Western University (Ontario)  Also known as University of Western Ontario
Finite Mathematics
MATH 1228

Fall 2015
W 1 o! 10
Let U be the set of all students in a particular class.
Let R be the set of all righthanded students in the class.
Let F be the set of all female students in the class.
Let B be the set of all students with beards.
Let M be the set of all stude
Western University (Ontario)  Also known as University of Western Ontario
Finite Mathematics
MATH 1228

Fall 2013
Math 1228A/B Online
Lecture 2:
Properties of Set Operations
(text reference: Section 1.1, pages 2  5)
c V. Olds 2008
5
1.1 Basic Set Theory
Properties of Union and Intersection
1. Both and are commutative
i.e. for any sets A and B ,
AB =B A
2. Both and a
Western University (Ontario)  Also known as University of Western Ontario
Finite Mathematics
MATH 1228

Spring 2016
Chapter 12
Perfect competition:
Recall: why firms enter and leave a market
In perfect competition there are many many firms
Minimum efficient scale is achieved
Short run: stay or to go
Long run equilibrium:
Minimizing loss at fixed cost =shut off point
Ju
Western University (Ontario)  Also known as University of Western Ontario
Finite Mathematics
MATH 1228

Spring 2016
Price discrimination is the practice of selling different units of a good or service for different
prices:
To be able to price discriminate, a monopoly must:
1) Identify and separate different buyer types
2) Sell a product that cannot be resold
Two ways o
Western University (Ontario)  Also known as University of Western Ontario
Finite Mathematics
MATH 1228

Spring 2016
Chapter 13 continued
A monopoly is a market that produces a good or service for which no close substitute exists
In which there is one supplier that is protected from competition by a barrier for entry
Two key features:
No close substitute
Barriers to ent
Western University (Ontario)  Also known as University of Western Ontario
Finite Mathematics
MATH 1228

Spring 2016
Chapter 16: Externalities
AntiCombine Law
The act distinguishes between criminal and noncriminal practices
Keep firms from combining and acting like monopolies
Criminal practices include
conspiracy to fix prices
bid rigging
false advertising
Noncrimin
Western University (Ontario)  Also known as University of Western Ontario
Finite Mathematics
MATH 1228

Spring 2016
Econ chapter 11
Output and costs
Decision time frames: the firm makes many decisions to achieve its main objective: profit
maximization
The short run: time frame in which the quantity of one ore more resources used in production is
fixed.
For most firms,
Western University (Ontario)  Also known as University of Western Ontario
Finite Mathematics
MATH 1228

Spring 2016
Econ chapter 17
Excludable or nonexcludable
Rival or nonrival
A good is excludable if only people who pay for it are able to enjoy its benefits tims coffee,
concert ticket
A good is nonexcludable if it is impossible to prevent anyone from enjoying the
Western University (Ontario)  Also known as University of Western Ontario
Finite Mathematics
MATH 1228

Spring 2016
University of Western Ontario
Final Examination
Winter 2012
Student Name (please print)
Signature
UWO Student ID Number
Course Abbreviation and Number
AM 1201B
Course Title
Calculus and Probability With Biological Applications
Section
g
001
Instructor
Dr.
Western University (Ontario)  Also known as University of Western Ontario
Finite Mathematics
MATH 1228

Spring 2016
Solutions
Please note that in all these solutions I treated C as an arbitrary constant
1.
R
9xe8x dx
Let:
u = 9x
du = 9dx
2.
R
9xe8x dx =
R
9 cos d
Let:
u = 9
du = 9d
3.
1 8x
e
8
dv = e8x dx
v=
9x 8x R 9 8x
9
9
e
e
+ C = e8x x e8x + C
8
8
8
64
v = sin
dv
Western University (Ontario)  Also known as University of Western Ontario
Finite Mathematics
MATH 1228

Spring 2016
The University of Western Ontario
Calculus 1201B Midterm Examination Version 111
February 12, 2009
7:00  10:00 pm
Instructions:
1. Please also enter your information correctly on the SCANTRON sheet.
2. Part I (pages 26) consists of 25 multiple choice qu
Western University (Ontario)  Also known as University of Western Ontario
Finite Mathematics
MATH 1228

Spring 2016
Chapter 10: organizing production
A firm is an institution that hires factors of production and organizes them to produce and sell
goods and services
The firms problem: what to produce and how much to produce, and how to produce and at
what price
The firm
Western University (Ontario)  Also known as University of Western Ontario
Finite Mathematics
MATH 1228

Winter 2015
Saturday, February 1, 2014
Page 1
Mathematics 1228B
Test 1
CODE 111
PART A (17 marks)
NOTE: YOUR ANSWERS TO THE PROBLEMS IN PART A MUST BE
CODED ON THE SCANTRON SHEET. ALSO CIRCLE YOUR ANSWERS
IN THIS BOOKLET.
1
mark
1. Let A = cfw_1, 2, 3, B = cfw_2, 4,
Western University (Ontario)  Also known as University of Western Ontario
Finite Mathematics
MATH 1228

Fall 2013
Math 1228A/B Online
Lecture 3:
Counting with Trees
(text reference: Section 1.2)
c V. Olds 2008
10
1.2
1 TECHNIQUES OF COUNTING
Tree Diagrams
A tree diagram is another way of organizing set information. These can be very useful in counting
problems. A tre
Western University (Ontario)  Also known as University of Western Ontario
Finite Mathematics
MATH 1228

Fall 2013
Math 1228A/B Online
Lecture 5:
Arranging Objects in a Line
(text reference: Section 1.4, pages 25  28)
c V. Olds 2008
22
1 TECHNIQUES OF COUNTING
1.4
Permutations
A fundamental question in counting problems is Does order matter?. If were talking about a
Western University (Ontario)  Also known as University of Western Ontario
Finite Mathematics
MATH 1228

Fall 2013
Math 1228A/B Online
Lecture 4:
Some Other Counting Tools
(text reference: Section 1.3)
c V. Olds 2008
1.3 Fundamental Counting Principle
1.3
15
Fundamental Counting Principle
Theorem (The FCP for 2 decisions)
If 2 decisions are to be made, where there are
Western University (Ontario)  Also known as University of Western Ontario
Finite Mathematics
MATH 1228

Fall 2013
Math 1228A/B Online
Lecture 6:
Arranging Objects in a Circle
(text reference: Section 1.4, pages 28  30)
c V. Olds 2008
27
1.4 Permutations
Circular Permutations
Question: In how many ways can 3 people be arranged in a circle?
Suppose the people are A, B
Western University (Ontario)  Also known as University of Western Ontario
Finite Mathematics
MATH 1228

Fall 2015
Set of rules that hold in all cases just because:
Commutative Laws:
Both and are are commutative
AB = BA
AB = BA
Commutative properties just say itdoesntmatterwhetherwestartwithsetAorwithsetB
Onceweputallelementsfrombothsetsintooneset(oronlythoseelementsw
Western University (Ontario)  Also known as University of Western Ontario
Finite Mathematics
MATH 1228

Winter 2015
Saturday, January 31, 2015
Page 1
Mathematics 1228B
Test 1
CODE 111
PART A (18 marks)
NOTE: YOUR ANSWERS TO THE PROBLEMS IN PART A MUST BE
CODED ON THE SCANTRON SHEET. ALSO CIRCLE YOUR ANSWERS
IN THIS BOOKLET.
1
mark
1. Let U = cfw_1, 2, 3, 4, 5, A = cfw_
Western University (Ontario)  Also known as University of Western Ontario
Finite Mathematics
MATH 1228

Winter 2015
Saturday, February 2, 2013
Page 1
Mathematics 1228B
Test 1
CODE 111
PART A (18 marks)
NOTE: YOUR ANSWERS TO THE PROBLEMS IN PART A MUST BE
CODED ON THE SCANTRON SHEET. ALSO CIRCLE YOUR ANSWERS
IN THIS BOOKLET.
1
mark
1. Let U = cfw_1, 2, 3, 4, 5, 6, A = c
Western University (Ontario)  Also known as University of Western Ontario
Finite Mathematics
MATH 1228

Spring 2016
University of Western Ontario
Midterm Examination
Winter 2012
Student Name (please print)
Signature
UWO Student ID Number
Course Abbreviation and Number
AM 1201B
Course Title
Calculus and Probability With Biological Applications
Section
g
001
Instructor
D