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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:2012
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UNIVERSITY EXAMINATIONS: 2011/2012
YEAR 1 EXAMINATION FOR THE BACHELOR OF COMMERCE
CMS 101 MANAGEMENT MATHEMATICS I (D+E)
DATE: APRIL 2012 TIME: 2 HOURS
INSTRUCTIONS: Answer Question One and Any other Two Questions
QUESTION ONE
a) A manufacturer makes two products, product Q and product M. The cost of making 15 units of
product Q and 10units of product M is sh 600. The cost of making 5 units of product Q and 8 units
of product M is sh 340. Determine the cost of making each product. (6 Marks)
b) Describe how sets can be used in making business decisions (4 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. (5 Marks)
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)
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(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
a) Explain the purpose of Venn diagrams (3 Marks)
b) The main daily newspapers in Nyeka are: The National, The New Era and The Citizen. The
management of one of the dailies is concerned about the low sales volume of their paper. In a
recent survey of 100 families in Yairobi, the numbers that read the various newspapers were found
to be as follows:
Newspaper Number of readers
Citizen 28
Citizen and New Era 8
New Era 30
Citizen and National 10
National 42
New Era and National 5
All three papers 3
Required
i) Present the above information in a Venn diagram (5 Marks)
ii) Determine the number of families who did not read any of the three newspapers.
(3 Marks)
iii) How many families read at least two newspapers (3 Marks)
iv) How many families read at most one of the three papers (3 Marks)
v) Mrembo Beauty advertising firm in Yairobi want to know which newspaper they should
advertise in so that they can reach the largest audience. Advise the company.
(3 Marks)
QUESTION THREE
a) State three assumptions that underlie break-even analysis. (3Marks)
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
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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)
v) The total basic salary to be earned by John Kimeu during a 30-year working life under
scheme B (4 Marks)
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QUESTION FIVE
a) How long will it take for a given sum to treble itself:
i) At 15% simple interest? (3 Marks)
ii) At 15% compound interest? (3 Marks)
b) A company sets up a sinking fund and invests £10,000 each year for 5 years at 9% compound
interest. What will the fund be worth after 5 years? (4 Marks)
c) Two investments have cash flows as follows:
Year 0 1 2 3
Project A (ksh) -24,000 8,000 12,000 16,000
Project B (ksh) -24,000 16,000 10,000 8,000
The cost of capital is 10%.
Required:
i) The net present value of each project (4 Marks)
ii) The internal rate of return of each project (4 Marks)
iii) Which of the two investments would you prefer (2 Marks)
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