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Business Mathematics I Question Paper
Business Mathematics I
Course:Bachelor Of Commerce
Institution: Strathmore University question papers
Exam Year:2008
1
STRATHMORE UNIVERSITY
FACULTY OF COMMERCE
Bachelor of Commerce
END OF SEMESTER EXAMINATION
MAT 1102: BUSINESS MATHEMATICS I (EVENING COURSE)
DATE: 13th August 2008 TIME: 2 Hours
Answer question ONE and any other two questions.
Question 1 (30 marks)
(a) List the elements in the following sets:
(i) A = {x | x?N, x < 5}
(ii) B = {x | x is a month whose name contains the letter r}
(iii) C = {x | x?N, 3 < x <11} (6 marks)
(b) State whether each statement is true or false:
(i) {1,3,5} ?{5,3,1}, (ii) {0} ?Ø, (iii){5,10} ?{2,4,6,8,...}
(6 marks)
(c) Let f (x) = 3x + 2 , and g(x) = x2 - 5, find the following composite
functions:
(i) f (g(x)) , (ii) g( f (x)) , (iii) g( f (2)) (6 marks)
(d) Define the term “absolute Value”, and solve the following x :
(i) x + 2 = 3 , (ii) 2x -1 = 5 (6 marks)
(e) Explain clearly what is meant by the term: “function”.
Find the domain of the function:
f (x) = 6 - x (6 marks)
Question 2 (20 marks)
(a) Show that (An B)' = A'? B' (6 marks)
(b) A recent survey of 125 college students showed that 70 registered for a
mathematics course, 60 registered for a commerce course, and 40 registered
for both mathematics course and commerce course.
2
(i) How many students registered only for a commerce course?
(ii) How many students did not register for a mathematics course?
(iii) How many students did not register for a commerce course?
(iv) How many students registered either for a mathematics course or
for a commerce course? (8 marks)
(c) (i) Define the term: “rational number”.
(ii) Show that 5 is an irrational number. (6 marks)
Question 3 (20 marks)
.
(a) State the “Principal of Mathematical Induction” and show that
1+ 2 + 22 + 23 + 24 +...+ 2n = 2n -1 (8 marks)
(b) Solve the following inequalities for x :
(i) 2x + 3 < 5 , (ii)
2 1 3 4
3 2
x - + x
= (6 marks)
(c) A company wholesales a certain brand of shampoo in a particular town.
Their marketing research department established the following weekly supply
and demand equations:
Supply equation:
1
450 2
p = x +
Demand equation:
p 6,300
x
=
(i) How many units x are required for supply to equal demand?
(ii) At what price p (in hundreds of Ksh) per bottle will supply equal
demand (6 marks)
Question 4 (20 marks)
a) Solve the following equations:
(i)
5x2 = 52-x , (ii) ln(x + 2) + ln x = ln 24 (6 marks)
b) An investment of £300,000 earns interest at the rate of 12%
per year. If the interest is compounded continuously:
(i) Find the exponential function which states the compound amount
as a function of years of investment t.
(ii) What will the £300,000 grow to if it is invested for 5 years?
(iii) Determine the length of time required for the investment to triple
in value. (6 marks)
3
c) The management of a company that manufactures roller skates has fixed
costs (costs at 0 output) of $ 250 per day and total costs of $ 3,450
per day at an output of 80 pairs of skates per day. Assume that cost C
is linearly related to output x .
(i) Find the slope of the line joining the points associated with outputs
of 0 and 80, i.e. the line passing through (0,250) and
(80,3450) .
(ii) Find an equation of the line relating output to cost. Write the final
answer in the form C = mx +b
(iii) Graph the cost equation from part (ii) above for 0 = x = 200
(8 marks)
Question 5 (20 marks)
(a) Use method of substitution / elimination to solve the following system:
3 2 2
2 6
x y
x y
(5 marks)
(b) Use Gaussian elimination to solve the following system:
1 2 3
1 2 3
1 2 3
2 10
3 2 4 20
3 6 9 30
(9 marks)
(c) It is estimated that the average cost C of processing an application is a
function of the number of analysts x
i.e. C = 0.006x2 -10ln x + 75
What is th+
e average cost if 20 analysts are hired? 35 analysts are hired?
Sketch the average costs function. (6 marks)
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