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Hbc 2110:Management Mathematics 1 Question Paper
Hbc 2110:Management Mathematics 1
Course:Bachelor Of Commerce
Institution: Dedan Kimathi University Of Technology question papers
Exam Year:2012
DEDAN KIMATHI UNIVERSITY OF TECHNOLOGY
University Examinations 2011/2012
FIRST YEAR SECOND SEMESTER EXAMINATION FOR BACHELOR
OF COMMERCE
HBC 2110: MANAGEMENT MATHEMATICS I
DATE: 13 TH DECEMBER 2011 TIME: 11.00 AM – 11.00 PM
Instructions: Answer question ONE AND ANY OTHER TWO QUESTIONS
QUESTION ONE (30 MARKS)
a) Calculate the future value of ordinary annuity with payments of $600 every six months for
16 years. The rate of return will be 8% compounded semiannually for the first five and half
years and 9% compounded semiannually for the subsequent ten and half years.
(6
marks)
b) The second, fourth, and eighth terms of an A.P are in G.P. and the sum of the third and fifth
terms is 20. Find the first four terms of the progression. (5 marks)
c) In the first week of production 1000 items were made. If the rise in weekly production is 5%
per week, how many weeks are necessary to produce a total of 15,000 items? (4 marks)
d) Solve for x in the following inequality: 5(x – 2) > 9x – 3(2x – 4) (2 marks)
e) Solve the equations y + 2x = 3 and x2 + y2 = 2 (3 marks)
f)
i) The twenty first term of an AP is
5 1
2
and the sum of the first 21 terms is 94½. Find
the first term, the common difference and the sum of the first 30 terms
(4 marks)
ii) Find the sum of the first terms of a geometric progression with third term 10 and
sixth term 80 (3 marks)
g) The simple interest rate being charged on a $5000 loan is three-quarters of 1% per month. If
the principal and interest are to be paid in nine months, how much interest will be charged?
(3
marks)
QUESTION TWO (20 MARKS)
a) Sinovet Researchers surveyed 520 people on how they get news. They found out that 340
read newspapers for their news, 180 listen to radio and 150 watch the Television. 80 read the
newspapers and listen to radio, 85 read news papers and watch television and 35 listen to
radio and watch television. If 25 utilize none of the three media, determine the number that
used utmost two sources of news. (6 marks)
b) CD solutions Ltd. manufactures and replicates CDs for software and music recording
companies. CD solutions sell each disc for $2.50. The variable costs per disc are $1.00.
a) To just break-even, how many CDs must be sold per month if the fixed costs are
$60,000 per month? (2 marks)
b) What must the sales be in order to have a profit of $7500 per month? (3 marks)
c) Calculate the missing quantities: (6 marks)
Part Sales ($) Variable
costs ($)
Contribution
margin ($)
Fixed
costs ($)
Net
income($)
Unit
sales
A 400,000 ? 20 100,000 60,000 ?
B ? 60,000 10 ? 12,500 4000
C 360,000 ? ? 90,000 60,000 5000
QUESTION THREE (20 MARKS)
a) A young couple wants to save Kshs 150,000 over the next 5 years and then use this amount
as a down payment on a home. In order to arrive at this goal, how much money must the
couple deposit at the end of each quarter into an account that earns interest at the rate of 5%,
compounded quarterly? (5 marks)
b) Calculate the amount of an annuity immediate of $2000 per annum for 20 years, the rate of
interest being 13 ½ % p. a. (5 marks)
c) Neno publishers Ltd. Are planning to produce a new text book in marketing. The fixed costs
are Sh. 3,300,000 and the variable costs are Sh. 312.50 per textbook. The wholesale price
will be Sh. 437.50 per textbook. How many textbooks must Neno publish and sell in order to
break-even? (4 marks)
d) Find the range of values of X which satisfy the inequalities 4 - 2x £ 4( x + 52) < x +11 (3
marks)
e) Graph the following inequalities simultaneously and show the wanted region
-x + 2y = 4, 2x + y = 8, 4x + 2y = 6, y = 0, and x = 0 (3 marks)
QUESTION FOUR (20 MARKS)
a) Using practical examples, describe the following type of sets:
i) Null set (1 marks)
ii) Universal set (1 marks)
iii) Finite set (1 marks)
iv) Overlapping sets (2 marks)
b) Rachel bought a piece of land for Sh. 1,500,000. Its value increases at 5% each year. How
much is it worth after six years? (3 marks)
c) For an in-service course in management, at least four but not more than nine members of
staff are to be chosen. The ratio of the number of male members of staff to number of female
must be less than 2: 1 and there must be more males than females. If x and y represent the
number of male members of staff and female members respectively, write down in their
simplest form the inequalities which x and y must satisfy. Represent these on graph paper
and find the composition of the in-service group of (a) the largest size, (b) the smallest size.
(6 marks)
d) An investment of Sh.200, 000 is made which earns some interest at the rate of 8% per year. If
interest is compounded continually determine
i) The exponential function which states the compound amount as a function of
years of investment. (1 mark)
ii) What will the sh.200, 000 amount to if it’s invested for 5yrs and 10yrs. (2 marks)
iii) Determine the length of time required for the investment to double (3 marks)
QUESTION FIVE (20 MARKS)
a) Distinguish between the following
i) Arithmetic progression and geometric progression (2 marks)
ii) Simple interest and compound interest (2 marks)
b) A firm is thinking of buying a machine costing $ 200,000 and the expected net cash flow
are:-
Year 1 2 3 4 5
Net cash flow 50,000 55,000 65,000 75,000 75,000
Using a discount rate of 10% calculate the percentage return over the 5 years on the
original investment. (5 marks)
c) A College offers a number of subjects namely Accounts, Secretarial, Computer studies and
others. The HOD of one of the subject areas is concerned about the low enrolment in his
subject area. I a recent survey of 200 students, the number of students who took the various
courses were found to be as follows:-
Subject No. of Students
Accounts 56
Accounts & Secretarial 16
Accounts & Computer studies 20
Secretarial & Computer studies 10
Computer studies 84
Accounts, Secretarial & Computer studies 6
d) Determine the number of students who took the other subjects (use Venn diagram)(6 marks)
e) A business man invested the same amount of money in two different banks at the same rate
of interest on bank paid compound interest and the other simple interest. After 2 years the
interest earned was Sh.920.25 and Sh.900 respectively. What was the principal and rate of
interest. (5 marks)
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