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POST UTME EKSU 2022 Mathematics | Objective

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Question 1 View Details

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

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

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

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

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

Correct Answer: C

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Question 2 View Details

A circle with center ( C(2, 3) ) and radius \(r = 5\) has a chord ( AB ) of length ( 10 ). Find the distance from the center ( C ) to the midpoint ( M ) of the chord ( AB ).

Correct A. \(\sqrt{5^2 - 5^2} = 0\)

B. \(\sqrt{5^2 - 5^2} = 5\)

C. \(\sqrt{5^2 - 5^2} = 10\)

D. \(\sqrt{5^2 - 5^2} = 15\)

Correct Answer: A

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Question 3 View Details

Find the volume of the solid formed by revolving the region bounded by the curve (y = \(x^2\)\), the x-axis, and the line \(x = 2\\((y = x^2), the x-axis, and the line\) about the x-axis.

A. \(\frac{32}{3} \pi\)

Correct B. \(\frac{64}{3} \pi\)

C. \(\frac{128}{3} \pi\)

D. \(\frac{256}{3} \pi\)

Correct Answer: B

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Question 4 View Details

A sequence is defined recursively as \(a_n = 2a_{n-1} + 1\), with \(a_1 = 3\). Find the sum of the first 5 terms of the sequence.

Correct A. \(3 + 7 + 15 + 31 + 63 = 119\)

B. \(3 + 7 + 15 + 31 + 63 = 119\)

C. \(3 + 7 + 15 + 31 + 63 = 119\)

D. \(3 + 7 + 15 + 31 + 63 = 119\)

Correct Answer: A

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Question 5 View Details

A set ( A ) contains 5 elements, and a set ( B ) contains 3 elements. If the number of elements in the intersection of ( A ) and ( B ) is 2, find the number of elements in the union of ( A ) and ( B ).

Correct A. \(5 + 3 - 2 = 6\)

B. \(5 + 3 - 2 = 6\)

C. \(5 + 3 - 2 = 6\)

D. \(5 + 3 - 2 = 6\)

Correct Answer: A

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Question 6 View Details

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

Correct A. 10

B. 100

C. 1000

D. 10000

Correct Answer: A

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Question 7 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. If 75% of the scores fall below 85, what is the z-score corresponding to a score of 85?

A. 0.5

Correct B. 1

C. 1.5

D. 2

Correct Answer: B

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Question 8 View Details

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

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

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

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

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

Correct Answer: C

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Question 9 View Details

A vector ( mathbf{a} ) has a magnitude of 5 and points in the direction of the positive x-axis. A vector ( mathbf{b} ) has a magnitude of 3 and points in the direction of the positive y-axis. Find the magnitude of the sum of these two vectors.

A. 5

B. 6

C. 7

Correct D. 8

Correct Answer: D

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Question 10 View Details

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

Correct A. -2

B. -1

C. 0

D. 1

Correct Answer: A

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Question 11 View Details

Find the volume of the frustum of a cone with height 12cm, lower base radius 6cm, and upper base radius 3cm.

A. 324\pi \(cm^3\)

Correct B. 648\pi \(cm^3\)

C. 972\pi \(cm^3\)

D. 1296\pi \(cm^3\)

Correct Answer: B

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Question 12 View Details

Solve for x in the equation \(2^x + 3^x = 5^x\).

A. \(x = 2\)

B. \(x = 3\)

Correct C. \(x = 4\)

D. \(x = 5\)

Correct Answer: C

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Question 13 View Details

Find the area of the triangle with vertices (1, 2), (3, 4), and (5, 6).

Correct A. 10

B. 20

C. 30

D. 40

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} 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 15 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 + \(y - 3\)^\(2 = 32\)

C. \(x - 2\)^2 + \(y - 3\)^\(2 = 64\)

D. \(x - 2\)^2 + \(y - 3\)^\(2 = 128\)

Correct Answer: A

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Question 16 View Details

In a binary system, what is the value of the number represented by the sequence 1011?

A. 3

Correct B. 5

C. 7

D. 9

Correct Answer: B

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Question 17 View Details

A histogram is constructed with the following data: 2, 4, 6, 8, 10, 12, 14, 16. What is the mean of the data?

A. 7

B. 8

Correct C. 9

D. 10

Correct Answer: C

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Question 18 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 + 3 \\)^2 + \(y - 2\)^\(2 = 16\) )

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

Correct Answer: A

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Question 19 View Details

Find the area under the curve \(y = x^2\) from \(x = 0\) to \(x = 4\).

A. 32

B. 64

Correct C. 96

D. 128

Correct Answer: C

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Question 20 View Details

Find the magnitude of the vector \(\vec{a} = 2hat{i} + 3hat{j}\).

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 21 View Details

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

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

B. f'\((x) =\)\(\frac{x}\){ \(x^2 + 1\) \)^{\(3/2\)}}\)

C. f'\((x) =\)\(\frac{1}\){ \(x^2 + 1\) \)^{\(3/2\)}}\)

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

Correct Answer: A

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Question 22 View Details

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

Correct A. \(-∞, -1\) ∪ (3, ∞)

B. \(-∞, -3\) ∪ (1, ∞)

C. \(-∞, 1\) ∪ (3, ∞)

D. \(-∞, -3\) ∪ (1, ∞)

Correct Answer: A

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Question 23 View Details

Find the equation of the line passing through the points (2, 3) and (4, 5).

Correct A. \(y = 2x - 1\)

B. \(y = 2x + 1\)

C. \(y = x - 1\)

D. \(y = x + 1\)

Correct Answer: A

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Question 24 View Details

A histogram of exam scores is shown below. What is the mean score?

A. 60

Correct B. 70

C. 80

D. 90

Correct Answer: B

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Question 25 View Details

Find the magnitude of the vector \(\vec{a} = 3\hat{i} + 4\hat{j}\).

Correct A. 5

B. 10

C. 15

D. 20

Correct Answer: A

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