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Cms 101: Management Mathematics I (Sunday Class) Question Paper
Cms 101: Management Mathematics I (Sunday Class)
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 (SUNDAY CLASS)
DATE: APRIL 2009 TIME: 2 HOURS
INSTRUCTIONS: Answer question ONE and any other TWO questions
QUESTION ONE (30 MARKS)
a) Define the following terms as used in set theory, giving examples
i) Compliment of a set
ii) Cardinality of a set.
iii) A subset. (6 Marks)
b) The cost C of producing x units of a certain item is given by
C = 0.001x2 - 0.5x + 800 .
i) What is the constant cost for this production.
ii) Find the cost of producing 1000 units. (5 Marks)
c) Emily bought a copier for $1800 and sold it 15 months later for $1200
i) Using linear depreciation, how much value did the copier lose
each month?
ii) Write the value V(t) of the copier after t months in the form:
V (t) = mt + b (4 Marks)
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d) A manufacturer makes two products T and C. The cost of making 15 units of T and 10 units of
C is Shs. 600. The cost of making 5 units of T and 8 units of C is Shs. 340. Calculate the
cost of making one unit of product T and C respectively. (5 Marks)
e) The fourth term of an arithmetic progression is 15 and the ninth term is 35. Find:
i) The first term and the common difference. (4 Marks)
ii) The sum of the first 14 terms. (3 Marks)
f) Find the period in years that an investment at simple interest rate of 16% p.a takes to double.
(3 Marks)
QUESTION TWO (20 MARKS)
a) Let U ={1,2,3,4,5, a, e,i,o,u} , A = {1,3,5, e,o } , B = {a, e,i,o,u} and
C = {2,3,4}
Find:
i) n(A n B)
ii) A - C
iii) A' ? B
iv) iv) A ? B ( 8 Marks)
b) A survey of 100 students produced the following statistics;
32 study Mathematics
20 study Physics
45 study Biology
15 study Mathematics and Biology
7 study Mathematics and Physics
10 study Physics and Biology
30 do not Study any of the three subjects
i) Find the number of students studying all the three subjects. (3 Marks)
ii) Present the above information in a Venn diagram. (6 Marks)
iii) Find the number of students taking exactly any one of the three subjects. (3 Marks)
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QUESTION THREE
a) Solve the following for x
i) 5(x - 2)= 3 (2 Marks)
ii) 3(x - 2)= 7 (2 Marks)
iii) 4x2 + 5x +1 = 0 (4 Marks)
b) Find the number of years required for a single deposit of $750 to amount to $1000 at 5%
interest compounded annually. (6 Marks)
c) Peter expects to receive Sh. 300,000 at the end of five years. The discounting rate is 13%.
Compute the present value of this amount. (6 Marks)
QUESTION FOUR (20 MARKS)
a) Solve the following simultaneous equations:
3 8
2 2 2
2
+ - =
- + = -
+ + =
x y z
x y z
x y z
(6 Marks)
b) Inflation is increasing at a rate of 6% compounded annually. In other words, $1 now is
equivalent to (1+ 6%)n dollars in n years. At this rate, how long will it take for an item
currently costing 10 dollars to cost 20 dollars?
c) Find the period in years that an investment at compound interest rate of 12.5% p.a takes to
triple. (5 Marks)
QUESTION FIVE (20 MARKS)
a) The amount S of a sum of money P invested at rate compounded continuously for T years
is governed by the exponential function S = PeRT . Suppose that an amount of KSh. 10000
is invested at 5% compounded continuously,
i) What will be the amount after three years. (3 Marks)
ii)How long will it take for the amount to double? ( 4 Marks)
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b) Joshua wishes to deposit Sh. 100,000 per annum for the next five years. The deposit is
made at the end of each year. The interest rate is 10% p.a. Compute the future value of the
annual deposit. (6 Marks)
c) Hellene has taken a loan of Sh. 400,000 from Industrial Development Bank. She expects to
liquidate the loan in 20 years time. The discounting rate is 12% p.a. Compute the amount
she has to pay each year in order to liquidate the loan. (7 Marks)
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