Week 1
0.3 Exponents and Radicals
In the expression xn , x is called the base and n is the exponent.
Properties of Exponents
If n is a positive ingteger, then
(i) xn = x x x x
(ii) xn =
(iii)
1
,x = 0
x x x x
1
= xn , x = 0
x n
(iv) x0 = 1
Examples
1.
1
2
1
MATH 109 Section 1  Fall 2014
School of Accounting and Finance
University of Waterloo
Waterloo, Canada
c 2014 Michelle Ashburner
2
Lectures: Week # 1
(0.3) Exponents: express in terms of positive exponents and
simplify.
(x2 )3 (x3 )4
(x5 )2
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IvIath 109 Test
$
6u5
Simpfify the foilowing:

+9uB
1
Page 2 of 9
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3u2
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a)
= 2vt + 3u 
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2, Solve the equations for
(a)
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V=l
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(+3+2,1[3+l1X
=?x1
J x+3
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Name (Print):
UW Student ID Number:
University of Waterloo
Term Test 2
Math 109
Mathematics for Accounting
Date: November 23, 2011
Time: 4:30 p.m.  6:20 p.m.
Number of pages: 9
(including cover page)
Test type: Closed Book
Additional material allowed:
No
Name (Print):
UW Student ID Number:
University of Waterloo
Term Test 1
Math 109
Mathematics for Accounting
Date: October 19, 2011
Time: 4:30 p.m.  6:20 p.m.
Number of pages: 9
(including cover page)
Test type: Closed Book
Additional material allowed:
Non
University of Waterloo
Final Examination
Term: Winter
Surname
Year: 2008
First Name
UW Student ID Number
Course Abbreviation and Number
MATH 109
Course Title
Mathematics for Accounting
Section(s)
001 to 002
Sections Combined Course(s)
N/A
Section Numbers
University of Waterloo
Final Examination
Term: Winter
Surname
Year: 2010
First Name
UW Student ID Number
Course Abbreviation and Number
MATH 109
Course Title
Mathematics for Accounting
Section(s)
001 to 002
Sections Combined Course(s)
N/A
Section Numbers
Week 9
6.4 & 6.5 Solving Systems of Equations by Reducing Matrices
A linear equation in the n unknowns x1 , x2 , . . . xn is an equation of the form
a1 x1 + a2 x2 + . . . an xn = b,
where a1 , a2 , . . . an , b are real constants.
The graphs of linear equ
Math 109 Final Exam Review Solutions
1. Find an equation of the tangent line to the curve x2 + xy + y 2 = 16 at the point (0, 2).
1
Solution: y = x + 2
2
2. Solve for x in the equation 2log2 x+log2 5 = 7.
7
Solution: x =
5
3. Find y ! if y = x3 + 3x .
Sol
Math 109 Final Exam Review Questions
1. Find an equation of the tangent line to the curve x2 + xy + y 2 = 16 at the point (0, 2).
2. Solve for x in the equation 2log2 x+log2 5 = 7.
3. Find y ! if y = x3 + 3x .
4. The average cost c for producing q units
Week 13
14.2 The Indenite Integral
Denition:
A function F is called an antiderivative of f if
F (x) = f (x)
An antiderivative of f is a function whose derivative is f .
Example 1:
Find the antiderivative of
(a) f (x) = 2x
(b) g (x) = ln x
(c) h(x) = x2
No
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INSTRUCTIONS:
1. This examination booklet contains 14 pages including this title page. Please ensure that it is
complete.
2. Only nonprogrammable, noncommunicating calculators may be used. You may not listen to
or use any communicating o
Exa11310: Solve for a: if 361+5 = 634
WAY 1: Exponential Rules rst.
WAY 2: Logarithm Rules rst. Example: Solve for a: if 5 + (3)4"51 : 12
WAY 1 does not work. We must use logs. Question:
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Answer: N9 \ /\/
bog/(x 0
ll)
' . ' l I I,  ) . . ' ,
(/lnhh lhtllhhlml. l [oblom .Solvmg Strategies
What do you nd most helpful when you have to solve a word
problem?
. gr, lv'qu ll! or?) lqltw.
What do you nd most difcult about solving a word problem?
b goluiw 111 ()folla CM
E
KIA1 109 (1:th and Study Nuns
Fi: A cfw_ll \ (\h:
_ Intzmiuetion to Smunmtion [Sigma Notation
 Review of Limits
 C omit nous Functions
School of Aomunting and Finance
University of \'ate1loo
Waterloo. Canada
2016 Michelle Ashbmner
Textbook Praetice Pr
Limits
The correct notation for expressing a limit of a function f (I) is:
l'mA (1\ =L
1)q
This means: As I approaches a, the values of f (I) approaCh
L.
a and L are always a real number. That is, a. L E R
Special Cases:
1. lim f(:c) # lim f(:z:)
313")0
MATH 109 Class and Study Notes
Fall 2016 Week 4:
Interest Calculations
AFM Denitions: Cost, Revenue, Prot
 Demand Functions
School of Accounting and Finance
University of Waterloo
Waterloo, Canada
2016 Michelle Ashbumer
Textbook Practice Problems for
m ._
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mg: 313% y'.';';a;j'. It earned 5:36. my. How Bong was
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151? LTKEJTEJ 353(13 Denitions:
FiXEd COStI TM gum 0C a C bgrg AAQFWAQ J GAP
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14
Application of Inequalities: To produce a The], Wee Easy but
ton, the 1nanufarmu'm determines that the material costs are
$250 and labor is $4.00. Fixed costs are $5,000.00. If the cost
to the wholesaler is $7.40 per button, find the least number of
19
Class Discussion: Problem Solving Strategies
What do you nd most helpful when you have to solve a word
problem?
Sulv'ml lll Yr) lolw
What do you nd most difcult about solving a word problem?
5 3 (Uhas
Exercise: Take a. few minutes to list your steps
10
Last season an NHL (lefenseman scored 14 goals by the end of
the third month and 20 goals by the end of the fth. Create a
linear equation for these statistics.
3 (a 0
vi a 6,101
mu5~
is
'2 1"
1 f
r51
. d
A cupcake store starts business with a $100,000
Exponential Emotions
An exponential function looks like: l: (w.
Examples:
Algebra _'
> <2. k guhlb
)Q h; 7:) TS Nhghgl\vg jnovxYLEuJNy
I
Domain of ex: [11 Range of 6": 51 v56 (1 \ W 7; 025
A logarithmic function looks like:
: \ 7Q
10(1) >1 BK l
b Is (L
Week 12
In Chapter 13, we are interested in curve sketching. We will use calculus and derivatives to help us
obtain the graph of a function. Before we begin, we will examine the graphs of some wellknown
economics curves: supply and demand.
Demand Functio
Week 11
12.1 Derivatives of Logarithmic Functions
d
1
ln x =
dx
x
1
d
ln x = .
In fact,
dx
x
Why?
Examples:
Find the derivative of each of the following:
1. y =
ln x
x2
2. y = x2 ln(4x + 2)
1
3. y = ln(p + 1)2 (p + 2)3 (p + 3)4
4. y = ln
1 + x2
x2 1
Die
Week 10
Chapter 10 Review: Limits and Continuity
This course will cover calculus and some linear algebra with an emphasis on their application to
economics. We will begin with a refresher in derivatives. In order to dene a derivative, we need to
recall th
Name (Print):
UW Student ID Number:
University of Waterloo
Term Test 1
Math 109
Mathematics for Accounting
Date: February 12, 2010
Time: 2:30 p.m.  4:00 p.m.
Number of pages: 9
(including cover page)
Test type: Closed Book
Additional material allowed:
No
University of Waterloo
Final Examination
Term: Winter
Surname
Year: 2010
First Name
UW Student ID Number
Course Abbreviation and Number
MATH 109
Course Title
Mathematics for Accounting
Section(s)
001 to 002
Sections Combined Course(s)
N/A
Section Numbers