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Cms 101: Management Mathematics I Question Paper
Cms 101: Management Mathematics I
Course:Bachelor Of Commerce
Institution: Kca University question papers
Exam Year:2009
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UNIVERSITY EXAMINATIONS: 2008/2009
FIRST YEAR STAGE 1 EXAMINATION FOR THE DEGREE OF
BACHELOR OF COMMERCE
CMS 101: MANAGEMENT MATHEMATICS I
DATE: APRIL 2009 TIME: 2 HOURS
INSTRUCTIONS: Answer question ONE and any other TWO questions
QUESTION ONE
a) Thirty books are bought for sh 10,800.Some cost sh 400 each and others cost sh 300 each.
How many books of each value are bought? (5 Marks)
b) In a recent survey of 600 students in a college ; 150 and 200 were registered for
Information technology and Business management courses respectively.60 were registered for
both courses.
Required
i) Present the above information in a venn diagram (4 Marks)
ii) Number of students registered for information technology only (2 Marks)
c) State and explain four applications of functions in business (4 Marks)
d) The 4th term of a geometric progression series is 27 and the 7th term is 729. Find the first term
and the common ratio. (5 Marks)
e) A credit union has issued a 4-year loan of ksh 500,000.Simple interest is charged at a rate of
10 % per year. The principal plus interest is to be repaid at the end of the 4th year. Compute
the interest and the total amount to be repaid at the end of the 4th year. (4 Marks)
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f) A major Bank offers a credit card which can be used domestically and internationally. Data
gathered over time indicate that the collection percentage for the credit issued in any month is
a function of the time,t, since the credit was issued. Specifically the relationship can be
approximated by the function P= 0.9( 1- e-0.08t ) where t =0 and P is the percentage of accounts
receivable collected t months after the credit is granted.
Required
i) What percentage is expected to be collected after 1 month? (2 Marks)
ii) What percentage is expected to be collected after 3 month? (2 Marks)
iii) What value does P approach to as t increases without limit? (2 Marks)
QUESTION TWO
Apex ltd is planning to launch a new product next year. It has carried out a survey on the products
prototype’s colour, brand name and packaging. 200 potential customers were given questionnaires and
were requested to indicate their liking or otherwise of each of the three attributes of the product. Their
responses were as follows:
i) 24 persons liked the packaging and brand name.
ii) 77 persons liked the brand name or the colour but not packaging.
iii) 40 persons liked the colour only.
iv) 120 persons liked the brand name or the colour.
v) 23 persons liked the colour and the packaging
vi) 43 persons liked at least two attributes.
vii) 5 persons did not like any of the three attributes
viii) 25 of the customers did not return the questionnaires
The company accepted an attribute to be incorporated in the product if at least 50% of those who
responded to the questionnaire liked it.
Required
a) Present the above information in a venn diagram (7 Marks)
b) The number of persons that liked all the three attributes (2 Marks)
c) Proportion of persons that liked the colour (3 Marks)
d) Proportion of persons that liked the brand name (3 Marks)
e) Proportion of persons that liked the packaging (3 Marks)
f) Attribute or attributes to be incorporated (2 Marks)
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QUESTION THREE
a) State three assumptions that underlie break-even analysis. (3 Marks)
b) Express limited, a manufacturing company, is considering an expansion of its current plant
capacity. The current fixed costs amount to sh.58.8 million and are expected to increase by
sh.17.5 million after the expansion. The current variable costs amount to sh.770 per unit and
are expected to reduce by sh. 126 per unit after the expansion. The current production capacity
is 160,000 units per annum and is expected to increase by 50% after the expansion. The
current selling price per unit is sh2,240 and is expected to remain unchanged after the
expansion. The targeted profit for the year is sh.210 million.
Required
i) The break even number of units before the expansion. (3 Marks)
ii) The break even number of units after the expansion. (4 Marks)
iii) Determine whether the targeted profit is achievable before the expansion.
(4 Marks)
iv) Determine whether the targeted profit is achievable after the expansion.
(3 Marks)
v) If the targeted profit is exceeded by 20% after the expansion, determine
the revenue realized by the company. (3 Marks)
QUESTION FOUR
a) Differentiate between arithmetic progression and geometric progression sequences. (4 Marks)
b) John Kimeu was recently employed by Maarifa consultants as an accountant with an initial
basic salary of sh.50,000 per month. The company has in place two salary schemes A and B.
Salary scheme A entails an annual salary increase of sh.90,000 at the end of each year of
service. Salary scheme B entails an annual increase of 10% of the previous year’s basic salary.
Required
i) Initial basic salary for the first year (2 Marks)
ii) Annual salary for year 3 of employment under scheme A (3 Marks)
iii) Annual salary for year 3 of employment under scheme B (3 Marks)
iv) The total basic salary to be earned by John Kimeu during a 30-year working life under
scheme A (4 Marks)
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v) The total basic salary to be earned by John Kimeu during a 30-year working life under
scheme B (4 Marks
QUESTION FIVE
a) Mary Mumbi owes Mary otieno sh.81,648 to be repaid in two years time. She would like to
invest a certain sum of money in XYZ Bank such that at the end of the first year, the sum of
money will amount to sh.75,600 and at the end of the second year, the amount will be enough
to settle the debt owed to Mary otieno
Required
i) The compound rate of interest if compounding is done annually (4 Marks)
ii) The amount of money mary mumbi has to invest in XYZ Bank in order to settle the
debt after two years if compounding is done annually. (4 Marks)
iii) The annual rate of interest if compounding is done quarterly. (4 Marks)
iv) The amount of money mary mumbi has to invest in XYZ Bank in order to settle the
debt after two years if compounding is done quarterly (4 Marks)
b) A salesman earns a commission of 3% on the sale of chairs and a commission of 4% on the
sale of tables. The selling price of a chair and a table are sh.6,000 and sh.15,000 respectively.
During the month of April 2006 , the number of chairs the salesman sold were 10 units more
than the number of tables sold. He received a total commission of sh.21,300.
Required
i) The number of chairs and tables the salesman sold in the month of April 2006
(2 Marks)
ii) The commission he received on the sale of chairs (1 Mark)
iii) The commission he received on the sale of tables (1 Mark)
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