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POST UTME SUMMIT UNIVERSITY 2021 Mathematics | Objective

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Question 1 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.

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

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

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

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

Correct Answer: A

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Question 2 View Details

The equation of a circle is given by \(x^2 + y^2 + 4x - 6y + 9 = 0\). Find the coordinates of the center of the circle.

Correct A. \(-2, 3\)

B. \(2, -3\)

C. \(-3, 2\)

D. \(3, -2\)

Correct Answer: A

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Question 3 View Details

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

Correct A. \(-\infty, -1\) \cup \(3, \infty\)

B. \(-\infty, 1\) \cup \(3, \infty\)

C. \(-\infty, -3\) \cup \(1, \infty\)

D. \(-\infty, 3\) \cup \(1, \infty\)

Correct Answer: A

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Question 4 View Details

Find the mean of the numbers 2, 4, 6, 8, 10.

A. 6

Correct B. 8

C. 10

D. 12

Correct Answer: B

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Question 5 View Details

The sum of the first n terms of an arithmetic progression is given by \(S_n = \frac{n}{2} 2a + (n - 1 \\) d) ). Find the value of d if \(a = 2\) and \(S_n = 120\).

A. 10

Correct B. 20

C. 30

D. 40

Correct Answer: B

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Question 6 View Details

Find the value of \(\frac{d}{dx}\left \frac{1}{x^2}\right\)\).

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

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

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

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

Correct Answer: A

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Question 7 View Details

Solve the inequality \(|x-2| > 3\).

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

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

C. \(-\infty, -1\) \cup (2, 5)

D. \(-\infty, 1\) \cup (2, 5)

Correct Answer: A

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Question 8 View Details

Find the equation of the tangent line to the curve \(y = x^2+2x-3\) at the point \\(tangent line to the curve (y = x^2+2x-3\((1, 2)\).

Correct A. \(y = 3x - 1\)

B. \(y = 3x + 1\)

C. \(y = x + 1\)

D. \(y = x - 1\)

Correct Answer: A

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Question 9 View Details

Solve the system of equations \nbegin{align*} \n 2x+y &= 4, \n 3x-2y &= 5. \nend{align*}

Correct A. (1, 2)

B. (2, 1)

C. (3, 4)

D. (4, 3)

Correct Answer: A

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Question 10 View Details

Find the area of the triangle with vertices \((0, 0), (3, 0),\) and \((0, 2)\).

Correct A. 6

B. 8

C. 10

D. 12

Correct Answer: A

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Question 11 View Details

Determine the value of x in the equation \(\frac{1}{x} + \frac{1}{x+1} = \frac{1}{2}\).

Correct A. 1

B. 2

C. 3

D. 4

Correct Answer: A

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Question 12 View Details

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

A. 8

Correct B. 10

C. 12

D. 14

Correct Answer: B

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Question 13 View Details

Solve the inequality \(\frac{x-1}{x+1} < 0\).

A. \(-1, 1\)

Correct B. \(-1, 0\) U (1, ∞)

C. \(-∞, -1\) U (0, 1)

D. \(-∞, ∞\) - \(-1, 1\)

Correct Answer: B

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Question 14 View Details

Find the derivative of the function ( f(x) = \(\sqrt{2x+1}\) ).

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

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

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

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

Correct Answer: B

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Question 15 View Details

Solve the system of equations \(egin{cases} x+y = 4 \ x-y = 2 \end{cases}\).

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

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

C. \(x = 2, y = 2\)

D. \(x = 4, y = 0\)

Correct Answer: A

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Question 16 View Details

Determine the mean of the following dataset: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?

A. 12

Correct B. 14

C. 16

D. 18

Correct Answer: B

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Question 17 View Details

Let \(\mathbf{a} = egin{pmatrix} 1 \ 2 \end{pmatrix}\) and \(\mathbf{b} = egin{pmatrix} 3 \ 4 \end{pmatrix}\). Find ( mathbf{a} cdot mathbf{b} ).

Correct A. 11

B. 13

C. 15

D. 17

Correct Answer: A

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Question 18 View Details

A random experiment has two independent events, A and B. The probability of event A occurring is 0.4, and the probability of event B occurring is 0.6. What is the probability that both events occur?

Correct A. 0.24

B. 0.36

C. 0.48

D. 0.60

Correct Answer: A

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Question 19 View Details

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

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 20 View Details

A set A contains the elements {1, 2, 3, 4, 5}. Find the number of subsets of A.

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 21 View Details

Find the equation of the circle passing through the points (1, 2), (3, 4), and (5, 6).

Correct A. \(x^2\) + \\((y^2 + 4x - 8y + 5\)\(= 0\)\)

B. \(x^2\) + \\((y^2 - 4x + 8y + 5\)\(= 0\)\)

C. \(x^2\) + \\((y^2 + 2x - 4y + 5\)\(= 0\)\)

D. \(x^2\) + \\((y^2 - 2x + 4y + 5\)\(= 0\)\)

Correct Answer: A

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Question 22 View Details

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

Correct A. x < -1 or \(x > 3/2\)\)

B. x > -1 or \(x < 3/2\)\)

C. x < -1 or \(x < 3/2\)\)

D. x > -1 or \(x > 3/2\)\)

Correct Answer: A

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Question 23 View Details

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.

Correct A. 2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374 + 13122 + 39366

B. 2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374 + 13122 + 39366 + 118098

C. 2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374 + 13122 + 39366 + 118098 + 354294

D. 2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374 + 13122 + 39366 + 118098 + 354294 + 1062882

Correct Answer: A

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Question 24 View Details

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

A. 9

Correct B. 18

C. 27

D. 36

Correct Answer: B

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Question 25 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 blue?

A. \(1/2\)

B. \(1/3\)

Correct C. \(2/5\)

D. \(3/5\)

Correct Answer: C

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