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Dms 101 Management Mathematics I Question Paper
Dms 101 Management Mathematics I
Course:Diploma In Business Management
Institution: Kca University question papers
Exam Year:2014
UNIVERSITY EXAMINATIONS: 2013/2014
STAGE II ORDINARY EXAMINATION FOR THE DIPLOMA IN
BUSINESS MANAGEMENT
DMS 101 MANAGEMENT MATHEMATICS I
DATE: APRIL 2014
TIME: 1 1/2 Hours
INSTRUCTION: Answer any THREE questions
QUESTION ONE: (20 MARKS)
a) Differentiate between the following terms as used in set theory:
i. Universal set and subset (2 Marks)
ii. Disjoint sets overlapping sets (2 Marks)
iii. Equivalent sets and equal sets (2 Marks)
b) A quick survey of 1,000 children in a refugee camp produced the following results:
320 children were fed on beans.
200 children were fed on rice.
450 children were fed on potatoes.
150 children were fed on beans and potatoes.
70 children were fed on beans and rice.
100 children were fed on potatoes and rice.
300 children were fed on none of the three types of food.
Required:
i. Represent the above information in the form of a venn diagram (5 Marks)
ii. The number of children who were fed on all the three types of food. (3 Marks)
iii. The number of children who were fed on exactly one of the three types of food.
(3 Marks)
iv.
The number of children who were fed on at least two types of food.
(3 Marks)
QUESTION TWO: (20 MARKS)
a) A car-leasing agency purchases new cars each year for use in the agency. The cars cost
sh.450, 000 new. They are used for three years after which they are sold for sh. 108,000. The
owner of the agency estimates that the variable costs of operating the cars, exclusive of fuel,
are sh. 4.8 per Km. cars are leased at a flat rate of sh. 9.9 per Km(fuel not
included).Required:
i. What is the break-even KMs for the 3-year period?
ii. What are the total revenue, total cost and total profit for the 3-year period if the car is
leased for 50,000KMs?
iii.
(3 Marks)
What price per KM must be charged in order to break even if the car is leased for
50,000KMs over a period of three years?
iv.
(3 Marks)
(2 Marks)
What price per KM must be charged in order to earn a profit of sh.150, 000 per car
over its 3 year if it is leased for a total of 50,000kms?
(2 Marks)
b) For a certain type of credit card the collection percentage of credit issued is an exponential
function of the time (months) since credit was issued. The function which approximates this
relationship is p=
Where:
t- Time in months
p- Percentage of debtors collected (in Sh.)
Required:
a. Calculate the percentage of debts recovered after
i. 3 months (4 Marks)
ii. 7 months (3 Marks)
b. What should be the provision for bad debts? (3 Marks)
QUESTION THREE: (20 MARKS)
a) Explain any three methods of evaluating projects giving two advantages and two
disadvantages for each.
(10 Marks)
b) ABC Companyintends to invest in two projects A and B which require initial cash outlay of
sh.60, 000 each. The two projects are mutually exclusive. The table below shows the annual
cash flow from the two projects:
year Project A
Project B
1 18000 2 18000 20000
3 18000 15000
4 18000 18000
5 18000
19000
14000
You are required to advice the management on which project to invest in using the internal rate
of return. The cost of capital of ABC is 12%.
(10 Marks)
QUESTION FOUR. : (20 MARKS)
a) Differentiate between the following terms:
i. Compounding and discounting (2 Marks)
ii. Geometric progression and arithmetic progression (2 Marks)
b) In a geometric progression the sum of the 2nd and 3rd is 6 and the sum of the 3rd and 4th is -12.
Required:
i. Find the 1st term and the common ratio. (5 Marks)
ii. Find the sum of the 1st 10 terms. (5 Marks)
c) The sum a number of consecutive terms of an arithmetic progression is -19.5, the 1st term is
16.5 and the common difference is -3.
Required: Find the number of terms.
(6 Marks)
QUESTION FIVE. : (20 MARKS)
a) Using appropriate examples differentiate between the following terms:-
i. Dependent variables and independent variables. (2 Marks)
ii. Discrete variables and continuous variables (2 Marks)
iii. Exponential growth function and decay exponential function (2 Marks)
b) The XYZ limited has a 3-year project whose initial cash outlay is Sh. 1.8 million. The project
is expected to generate Sh. 800,000, Sh. 700,000 and Sh. 1 million in year 1, 2 and 3
respectively.
The cost of capital is 12%.
Required:
Compute:
i. The Payback period (3 Marks)
ii. The Net Present Value of the project (4 Marks)
c) Profitability Index of the project
(2 Marks)
A revenue function is quadratic in nature. When x=5, R=50 whereas when x=4, R=48.
Where x is quantity sold and R is revenue.
Required:
Determine the revenue function.
(5 Marks)
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