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POST UTME PAN-ATLANTIC UNIVERSITY 2023 Mathematics | Objective

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Question 1 View Details

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. \(-1, 0\) \cup \(-∞, -1\)\)

D. \(-1, 0\) ∪ (0, 1)

Correct Answer: A

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Question 2 View Details

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 View Details

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 View Details

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 View Details

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

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

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

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

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

Correct Answer: A

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Question 6 View Details

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 View Details

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 \\(text{otherwise} end{cases} ). Find \\) ).

A. 0.3

B. 0.4

Correct C. 0.5

D. 0.6

Correct Answer: C

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Question 8 View Details

A histogram of exam scores has a mean of 60 and a standard 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 View Details

Find the derivative of the function ( f(x) = \(\frac{1}{x^2 + 1}\)\)\) \) using 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 View Details

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

A. 3.6

B. 4.2

Correct C. 4.5

D. 5.0

Correct Answer: C

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Question 11 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 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.

A. 63

B. 65

C. 67

Correct D. 69

Correct Answer: D

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Question 20 View Details

A set of 5 numbers has a mean of 10 and a standard 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 View Details

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

Correct A. \(x > 4 \\)

B. \(x < 4 \\)

C. \(x = 4 \\)

D. \(x = 2 \\)

Correct Answer: A

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Question 22 View Details

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 View Details

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 View Details

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 View Details

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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