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POST UTME SKYLINE UNIVERSITY 2023 Mathematics | Objective

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Question 1 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 2 View Details

Solve for y in the equation \(y = \frac{1}{2} \left \frac{1}{x} + \frac{1}{x^2} \right \\) ).

Correct A. \(x^2 + 2x + 1\)

B. \(x^2 - 2x + 1\)

C. \(x^2 + x + 1\)

D. \(x^2 - x + 1\)

Correct Answer: A

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Question 3 View Details

A circle has a radius of 5 cm. Find the area of the circle.

A. 50π

Correct B. 100π

C. 150π

D. 200π

Correct Answer: B

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Question 4 View Details

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

A. 0

Correct B. -2

C. 2

D. -4

Correct Answer: B

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Question 5 View Details

A right-angled triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.

A. 4

B. 6

Correct C. 8

D. 12

Correct Answer: C

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Question 6 View Details

Find the derivative of the function ( f(x) = \(\frac{1}{2x^2 + 3x - 1}\)\)\) ) using the quotient rule.

Correct A. \(\frac{-4x + 3}{2x^2 + 3x - 1\) ^2}\)\)

B. \(\frac{4x + 3}{2x^2 + 3x - 1\) ^2}\)\)

C. \(\frac{4x - 3}{2x^2 + 3x - 1\) ^2}\)\)

D. \(\frac{-4x - 3}{2x^2 + 3x - 1\) ^2}\)\)

Correct Answer: A

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Question 7 View Details

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

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

B. \begin{bmatrix} 1 \ 2 \end{bmatrix}

C. \begin{bmatrix} 2 \ 1 \end{bmatrix}

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

Correct Answer: A

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Question 8 View Details

A binary operation (\ast\) is defined as \\((ast\(a ast b = a^2 + b^2\). Find the value of \(2 \\(ast b = a^2 + b^2). Find the value of \ast 3\).

Correct A. 13

B. 14

C. 15

D. 16

Correct Answer: A

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Question 9 View Details

Find the value of ( x ) in the equation \(2^x + 3^x = 10\).

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 10 View Details

Solve the inequality \(2x^2 + 3x - 1 > 0\).

A. \(x < -1\)

Correct B. \(x > -1\)

C. \(x < 1\)

D. \(x > 1\)

Correct Answer: B

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Question 11 View Details

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

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

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

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

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

Correct Answer: A

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Question 12 View Details

A right circular cylinder has a height of 10 cm and a radius of 4 cm. Find the volume of the cylinder.

A. ( 40pi ) \(cm^3\)

B. ( 80pi ) \(cm^3\)

Correct C. ( 160pi ) \(cm^3\)

D. ( 320pi ) \(cm^3\)

Correct Answer: C

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Question 13 View Details

Find the equation of the circle with center \(-2, 3\) and radius 5.

Correct A. \(x + 2 \\)^2 + \(y - 3\)^\(2 = 25\) )

B. \(x - 2 \\)^2 + \(y + 3\)^\(2 = 25\) )

C. \(x + 2 \\)^2 + \(y + 3\)^\(2 = 25\) )

D. \(x - 2 \\)^2 + \(y - 3\)^\(2 = 25\) )

Correct Answer: A

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Question 14 View Details

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

Correct A. \(x < -\frac{5}{4}\) or \(x > \frac{3}{2}\)

B. \(x < -\frac{3}{2}\) or \(x > \frac{5}{4}\)

C. \(x < -\frac{3}{2}\) or \(x < \frac{5}{4}\)

D. \(x > -\frac{5}{4}\) or \(x < \frac{3}{2}\)

Correct Answer: A

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Question 15 View Details

Find the value of ( x ) in the equation \(2^x + 3^x = 5^x\).

A. \(x = 2\)

Correct B. \(x = 3\)

C. \(x = 4\)

D. \(x = 5\)

Correct Answer: B

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Question 16 View Details

Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 64\pi \(cm^3\)

Correct B. 128\pi \(cm^3\)

C. 256\pi \(cm^3\)

D. 512\pi \(cm^3\)

Correct Answer: B

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Question 17 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?

A. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

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Question 18 View Details

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

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 19 View Details

In the triangle ABC, the length of side AB is 5 cm, the length of side BC is 7 cm, and the length of side AC is 9 cm. What is the measure of angle A in degrees?

A. 30

B. 45

Correct C. 60

D. 90

Correct Answer: C

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Question 20 View Details

A circle has a radius of 4 cm. What is the area of the circle?

Correct A. 16\pi \(cm^2\)

B. 32\pi \(cm^2\)

C. 64\pi \(cm^2\)

D. 128\pi \(cm^2\)

Correct Answer: A

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Question 21 View Details

Find the determinant of the matrix [ egin{array}{ccc} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{array} ].

A. -120

B. 120

Correct C. 0

D. -60

Correct Answer: C

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Question 22 View Details

A histogram is constructed using the following data: [ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 ]. The width of each bar is 1 unit. Find the mean of the data.

A. 6

Correct B. 7

C. 8

D. 9

Correct Answer: B

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Question 23 View Details

Find the volume of the solid formed by revolving the region bounded by the curve [\((y = x\)\^2\) ] and the line [ \\((y = x^2\(y = 4\) ] about the x-axis.

A. 64\pi

B. 128\pi

Correct C. 256\pi

D. 512\pi

Correct Answer: C

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Question 24 View Details

A sequence is defined by [ \(a_n = 2n + 1\) ]. Find the sum of the first 5 terms of the sequence.

A. 15

B. 25

C. 35

Correct D. 45

Correct Answer: D

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Question 25 View Details

A set of 5 numbers has a mean of 10. If 2 more numbers are added to the set, the mean becomes 12. Find the sum of the original 5 numbers.

A. 40

Correct B. 50

C. 60

D. 70

Correct Answer: B

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