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Management Mathematics I Question Paper
Management Mathematics I
Course:Bachelor Of Science In Information Technology
Institution: Kca University question papers
Exam Year:2009
1
UNIVERSITY EXAMINATIONS: 2008/2009
STAGE I EXAMINATION FOR DIPLOMA IN BUSINESS MANAGEMENT
DMS 101: MANAGEMENT MATHEMATICS I
DATE: APRIL 2009 TIME: 1½HOURS
INSTRUCTIONS: Answer any THREE questions
QUESTION ONE
a) Define the following terms as used in Set Theory:
(i) Finite set
(ii) Equality of sets
(iii) The null set
(iv) The power set
(v) The intersection set [10 Marks]
b) Two points (p, q) on a linear demand function are (Sh24, 60000) and (Sh32, 44400).
(i) Determine the demand function q = f (p).
(ii) What price would result in demand of 80000 units?
(iii) Interpret the slope of the function. [5 Marks]
(c) The supply function q s = f (p) for a product is quadratic. Three points which lie on the function
are (30, 1500), (40, 3600), and (50, 6,300).
Required:
Determine the supply function. [5 Marks]
2
QUESTION TWO
(a) 120 consumers in a shopping mall were asked about their buying preferences concerning a
certain product that is sold in the market under three labels. The results follow:
12 buy only those sold under label A
25 buy only those sold under label B
26 buy only those sold under label C
15 buy only those sold under labels A and B
10 buy only those sold under labels A and C
12 buy only those sold under labels B and C
8 buy the product sold under all three labels
How many of the consumers surveyed buy the product sold under
i. At least one of the three labels?
ii. Labels A and B but not C?
iii. Label A
iv. None of these labels? [8 Marks]
b) Wega Wega Auditors claim that among their 200 clients, 106 had computerized their accounts, 124
operated a manual system, 35 had both systems (computerized and manual), and 23 had neither on
regular basis.
Required:
Determine whether the above figures are compatible or incompatible? Explain your answer.
[4 Marks]
(c) (i) Given the first term and the common difference of an AP are 2 and 5 respectively, obtain the 7th
term and the sum of the first 15 terms [4 Marks]
(ii) Given the first term and the common ratio of a GP are 3 and 2 respectively, find the 5th term
and the sum of the first 8 terms. [4
Marks]
QUESTION THREE
(a) A survey of high school and college football players suggests that the number of career-ending
injuries in this sport is increasing. In 2000 the number of such injuries was 925; in 2008 the
number was 1,235. If it is assumed that the injuries are increasing at a linear rate:
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(i) Determine the function n = f (t), where n equals the estimated number of injuries per year and
t equals time measured in years since 2000. [5 Marks]
(ii) Interpret the meaning of the slope of this function [3 Marks]
(b) The resale value, V, of a piece of industrial equipment has been found to behave according to
the function
V = 250,000 e -0.06t
Where t = years since original purchase.
(i) What was the original value of the piece of equipment? [2 Marks]
(ii) What is the expected resale value after 5 years? [2 Marks]
(iii) How long would it take for the value of the equipment to be 100, 000? [3 Marks]
(c) Explain why functions are important in business management and economics [5 Marks]
QUESTION FOUR
(a) A small scale trader has observed that at a unit price of Sh.20 of product “Beta”, 600 units were
sold, while at an increased unit price of Sh.70, the sales of product “Beta” decreased to 100 units.
He estimates that the relationship between the price of the product “Beta” and the quantity sold of
product “Beta” can be described by a linear function. The total cost C of the product “Beta” is
given by the equation
C = 0.9q2 – 30q + 1000
Where q is the number of units of product “Beta” sold.
Required:
(i) The profit function. [6 Marks]
(ii) The break-even quantity of product “Beta” [6 Marks]
(c) Consider that an investor has an opportunity of receiving Sh.1000, Sh.1500, Sh.800, Sh.1100
and Sh.400 respectively at the end of one through five years. Find out the present value of this
stream of cash flows. The investor’s required interest rate is 8% p.a. [8 Marks]
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QUESTION FIVE
a) Define the following terms as used in financial mathematics
(i) Principle [1 Mark]
(ii) Interest [1 Mark]
(iii) Rate of interest [2 Marks]
b) James invested Sh.35, 000 in a financial institution that pays compound interest at 25%. The
amount accrued after a given period of time is Sh.208, 616.2567. Find the time taken to accrue this
amount? [5 Marks]
c) Given the universal set ? = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {2, 3, 5, 6, 8} and B = {3, 4, 5, 6, 9,
10}. Find (i) A ?B (ii) A n B (iii) A’ [6 Marks]
d) AK Ltd. has a machine that they intend to replace in 8 years time from now. A new machine is
expected to cost Sh.7 million. If money can earn interest at 15% p.a., what constant sum of money
should be deposited in an investment account at the start of each year so as to be able to realize the
required amount to buy the new machine? [5 Marks]
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