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Business Mathematics I Question Paper
Business Mathematics I
Course:Bachelor Of Commerce
Institution: Strathmore University question papers
Exam Year:2007
STRATHMORE UNIVERSITY
FACULTY OF COMMERCE
Bachelor of Commerce
END OF SEMESTER EXAMINATION (EVENING COURSE)
MAT 1101: BUSINESS MATHEMATICS I
DATE: August 2007 TIME: 2 Hours
Answer question ONE and any other two questions.
Question 1 (30 marks)
(a) Represent the following sets using descriptive properties of a set:
(i) A = {a,e,i,o,u}
(ii) B = {1,3,5,7,9,11,13,15,17,19}
(iii) C = {1,-8,-27,-64,-125} (6 marks)
(b) State which of the following sets are equal:
C = {x | x is a natural number less than 5}
A = {1,2,4} , B = {2, 4,1} , D = {1,2,3,4} (6 marks)
(c) Given g(x) = x , and h(x) = 2x2 - 3x + 5, find the following composite
functions:
(i) g(h(x)) , (ii) g(h(2)) (4 marks)
(d) Define the term “rational number”. Given that a , b are rational numbers,
and c is irrational. Determine whether: or not:
(i) a +b is a rational number?
(ii) a + c is a rational number? (6 marks)
(e) Explain clearly what is meant by the term: “function”. Two people are discussing
the function and one says to the other “ f (2) exists but f (3) does not”.
(i) Explain what they are talking about
(ii) Find f (-2) and f (-3) exist? Explain the result”. (8 marks)
Question 2 (20 marks)
(a) Show that 3 is an irrational number number. (6 marks)
(b) State the “Principal of Mathematical Induction”. Use it to show that
(i) 24n -1 is divisible by 15.
(ii) 2 + 22 + 23 + 24 +...+ 2n = 2(2n -1) (6 marks)
(c) A recent survey of 500 people who read the local news papers found that
• 280 read the “Nation”,
• 230 read the “Standard”
• 40 read both papers
(i) How many read either the Nation or the Standard?
(ii) How many did not read either the Nation or the Standard?
(iii) How many read the Nation but not the Standard?
(iv) How many did not read both Nation or Standard? (8 marks)
Question 3 (20 marks)
(a) The demand function for a particular commodity is given by:
d = f ( p) = p2 - 90 p + 2025, 0 = p = 45
where d is the number of units demanded and p is price per unit, stated in
Kenyan Pounds.
(i) What type of equation is this?
(ii) How many units will be demanded at a price of K£30?
(iii) What price(s) would result in zero demand for the product?
(6 marks)
(b) Solve the following inequality;
6x - 2 = 7 (6 marks)
(c) A company manufactures two products A and B. Each unit of A requires 3
labour hours, and each unit of B requires 2 labour hours. Daily
manufacturing capacity is 120 hours.
(i) If x units of product A and y units of product B are manufactured each day, and
all labour hours are to be used, determine the linear equation that requires the
use of 120 labour hours per day.
(ii) How many units of A can be made each day if 20 units of B are manufactured
each day?
(iii) How many units of A can be made each week if 10 units of B are made each
day? (Assume a 5-day working week). (8 marks)
3
Question 4 (20 marks)
(a) Given the equation 24
3
x y x
? + ? ? ? = -
? ?
(i) Rewrite the equation and make y the subject of the equation.
(ii) Identify and interpret the slope.
(iii) Identify the y- intercept (6 marks)
(b) The Red Cross wants to airlift supplies into Dafur Southern Sudan, which has
experienced a severe drought. Four types of supplies, each of which would be
shipped in containers, are being considered. One container of a particular item
weighs 100, 200, 300 and 400 kilograms respectively, for the four items. If the
airplane to be used has a weight capacity of 60,000 kilograms and j x equals the
number of containers shipped of items j ( j =1,2,3,4 ):
(i) Determine the equation which ensures that the plane will be loaded to its
weight capacity.
(ii) If it is decided to devote this plane to one supply item only, how many
containers could be shipped of each item? (6 marks)
(c) The equation p = 240,000 - 7,500t expresses the relationship between the
estimated population p of a rare bird which is endangered and time t is
measured in years since 1990 (t = 0 corresponds to 1990). Identify and
interpret the meaning of the
(i) “Slope”, (ii) “p intercept” and (iii) the “t intercept”. (8 marks)
Question 5 (20 marks)
(a) (i) Solve the equation ln x4 - ln x2 = 8
(ii) It is estimated that the average cost C of processing an application is a
function of the number of analysts x
i.e. C = 0.005x2 -10ln x + 70
What is the average cost if 20 analysts are hired? 30 analysts are hired?
Sketch the average costs function. (6 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
x x x
x x x
x x x
- + =
- + =
- + - =-
(7 marks)
(c) If you borrow K£4800 and repay the loan by paying K£200 per month
to reduce the loan, and 1% of the unpaid balance each month for the use of
the money. What is the total cost of the loan over 24 months? (7 marks)
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