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Principles Of Marketing Question Paper
Principles Of Marketing
Course:Bachelor Of Commerce
Institution: Strathmore University question papers
Exam Year:2005
STRATHMORE UNIVERSITY
FACULTY OF COMMERCE
Bachelor of Commerce
END OF SEMESTER EXAMINATION
MAT 1101: BUSINES MATHEMATICS I
DATE: 19th October 2005 TIME: 2 Hours
INSTRUCTIONS: ANSWER QUESTION ONE AND ANY OTHER TWO
QUESTIONS
Question 1 (30 marks)
(a) List the elements in the following sets:
(i) The set A of positive prime numbers less than or equal to 31.
(ii) The set B ={x | x2 + x -12 = 0, xÎR,}
(iii) The set C consisting of letters in the word SUBSET. (6 marks)
(b) (i) Define clearly the term: “rational number”.
(ii) Show that 3 is an irrational number. (6 marks)
(c) Define clearly the term “function”.
Given 2 ( ) (1 2 )
f x x = - x , and g(x) = x - 5 , find the following
composite functions:
(i) f (g(x)) , (ii) g( f (x)) , (iii) f (g(-5)) (6 marks)
(d) Use Gaussian elimination method to solve the following:
5 20 25
4 7 26
x y
x y
(6 marks)
(e) Solve the following:
(i) e-5x = 80
(ii) ln(x + 2) + ln x = ln 24 (6 marks)
Question 2 (20 marks)
(a) Show without using Venn diagram that
(AÈB)¢ = A¢ÇB¢ (6 marks)
2
(b) A recent survey to determine drag usage gave the following result:
· 10 people tried both marijuana and hard drags
· 90 people tried marijuana
· 20 people tried hard drags
Let M = the set of people who tried marijuana
H = the set of people who tried hard drags
(i) Display the survey results on a Venn diagram
(ii) How many tried marijuana or hard drags but not both.
(iii) Find n(Mc ÇHc ) and n(M ÇHc ) (8 marks)
(c) The revenue from selling a particular products upon the price charged per unit
. Specifically the revenue function in:
R =1500 p - 50 p2 .
(i) What type of equation is this?
(ii) What is the total revenue expected to be if the price per unit is £10
(iii) What price(s) would result in total revenue equalling zero (6 marks)
Question 3 (20 marks)
(a) Define the term: “Modulus of x”. Hence or otherwise solve the
following for x:
(i) x = -x + 5
(ii) 3x -5 > 4 (6 marks)
(b) State the “Principle of Mathematical Induction”. Use it to show that
(i) 4 +8 +12 +...+ 4n = 2n, for all n ³1
(ii) 2n > n, for all n ³1 (8 marks)
(c) The Red Cross wants to airlift supplies into Southern Sudan, which has
experienced a severe drought. Four types of supplies, each of which would be
shipped in containers, are being considered. One container of a particular item
weighs 150, 250, 300 and 400 kilograms respectively, for the four items. If
the airplane to be used has a weight capacity of 60,000 kilograms and j x
equals the number of containers shipped of items j ( j =1,2,3,4):
(i) Determine the equation which ensures that the plane will be loaded to
its weight capacity.
(ii) If it is decided to devote this plane to one supply item only, how many
containers could be shipped of each item? (6 marks)
3
Question 4 (20 marks)
(a) Solve the following equations:
(i)
45x-x2 = 4-6
(ii) ln(x2 + 3) + ln x2 =1 (6 marks)
(b) An investment of £200,000 is made which earns interest at the rate of 8%
per year. If the interest is compounded continuously.
(i) Determine the exponential function which states the compound amount as a
function of years of investment t:
(ii) What will the £200,000 grow to if it is invested for 5 years?
(iii) Determine the length of time required for the investment to double in value.
(9 marks)
(c) How many years (to 2 decimal places) will it take £5,000 to grow to £7,500 if it
is invested at 8% compounded continuously. (5 marks)
Question 5 (20 marks)
(a) Use Gaussian elimination to solve the following system:
1 2 3
1 2 3
1 2 3
3 2 2
2 3
2 3 3
x x x
x x x
x x x
+ - =
- + =
- - =
(8 marks)
(b) Find the sum of all even integers between 13 and 70 (5 marks)
(c) If you borrow K£4800 and repay the loan by paying K£200 per month
to reduce the loan, and 1% of the unpaid balance each month for the use of
the money. What is the total cost of the loan over 24 months? (7 marks)
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