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POST UTME SKYLINE UNIVERSITY 2020 Mathematics | Objective

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Question 1 View Details

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

Correct A. \(\frac{16}{3}\)

B. \(\frac{32}{3}\)

C. \(\frac{64}{3}\)

D. \(\frac{128}{3}\)

Correct Answer: A

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Question 2 View Details

Solve the equation \(2x^2 + 5x - 3 = 0\) using the quadratic formula.

A. \(x = \frac{-5 \pm \sqrt{109}}{4}\)

B. \(x = \frac{-5 \pm \sqrt{121}}{4}\)

Correct C. \(x = \frac{-5 \pm \sqrt{169}}{4}\)

D. \(x = \frac{-5 \pm \sqrt{225}}{4}\)

Correct Answer: C

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Question 3 View Details

Find the equation of the circle with center ( (3, 4) ) and radius ( 5 ).

Correct A. \(x - 3 \\)^2 + \(y - 4\)^\(2 = 25\) )

B. \(x - 4 \\)^2 + \(y - 3\)^\(2 = 25\) )

C. \(x - 5 \\)^2 + \(y - 3\)^\(2 = 25\) )

D. \(x - 3 \\)^2 + \(y - 5\)^\(2 = 25\) )

Correct Answer: A

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Question 4 View Details

Find the volume of the cylinder with radius ( 4 ) and height ( 6 ).

Correct A. ( 96pi )

B. ( 192pi )

C. ( 384pi )

D. ( 768pi )

Correct Answer: A

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Question 5 View Details

Solve the inequality \(x^2 - 4x + 3 > 0\).

Correct A. \(x < -1\) or \(x > 3\)

B. \(x < 1\) or \(x > 3\)

C. \(x < -3\) or \(x > 1\)

D. \(x < 3\) or \(x > 1\)

Correct Answer: A

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Question 6 View Details

Find the area under the curve \(y = \frac{1}{2}x^2 + 3x - 2\) 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 circle has equation \(x - 2 \\)^2 + \(y - 3)^\(2 = 4\) ). Find the equation of the \\\\((()^(2\) = 4\)\tangent line at point ( (3, 5) ).

Correct A. \(y = -x + 7\)

B. \(y = x + 1\)

C. \(y = 2x - 3\)

D. \(y = -2x + 9\)

Correct Answer: A

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Question 8 View Details

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

A. x < -1 or \(x > 3\)

Correct B. \(x < 1\) or \(x > 3\)

C. x < -3 or \(x > 1\)

D. \(x < 3\) or \(x > 1\)

Correct Answer: B

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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.

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

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

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

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

Correct Answer: A

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Question 10 View Details

A binary number is represented as \(1011_2\). Convert it to decimal.

A. 11

B. 13

Correct C. 15

D. 17

Correct Answer: C

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Question 11 View Details

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

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 12 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 13 View Details

The mean of five numbers is (25\). If one of the numbers is \(10\\((25). If one of the numbers is\), find the sum of the other four numbers.

Correct A. 90

B. 100

C. 110

D. 120

Correct Answer: A

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Question 14 View Details

Solve the inequality \(\log_{10} x^2\)\(> 4\)\).

Correct A. \(x > 10\)

B. \(x < -10\)

C. \(x > 100\)

D. \(x < -100\)

Correct Answer: A

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Question 15 View Details

A fair six-sided die is rolled. What is the probability that the number rolled is greater than \(4\)?

A. \(\frac{1}{6}\)

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

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

Correct D. \(\frac{5}{6}\)

Correct Answer: D

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Question 16 View Details

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 24\pitext{ cm}^3

B. 48\pitext{ cm}^3

Correct C. 72\pitext{ cm}^3

D. 96\pitext{ cm}^3

Correct Answer: C

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Question 17 View Details

Solve the system of linear equations using matrices: \begin{align*} x + 2y - z &= 3 \ 2x - 3y + 4z &= 2 \ 3x + y - 2z &= 1 \end{align*}

Correct A. \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}

B. \begin{pmatrix} 2 \ -1 \ 1 \end{pmatrix}

C. \begin{pmatrix} 3 \ 1 \ -2 \end{pmatrix}

D. \begin{pmatrix} 4 \ 2 \ 1 \end{pmatrix}

Correct Answer: A

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Question 18 View Details

Find the area under the curve (f(x) = \begin{cases} 2x + 1, & \text{if}\(x < 2\)\\((f(x) = begin{cases} 2x + 1, & \ 3x - 2, & text{if} x \geq 2 \\(text{if} x \end{cases}\) from \(x = 0\) to \(x = 4\).

A. 14

Correct B. 16

C. 18

D. 20

Correct Answer: B

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Question 19 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 + \(y - 3\)^\(2 = 20\)

C. \(x - 2\)^2 + \(y - 3\)^\(2 = 24\)

D. \(x - 2\)^2 + \(y - 3\)^\(2 = 28\)

Correct Answer: A

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Question 20 View Details

Find the sum of the first 10 terms of the geometric progression 3, 6, 12, ...

A. 124

B. 126

Correct C. 128

D. 130

Correct Answer: C

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Question 21 View Details

Find the determinant of the matrix \(egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix}\).

A. 1

Correct B. -1

C. 5

D. 10

Correct Answer: B

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Question 22 View Details

A circle has a diameter of 10 cm. Find the area of the circle.

A. 50π

Correct B. 100π

C. 200π

D. 250π

Correct Answer: B

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Question 23 View Details

A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the prism.

Correct A. 30

B. 50

C. 60

D. 70

Correct Answer: A

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Question 24 View Details

A line passes through the points (2, 3) and (4, 5). Find the equation of the line in slope-intercept form.

Correct A. \(y = x + 1\)

B. \(y = x - 1\)

C. \(y = -x + 3\)

D. \(y = x - 3\)

Correct Answer: A

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Question 25 View Details

A random experiment consists of rolling a fair six-sided die. If the number rolled is even, the experiment is a success. Find the probability of success.

Correct A. \(1/2\)

B. \(1/3\)

C. \(2/3\)

D. \(3/4\)

Correct Answer: A

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