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Business Mathematics I Question Paper
Business Mathematics I
Course:Bachelor Of Commerce
Institution: Strathmore University question papers
Exam Year:2009
1
STRATHMORE UNIVERSITY
FACULTY OF COMMERCE
Bachelor of Commerce
END OF SEMESTER EXAMINATION
MAT 1102: BUSINESS MATHEMATICS I
Venue: LT 6
DATE: 14th October, 2009 TIME: 2 hours
ATTEMPT QUESTION ONE AND ANY OTHER TWO QUESTIONS
Question 1 (30 marks)
(a) Prove that A ? B if and only if AnBc =f
(6 marks)
(b) What do you understand by a function?
Given f (x) = 3- x5 and
g(x) 1 x
Find f (g(x)) , g( f (x)) , what do we call the functions you obtain?
(6 marks)
(c) Define the term “rational number”. Prove that 11 is an irrational number.
(6 marks)
(d) What is the sum of all 3 digit numbers that leave a remainder of '2' when divided
by 3?
(6 marks)
(e) Prove that 4
2 2
P(n): 1+8+27+···+n3 = n (n+1) , is true for n = 1
2
(6 marks)
Question 2 (20 marks)
(a) Let x, y?R , where R is the set of real numbers.
(i.) Proof that x + y = x + y
(ii.) Solve the inequality below and represent the solution sets on a number
line: 2
0 = x - 3 < 6
(6 marks)
(b) In a class 40% of the students enrolled for Math and 70% enrolled for Economics.
If 15% of the students enrolled for both Math and Economics, what % of the
students of the class did not enroll for either of the two subjects?
(6 marks)
(c) Briefly state the “Principle of Mathematical Induction” and use it to show that:
( 1)
4
P(n): 5+52+53+···+5n = 5 5n - , is true for n = 1
(8 marks)
Question 3 (20 marks)
(a) "An investor starts with £500 in an investment account, and each month it earns a
constant £32 interest. After how many years will the sum in the account exceed
£700?"
(6 marks)
(b) Three numbers are in A.P. and their sum is 21. If 2, 2 and 14 are added to these
numbers respectively, the resulting numbers are in G.P. Find the numbers.
(8 marks)
(c) The country music group, Nashville Alive agrees to a contract by which they
make $60,000 for their first recording and half as much on each succeeding
release of that recording.
How much does the group make on their 5th release of their first recording?
What is the total amount they have made in 5 releases?
(6 marks)
Question 4 (20 marks)
(a)Find
(i) P2
(ii) f (P) , where f (x) = -2x2 - 5
(4 marks)
(a) Determine whether the following are linear functions or not
(i.) f(x)=5x-10+2x10
(ii.) f(x)=x 2+12
(iii.)
f(x) 1
2 4=2- 2+x
(4 marks)
(b) A welfare agency wants to determine how many analysts to hire for processing of
welfare applications. it’s estimated that the average cost C of processing an
application is a function of the number of analysts x . The cost function is
C(x)=x(x2+100)-9
What is the average cost if 10 analysts are hired? 13 analysts? What type of
function is this? Sketch the average cost function.
(4 marks)
(a) The book value of a machine is expressed by the function
V = f(t)=105, 000-500t , where V stands for the book value in $, and t
represents the age of the machine in yrs.
i) Identify t and V intercepts and interpret.
ii) Sketch the graph
iii) Find the slope of the graph and interpret
iv) Find the domain and the range of the function and interpret.
(8 marks)
4
Question 5 (20 marks)
(a)
verify that (AB)-1 = B-1A-1 .
(6 marks)
(b) Your breakfast consists of orange juice, cereal, and eggs with the following nutritional
information:
OJ Cereal Eggs
Protein 0% 10% 20%
Vitamin C 20% 15% 0%
Calories 100 120 100
If you must have 30% protein, 30% Vitamin C and 300 calories for your
breakfast. Form the system of linear equations and determine how many servings
of OJ, Cereal, and Eggs you should have.
(8 marks)
(c) For what values of ‘ k ’ will the pair of equations
3 4 12
12 30
x y
kx y
+ =
+ =
not have a unique solution?
(6 marks)
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