POST UTME GREENFIELD UNIVERSITY 2019 Mathematics | Objective

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Question 1 View Details
Determine the value of x in the equation \(\frac{x}{2} + 5 = 11\).
Correct A. 6
B. 7
C. 8
D. 9

Correct Answer: A

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Question 2 View Details
A histogram is constructed with the following data: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. What is the class width?
A. 2
Correct B. 4
C. 6
D. 8

Correct Answer: B

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Question 3 View Details
Solve the quadratic equation \(x^2 + 5x + 6 = 0\).
A. -2
Correct B. -3
C. -4
D. -5

Correct Answer: B

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Question 4 View Details
Find the sum of the first 10 terms of the arithmetic progression 2, 5, 8, 11, ...
Correct A. 55
B. 60
C. 65
D. 70

Correct Answer: A

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Question 5 View Details
A set of numbers has a mean of 10 and a standard deviation of 2. What is the probability that a randomly selected number from this set is greater than 12?
A. 0.25
B. 0.5
C. 0.75
Correct D. 0.9

Correct Answer: D

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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} ].
A. -120
B. 120
Correct C. 0
D. -60

Correct Answer: C

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Question 7 View Details
If f(x) = \(3x^2 + 2x - 5\), find f'(x) using the chain rule.
Correct A. 6x + 2
B. 6x + 2 - 5
C. 6x + 2
D. 6x + 2 - 5

Correct Answer: A

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Question 8 View Details
A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find its volume.
Correct A. 30
B. 60
C. 30
D. 60

Correct Answer: A

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Question 9 View Details
Two events A and B are independent. If P(A) = 0.4 and P(B) = 0.6, find P(\(A \cap B\)).
Correct A. 0.24
B. 0.24
C. 0.24
D. 0.24

Correct Answer: A

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Question 10 View Details
Find the equation of the circle with center (2, 3) and radius 4.
A. \(x - 2\)^2 + \(y - 3\)^\(2 = 16\)
B. \(x - 2\)^2 + \(y - 3\)^\(2 = 4\)
Correct C. \(x - 2\)^2 + \(y - 3\)^\(2 = 16\)
D. \(x - 2\)^2 + \(y - 3\)^\(2 = 4\)

Correct Answer: C

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

Correct Answer: A

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

Correct Answer: C

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Question 13 View Details
Find the area under the curve \(y = $1x\) from \(x = 0\) to \(x = \frac{\pi}{2}\).
A. ( 1 )
Correct B. \(\frac{1}{2}\)
C. \(\frac{\pi}{2}\)
D. ( pi )

Correct Answer: B

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Question 14 View Details
Solve the inequality \(\frac{x^2 - 4}{x^2 - 9} > 0\).
Correct A. x in \( -infty, -3 \ cup (1, infty) )
B. x in \( -infty, -3 \ cup (3, infty) )
C. x in \( -infty, -1 \ cup (1, infty) )
D. x in \( -infty, -1 \ cup (3, infty) )

Correct Answer: A

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Question 15 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 16 View Details
Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 5 & 2 \ 1 & 2 & 3 \end{pmatrix} ].
Correct A. 18
B. -18
C. 20
D. -20

Correct Answer: A

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Question 17 View Details
A histogram of exam scores has a mean of 75 and a standard deviation of 10. What is the probability that a randomly selected score is between 60 and 90?
Correct A. 0.68
B. 0.95
C. 0.99
D. 0.999

Correct Answer: A

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Question 18 View Details
Find the volume of the solid formed by revolving the region bounded by the curves \(y = x\^2\) and \(y = 4 - x\^2\) 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 19 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?
Correct A. \(\frac{2}{3}\)\)
B. \(\frac{3}{5}\)\)
C. \(\frac{5}{8}\)\)
D. \(\frac{7}{10}\)\)

Correct Answer: A

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Question 20 View Details
Find the area under the curve \(y = x\^3\) from \(x = 0\) to \(x = 2\).
A. 8
Correct B. 16
C. 32
D. 64

Correct Answer: B

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Question 21 View Details
If \(\vec{a} = egin{pmatrix} 2 \ 3 \end{pmatrix}\) and \(\vec{b} = egin{pmatrix} -1 \ 4 end{pmatrix}\), find the unit vector in the direction of \(\\(end{pmatrix}), find the unit vector in the direction of \vec{a} + \vec{b}\).
Correct A. \begin{pmatrix} \(\frac{1}\){\(\sqrt{26}\)}\) \\ \(\frac{3}\){\(\sqrt{26}\)}\) \end{pmatrix}
B. \begin{pmatrix} \(\frac{1}\){\(\sqrt{26}\)}\) \\ -\(\frac{3}\){\(\sqrt{26}\)}\) \end{pmatrix}
C. \begin{pmatrix} -\(\frac{1}\){\(\sqrt{26}\)}\) \\ \(\frac{3}\){\(\sqrt{26}\)}\) \end{pmatrix}
D. \begin{pmatrix} -\(\frac{1}\){\(\sqrt{26}\)}\) \\ -\(\frac{3}\){\(\sqrt{26}\)}\) \end{pmatrix}

Correct Answer: A

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Question 22 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 23 View Details
Find the equation of the circle with center at ( (2, 3) ) and radius ( 4 ).
A. \(x - 2\)^2 + \(y - 3\)^\(2 = 16\)
B. \(x - 2\)^2 + \(y - 3\)^\(2 = 25\)
Correct C. \(x - 2\)^2 + \(y - 3\)^\(2 = 36\)
D. \(x - 2\)^2 + \(y - 3\)^\(2 = 49\)

Correct Answer: C

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Question 24 View Details
If ( f(x) = \(2x^2 + 3x - 1\) ), find the derivative of ( f(x) ) using the power rule.
Correct A. f'\((x) = 4x + 3\)
B. f'\((x) =\)\(4x^2 + 3\)
C. f'\((x) = 2x + 3\)
D. f'\((x) =\)\(2x^2 + 3x\)

Correct Answer: A

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Question 25 View Details
Solve the inequality \(2x^2 + 5x - 3 > 0\).
Correct A. x < -1 or x > \(\frac{3}{2}\)\)
B. x < -1 or x < \(\frac{3}{2}\)\)
C. x > -1 or x > \(\frac{3}{2}\)\)
D. x > -1 or x < \(\frac{3}{2}\)\)

Correct Answer: A

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