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POST UTME PAN-ATLANTIC UNIVERSITY 2020 Mathematics | Objective

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Question 1 View Details

Determine the value of the determinant of the matrix [ egin{pmatrix} 2 & 3 \ 4 & 5 \end{pmatrix} ].

Correct A. -1

B. 1

C. 2

D. 3

Correct Answer: A

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

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

Correct Answer: B

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Question 3 View Details

A set of exam scores has a mean of 80 and a standard deviation of 10. If a new score of 90 is added to the set, what is the new mean?

A. 79.5

Correct B. 80.5

C. 81.5

D. 82.5

Correct Answer: B

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Question 4 View Details

Solve the equation [ \(2^x\) + \\((3^x\)\(= 5\)\\()^x\) ].

Correct A. \(x = 1\)

B. \(x = 2\)

C. \(x = 3\)

D. \(x = 4\)

Correct Answer: A

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Question 5 View Details

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. 20

Correct C. 25

D. 30

Correct Answer: C

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Question 6 View Details

Solve the inequality \(\frac{x^2 - 4}{x + 2} \geq 0\) for ( x in mathbb{R} ).

Correct A. \(-\infty, -2 \\) cup [0, infty) )

B. \(-\infty, -2 \\) cup \(-2, 0\) cup (0, infty) )

C. \(-\infty, -2 \\) cup (0, infty) )

D. \(-\infty, -2 \\) cup [0, 2] )

Correct Answer: A

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Question 7 View Details

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

Correct A. -120

B. 120

C. -60

D. 60

Correct Answer: A

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Question 8 View Details

Solve the system of linear equations \(egin{cases} x + y + z = 6 \ x + 2y + 3z = 12 \ 2x + 3y + 4z = 20 \end{cases}\).

Correct A. \(x = 1, y = 2, z = 3\)

B. \(x = 2, y = 1, z = 3\)

C. \(x = 1, y = 3, z = 2\)

D. \(x = 2, y = 3, z = 1\)

Correct Answer: A

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Question 9 View Details

Find the derivative of the function ( f(x) = \(\frac{x^2 + 2x - 3}{x^2 - 4}\)\)\) ) using the quotient rule.

Correct A. ( f'\((x) =\)\(\frac{x^2 - 4\) 2x + 2 - \(x^2 + 2x - 3\) (2x)}{ \(x^2 - 4\) ^2}\)\) )

B. ( f'\((x) =\)\(\frac{x^2 - 4\) 2x + 2 - \(x^2 + 2x - 3\) (2x)}{ \(x^2 - 4\) ^2}\)\) )

C. ( f'\((x) =\)\(\frac{x^2 - 4\) 2x + 2 - \(x^2 + 2x - 3\) (2x)}{ \(x^2 - 4\) ^2}\)\) )

D. ( f'\((x) =\)\(\frac{x^2 - 4\) 2x + 2 - \(x^2 + 2x - 3\) (2x)}{ \(x^2 - 4\) ^2}\)\) )

Correct Answer: A

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Question 10 View Details

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

Correct A. \(x = -2 \pm 0i\)

B. \(x = -2 \pm 2i\)

C. \(x = -2 \pm 4i\)

D. \(x = -2 \pm 6i\)

Correct Answer: A

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Question 11 View Details

Find the derivative of ( f(x) = \(\frac{x^2 + 2x - 3}{x^2 - 4}\)\)\) ) using the quotient rule.

A. \(\frac{2x x^2 - 4 - x^2 + 2x - 3\) (2x)}{ \(x^2 - 4\) ^2}\)\)

B. \(\frac{2x x^2 - 4 + x^2 + 2x - 3\) (2x)}{ \(x^2 - 4\) ^2}\)\)

Correct C. \(\frac{2x x^2 - 4 - x^2 + 2x - 3\) (2x)}{ \(x^2 - 4\) ^2}\)\)

D. \(\frac{2x x^2 - 4 + x^2 + 2x - 3\) (2x)}{ \(x^2 - 4\) ^2}\)\)

Correct Answer: C

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Question 12 View Details

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

A. \left\(-\frac{5}{4}, \frac{3}{2} \right\)

Correct B. \left\(-\infty, -\frac{5}{4} \right\) \cup \left\(\frac{3}{2}, \infty \right\)

C. \left\(-\infty, -\frac{5}{4} \right\) \cup \left\(-\frac{3}{2}, \infty \right\)

D. \left\(-\infty, \frac{3}{2} \right\)

Correct Answer: B

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Question 13 View Details

Find the sum of the first 5 terms of the geometric series \(2 + 6 + 18 + \cdots\).

Correct A. 120

B. 150

C. 180

D. 200

Correct Answer: A

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Question 14 View Details

Solve the matrix equation \(\begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 6 \end{bmatrix}\).

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

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

C. \begin{bmatrix} 5 \ 6 \end{bmatrix}

D. \begin{bmatrix} 7 \ 8 \end{bmatrix}

Correct Answer: A

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Question 15 View Details

Find the probability that at least one of the events A and B occurs, given that P(A) = 0.4,\(P(B) = 0.3\), and P\(A \cap B\)\(= 0.1.\)

A. 0.5

Correct B. 0.6

C. 0.7

D. 0.8

Correct Answer: B

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Question 16 View Details

Find the value of x in the equation \(\log_{10} x^2 \\)\(= 4 ).\)

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 17 View Details

Solve for y in the equation \(2y^2 + 5y - 3 = 0\).

A. -1

Correct B. 1

C. 3

D. -3

Correct Answer: B

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Question 18 View Details

Find the sum of the first 5 terms of the geometric sequence with first term 2 and common ratio 3.

A. 10

B. 20

Correct C. 30

D. 40

Correct Answer: C

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Question 19 View Details

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

A. \(-∞, 1\) ∪ (3, ∞)

Correct B. \(-∞, 3\) ∪ (1, ∞)

C. \(-∞, 1\) ∪ (1, 3)

D. \(-∞, 3\) ∪ (3, ∞)

Correct Answer: B

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Question 20 View Details

Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).

A. 6

B. 12

Correct C. 18

D. 24

Correct Answer: C

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Question 21 View Details

A right circular cone has a height of 15 cm and a base radius of 8 cm. Find the volume of the cone in terms of π.

Correct A. \(\frac{4000\pi}{3}\)\)

B. \(\frac{800\pi}{3}\)\)

C. \(\frac{1600\pi}{3}\)\)

D. \(\frac{3200\pi}{3}\)\)

Correct Answer: A

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Question 22 View Details

Solve the 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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Question 23 View Details

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 + \(y - 3\)^\(2 = 16\) \)

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

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

Correct Answer: A

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Question 24 View Details

A set A contains 3 elements. Find the number of subsets of A.

Correct A. 8

B. 16

C. 32

D. 64

Correct Answer: A

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Question 25 View Details

Find the sum of the first 5 terms of the geometric progression 2, 6, 18, ...

Correct A. 312

B. 3120

C. 31200

D. 312000

Correct Answer: A

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