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Business Mathematics I Question Paper

Business Mathematics I

Course:Bachelor Of Commerce

Institution: Strathmore University question papers

Exam Year:2011

` STRATHMORE UNIVERSITY
SCHOOL OF MANAGEMENT AND COMMERCE
Bachelor of Commerce
END OF SEMESTER EXAMINATION
MAT 1102: BUSINESS MATHEMATICS 1
DATE: 9th March, 2011 TIME: 2 Hours
INSTRUCTIONS
Answer question ONE and any other TWO questions
Question 1 (30 Marks)
a) Given f (x) = (x -1)2 + 3 and g(x) = - x - 3 , find
i. Domain and range of g(x) (4 marks)
ii. f -1 (3 marks)
iii. g( f (x)) (3 marks)
iv. Is g(x) a function or a relation? Why? (2 marks)
b) The 2rd term of an arithmetic progression is 3 and the 8th term -3. What is the
sum of the first three terms. (4 marks)
c) For what values of ‘k’ will the pair of equations
2 3 4
2
x y
(3 marks)
not have a unique solutions?
d) i. Explain clearly what is meant by the term: “absolute value”. (2 marks)
ii. Solve the following inequality for x :
|1- 2x |= 9 (3 marks)
2
e) i. Sketch the region represented by (A? B)?(AnB) , where A, B?U on a
Venn diagram (2 marks)
ii. Use set algebras to write (A? B)?(AnB) in its simplest form
(4 marks)

Question 2 (20 Marks)
a) Show that 7 is an irrational number (6 marks)
b) State the principle of mathematical induction and use it to show that
i. 2 7 12 ... (5 3) 1 (5 1)
2
+ + + + n - = n n - , where (n =1) (6 marks)
ii. Hence find the following summation:
2 + 7 +12 +...+ 52 (4 marks)
c) A parent saved Ksh 350 on his sons first birthday, Ksh700 on his second, Ksh
1050 on his third and so on, increasing the amount by Ksh 350 on each birthday.
How much will have been saved by the time the son reaches 15 years excluding
the interest accrued. (4 marks)

Question 3 (20 Marks)
a) A small firm manufactures some products on weekly bases. The firm’s accountant
has indicated that overhead cost is Ksh 1,500,000. On average, the production
cost per item is Ksh2, 000. The firm has a long term contract with a major
customer who has agreed to buy all the firms output at a price of Ksh 2250 per
unit.
i. How many units does the company need to produce to break even on
weekly bases? (4 marks)
ii. What will be the total cost for the company to meet the breakeven?
(2 Marks)
b) A committee of 5 is to be selected from among 11 men and 9 women. The
majority in the committee should be men. How many possible committees can be
formed?
(6 Marks)

c) Solve the following simultaneous equations using the Gauss Jordan Elimination
method
1 2 3
1 2 3
1 2 3
3 2 10
2 5 4 20
7 8 5 34
x x x
x x x
x x x
- + =
- + =
- + - =-
(8 Marks)

Question 4 (20 marks)
a) Let A, B and C be sets. Suppose A ? B , B ? C andC ? A. Show that
A = B = C . (6 marks)
b) Show without using Venn diagram that if U is the universal set and A, B?U
then (A?B)c = Ac nBc (6 marks)
c) In a survey of 400 students found that 240 take “Calculus”, 220 take
“Economics”, 180 take “Accounting”, 80 take “Calculus and Accounting”, 130
take
“Calculus and Economics”, 70 take “Economics and Accounting”, and 10 take all
three subjects
i. Draw a Venn diagram representing the above information (4 marks)
ii. How many students take Calculus but not Accounting? (2 marks)
iii. How many took exactly one of the three subjects? (2 marks)
4
Question 5 (20 Marks)
a) Solve the following equations:
i. 2log3x = 2 + log9x (5 marks)
ii. ln 1 (ln16 2ln 2)
3
x= + (4 marks)
b) A police department has found that the average daily crime rate depends on
the number of officers assigned to each shift. The function representing this
relationship is
N = f (x) = 700e0.05x -1000
where N equals the average daily crime rate and x equals the number of officers
assigned to each shift.
What is the average daily crime rate if
i. 20 officers are assigned? (3 marks)
ii. Write x as a function of N (5 marks)
iii. How many officers were on duty when 400 crimes were reported
(3 marks)

Business Mathematics I Question Paper

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