Bms 100: Management Mathematics I Question Paper

Bms 100: Management Mathematics I

Course:Bachelor Of Commerce

Institution: Kenyatta University question papers

Exam Year:2008

KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2007/2008
INSTITUTE OF OPEN LEARNING
EXAMINATION FOR THE DEGREE OF BACHELOR OF COMMERCE,
BACHELOR OF EDUCATION, BACHELOR OF ARTS AND BACHELOR OF
ARTS (HUMAN RESOURCE MANAGEMENT)
BMS 100: MANAGEMENT MATHEMATICS I

DATE: Thursday 10th January, 2008 TIME: 8.00 a.m. – 10.00 a.m.
________________________________________________________________________
INSTRUCTIONS
Answer question ONE and any other TWO questions.

Question One

(a)
Differentiate the following terms giving examples:
(i)
Universal set and Complement of asset
(ii)
Simple Interest and Compound Interest.
(iii)
Average rate of change and Instantaneous Rate of Change.
(iv)
Amortization and Sinking fund.
(v)
Linear equation and Quadratic equation.

[10 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

2 excel in none

x students excel in all the three subjects.

2

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.
Required:
(i)
Represent this information in venn diagram and solve fore x.

(ii)
How many students excel in two subjects.

[10 marks]
(c)
Solve the simultaneous equations giving your answers in terms of V.

x2 + y2 = 25v2

2y + x = 10v2

[5 marks]
(d)
XYZ Limited expects the cash inflow from an investment to be shs.40,000 after
two years and another shs.30,000 after 3 years. Its target rate of returns is 12%.
Calculate the present value of this future returns.

[5
marks]

Question Two
(a)
The rate of change of the monthly sales of a new product is given by
1

S'(t) = 500t 4 where t is the number of months since the product was launched
and S(t) is the number of products sold each month. When will the monthly sales
reach 20,000 products.

[10 marks]
(b)
Integrate the following functions:

(i)
? 2x
3 dx

(ii)
??2x2 ?3x3?dx

(iii)
?5x dx
Question Three
a)
A firm produces three types of Pans, Round bottom Square bottom and
Triangular bottom. These three products use three available inputs, raw materials,
man hours and machine hours, one Unit of round bottom requires 12 units of raw
materials, 8 man-hours and 14 machine hours. One unit of square bottom requires
10, 4 and 6 units of raw materials, man hours and machines hours respectively.

3

One unit of triangular bottom requires 6, 5 and 6 units of raw material, man hours
and machine hours respectively. 250, 130 and 225 units of raw materials, man
hours and machine hours respectively are available.
(i)
Model the above problem as a system of simultaneous equations.
(ii)
Solve the model above to find the number of units of each product to
produce in order to utilize completely the available resources.
[15 marks]
(b)
Use quadratic formula to solve the following:
(i)
3x2 – 6x + 2 = 0
(ii)
x2 – 2x = -2

[5 marks]

Question Four
(a)
Given the following revenue and cost function

R(x) = x (1,190 – 36x) ? Revenue function

C(x) = 4320 + 146x ? Cost function

Where x is thousand of computers and R(x) and C(x) are in thousand of shillings.

(i)
Derive the profit function

[6 marks]

(ii)
Find the value of x that maximize profit and what is the maximum profit.

[9 marks]
(b)
Differentiate the following functions:

(i)
f(x) = 2x2 + 3x + 10

[2.5 marks]
x3 4x
-

2

(ii)
f(x) =

[2.5 marks]
4x ?1

………………

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