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POST UTME MADONNA UNIVERSITY 2023 Mathematics | Objective

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Question 1 View Details

In the diagram below, what is the equation of the circle with center at point A?

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

B. \(x^2 + y^2 = 9\)

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

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

Correct Answer: A

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Question 2 View Details

If the polynomial ( p(x) = \((x^3 - 6x^2 + 11x - 6\)\) ) has a factor of \(x - 1\\((x^3 - 6x^2 + 11x - 6) ) has a factor of\), what is the other factor?

Correct A. \(x^2 - 5x + 6\)

B. \(x^2 - 5x + 5\)

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

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

Correct Answer: A

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Question 3 View Details

A right circular cone has a height of 8 cm and a base radius of 4 cm. What is the volume of the cone?

A. ( 32pi ) \(cm^3\)

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

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

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

Correct Answer: C

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Question 4 View Details

In a set of 10 integers, the average of the first 5 integers is 10, and the average of the next 3 integers is 15. What is the average of all 10 integers?

A. 12

Correct B. 13

C. 14

D. 15

Correct Answer: B

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Question 5 View Details

If the matrix \(A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}\) is multiplied by the matrix \(B = egin{bmatrix} 5 & 6 \ 7 & 8 \end{bmatrix}\), what is the value of the element in the first row and second column of the product matrix?

A. 19

B. 20

Correct C. 21

D. 22

Correct Answer: C

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Question 6 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. 64\pi

B. 128\pi

Correct C. 256\pi

D. 512\pi

Correct Answer: C

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Question 7 View Details

Solve the inequality \(\frac{x^2 - 4}{x^2 - 9}\)\)\\() > 0.\)

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

B. \(-3, -1\) \cup (1, 3) \cup (4, 5)

C. \(-3, -1\) \cup (1, 3) \cup (4, 5) \cup (6, 7)

D. \(-3, -1\) \cup (1, 3) \cup (4, 5) \cup (6, 7) \cup (8, 9)

Correct Answer: A

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Question 8 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. \(\frac{x}{x^2 + 1\) ^2}\)\)

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

Correct Answer: A

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Question 9 View Details

Solve the equation \\(\sin^2\) x + \\(\cos^2\) \(x = 1\) for x in the interval [0, 2\pi].

A. \(\frac{\pi}{4}\)\)

Correct B. \(\frac{\pi}{2}\)\)

C. \(\frac{3\pi}{4}\)\)

D. \(\frac{5\pi}{4}\)\)

Correct Answer: B

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Question 10 View Details

Find the area of the region bounded by the curves \(y = x\^2\), \(y = 0\), and \(x = 2\).

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

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

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

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

Correct Answer: A

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Question 11 View Details

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

Correct A. 27

B. 30

C. 33

D. 36

Correct Answer: A

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Question 12 View Details

Solve the inequality \\((x^2 - 4x - 5\)\(> 0.\)\)

Correct A. \(-∞, -1\) ∪ (5, ∞)

B. \(-∞, -5\) ∪ (1, ∞)

C. \(-∞, 1\) ∪ (5, ∞)

D. \(-∞, -5\) ∪ (1, ∞)

Correct Answer: A

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Question 13 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 14 View Details

A die is rolled. What is the probability that the number obtained is greater than 4?

A. \(1/3\)

B. \(1/2\)

Correct C. \(2/3\)

D. \(1/6\)

Correct Answer: C

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Question 15 View Details

Find the sum of the first 10 terms of the geometric series \(3x^2 + 6x + 12\).

Correct A. \(300x^2 + 600x + 1200\)

B. \(300x^2 + 600x + 12000\)

C. \(300x^2 + 6000x + 1200\)

D. \(300x^2 + 6000x + 12000\)

Correct Answer: A

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Question 16 View Details

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

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

Correct B. f'\((x) =\)\(\frac{x^2 + 2x - 3\) 2x - 8 - \(x^2 - 4\) 2x + 2 }{ \(x^2 - 4\) ^2}\)\)

C. f'\((x) =\)\(\frac{x^2 + 2x - 3\) 2x + 8 - \(x^2 - 4\) 2x - 2 }{ \(x^2 - 4\) ^2}\)\)

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

Correct Answer: B

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Question 17 View Details

A rectangular box has dimensions 5 cm, 8 cm, and 3 cm. Find the surface area of the box.

Correct A. \(A = 2(5)(8) + 2(5)(3) + 2(8)(3)\)

B. \(A = 2(5)(8) + 2(5)(3) + 2(8)(5)\)

C. \(A = 2(5)(8) + 2(3)(8) + 2(5)(3)\)

D. \(A = 2(5)(8) + 2(3)(5) + 2(8)(3)\)

Correct Answer: A

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Question 18 View Details

The mean of a set of numbers is 25. If the sum of the numbers is 100, what is the median?

Correct A. The median is 25.

B. The median is 20.

C. The median is 30.

D. The median is 35.

Correct Answer: A

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Question 19 View Details

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

Correct A. x < -3 or x > \(\frac{1}{2}\)\)

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

C. x > -3 or x > \(\frac{1}{2}\)\)

D. x < -3 or x > \(\frac{1}{2}\)\)

Correct Answer: A

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Question 20 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. \(y = -2x + 1\)

D. \(y = -2x - 1\)

Correct Answer: A

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Question 21 View Details

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

Correct A. \(x^2\) + \\((y^2 - 6x + 4y + 7\)\(= 0\)\)

B. \(x^2\) + \\((y^2 - 4x - 2y + 3\)\(= 0\)\)

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

D. \(x^2\) + \\((y^2 + 6x - 2y + 1\)\(= 0\)\)

Correct Answer: A

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Question 22 View Details

If f(x) = \(x^3 - 6x^2 + 11x - 6\), find f'(x) using the chain rule.

Correct A. \(3x^2 - 12x + 11\)

B. \(3x^2 - 12x + 6\)

C. \(3x^2 - 12x - 11\)

D. \(3x^2 - 12x + 5\)

Correct Answer: A

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Question 23 View Details

Solve the system of equations using matrices: \(x + 2y - z = 4\),\(2x - 3y + z = -3\), \(x + y + 2z = 2\).

Correct A. [\(x = 1\), \(y = 1\), \(z = 1\)]

B. [\(x = 2\), \(y = 1\), \(z = 0\)]

C. [\(x = 1\), \(y = 2\), \(z = 0\)]

D. [\(x = 0\), \(y = 1\), \(z = 2\)]

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 \(x = 2\).

A. 10

Correct B. 12

C. 15

D. 20

Correct Answer: B

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Question 25 View Details

A car travels from city A to city B at an average speed of 60 \((km/h\)\) and returns at an average speed of 40 \(km/h\\((km/h) and returns at an average speed of 40\). What is the average speed for the round trip?

A. 48 \(km/h\)

B. 50 \(km/h\)

Correct C. 52 \(km/h\)

D. 55 \(km/h\)

Correct Answer: C

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