POST UTME NILE UNIVERSITY 2018 Mathematics | Objective

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Question 1 View Details
Find the area under the curve \(y = \frac{1}{2}x^2 + 3x - 2\) from \(x = 0\) to \(x = 4\).
Correct A. 24
B. 28
C. 30
D. 32

Correct Answer: A

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

Correct Answer: D

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Question 3 View Details
A fair six-sided die is rolled. What is the probability that the number obtained is a multiple of 3?
Correct A. \(1/6\)
B. \(1/3\)
C. \(2/3\)
D. \(5/6\)

Correct Answer: A

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Question 4 View Details
Find the derivative of the function ( f(x) = \(\frac{1}{x^2 + 1}\)\)\) ) using the chain rule.
A. \(\frac{-2x}{x^2 + 1\) ^2}\)\)
Correct B. \(\frac{2x}{x^2 + 1\) ^2}\)\)
C. \(\frac{-x}{x^2 + 1\) ^2}\)\)
D. \(\frac{x}{x^2 + 1\) ^2}\)\)

Correct Answer: B

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Question 5 View Details
A random variable ( X ) has a probability density function (pdf) given by ( f(x) = \(\frac{1}{2}\)\\()e^{-\)|x|} ). Find the probability that ( X ) is greater than 1.
Correct A. \(1/4\)
B. \(1/2\)
C. \(3/4\)
D. 1

Correct Answer: A

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Question 6 View Details
Find the equation of the line passing through the points ((2,3)) and \(-1,4 \\)).
Correct A. \(y = -x + 5\)
B. \(y = x + 1\)
C. \(y = -2x + 7\)
D. \(y = 2x - 3\)

Correct Answer: A

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Question 7 View Details
A histogram of exam scores is shown below. What is the mean score of the exam?
A. 25
B. 30
Correct C. 35
D. 40

Correct Answer: C

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Question 8 View Details
Solve for ( x ) in the equation \(2^x + 5^x = 7^x\).
A. \(x = 2\)
Correct B. \(x = 3\)
C. \(x = 4\)
D. \(x = 5\)

Correct Answer: B

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Question 9 View Details
Find the equation of the circle with center ( (3,4) ) and radius ( 5 ).
Correct A. \(x - 3 \\)^2 + \(y - 4\)^\(2 = 25\) )
B. \(x - 4 \\)^2 + \(y - 3\)^\(2 = 25\) )
C. \(x - 3 \\)^2 + \(y - 4\)^\(2 = 16\) )
D. \(x - 4 \\)^2 + \(y - 3\)^\(2 = 16\) )

Correct Answer: A

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Question 10 View Details
A polynomial function is defined as ( f(x) = \((ax^3 + bx^2 + cx + d\)\) ). If \(f -1 \\((ax^3 + bx^2 + cx + d) ). If \\)\(= 2 )\),\(( f(1) = 4 )\), and ( f(2) = 12 ), find the value of \(a + b + c + d\).
A. ( 10 )
B. ( 12 )
Correct C. ( 14 )
D. ( 16 )

Correct Answer: C

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Question 11 View Details
Let \(X\) and \(Y\) be independent random variables with probability density functions \(f_X(x) = egin{cases} 2x & 0 \leq x \leq 1 \ 0 & \text{otherwise} \end{cases}\) and \(f_Y(y) = egin{cases} 3y^2 & 0 \leq y \leq 1 \ 0 & \text{otherwise} end{cases}\). Find the probability that \(X + Y \\(end{cases}). Find the probability that \leq 1\).
Correct A. \(\frac{1}{4}\)\)
B. \(\frac{1}{2}\)\)
C. \(\frac{3}{4}\)\)
D. \(\frac{5}{8}\)\)

Correct Answer: A

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Question 12 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. \(x + 2\)^2 + \(y + 3\)^\(2 = 16\)
D. \(x + 2\)^2 + \(y + 3\)^\(2 = 4\)

Correct Answer: A

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Question 13 View Details
If \(f(x) = egin{cases} x^2 & x \geq 0 \ 0 & x < 0 end{cases}\), find \(f'(x)\\(end{cases}), find\).
Correct A. 2x
B. \(x^2\)
C. 0
D. \(x^3\)

Correct Answer: A

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Question 14 View Details
Solve the inequality \(\frac{x^2 - 4}{x + 2} \geq 0\).
Correct A. \(-\infty, -2\) \cup [0, \infty)
B. \(-\infty, -2\) \cup \(0, \infty\)
C. \(-\infty, -2\) \cup [2, \infty)
D. \(-\infty, -2\) \cup \(-2, \infty\)

Correct Answer: A

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Question 15 View Details
Find the mean of the data set \(\{2, 4, 6, 8, 10 \}\).
Correct A. 4
B. 5
C. 6
D. 7

Correct Answer: A

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Question 16 View Details
Find the area under the curve \(y = \frac{1}{2}x^2 + 3x - 2\) from \(x = 0\) to \(x = 4\).
A. 24
B. 30
Correct C. 36
D. 40

Correct Answer: C

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Question 17 View Details
A rectangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find its volume.
Correct A. 72
B. 80
C. 90
D. 100

Correct Answer: A

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Question 18 View Details
Find the derivative of the function \(y = \sqrt{x^2 + 1}\) using the chain rule.
Correct A. \(\frac{x}\){\sqrt{\(x^2 + 1}}\)\)
B. \(\frac{1}{2}\)\) \(\sqrt{x^2 + 1}\)\)
C. \(\frac{x^2}\)\){\sqrt{\(x^2 + 1}}\)\)
D. \(\frac{1}{x^2 + 1}\)\)\)

Correct Answer: A

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Question 19 View Details
Solve the inequality \(2x^2 - 5x - 3 > 0\).
Correct A. \(-∞, -1\) ∪ (3, ∞)
B. \(-∞, 1\) ∪ (3, ∞)
C. \(-∞, -1\) ∪ (1, ∞)
D. \(-∞, 3\) ∪ (5, ∞)

Correct Answer: A

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Question 20 View Details
A circle has a radius of 4 cm. Find its circumference.
A. 8\pi
B. 10\pi
Correct C. 12\pi
D. 16\pi

Correct Answer: C

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Question 21 View Details
In a survey of 100 students, the mean height was 175 cm with a standard deviation of 5 cm. If the heights of the students are normally distributed, what is the probability that a randomly selected student will be taller than 180 cm?
A. 0.1587
B. 0.3413
C. 0.5
Correct D. 0.8413

Correct Answer: D

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Question 22 View Details
A rectangular prism has a length of 10 cm, a width of 5 cm, and a height of 8 cm. What is the volume of the prism in cubic centimeters?
Correct A. 400
B. 500
C. 600
D. 800

Correct Answer: A

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Question 23 View Details
Solve the quadratic equation \(x^2 + 4x + 4 = 0\)
Correct A. -2
B. 0
C. 2
D. 4

Correct Answer: A

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Question 24 View Details
A set 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 will be less than 70?
A. 0.1587
B. 0.3413
Correct C. 0.5
D. 0.8413

Correct Answer: C

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Question 25 View Details
A rectangular garden has a length of 15 m and a width of 8 m. If a path that is 2 m wide is built around the garden, what is the area of the path?
A. 48
B. 64
C. 80
Correct D. 96

Correct Answer: D

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