Get premium membership and access revision papers, questions with answers as well as video lessons.
Got a question or eager to learn? Discover limitless learning on WhatsApp now -
Start Now!
Cms 101: Management Mathematics I Question Paper
Cms 101: Management Mathematics I
Course:Bachelor Of Commerce
Institution: Kca University question papers
Exam Year:2009
1
UNIVERSITY EXAMINATIONS: 2009/2010
SECOND YEAR STAGE 2 EXAMINATION FOR THE DEGREE OF
BACHELOR OF COMMERCE
CMS 101: MANAGEMENT MATHEMATICS I
(DAY & EVENING CLASS)
DATE: DECEMBER 2009 TIME: 2 HOURS
INSTRUCTIONS: Answer ONE and Any other TWO Questions
QUESTION ONE
a) Using appropriate examples, differentiate between the following terms as used in set theory:
i) Disjoint sets and Overlapping sets [2 Marks]
ii) Union of sets and Intersection of sets [2 Marks]
b) The weights (w) of male college students are linearly related to their heights (h) . If a student of
height 62 inches weighs 120 pounds and a student of height 72 inches weighs 170 pounds,
determine the equation that expresses their weight in terms of height. [4 Marks]
c) The sum of the first six terms of an arithmetic progression is 21 and the seventh term is three times
the sum of the third and fourth terms. Find the first term and common difference of this arithmetic
progression. [4 Marks]
d) ABC Ltd has a project which is expected to generate the following cash flows
Year 1 - 5 6 - 9 10 – 12 13 - 8
Cash flows (Sh. ‘000) 250 380 430 550
Compute the present value of these cash flows. Discounting rate is 14%.
[6 Marks]
2
e) The atmospheric pressure P in pounds per square inch at x miles above sea level is given
approximately by P = 14.7l -0.21x . At what height will the atmospheric pressure be half the sea-level
pressure? [5 Marks]
f) A researcher surveyed 520 people. He found out that 340 read newspapers for news, 180 listen to
Radio and 150 watch the Television. 80 read the newspaper and listen to Radio, 85 read the
newspaper and watch television and 35 listen to radio and watch Television. If 25 utilize none of
the three media, determine the number that used all the three sources of news. [7 Marks]
QUESTION TWO
a) In a geometric progression, the sum is 224 and the last term is 128 and the common ratio is 2. Find
the first term and the number of terms. [4 Marks]
b) In a class of 52 students, 13 excel in Science and Mathematics, 16 excel in Science and Arts, 12
excel in Mathematics and Arts, 24 excel in Arts and 2 excel in none. Twice as many students excel
in Science only as do in Mathematics only. The number of students who excel in Mathematics only
is six times the number of students who excel in Arts only. Determine the number of students who
excelled in:
i) All the three subjects [6 Marks]
ii) Two subjects [2 Marks]
c) A company manufacturing three products X, Y and Z, each of which must go through three
processes A, B and C for the following times:
Product
Time spent in the process
A B C
X
Y
Z
2
1
2
5
2
2
1
3
3
The maximum capacities of processes A, B and C are 1100, 1800 and 1400 respectively.
Calculate the number of units to be produced of products X, Y and Z to ensure the utilization of
maximum capacity? [8 Marks]
3
QUESTION THREE
a) Briefly explain four types of annuities [4 Marks]
b) A lump sum of money is invested at a rate of 10% per annum compounded quarterly. How long
will it take for the investment to:-
i) Double [4 Marks]
ii) Triple [4 Marks]
c) The following information relate to Kathurima Ltd, a dealer in standard wooden furniture on the
outskirts of the city of Nairobi. The company realized profits of Sh. 120,000 from 7 tables, Sh.
124,000 from 9 tables and Sh. 113,000 from 4 tables made and sold. Kathurima has now
approached you for assistance in forecasting future profits. The profit function is believed to be
quadratic in nature. What will be Kathurima Ltd’s profit function to be used in forecasting?
[8 Marks]
QUESTION FOUR
a) Using appropriate examples, differentiate between the following terms as used in management
mathematics:-
i) Discrete variables and continuous variables [2 Marks]
ii) Independent variables and dependent variables [2 Marks]
iii) Simple interest and compound interest [2 Marks]
iv) Arithmetic series and Geometric series [2 Marks]
b) The research department in a company that manufactures AM / FM clock watches established the
following price-demand, cost and revenue functions
( ) 20 1000
( ) ( ) (200 10 )
( ) 200 10
= 2 - +
= = -
= -
C x x x
R x xP x x x
P x x
Where x is in thousands of units and C(x) and R(x) are in thousands of shillings. Using the
method of completing the square:
i) Find the output that will produce maximum revenue hence the maximum value of
revenue. [4 Marks]
4
ii) Find the output that will produce the maximum profit hence the maximum value of
profit. [4 Marks]
iii) Determine the break-even point. [4 Marks]
QUESTION FIVE
a) XYZ ltd has a 10 year project which is expected to generate the following cash flows:
Year 1 – 4 5 – 8 9 - 10
Cash flows (Sh. ‘000) 300 200 100
The discounting rate is 10%. Compute the present value of the cash flows.
[8 Marks]
b) XYZ Ltd has a five-year project, which is expected to generate the following cash flows:
Year 1 2 3 4 5
Cash flows 60,000 45,000 55,000 70,000 40,000
The initial cash outlay of the project is Shs. 200,000. The cost of capital of the firm is 12%.
Compute the values of the following:-
i) Pay back period [2 Marks]
ii) The Net present value [2 Marks]
iii) The Profitability index [2 Marks]
iv) Internal Rate of return [4 Marks]
v) Discounted Payback period [2 Marks]
More Question Papers
Popular Exams
Return to Question Papers