FPMA 0901 Sultanate of Oman Applied Mathematics Applied Math Worksheet

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Sultanate of Oman
Ministry of Higher Education
University of Technology and Applied Sciences Nizwa
Assignment
SP 2021
Course
Name
Applied Mathematics
Course
Code
FPMA0901
Date
Saturday, 05/06/2021
Time
08:00 am – 06:00 pm
Student Name :
Section :
Student ID No:
General Instructions:
This assignment is for 25 Marks.
Write your Name, Registration No and place your signature on the answer sheets. Any answer
sheet without Name, Registration No, and signature will be graded zero.
No need to write the statement of a question, just write the appropriate question number.
Be clear, neat and concise.
If needed, rough work may be done at a side of the answer sheet. Rough work will not be graded.
Upload the answers of all questions in the Black Board in a single PDF file.
Any answer sheet send to e-mail of the teacher will be graded zero.
Questions
Marks Allotted
Marks Scored
Q1
Q2
Q3
Q4
Q5
5
5
5
5
5
Total
25
Q1. A ladder is placed against a wall such that it reaches the top of the wall of height 6 m and
the ladder is inclined at an angle of 60 degree and ∠𝐶𝐴𝐵 = ϕ. Find
a. How far the ladder is from the foot of the wall?
b. How far the ladder is from the top of the wall?
c. Find an angle ϕ between ladder and the wall?
d. Convert an angle ϕ in degrees to radians
Q2. The diameter of an iron ball (in the box) is given in mm. The sample of 50 iron balls
is summarized in the following frequency table:
(5)
Diameter of an iron ball (mm)
Number of iron balls
35 – 39
6
40 – 44
45 – 49
12
15
50 – 54
10
55 – 60
7
Find the mean and the variance of the iron balls in this sample.
Q3. (i) Solve for x :
a. 32𝑥 = 22𝑥−4
(3)
3
b. √𝑙𝑜𝑔2 (𝑥 − 8) + 𝑙𝑜𝑔2 (𝑥 + 8) = 64
(ii) Mr. Ahmed wants to start the savings out of the money earned by him. He decides to
deposit the initial amount of $ 22,000 into the high-interest savings account. The rate of
interest in this case is 22 % per annum compounded yearly. Currently, the age of Ahmed
is 42 years and he plans to take retirement at the age of 60 years. Calculate the amount of
money that Ahmed is going to receive at the age of 60 years.
(2)
Q4. (i) Let 𝑓: 𝑅 → 𝑅 be the quadratic function defined by 𝑓 (𝑥) = −2𝑥 2 − 6𝑥 + 8.
Complete the following statements:
(3.5)
1.
The vertex is
2.
The axis of symmetry is
3.
The range is
4.
The 𝑥 −intercepts are
5.
The 𝑦 −intercept is
6.
The minimum value of the function is
7.
The graph of the function 𝑓(𝑥)
4
3
2
1
-3
-2 -1 0
1
2
3
4 5
-2
-3
-4
(ii) Jill stands on a balcony and throws a ball to her dog, who is at ground level. The ball’s
height (in meters above the ground) 𝑥 seconds after Jill threw it, is modeled by
ℎ(𝑥) = 2𝑥2 + 4𝑥 + 16. What is the height of the ball at the time it is thrown?
Q5. (i) Prices of chocolates each (OMR.):
(1.5)
(4)
0.10, 0.19, 0.11, 0.19, 0.17, 0.12, 0.12, 0.12, 0.10, 0.11, 0.13, 0.10, 0.09, 0.11, 0.15,
0.13, 0.10, 0.18, 0.09, 0.07, 0.08, 0.06, 0.08, 0.05, 0.07, 0.08, 0.08, 0.07, 0.09, 0.06,
0.07, 0.08, 0.07, 0.07, 0.07, 0.08, 0.06, 0.07, 0.06
Using 6 class intervals with the lowest starting at 0.05
.Set up frequency distribution
Construct frequency histogram
(ii) How many ways of four-digit odd numbers can be formed from the set of digits
A= {5,6,2,7,4,9,3} if the repetition of digit is not allowed
(1)

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Explanation & Answer:
5 Questions

Tags:
frequency table

applied math

Math Problems

y intercept

Applied mathematics

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