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POST UTME SUMMIT UNIVERSITY 2022 Mathematics | Objective

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Question 1 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\pi

B. 32\pi

Correct C. 48\pi

D. 64\pi

Correct Answer: C

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Question 2 View Details

Solve the inequality \(\frac{x^2 - 4x - 5}{x + 1}\)\)\\() > 0.\)

Correct A. \(-\infty, -1\) \cup \(5, \infty\)

B. \(-\infty, -1\) \cup \(-1, 5\)

C. \(-\infty, 5\) \cup \(5, \infty\)

D. \(-\infty, -1\) \cup \(5, \infty\)

Correct Answer: A

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Question 3 View Details

A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is not blue?

A. \(\frac{1}{2}\)\)

B. \(\frac{3}{5}\)\)

Correct C. \(\frac{5}{8}\)\)

D. \(\frac{3}{8}\)\)

Correct Answer: C

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Question 4 View Details

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

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

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

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

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

Correct Answer: D

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Question 5 View Details

A bakery sells 250 loaves of bread per day. If they make a profit of ₦5 per loaf, how much profit do they make in a day?

Correct A. ₦1250

B. ₦12500

C. ₦125000

D. ₦1250000

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 \(x = 4\).

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

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

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

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

Correct Answer: A

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Question 7 View Details

Solve for ( x ) in the equation \(\log_{10} x^2 \\)\(= 4 ).\)

Correct A. \(x = 10^4\)

B. \(x = 10^2\)

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

D. \(x = 10^{-4}\)

Correct Answer: A

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Question 8 View Details

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

A. \(\frac{8}{3} \pi\)

Correct B. \(\frac{16}{3} \pi\)

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

D. \(\frac{64}{3} \pi\)

Correct Answer: B

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Question 9 View Details

A right-angled triangle has sides of length 3, 4, and 5. Find the area of the triangle.

Correct A. \(\frac{1}{2} \times 3 \times 4\)

B. \(\frac{1}{2} \times 3 \times 5\)

C. \(\frac{1}{2} \times 4 \times 5\)

D. \(\frac{1}{2} \times 3 \times 5\)

Correct Answer: A

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Question 10 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 + \(y - 3\)^\(2 = 4\) )

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

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

Correct Answer: A

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Question 11 View Details

In the diagram below, a right-angled triangle has a hypotenuse of length 10 cm. If the ratio of the lengths of the two legs is 3:4, what is the area of the triangle in square centimeters?

Correct A. 30

B. 40

C. 50

D. 60

Correct Answer: A

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Question 12 View Details

A polynomial function f(x) has a degree of 4 and a leading coefficient of 2. If f(1) = 10 and f\(-2 = -20\), what is the value of f(0)?

A. 0

B. 5

Correct C. 10

D. 15

Correct Answer: C

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Question 13 View Details

A circle has a radius of 5 cm. If a chord of the circle is 8 cm long, what is the area of the sector formed by the chord and the center of the circle?

A. 20

Correct B. 30

C. 40

D. 50

Correct Answer: B

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Question 14 View Details

A right-angled triangle has a hypotenuse of length 10 cm. If the ratio of the lengths of the two legs is 3:4, what is the length of the longer leg?

A. 6

Correct B. 8

C. 10

D. 12

Correct Answer: B

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Question 15 View Details

A polynomial function f(x) has a degree of 3 and a leading coefficient of 1. If f(0) = 2 and f(1) = 5, what is the value of f\(-1\)?

A. 2

B. 3

Correct C. 4

D. 5

Correct Answer: C

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Question 16 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 17 View Details

A fair six-sided die is rolled. If the number on the die is even, a second die is rolled. What is the probability that the sum of the numbers on the two dice is 7?

Correct A. \(1/6\)

B. \(1/12\)

C. \(1/24\)

D. \(1/36\)

Correct Answer: A

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Question 18 View Details

Solve for ( x ) in the equation \(2^x + 5^x = 7^x\).

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 19 View Details

Find the value of ( x ) in the equation \(2x + 5 = 11\).

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 20 View Details

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

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 21 View Details

Find the volume of the solid formed by revolving the region bounded by the curves \(y = x\^2\), \(y = 0\), and \(x = 2\) 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 22 View Details

A binary operation ast on the set of real numbers is defined as a \ast \(b = ab + 2\\(ast on the set of real numbers is defined as a ast\). Find the value of 2 \ast 3.

A. 6

B. 8

Correct C. 10

D. 12

Correct Answer: C

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Question 23 View Details

A random experiment consists of rolling a fair six-sided die and then flipping a fair coin. If the number on the die is even and the coin lands heads up, what is the probability that the number on the die is greater than 4?

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

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

C. \(\frac{1}{2}\)\)

Correct D. \(\frac{2}{3}\)\)

Correct Answer: D

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Question 24 View Details

Find the area under the curve \(y = x\^3 - 6x^2 + 9x + 2\) from \(x = 0\) to \(x = 4\).

A. 64

B. 128

Correct C. 192

D. 256

Correct Answer: C

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Question 25 View Details

A solid is formed by revolving the region bounded by the curves \(y = x\^2\), \(y = 0\), and \(x = 2\) about the y-axis. Find the volume of the solid.

A. 16\pi

B. 32\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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