_1 = 2 \) and \( a_2 = 3 \). Find the magnitude of the vector \( \vec{a} \).

A. 3.6

B. 4.2

Correct C. 4.5

D. 5.0

Correct Answer: C

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Question 11

Solve for x in the equation \( \frac{1}{x+2} + \frac{1}{x-3} = \frac{1}{2} \).

A. x = -1

B. x = 2

Correct C. x = 5

D. x = -5

Correct Answer: C

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Question 12

In the diagram below, find the value of x.

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 13

Find the sum of the infinite geometric series \( 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots \).

Correct A. 2

B. 4

C. 8

D. 16

Correct Answer: A

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Question 14

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

Correct A. x < -1

B. x > -1

C. x < 3

D. x > 3

Correct Answer: A

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Question 15

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

A. x = 1

Correct B. x = -1

C. x = 5

D. x = -5

Correct Answer: B

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Question 16

A random variable X has a probability distribution given by the following histogram. What is the expected value of X?

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 17

Solve for x in the equation \( \log_{10} \( x^2 \) = 4 \).

A. 10

B. 100

Correct C. 1000

D. 10000

Correct Answer: C

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Question 18

Find the volume of the solid formed by revolving the region bounded by the curves \( y = x^2 \) and \( y = 2x \) 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 19

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.

A. 63

B. 65

C. 67

Correct D. 69

Correct Answer: D

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Question 20

A set of 5 numbers has a mean of 10 and a s\tandard deviation of 2. Find the range of the set.

A. 16

B. 18

C. 20

Correct D. 22

Correct Answer: D

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Question 21

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

Correct A. \( x > 4 \ \)

B. \( x < 4 \ \)

C. \( x = 4 \ \)

D. \( x = 2 \ \)

Correct Answer: A

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Question 22

Find the area under the curve \( y = x^2 - 4x + 3 \) from \( x = 1 \) to \( x = 3 \).

A. \( 4 \ \)

Correct B. \( 6 \ \)

C. \( 8 \ \)

D. \( 10 \ \)

Correct Answer: B

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Question 23

Solve the matrix equation \( \begin{bmatrix} 2 & 1 \ 1 & 2 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 3 \end{bmatrix} \).

A. \( x = 1, y = 1 \ \)

B. \( x = 2, y = 2 \ \)

Correct C. \( x = 3, y = 3 \ \)

D. \( x = 4, y = 4 \ \)

Correct Answer: C

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Question 24

A fair six-sided die is rolled. What is the probability that the number rolled is a multiple of 3?

A. \( \frac{1}{2} \ \)

Correct B. \( \frac{1}{3} \ \)

C. \( \frac{2}{3} \ \)

D. \( \frac{4}{5} \ \)

Correct Answer: B

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Question 25

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

Correct A. \( x = -2 \ \)

B. \( x = 2 \ \)

C. \( x = -1 \ \)

D. \( x = 1 \ \)

Correct Answer: A

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