POST UTME COVENANT UNIVERSITY 2017 Mathematics | Objective

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Question 1 View Details
In a certain number base, the number 1011 is equivalent to 11 in base 10. What is the value of the number base?
Correct A. 6
B. 8
C. 10
D. 12

Correct Answer: A

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Question 2 View Details
Solve for x in the equation \(\sin^2 x \\) + \\(\cos^2(x)\)\(= 1 ).\)
Correct A. \(x = \frac{\pi}{4}\)
B. \(x = \frac{\pi}{2}\)
C. \(x = \frac{\pi}{3}\)
D. \(x = \frac{\pi}{6}\)

Correct Answer: A

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Question 3 View Details
A polynomial function f(x) has a degree of 3 and a leading coefficient of 2. If f\(-2 = -23\), find the value of f(1).
Correct A. -5
B. -3
C. -1
D. 1

Correct Answer: A

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Question 4 View Details
A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If a marble is drawn at random, what is the probability that it is not blue?
Correct A. \(\frac{1}{2}\)\)
B. \(\frac{2}{3}\)\)
C. \(\frac{3}{4}\)\)
D. \(\frac{4}{5}\)\)

Correct Answer: A

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Question 5 View Details
A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. What is the volume of the prism?
Correct A. 30 \(cm^3\)
B. 40 \(cm^3\)
C. 50 \(cm^3\)
D. 60 \(cm^3\)

Correct Answer: A

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Question 6 View Details
Determine the volume of the frustum of a cone with a height of 15 cm, a lower base radius of 4 cm, and an upper base radius of 6 cm.
A. 300\pitext{ cm}^3
B. 400\pitext{ cm}^3
Correct C. 500\pitext{ cm}^3
D. 600\pitext{ cm}^3

Correct Answer: C

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Question 7 View Details
Find the area under the curve of the function f(x) = \(2x^2 + 3x - 1\) from \(x = 0\) to \(x = 2\).
A. 17
Correct B. 19
C. 21
D. 23

Correct Answer: B

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Question 8 View Details
A set of 10 consecutive integers has a mean of 12. Find the sum of the integers.
A. 120
B. 130
Correct C. 140
D. 150

Correct Answer: C

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Question 9 View Details
Find the surface area of the sphere with a radius of 5 cm.
A. 50\pitext{ cm}^2
Correct B. 100\pitext{ cm}^2
C. 150\pitext{ cm}^2
D. 200\pitext{ cm}^2

Correct Answer: B

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Question 10 View Details
A number is 5 times the sum of its digits. If the number is divisible by 3, what is the sum of its digits?
A. 3
B. 4
Correct C. 5
D. 6

Correct Answer: C

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Question 11 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.
Correct A. \(\frac{32\pi}{5}\)\)
B. \(\frac{64\pi}{5}\)\)
C. \(\frac{128\pi}{5}\)\)
D. \(\frac{256\pi}{5}\)\)

Correct Answer: A

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Question 12 View Details
If f(x) = \(\frac{1}{x^2 + 1}\)\)\), find f'(x) 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. \(\frac{2}{x^2 + 1\) ^2}\)\)

Correct Answer: A

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Question 13 View Details
Solve the equation \\(\sin^2\) x + \\(\cos^2\) \(x = 1\) for x in the interval [0, 2\pi].
Correct A. \(x =\)\(\frac{\pi}{4}\)\)
B. \(x =\)\(\frac{3\pi}{4}\)\)
C. \(x =\)\(\frac{5\pi}{4}\)\)
D. \(x =\)\(\frac{7\pi}{4}\)\)

Correct Answer: A

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Question 14 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 + \(y - 3\)^\(2 = 9\)
C. \(x - 2\)^2 + \(y - 3\)^\(2 = 25\)
D. \(x - 2\)^2 + \(y - 3\)^\(2 = 36\)

Correct Answer: A

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Question 15 View Details
A circle has equation \(x^2\) + \\((y^2) = 25.\) Find the length of the arc intercepted by the line \(y = x\\() = 25.) Find the length of the arc intercepted by the line\).
Correct A. \(\frac{\pi}{2}\)\)
B. \(\frac{\pi}{4}\)\)
C. \(\frac{\pi}{6}\)\)
D. \(\frac{\pi}{8}\)\)

Correct Answer: A

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Question 16 View Details
Find the derivative of the function ( f(x) = \(\frac{1}\){\sqrt{1 - \(x^2}}\)\) ) using the chain rule.
Correct A. f'\((x) =\)\(\frac{x}\){ 1 - \(x^2\) \)^{\(3/2\)}}\)
B. f'\((x) =\)\(\frac{-x}\){ 1 - \(x^2\) \)^{\(3/2\)}}\)
C. f'\((x) =\)\(\frac{1}\){ 1 - \(x^2\) \)^{\(3/2\)}}\)
D. f'\((x) =\)\(\frac{-1}\){ 1 - \(x^2\) \)^{\(3/2\)}}\)

Correct Answer: A

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Question 17 View Details
Solve the inequality \(2x^2 + 5x - 3 > 0\).
Correct A. \(-∞, -1\) ∪ (3, ∞)
B. \(-∞, -3\) ∪ (1, ∞)
C. \(-∞, 1\) ∪ (3, ∞)
D. \(-∞, -3\) ∪ (1, ∞)

Correct Answer: A

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Question 18 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 19 View Details
Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).
Correct A. 6
B. 12
C. 18
D. 24

Correct Answer: A

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Question 20 View Details
Find the derivative of the function ( f(x) = \(x^2\) \sin x ) using the product rule.
Correct A. f'\((x) = 2x\)\sin x + \(x^2\) \cos x
B. f'\((x) =\)\(x^2\) \cos x - 2x \sin x
C. f'\((x) = 2x\)\cos x + \(x^2\) \sin x
D. f'\((x) =\)\(x^2\) \sin x - 2x \cos x

Correct Answer: A

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Question 21 View Details
Find the area under the curve of ( f(x) = \(\frac{1}{x^2}\)\)\) ) from \(x = 1\) to \(x = 2\).
A. 1
B. 2
Correct C. 3
D. 4

Correct Answer: C

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Question 22 View Details
Solve for ( x ) in the equation \(2x^2 + 5x - 3 = 0\).
A. 1
Correct B. 2
C. 3
D. 4

Correct Answer: B

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Question 23 View Details
Find the value of (\(12x \\) ) given that \\((\)12x \(\(1x \\) = \(\frac{3}{5}\)\) ) and 1x \\) = \(\frac{4}{5}\)\) ).
A. 1
B. 2
C. 3
Correct D. 4

Correct Answer: D

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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. 20
Correct C. 25
D. 30

Correct Answer: C

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Question 25 View Details
A matrix is given by \(A = \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix}\). Find the determinant of the matrix.
A. 1
B. 2
C. 3
Correct D. 4

Correct Answer: D

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