MAC 1140 Topics (Ratti) 2nd Ed
This page contains the Main Topics of the course and the Main Concepts for each test.
The Main Topics list the material/examples required to be read from the e-book.
The Main Concepts must be study before taking the tests. The listed problems must be worked after you have worked the suggested examples below, and you have worked the book homework. To make sure you are prepared for the test, these problems must be worked without referring to your book/ notes.
Ch 1 Graphs and Functions
This book contains more material than is required for this course. The only material/examples required to be read from the book is listed below.
Chapter 1 PowerPoint Presentation of the Main Topics (Click Link)
If you do not have Power Point, go to Get Power Point Viewer
1.1 Graphs of Equations P5 (Video Link)
The Distance Formula: Ex3 (Study example 3) All example are followed by a Practice Problem. You should do the Practice Problems to check your understanding.
The Midpoint Formula: Ex4
Symmetry: Ex7
Circles: Ex 9,10
Semicircles: Ex 11
Appendix 7
Using Test Points to Solve Inequalities A.7 P838: Ex6,7
Inequalities Involving Absolute Values A.7 P840: Ex8,9,10
Slope of a Line: Ex1
Point-Slope Form: Ex2,3
Slope-Intercept Form: Ex4.5
Equations of Horizontal and Vertical Lines: Ex6
General Form of the Equation of a Line: Ex7
Parallel and perpendicular Lines: Ex9
1.3 Functions P37 (Video Link)
The Domain of a Function: Ex5
See an animation of domain and range at http://www.mathdemos.org/mathdemos/domainrange/domainrange.html
Average rate of Change: Ex10,11
1.4 A Library of Functions P52 (Video Link)
Increasing and Decreasing Functions: Ex2
Relative Minimum and Maximum Values:
Even-Odd Functions and Symmetry: Ex3
Piecewise functions: Ex4,5
Graphing Piecewise Functions: Ex6
Basic Functions:
1.5 Transformations of Functions P64 (Video Link)
Transformations:
Vertical and Horizontal Shifts: Ex1,2,3
Reflections: Ex4,5
Stretching and Compressing: Ex6,7
Multiple Transformations in Sequence: Ex8
1.6 Combining Functions; Composition of Functions P83 (Video Link)
Composition of Functions: Ex2,3
Domain of composite:Ex4,5
Decomposition of Functions Ex6:
Application of Composite Functions: Ex7,8
1.7 The Inverse Function P93 (Video Link)
Inverses: Ex1,2,3
Finding the Inverse of a Function: Ex4,5,6
Finding the Range of a One-to-One Function: Ex7,8
This concludes the Main Topics for TEST #1
Review Concepts for TEST #1
Only doing these problems will not be enough to learn the material and pass the tests.
To make sure you have learned the material, you must work these problems without referring back to your book/notes.
Ch 1 Graphs and Functions
Distance Formula: 13p14
Midpoint Formula: 19p14
Symmetry: 61p15
Circles: 69p15
Solving Inequalities algebraically 31,37,47,51,53p844
Lines: 31,43p28;77,79p29;97p30
Domain of Functions: 41,43p47
Average rate of Change: 67,71,80,83p48
Increasing and Decreasing Functions: 35p60
Relative Minimum and Maximum Values: p53-54
Even-Odd Functions: 7,29p60
Piecewise functions:45p61
Basic Functions: p58
Transformations of Functions: 11p77;27p78;57,71p79;111p80
Composition of Functions: 25,35p90
Domain of composite: 53p90
Decomposition of Functions: 65p90
Applications: 77p92
Inverses of a Function:27,33,39,49p103;55p104
Review the Summary for Covered Sections in Chapter 1 P106-107
Do Practice Tests A and B P 110-112 Answers on page A-14-A-15
This concludes the Main Concepts for TEST #1
Ch 2 Polynomials and Rational Functions
Chapter 2 PowerPoint Presentation of the Main Topics (Click Link)
2.1 Quadratic Functions P114 (Video Link)
Quadratic Function:
Standard form of a Quadratic Function: Ex1,2
Graphing a Quadratic Function f(x) =ax2 + bx + c: Ex3,4
Applications: Ex5
2.2 Polynomial Functions P125 (Video Link)
Polynomial Functions: Ex1
Power Functions:
End Behavior of Polynomial Functions: Ex2,3
Zeros of a Function: Ex4
Zero and Turning Points: Ex6-8
Graphing a polynomial Function: Ex9
2.3 Dividing Polynomials and the Rational Zeros Test P143 (Video Link)
The Division Algorithm: Ex1
There are animations of long division at http://www.mathsisfun.com/algebra/polynomials-division-long.html
There is an example of long division at http://www.purplemath.com/modules/polydiv2.htm
Appendix 2
Synthetic Division A.2 P797: Ex3
Concept of synthetic division with examples at http://www.purplemath.com/modules/synthdiv.htm
The Remainder and Factor Theorem: Ex2-4
The Rational Zeros Test: Ex6
2.4 Zeros of Polynomial Functions P153 (Video Link)
Appendix 8
Complex Numbers A.8 P845:
Addition and Subtraction A.8 P845: Ex1
Multiplying and Dividing Complex Numbers A.8 P846: Ex 2-4
Powers of I A.8 P848:
Complex Zeros of Polynomials: Ex3
Conjugate Pairs Theorem: Ex4-6
2.5 Rational Functions P163 (Video Link)
Rational Functions: Ex1
Vertical and Horizontal Asymptotes:
Translation of 1/x: Ex2-5
Graphing Rational Functions: Ex6-8
Oblique Asymptotes: Ex9
This concludes the Main Topics for TEST #2
Review Concepts for TEST #2
Only doing these problems will not be enough to learn the material and pass the tests.
To make sure you have learned the material, you must work these problems without referring back to your book/notes.
Ch 2 Polynomials and Rational Functions
Standard form of a Quadratic Function: 25,33p121;99p124
Completing the square: 49,59,67p122
Applications: 82,92p123
Polynomial Functions: 11p137;37,40p138
Graphing a polynomial Function: 55,57p138
Polynomial Division: 71,75p801
Synthetic Division: 83,89p801;113p802
Remainder Theorem:19p149
Factor Theorem:25p149
Rational Zeros Test:43,47,51p150
Addition and Subtraction of complex numbers:7p849
Multiplying and Dividing Complex Numbers 19,29,33p849
Powers of I 35p149
Complex Zeros of Polynomials: 27,42,43,53,p161
Rational Functions: 13p177
Vertical and Horizontal Asymptotes: 37,47,p178
Graphing Rational Functions:65,67p178;73p179
Oblique Asymptotes: 77p179
Review the Summary for Covered Sections in Chapter 2 P192-193
Do Practice Tests A and B P 196-198 Answers on page A-26-A-27
This concludes the Main Concepts for TEST #2
Ch 3 Exponential and Logarithmic Functions
Chapter 3 PowerPoint Presentation of the Main Topics (Click Link)
3.1 Exponential Functions P200 (Video Link)
Exponential Functions:
Evaluate Exponential Functions: Ex1
Graph Exponential Functions: Ex2-4
Simple Interest: Ex5
Compound Interest: Ex6-8
Continuous Compounded Interest Formula: Ex9
The Natural Exponential Function: Ex10
Natural Exponential Growth and Decay: Ex11,12
3.2 Logarithmic Function P218 (Video Link)
Logarithmic Functions: Ex1,2
Evaluating Logarithms: Ex3,4
Domain of Logarithmic Functions: Ex5
Graphs of Logarithmic Functions: Ex6,7
Common Logarithms: Ex8
Natural Logarithms: Ex9
Investments: Ex10
Newton’s law of Cooling: Ex11,12
3.3 Rules of Logarithms P233 (Video Link)
Rules of Logarithms: Ex1-3
Change of Base Formula: Ex5,6
Growth and Decay:
Half Life: Ex7
3.4 Exponential and Logarithmic Equations and Inequalities P246 (Video Link)
Solving Exponential Equations: Ex1-4
Applications of Exponential Equations: Ex5
Solving Logarithmic Equations: Ex6-9
Logarithmic and Exponential Inequalities: Ex10,11
3.5 Logarithmic Scales P258 (Video Link)
pH Scale: Ex1,2
Earthquake Intensity: Ex3-5
Loudness of Sound:Ex6-8
Review the Summary for Covered Sections in Chapter 3 P271-272
Do Practice Tests A and B P275-277 Answers on page A-32
This concludes the Main Topics for TEST #3
Review Concepts for TEST #3
Only doing these problems will not be enough to learn the material and pass the tests.
To make sure you have learned the material, you must work these problems without referring back to your book/notes.
Ch 3 Exponential and Logarithmic Functions
Exponential Functions:
Graph Exponential Functions: 31p214;49,55,57p215
Simple Interest: 63p215
Future Value: 65p215
Compound Interest: 69p215
Continuous Compounding: 67p215;85p244
The Natural Exponential Function:79p215
Logarithmic Functions: 11p229;25p230
Evaluating Logarithms: 35,47p230
Domain of Logarithmic Functions: 57p230
Graphs of Logarithmic Functions: 67,75p231
Common Logarithms: 85p231
Natural Logarithms: 89p231
Newton’s law of Cooling: 101p231
Rules of Logarithms: 31,41p243 108p245
Change of Base Formula:57p243
Evaluate logarithms: 65p243
Half Life: 89p244
Solving Exponential Equations: 19,31,45p255
Applications of Exponential Equations: 89p256
Solving Logarithmic Equations: 61p255
Logarithmic and Exponential Inequalities: 83p256
Applications of Logarithms 43,55,59p269
Review the Summary for Covered Sections in Chapter 3 P271-272
Do Practice Tests A and B P275-277 Answers on page A-32
This concludes the Main Concepts for TEST #3
Ch 7 Systems of Equations and Inequalities
Chapter 7 PowerPoint Presentation of the Main Topics (Click Link)
7.2 System of Equations in Three Variables P541 (Video Link)
Systems of Linear Equations:Ex1,2
Number of Solutions of a Linear System:Ex3,4
Non-square Systems:Ex5
An Application to CAT Scans: Ex6
7.4 Determinants and Cramer’s Rule P568 (Video Link)
The Determinant of a 2 X 2 Matrix: Ex1
Minors and Cofactors: Ex2
The Determinant of a n x n Matrix: Ex3
Cramer’s Rule: Ex4 Only Cramer’s rule of 2x2 matrices will be covered.
7.5 Partial Fraction Decomposition P579 (Video Link)
Partial Fractions: See an alternative method at (handout on Partial Fractions Link ): you must learn this method!
Q(x) Has Only Distinct Linear Factors: Ex1,2
Q(x) Has Repeated linear Factors: Ex3
Q(x) Has Distinct Irreducible Quadratic Factors: Ex4,6,7
Review the Summary for Covered Sections in Chapter 7 P631
Do Practice Tests A and B p635-636 Answers on page A-57
Ch 8 Analytic Geometry
Chapter 8 PowerPoint Presentation of the Main Topics (Click Link)
8.1 Conic Sections Overview P640
8.2 The Parabola (Video Link)
Geometric Definition of a Parabola:
Equations of a Parabola: Ex1,2 and Summary of Main Facts
Translation of Parabolas: Ex3 and Summary of Main Facts
Reflecting Properties of Parabolas: Ex4
8.3 The Ellipse (Video Link)
Definition of Ellipse:
Equation of an Ellipse: Summary of Main Facts, Ex1,2
Translation of Ellipses: Ex3,4
Applications: Ex5
8.4 The Hyperbola (Video Link)
Definition of Hyperbola: Summary of Main Facts, Ex1-3
The Asymptotes of a Hyperbola: Ex4
Graphing a Hyperbola with Center at (0,0):Ex5
Translation of Hyperbolas: Summary of Main Facts, Ex6
Review the Summary for Covered Sections in Chapter 8 P706
Do Practice Tests A and B P709-710 Answers on page A-70-A-71
Ch 9 Further Topics in Algebra
Chapter 9 PowerPoint Presentation of the Main Topics (Click Link)
9.1 Sequences and Series (Video Link)
Sequences: Ex 1-2
Recursive Formulas: Ex 3
Factorial Notation: Ex 5,6
Summation Notation: Ex 7
Series: Ex 8
9.5 The Binomial Theorem (Video Link)
Pascal's Triangle: Ex1
The Binomial Theorem: Ex 2,3
Binomial Coefficients: Ex 4,5
This concludes the Main Topics for TEST #4
Review Concepts for TEST #4
Only doing these problems will not be enough to learn the material and pass the tests.
To make sure you have learned the material, you must work these problems without referring back to your book/notes.
Ch 7 Systems of Equations and Inequalities
Systems of Linear Equations in 3 variables: 13p549;41p550;63p551
The Determinant of a Matrix:27p576
Cramer’s Rule: 39p576
Applications: 57,61,67p577
An Alternative of Partial Fractions (Handout on Partial Fractions Link )
Distinct Linear Factors: 23p588
Repeated linear Factors:31p588
Distinct Irreducible Quadratic Factors: 47p589
Review the Summary for Covered Sections in Chapter 7 P631
Do Practice Tests A and B p635-636 Answers on page A-57
Ch 8 Analytic Geometry
Equations of a Parabola: 17,25,31,p650;45,51p651
Applications:59p651
Equation of an Ellipse: 13,31,45,53p661
Applications: 61p661
Graphing Hyperbolas: 19,33,35,37,43,51p675
Review the Summary for Covered Sections in Chapter 8 P706
Do Practice Tests A and B P709-710 Answers on page A-70-A-71Ch 9 Further Topics in Algebra
Sequences: 37p721
Factorial Notation: 61p721
Summation Notation:69p721
Series: 83p721
Pascal's Triangle: 19p753
The Binomial Theorem: 25,41p753
Binomial Coefficients: 11,15p753
Review the Summary for Covered Sections in Chapter 9 P776
Do Practice Tests A and B P799-780 Answers on page A-74 in e-bookThis concludes the Main Concepts for TEST #4
The Limits topics will be tested in the comprehensive (cumulative) Final
Limits: A Preview of Calculus Handout
Limits PowerPoint Presentation of the Main Topics (Click Link)
An Introduction To Limits
Definition of a Limit:
Estimating Limits Numerically and Graphically: (Video Link)
Limits That Fail to Exist:
One Sided Limits: (Video Link)
The Limits Laws:
Applying the Limits Laws:
Finding Limits Using Algebra and the Limits Laws:
Limits at Infinity (Video Link)
Main Extra Concepts in the Final Exam
Limits: A Preview of Calculus Handout
Definition of a Limit:
Estimating Limits Numerically and Graphically:
Limits That Fail to Exist:
One Sided Limits:
The Limits Laws:
Applying the Limits Laws:
Finding Limits Using Algebra and the Limits Laws: