POST UTME BSU 2024 Mathematics | Objective

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

Correct Answer: A

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Question 2 View Details
A box contains 5 red balls and 3 blue balls. If two balls are drawn at random, what is the probability that they are of different colors?
Correct A. \(\frac{5}{14}\)\)
B. \(\frac{3}{14}\)\)
C. \(\frac{2}{7}\)\)
D. \(\frac{1}{2}\)\)

Correct Answer: A

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Question 3 View Details
The volume of a cylinder is given by \(V = \pi r^2 h\). If the radius of the cylinder is increased by 20% and the height is decreased by 15%, what is the new volume?
Correct A. \(\frac{21}{16}\)\) \pi \(r^2\) h
B. \(\frac{25}{16}\)\) \pi \(r^2\) h
C. \(\frac{27}{16}\)\) \pi \(r^2\) h
D. \(\frac{29}{16}\)\) \pi \(r^2\) h

Correct Answer: A

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Question 4 View Details
The mean of a set of numbers is 25. If the set is increased by 10% and then decreased by 5%, what is the new mean?
Correct A. 24.5
B. 25.5
C. 26.5
D. 27.5

Correct Answer: A

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Question 5 View Details
A histogram of exam scores has a mean of 80 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 70 and 90?
Correct A. 0.68
B. 0.69
C. 0.70
D. 0.71

Correct Answer: A

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Question 6 View Details
Find the value of \(\int_0^1 \frac{1}{1+x^2} dx\).
Correct A. \(\frac{\pi}{4}\)\)
B. \(\frac{\pi}{2}\)\)
C. \(\frac{\pi}{3}\)\)
D. \(\frac{\pi}{6}\)\)

Correct Answer: A

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Question 7 View Details
Solve for \(x\): \(\log_2 x + \log_2 x-1\)\(= 2\)\).
A. 3
B. 4
Correct C. 5
D. 6

Correct Answer: C

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Question 8 View Details
Find the area of the region bounded by the curves \(y = x^2\) and \(y = 2x\).
A. \(\frac{1}{3}\)\)
Correct B. \(\frac{2}{3}\)\)
C. 1
D. 2

Correct Answer: B

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Question 9 View Details
Solve for \(x\): \(\sin^2 x + \cos^2 x = 1\).
Correct A. \(x =\)\(\frac{\pi}{4}\)\)
B. \(x =\)\(\frac{\pi}{2}\)\)
C. \(x =\)\(\frac{3\pi}{4}\)\)
D. \(x =\)\pi

Correct Answer: A

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Question 10 View Details
Find the value of \(\frac{d}{dx} \left \frac{1}{x} \right\)\).
Correct A. -\(\frac{1}{x^2}\)\)\)
B. \(\frac{1}{x^2}\)\)\)
C. -\(\frac{1}{x}\)\)
D. \(\frac{1}{x}\)\)

Correct Answer: A

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Question 11 View Details
Find the area under the curve \(y = \frac{1}{2}x^2 + 3x - 2\) from \(x = 0\) to \(x = 4\).
A. 40
B. 50
Correct C. 60
D. 70

Correct Answer: C

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Question 12 View Details
Solve the matrix equation \(\begin{bmatrix} 2 & 1 \ 1 & 3 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 5 \ 7 \end{bmatrix}\).
Correct A. \begin{bmatrix} 1 \ 2 \end{bmatrix}
B. \begin{bmatrix} 2 \ 1 \end{bmatrix}
C. \begin{bmatrix} 3 \ 4 \end{bmatrix}
D. \begin{bmatrix} 4 \ 3 \end{bmatrix}

Correct Answer: A

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Question 13 View Details
A histogram of exam scores has a mean of 60 and a standard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 50 and 70?
A. 0.68
Correct B. 0.85
C. 0.95
D. 0.99

Correct Answer: B

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Question 14 View Details
A right circular cone has a radius of 6 cm and a height of 8 cm. Find the volume of the cone.
A. 288\pi
Correct B. 384\pi
C. 480\pi
D. 576\pi

Correct Answer: B

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Question 15 View Details
Solve the trigonometric equation \(\sin^2 x + \cos^2 x = 1\).
Correct A. \(x =\)\(\frac{\pi}{4}\)\)
B. \(x =\)\(\frac{\pi}{2}\)\)
C. \(x =\)\(\frac{3\pi}{4}\)\)
D. \(x =\)\pi

Correct Answer: A

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Question 16 View Details
In the diagram below, the graph of \(y = \frac{1}{2} $12x \\) ) is shown. What is the amplitude of the graph?
A. 1
Correct B. 0.5
C. 2
D. 0.25

Correct Answer: B

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Question 17 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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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
A right-angled triangle has sides of length ( 3 ), ( 4 ), and ( 5 ). Find the area of the triangle.
Correct A. 6
B. 8
C. 10
D. 12

Correct Answer: A

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Question 20 View Details
Solve the equation \(x^2 - 4x + 4 = 0\).
Correct A. \(x = 2\)
B. \(x = 1\)
C. \(x = 3\)
D. \(x = 4\)

Correct Answer: A

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Question 21 View Details
Solve for x in the equation \(\frac{1}{x} + \frac{1}{x+1} = \frac{1}{2}\).
A. \(x = 2\)
B. \(x = -1\)
Correct C. \(x = 1\)
D. \(x = -2\)

Correct Answer: C

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Question 22 View Details
Find the volume of the frustum of a cone with height 10 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. \(V = 100\)\pi \(cm^3\)
B. \(V = 200\)\pi \(cm^3\)
Correct C. \(V = 300\)\pi \(cm^3\)
D. \(V = 400\)\pi \(cm^3\)

Correct Answer: C

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Question 23 View Details
A set of 5 consecutive integers has a median of 8. What is the sum of the integers?
A. 40
B. 50
Correct C. 60
D. 70

Correct Answer: C

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Question 24 View Details
A right triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.
Correct A. 8 cm
B. 6 cm
C. 4 cm
D. 2 cm

Correct Answer: A

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Question 25 View Details
A sequence is defined recursively as (a_\(n = 2a\)_{n-1} + 1\), where \(a_1 = 3\\((a_n = 2a_{n-1} + 1), where\). Find the value of \(a_{10}\).
A. 1023
Correct B. 1025
C. 1027
D. 1029

Correct Answer: B

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