POST UTME BELLS UNIVERSITY 2017 Mathematics | Objective

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

Correct Answer: A

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Question 2 View Details
A particle moves along the x-axis with its position given by ( x(t) = \((2t^3 - 5t^2 + 3t + 1\)\) ). Find the velocity of the particle at time \(t = 2\\((2t^3 - 5t^2 + 3t + 1) ). Find the velocity of the particle at time\) seconds.
Correct A. \(12t^2 - 10t + 3\)
B. \(6t^2 - 10t + 3\)
C. \(12t^2 - 10t - 3\)
D. \(6t^2 - 10t - 3\)

Correct Answer: A

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Question 3 View Details
Find the area under the curve \(y = x^2 - 4x + 3\) from \(x = 1\) to \(x = 3\).
A. \(\frac{2}{3}\)
Correct B. \(\frac{4}{3}\)
C. \(\frac{6}{3}\)
D. \(\frac{8}{3}\)

Correct Answer: B

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Question 4 View Details
Solve the system of equations \(egin{cases} x + y = 2 \ 2x - y = 3 \end{cases}\).
Correct A. \(x = 1, y = 1\)
B. \(x = 2, y = 0\)
C. \(x = 0, y = 2\)
D. \(x = 1, y = 2\)

Correct Answer: A

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Question 5 View Details
Find the determinant of the matrix \(egin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 1 & 3 & 2 \end{bmatrix}\).
Correct A. ( 0 )
B. ( 1 )
C. ( 2 )
D. ( 3 )

Correct Answer: A

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Question 6 View Details
Find the determinant of the matrix [ egin{pmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{pmatrix} ].
Correct A. 0
B. 1
C. 2
D. 3

Correct Answer: A

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Question 7 View Details
A histogram is constructed with 5 classes of equal width. The first class has a frequency of 5, the second class has a frequency of 7, the third class has a frequency of 3, the fourth class has a frequency of 2, and the fifth class has a frequency of 4. What is the mean of the histogram?
A. 4
Correct B. 5
C. 6
D. 7

Correct Answer: B

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Question 8 View Details
Find the volume of the solid formed by revolving the region bounded by the parabola (y = x\^2\), the x-axis, and the line \\((y = x^2\(x = 2\) about the x-axis.
Correct A. 32\pi
B. 64\pi
C. 128\pi
D. 256\pi

Correct Answer: A

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Question 9 View Details
A circle with center (0, 0) and radius 4 passes through the point (3, 4). What is the equation of the circle?
Correct A. \(x - 0\)^2 + \(y - 0\)^\(2 = 16\)
B. \(x - 3\)^2 + \(y - 4\)^\(2 = 16\)
C. \(x - 0\)^2 + \(y - 0\)^\(2 = 9\)
D. \(x - 3\)^2 + \(y - 4\)^\(2 = 9\)

Correct Answer: A

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Question 10 View Details
Find the mean deviation of the data set {2, 4, 6, 8, 10} about the mean.
A. 4
Correct B. 6
C. 8
D. 10

Correct Answer: B

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Question 11 View Details
Find the derivative of the function ( f(x) = \(\frac{1}\){\sqrt{\(x^2 + 1}}\)\) ) using the chain rule.
Correct A. f'\((x) =\)\(\frac{-x}\){ \(x^2 + 1\) \)^{\(3/2\)}}\)
B. f'\((x) =\)\(\frac{x}\){ \(x^2 + 1\) \)^{\(3/2\)}}\)
C. f'\((x) =\)\(\frac{1}\){ \(x^2 + 1\) \)^{\(3/2\)}}\)
D. f'\((x) =\)\(\frac{-1}\){ \(x^2 + 1\) \)^{\(3/2\)}}\)

Correct Answer: A

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Question 12 View Details
Solve the inequality \(2^x > 3^x\) for ( x ).
Correct A. \(x < 0\)
B. \(x > 0\)
C. \(x < 1\)
D. \(x > 1\)

Correct Answer: A

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Question 13 View Details
Find the volume of the solid formed by revolving the region bounded by the curves \(y = x^2\) and \(y = 2x\) about the x-axis.
Correct A. \(\frac{4}{3}\)\)\pi
B. \(\frac{2}{3}\)\)\pi
C. \(\frac{1}{3}\)\)\pi
D. \(\frac{1}{2}\)\)\pi

Correct Answer: A

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Question 14 View Details
Find the derivative of the function ( f(x) = \\(\sin^2\) x ) using the chain rule.
Correct A. f'\((x) = 2\)\sin x \cos x
B. f'\((x) =\)\sin x \cos x
C. f'\((x) =\)\cos x
D. f'\((x) =\)\sin x

Correct Answer: A

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Question 15 View Details
Solve the equation \(x^3 + 2x^2 - 7x + 12 = 0\) for ( x ).
Correct A. \(x = -3\)
B. \(x = -1\)
C. \(x = 3\)
D. \(x = 4\)

Correct Answer: A

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Question 16 View Details
Find the area of the region bounded by the curves \(y = x^2\) and \(y = 2x\) for \(0 \leq x \leq 2\).
A. 4
Correct B. 6
C. 8
D. 10

Correct Answer: B

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Question 17 View Details
Find the derivative of the function ( f(x) = \(\frac{1}{x^2}\)\)\) ) using the chain rule.
Correct A. f'\((x) = -\)\(\frac{2}{x^3}\)\)\)
B. f'\((x) =\)\(\frac{2}{x^3}\)\)\)
C. f'\((x) = -\)\(\frac{1}{x^3}\)\)\)
D. f'\((x) =\)\(\frac{1}{x^3}\)\)\)

Correct Answer: A

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Question 18 View Details
Solve the inequality \(x^2 - 4x + 3 > 0\) for ( x ).
A. \(x < 1\)
Correct B. \(x > 1\)
C. \(x < 3\)
D. \(x > 3\)

Correct Answer: B

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Question 19 View Details
Solve the quadratic equation \(x^2 + 5x + 6 = 0\) using the quadratic formula.
A. \(x = -2\)
B. \(x = -3\)
Correct C. \(x = 2\)
D. \(x = 3\)

Correct Answer: C

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Question 20 View Details
Find the volume of a cylinder with radius 4 cm and height 6 cm.
A. 48\pi
B. 64\pi
Correct C. 72\pi
D. 96\pi

Correct Answer: C

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Question 21 View Details
Solve the inequality \(2x - 5 > 3\).
Correct A. \(x > 4\)
B. \(x < 4\)
C. \(x > 2\)
D. \(x < 2\)

Correct Answer: A

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Question 22 View Details
Find the surface area of a sphere with radius 5 cm.
A. 100\pi
B. 200\pi
Correct C. 300\pi
D. 400\pi

Correct Answer: C

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Question 23 View Details
Solve the equation \(x^2 + 2x - 6 = 0\) by factoring.
Correct A. \(x + 3\), \(x - 2 = 0\)\)
B. \(x + 2\), \(x - 3 = 0\)\)
C. \(x - 3\), \(x + 2 = 0\)\)
D. \(x - 2\), \(x + 3 = 0\)\)

Correct Answer: A

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Question 24 View Details
Find the area of a triangle with base 6 cm and height 8 cm.
A. 24
B. 30
Correct C. 36
D. 48

Correct Answer: C

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Question 25 View Details
Solve the inequality \(x^2 - 4x + 4 > 0\).
A. \(x > 2\)
Correct B. \(x < 2\)
C. \(x > 1\)
D. \(x < 1\)

Correct Answer: B

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