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Overview
Take the TExES and Start Teaching High School Math!
New TestWare CD Edition!
REA’s new Texas TExES test prep with CD was designed to help teacher candidates in Texas pass the TExES 135 Mathematics exam and start teaching!
Our test prep is perfect for students, outofstate teachers, and careerchanging professionals who are looking to become a Texas High School (Grades 812) Mathematics teacher.
The book is completely aligned with the most recent TExES 135 exam and targets exactly what teacher candidates need to know to excel on the test. A comprehensive review guides prospective high school teachers through all the content topics tested on the TExES, including: Number Concepts, Patterns & Algebra, Geometry & Measurement, Probability & Statistics, Mathematical Processes & Perspectives, Mathematical Learning, Instruction, and Assessment.
This enhanced TestWare edition includes the book’s two fulllength practice tests on CD with automatic, instant scoring, and onscreen detailed explanations of answers. Our timed, computerized exam format gives testtakers the closest experience to taking the actual exam.
Teacher candidates can identify their strengths and weaknesses while reinforcing their skills and testing their teaching knowledge. Book comes complete with a customized study schedule and REA’s testtaking strategies and tips.
This book is a must for anyone seeking certification as a Math teacher in Texas!
REA books and software have proven to be the extra support teacher candidates need to pass their challenging test for state licensure. Our comprehensive test preps are teacherrecommended and written by educators who have mastered the test and the related program of study.
Product Details
ISBN13:  9780738606477 

Publisher:  Research & Education Association 
Publication date:  09/28/2009 
Series:  TExES Teacher Certification Test Prep Series 
Pages:  456 
Product dimensions:  8.30(w) x 10.60(h) x 1.40(d) 
Age Range:  18 Years 
About the Author
About the Author
Author Mel Friedman, M.S., is a former classroom teacher at the high school and university levels. He has also worked as a testitem writer for Educational Testing Service and ACT, Inc.
Contributing Authors
Stephen Reiss, M.B.A., is the founder and owner of the Math Magician and the Reiss SAT Seminars. He also tutors students in the math portions of the SAT, SAT II and the ACT. Reiss serves as a consultant to San Diego area high schools, teaching his SAT seminars on campus.
Adel Arshaghi, M.S., has taught mathematics at both the high school and college level. He has been a frequent contributor to mathematics books.
Read an Excerpt
About This Book
REA’s The Best Teachers’ Test Preparation for the TExES 135 Mathematics 812 Test is a comprehensive guide designed to assist you in preparing to take this TExES test, the purpose of which is to ensure that you have the prerequisite content and professional knowledge necessary for an entrylevel position in Texas public schools.
To help you to succeed in this important step toward your teaching career in Texas schools, this test guide features:
• An accurate and complete overview of the TExES 135 Mathematics 812 Test
• The information you need to know about the exam
• A targeted review of each domain
• Tips and strategies for successfully completing standardized tests
• Diagnostic tools to identify areas of strength and weakness
• Two fulllength, truetoformat practice tests based on the most recently administered TExES 135
Mathematics 812 Test are included in two formats: in printed form in this book and in TestWare® format on the enclosed CD.
• Detailed explanations for each answer on the practice tests. These allow you to identify correct answers and understand not only why they are correct but also why the other answer choices are incorrect.
When creating this test prep, the authors and editors considered the most recent test administrations and professional standards. They also researched information from the Texas Department of Education, professional journals, textbooks, and educators. The result is the best TExES test preparation materials based on the latest information available.
About the TExES 135 Mathematics 812 Test
The purpose of the TExES 135 Mathematics 812 Test is to assess the knowledge and skills of prospective Texas teachers in the areas of mathematics. The Mathematics 8–12 test will contain 80 scorable multiplechoice items and approximately 10 nonscorable items. Your final scaled score will be based only on scorable items. The nonscorable multiplechoice items are included for the purpose of pilottesting of proposed new questions. These pilot questions do not count toward your score. However, they are not identified on the test either.
There will be four answer choices for each multiple choice question. Answers will be marked on a separate answer sheet. A Definitions/Formula Page will be provided for you. If you wish to use a calculator you must bring your own to the test site. However, it is very important that you bring a calculator that is listed with the brands and models seen on the TExES registration bulletin.
The approved list of calculator brands and models could change. The test administration promises that you will be notified if such a change occurs. All of the calculators on the approved list are graphing calculators, which perform all the operations of typical scientific calculators.
As some test questions are designed to be solved with a graphing calculator, it makes good sense to bring a graphing calculator with you to the test site. However, you will not be allowed to share calculators. The testing staff will clear your calculator’s memory both before and after the test.
Who Administers the Test?
The Texas Education Agency has contracted with Educational Testing Service (ETS) to assist in the
development and administration of the TExES.
For additional information you can contact:
ETSTexas Educator Certification Program
PO Box 6001
Princeton, NJ 085416001
Telephone: 18002052626 (U.S., U.S. Territories, and Canada)
16097717393 (all other locations)
Hours: MondayFriday 8:00 a.m.5:00 p.m. Central time
Fax: 19737350156 or 18664845860
Email: texesexcet_inquiries@ets.org
Test Administration
The TExES tests are administered six times during the testing year. Each test date has morning and afternoon test sessions. Each session is five hours long.
Do I Pay a Registration Fee?
To take the TExES, you must pay a registration fee. For information about the fee, log on to http://www.texes.ets.org/texes/AboutTheTest/.
How Is the TExES 135 Mathematics 812 Test Scored?
Test results are reported as scaled scores in a range from 100 to 300. Your total scaled score shows how you performed on the test as a whole and whether you passed the test.
The scale score allows comparison among any version of the same test. The raw scores cannot be compared from one version of a test to another. You receive one point for each correct response and no points for each incorrect response. Most tests will also include nonscorable questions. Therefore the total number of questions reported on your score report is usually less than the total number of questions that you saw on the test. The nonscorable questions will not be used in the calculation of your score.
When Should I Start Studying?
It is never too early to start studying for the TExES 135 Mathematics 812 Test. The earlier you begin, the more time you will have to sharpen your skills. Do not procrastinate! Cramming is not an effective way to study because it does not allow you the time you need to think about the
content, review the domains, and take the practice tests.
What Do the Review Sections Cover?
The targeted review in this book is designed to help you sharpen the mathematical skills you need to
approach the TExES 135 Mathematics 812 Test, as well as provide strategies for attacking the questions.
Each competency area included in the TExES 135 Mathematics 812 test is examined in a separate chapter. The skills required for all domains are extensively discussed to optimize your understanding of what the examination covers.
Your schooling has taught you most of the information you need to answer the questions on the test. The review sections in this book are designed to help you fit the information you have acquired into the domains and competencies specifi ed on the TExES. Going over your class notes and textbooks together with the reviews provided here will give you an excellent springboard for passing the examination
First Chapter
About This Book
REA’s The Best Teachers’ Test Preparation for the TExES 135 Mathematics 812 Test is a comprehensive guide designed to assist you in preparing to take this TExES test, the purpose of which is to ensure that you have the prerequisite content and professional knowledge necessary for an entrylevel position in Texas public schools.
To help you to succeed in this important step toward your teaching career in Texas schools, this test guide features:
• An accurate and complete overview of the TExES 135 Mathematics 812 Test
• The information you need to know about the exam
• A targeted review of each domain
• Tips and strategies for successfully completing standardized tests
• Diagnostic tools to identify areas of strength and weakness
• Two fulllength, truetoformat practice tests based on the most recently administered TExES 135
Mathematics 812 Test are included in two formats: in printed form in this book and in TestWare® format on the enclosed CD.
• Detailed explanations for each answer on the practice tests. These allow you to identify correct answers and understand not only why they are correct but also why the other answer choices are incorrect.
When creating this test prep, the authors and editors considered the most recent test administrations and professional standards. They also researched information from the Texas Department of Education, professional journals, textbooks, and educators. The result is the best TExES test preparation materials based on the latest information available.
About the TExES 135 Mathematics 812 Test
The purpose of the TExES 135 Mathematics 812 Test is to assess the knowledge and skills of prospective Texas teachers in the areas of mathematics. The Mathematics 8–12 test will contain 80 scorable multiplechoice items and approximately 10 nonscorable items. Your final scaled score will be based only on scorable items. The nonscorable multiplechoice items are included for the purpose of pilottesting of proposed new questions. These pilot questions do not count toward your score. However, they are not identified on the test either.
There will be four answer choices for each multiple choice question. Answers will be marked on a separate answer sheet. A Definitions/Formula Page will be provided for you. If you wish to use a calculator you must bring your own to the test site. However, it is very important that you bring a calculator that is listed with the brands and models seen on the TExES registration bulletin.
The approved list of calculator brands and models could change. The test administration promises that you will be notified if such a change occurs. All of the calculators on the approved list are graphing calculators, which perform all the operations of typical scientific calculators.
As some test questions are designed to be solved with a graphing calculator, it makes good sense to bring a graphing calculator with you to the test site. However, you will not be allowed to share calculators. The testing staff will clear your calculator’s memory both before and after the test.
Who Administers the Test?
The Texas Education Agency has contracted with Educational Testing Service (ETS) to assist in the
development and administration of the TExES.
For additional information you can contact:
ETSTexas Educator Certification Program
PO Box 6001
Princeton, NJ 085416001
Telephone: 18002052626 (U.S., U.S. Territories, and Canada)
16097717393 (all other locations)
Hours: MondayFriday 8:00 a.m.5:00 p.m. Central time
Fax: 19737350156 or 18664845860
Email: texesexcet_inquiries@ets.org
Test Administration
The TExES tests are administered six times during the testing year. Each test date has morning and afternoon test sessions. Each session is five hours long.
Do I Pay a Registration Fee?
To take the TExES, you must pay a registration fee. For information about the fee, log on to http://www.texes.ets.org/texes/AboutTheTest/.
How Is the TExES 135 Mathematics 812 Test Scored?
Test results are reported as scaled scores in a range from 100 to 300. Your total scaled score shows how you performed on the test as a whole and whether you passed the test.
The scale score allows comparison among any version of the same test. The raw scores cannot be compared from one version of a test to another. You receive one point for each correct response and no points for each incorrect response. Most tests will also include nonscorable questions. Therefore the total number of questions reported on your score report is usually less than the total number of questions that you saw on the test. The nonscorable questions will not be used in the calculation of your score.
When Should I Start Studying?
It is never too early to start studying for the TExES 135 Mathematics 812 Test. The earlier you begin, the more time you will have to sharpen your skills. Do not procrastinate! Cramming is not an effective way to study because it does not allow you the time you need to think about the
content, review the domains, and take the practice tests.
What Do the Review Sections Cover?
The targeted review in this book is designed to help you sharpen the mathematical skills you need to
approach the TExES 135 Mathematics 812 Test, as well as provide strategies for attacking the questions.
Each competency area included in the TExES 135 Mathematics 812 test is examined in a separate chapter. The skills required for all domains are extensively discussed to optimize your understanding of what the examination covers.
Your schooling has taught you most of the information you need to answer the questions on the test. The review sections in this book are designed to help you fit the information you have acquired into the domains and competencies specifi ed on the TExES. Going over your class notes and textbooks together with the reviews provided here will give you an excellent springboard for passing the examination
Table of Contents
TABLE OF CONTENTS
ABOUT THIS BOOK AND TestWare®
About the TExES 135 Mathematics 812 Test
Studying for the TExES 135 Mathematics 812 Test
The Day of the Test
CHAPTER 1
THE REAL NUMBER SYSTEM
Number Categories
Number Properties Models
CHAPTER 2
THE COMPLEX NUMBER SYSTEM
Arithmetic Operations
Solutions to Quadratic Equations
Equivalent Representations
Powers and Roots
Vectors
CHAPTER 3
NUMBER THEORY
Prime Numbers and Factorization
Greatest Common Factor
Congruence Classes
Properties of Vectors and Matrices
CHAPTER 4
SEQUENCES AND SERIES
Patterns and Properties of Series
Application of Sequences and Series to Finance
CHAPTER 5
FUNCTIONS
Relations
Domain and Range of Functions
Transformations of Functions
CHAPTER 6
LINEAR AND QUADRATIC FUNCTIONS
Properties of Lines and Their Equations
Systems of Linear Equations
The Application of Quadratic Equations in One Variable to Verbal Problems
CHAPTER 7
RATIONAL AND RADICAL FUNCTIONS
Special Functions
Polynomial Inequalities
Radical Equations
CHAPTER 8
EXPONENTIAL AND LOGARITHMIC FUNCTIONS
Algebraic Properties
Equations
Graphic Features of Logarithmic and Exponential Functions
Exponential Growth, Exponential Decay, Proportions
CHAPTER 9
TRIGONOMETRIC AND CIRCULAR FUNCTIONS
The Cartesian Coordinate System
Basic Trigonometric Functions
Inverse Trigonometric Functions
Right Triangle Trigonometry
Graphic Features of Trigonometric Functions
Trigonometric Identities and Equations
Unit Circle
CHAPTER 10
DIFFERENTIAL AND INTEGRAL CALCULUS
Limits and Continuity of Functions
Continuity of Functions
Average Rate of Change
Instantaneous Rate of Change
Rules for Finding First Derivatives
Rules for Finding Second Derivatives
Applications of First and Second Derivatives to a Graph
Antiderivatives
Definite Integral
CHAPTER 11
MEASUREMENT IN GEOMETRY
Perimeters and Areas of Twodimensional Figures
Threedimensional Figures
Using Calculus for Areas between Curves and Arc Length
CHAPTER 12
AXIOMS, PROPERTIES, AND THEOREMS OF EUCLIDEAN GEOMETRY
Properties of Points, Line Segments, Rays, Angles, Planes, and Distances
Properties of Sides and Angles of Triangles
Theorems Concerning Congruent and Similar Triangles
Properties of Quadrilaterals
Similarity for Threedimensional Figures
Geometric Constructions Using a Compass and a Straightedge
CHAPTER 13
APPLICATIONS OF EUCLIDEAN GEOMETRY TO CIRCLES
AND COMPOSITE FIGURES
Properties of Lines and Angles Related to Circles
Areas of Circles and Portions of Circles
Properties of Regular Polygons
Perimeters and Areas of Composite Figures
Crosssections and Nets of Threedimensional Figures
Geometric Constructions Related to Circles
CHAPTER 14
COORDINATE, TRANSFORMATIONAL, AND VECTOR GEOMETRY
Transformations and their Properties
Concepts and Properties of Slope, Midpoint, and Distance in the Coordinate Plane
Equations and Properties of Conic Sections Geometric Properties of Matrices and Vectors
CHAPTER 15
GRAPHICAL AND NUMERICAL TECHNIQUES TO ANALYZE DATA
Measurement Scales for Data
Various Displays to Represent Data
Measures of Central Tendency and Dispersion
Linear Transformation of Data
Summary of Formulas
CHAPTER 16
PROBABILITY CONCEPTS AND APPLICATIONS
Sample Spaces Categories of Probability Permutations and Combinations
Application of Probability to Permutations and Combinations
Application of Probability to Geometric Figures
CHAPTER 17
PROBABILITY DISTRIBUTIONS, SAMPLING, AND STATISTICAL INFERENCE
Probability Distribution
Binomial Distribution
Hypothesis Testing
Regression Analysis
CHAPTER 18
MATHEMATICAL REASONING AND PROBLEM SOLVING
Indirect Proof
Deductive Reasoning
Inductive Reasoning Counterexamples
CHAPTER 19
COMMUNICATING MATHEMATICAL CONCEPTS
Application to Biology
Application to Engineering
Business and Finance
Leisure and Entertainment
Connections to Mathematics
CHAPTER 20
INSTRUCTION AND ASSESSMENT
Mathematical Instruction: Then and Now
Assessment
PRACTICE TEST 1
TExES Mathematics 135 Practice Test 1
Answer Key Practice Test 1
Practice Test 1 Progress Chart
Detailed Solutions
PRACTICE TEST 2
TExES Mathematics 135 Practice Test 2
Answer Key Practice Test 2
Practice Test 2 Progress Chart
Detailed Solutions
INDEX
INSTALLING REA’S TestWare®
Reading Group Guide
TABLE OF CONTENTS
ABOUT THIS BOOK AND TestWare®
About the TExES 135 Mathematics 812 Test
Studying for the TExES 135 Mathematics 812 Test
The Day of the Test
CHAPTER 1
THE REAL NUMBER SYSTEM
Number Categories
Number Properties Models
CHAPTER 2
THE COMPLEX NUMBER SYSTEM
Arithmetic Operations
Solutions to Quadratic Equations
Equivalent Representations
Powers and Roots
Vectors
CHAPTER 3
NUMBER THEORY
Prime Numbers and Factorization
Greatest Common Factor
Congruence Classes
Properties of Vectors and Matrices
CHAPTER 4
SEQUENCES AND SERIES
Patterns and Properties of Series
Application of Sequences and Series to Finance
CHAPTER 5
FUNCTIONS
Relations
Domain and Range of Functions
Transformations of Functions
CHAPTER 6
LINEAR AND QUADRATIC FUNCTIONS
Properties of Lines and Their Equations
Systems of Linear Equations
The Application of Quadratic Equations in One Variable to Verbal Problems
CHAPTER 7
RATIONAL AND RADICAL FUNCTIONS
Special Functions
Polynomial Inequalities
Radical Equations
CHAPTER 8
EXPONENTIAL AND LOGARITHMIC FUNCTIONS
Algebraic Properties
Equations
Graphic Features of Logarithmic and Exponential Functions
Exponential Growth, Exponential Decay, Proportions
CHAPTER 9
TRIGONOMETRIC AND CIRCULAR FUNCTIONS
The Cartesian Coordinate System
Basic Trigonometric Functions
Inverse Trigonometric Functions
Right Triangle Trigonometry
Graphic Features of Trigonometric Functions
Trigonometric Identities and Equations
Unit Circle
CHAPTER 10
DIFFERENTIAL AND INTEGRAL CALCULUS
Limits and Continuity of Functions
Continuity of Functions
Average Rate of Change
Instantaneous Rate of Change
Rules for Finding First Derivatives
Rules for Finding Second Derivatives
Applications of First and Second Derivatives to a Graph
Antiderivatives
Definite Integral
CHAPTER 11
MEASUREMENT IN GEOMETRY
Perimeters and Areas of Twodimensional Figures
Threedimensional Figures
Using Calculus for Areas between Curves and Arc Length
CHAPTER 12
AXIOMS, PROPERTIES, AND THEOREMS OF EUCLIDEAN GEOMETRY
Properties of Points, Line Segments, Rays, Angles, Planes, and Distances
Properties of Sides and Angles of Triangles
Theorems Concerning Congruent and Similar Triangles
Properties of Quadrilaterals
Similarity for Threedimensional Figures
Geometric Constructions Using a Compass and a Straightedge
CHAPTER 13
APPLICATIONS OF EUCLIDEAN GEOMETRY TO CIRCLES
AND COMPOSITE FIGURES
Properties of Lines and Angles Related to Circles
Areas of Circles and Portions of Circles
Properties of Regular Polygons
Perimeters and Areas of Composite Figures
Crosssections and Nets of Threedimensional Figures
Geometric Constructions Related to Circles
CHAPTER 14
COORDINATE, TRANSFORMATIONAL, AND VECTOR GEOMETRY
Transformations and their Properties
Concepts and Properties of Slope, Midpoint, and Distance in the Coordinate Plane
Equations and Properties of Conic Sections Geometric Properties of Matrices and Vectors
CHAPTER 15
GRAPHICAL AND NUMERICAL TECHNIQUES TO ANALYZE DATA
Measurement Scales for Data
Various Displays to Represent Data
Measures of Central Tendency and Dispersion
Linear Transformation of Data
Summary of Formulas
CHAPTER 16
PROBABILITY CONCEPTS AND APPLICATIONS
Sample Spaces Categories of Probability Permutations and Combinations
Application of Probability to Permutations and Combinations
Application of Probability to Geometric Figures
CHAPTER 17
PROBABILITY DISTRIBUTIONS, SAMPLING, AND STATISTICAL INFERENCE
Probability Distribution
Binomial Distribution
Hypothesis Testing
Regression Analysis
CHAPTER 18
MATHEMATICAL REASONING AND PROBLEM SOLVING
Indirect Proof
Deductive Reasoning
Inductive Reasoning Counterexamples
CHAPTER 19
COMMUNICATING MATHEMATICAL CONCEPTS
Application to Biology
Application to Engineering
Business and Finance
Leisure and Entertainment
Connections to Mathematics
CHAPTER 20
INSTRUCTION AND ASSESSMENT
Mathematical Instruction: Then and Now
Assessment
PRACTICE TEST 1
TExES Mathematics 135 Practice Test 1
Answer Key Practice Test 1
Practice Test 1 Progress Chart
Detailed Solutions
PRACTICE TEST 2
TExES Mathematics 135 Practice Test 2
Answer Key Practice Test 2
Practice Test 2 Progress Chart
Detailed Solutions
INDEX
INSTALLING REA’S TestWare®
Interviews
TABLE OF CONTENTS
ABOUT THIS BOOK AND TestWare®
About the TExES 135 Mathematics 812 Test
Studying for the TExES 135 Mathematics 812 Test
The Day of the Test
CHAPTER 1
THE REAL NUMBER SYSTEM
Number Categories
Number Properties Models
CHAPTER 2
THE COMPLEX NUMBER SYSTEM
Arithmetic Operations
Solutions to Quadratic Equations
Equivalent Representations
Powers and Roots
Vectors
CHAPTER 3
NUMBER THEORY
Prime Numbers and Factorization
Greatest Common Factor
Congruence Classes
Properties of Vectors and Matrices
CHAPTER 4
SEQUENCES AND SERIES
Patterns and Properties of Series
Application of Sequences and Series to Finance
CHAPTER 5
FUNCTIONS
Relations
Domain and Range of Functions
Transformations of Functions
CHAPTER 6
LINEAR AND QUADRATIC FUNCTIONS
Properties of Lines and Their Equations
Systems of Linear Equations
The Application of Quadratic Equations in One Variable to Verbal Problems
CHAPTER 7
RATIONAL AND RADICAL FUNCTIONS
Special Functions
Polynomial Inequalities
Radical Equations
CHAPTER 8
EXPONENTIAL AND LOGARITHMIC FUNCTIONS
Algebraic Properties
Equations
Graphic Features of Logarithmic and Exponential Functions
Exponential Growth, Exponential Decay, Proportions
CHAPTER 9
TRIGONOMETRIC AND CIRCULAR FUNCTIONS
The Cartesian Coordinate System
Basic Trigonometric Functions
Inverse Trigonometric Functions
Right Triangle Trigonometry
Graphic Features of Trigonometric Functions
Trigonometric Identities and Equations
Unit Circle
CHAPTER 10
DIFFERENTIAL AND INTEGRAL CALCULUS
Limits and Continuity of Functions
Continuity of Functions
Average Rate of Change
Instantaneous Rate of Change
Rules for Finding First Derivatives
Rules for Finding Second Derivatives
Applications of First and Second Derivatives to a Graph
Antiderivatives
Definite Integral
CHAPTER 11
MEASUREMENT IN GEOMETRY
Perimeters and Areas of Twodimensional Figures
Threedimensional Figures
Using Calculus for Areas between Curves and Arc Length
CHAPTER 12
AXIOMS, PROPERTIES, AND THEOREMS OF EUCLIDEAN GEOMETRY
Properties of Points, Line Segments, Rays, Angles, Planes, and Distances
Properties of Sides and Angles of Triangles
Theorems Concerning Congruent and Similar Triangles
Properties of Quadrilaterals
Similarity for Threedimensional Figures
Geometric Constructions Using a Compass and a Straightedge
CHAPTER 13
APPLICATIONS OF EUCLIDEAN GEOMETRY TO CIRCLES
AND COMPOSITE FIGURES
Properties of Lines and Angles Related to Circles
Areas of Circles and Portions of Circles
Properties of Regular Polygons
Perimeters and Areas of Composite Figures
Crosssections and Nets of Threedimensional Figures
Geometric Constructions Related to Circles
CHAPTER 14
COORDINATE, TRANSFORMATIONAL, AND VECTOR GEOMETRY
Transformations and their Properties
Concepts and Properties of Slope, Midpoint, and Distance in the Coordinate Plane
Equations and Properties of Conic Sections Geometric Properties of Matrices and Vectors
CHAPTER 15
GRAPHICAL AND NUMERICAL TECHNIQUES TO ANALYZE DATA
Measurement Scales for Data
Various Displays to Represent Data
Measures of Central Tendency and Dispersion
Linear Transformation of Data
Summary of Formulas
CHAPTER 16
PROBABILITY CONCEPTS AND APPLICATIONS
Sample Spaces Categories of Probability Permutations and Combinations
Application of Probability to Permutations and Combinations
Application of Probability to Geometric Figures
CHAPTER 17
PROBABILITY DISTRIBUTIONS, SAMPLING, AND STATISTICAL INFERENCE
Probability Distribution
Binomial Distribution
Hypothesis Testing
Regression Analysis
CHAPTER 18
MATHEMATICAL REASONING AND PROBLEM SOLVING
Indirect Proof
Deductive Reasoning
Inductive Reasoning Counterexamples
CHAPTER 19
COMMUNICATING MATHEMATICAL CONCEPTS
Application to Biology
Application to Engineering
Business and Finance
Leisure and Entertainment
Connections to Mathematics
CHAPTER 20
INSTRUCTION AND ASSESSMENT
Mathematical Instruction: Then and Now
Assessment
PRACTICE TEST 1
TExES Mathematics 135 Practice Test 1
Answer Key Practice Test 1
Practice Test 1 Progress Chart
Detailed Solutions
PRACTICE TEST 2
TExES Mathematics 135 Practice Test 2
Answer Key Practice Test 2
Practice Test 2 Progress Chart
Detailed Solutions
INDEX
INSTALLING REA’S TestWare®
Recipe
TABLE OF CONTENTS
ABOUT THIS BOOK AND TestWare®
About the TExES 135 Mathematics 812 Test
Studying for the TExES 135 Mathematics 812 Test
The Day of the Test
CHAPTER 1
THE REAL NUMBER SYSTEM
Number Categories
Number Properties Models
CHAPTER 2
THE COMPLEX NUMBER SYSTEM
Arithmetic Operations
Solutions to Quadratic Equations
Equivalent Representations
Powers and Roots
Vectors
CHAPTER 3
NUMBER THEORY
Prime Numbers and Factorization
Greatest Common Factor
Congruence Classes
Properties of Vectors and Matrices
CHAPTER 4
SEQUENCES AND SERIES
Patterns and Properties of Series
Application of Sequences and Series to Finance
CHAPTER 5
FUNCTIONS
Relations
Domain and Range of Functions
Transformations of Functions
CHAPTER 6
LINEAR AND QUADRATIC FUNCTIONS
Properties of Lines and Their Equations
Systems of Linear Equations
The Application of Quadratic Equations in One Variable to Verbal Problems
CHAPTER 7
RATIONAL AND RADICAL FUNCTIONS
Special Functions
Polynomial Inequalities
Radical Equations
CHAPTER 8
EXPONENTIAL AND LOGARITHMIC FUNCTIONS
Algebraic Properties
Equations
Graphic Features of Logarithmic and Exponential Functions
Exponential Growth, Exponential Decay, Proportions
CHAPTER 9
TRIGONOMETRIC AND CIRCULAR FUNCTIONS
The Cartesian Coordinate System
Basic Trigonometric Functions
Inverse Trigonometric Functions
Right Triangle Trigonometry
Graphic Features of Trigonometric Functions
Trigonometric Identities and Equations
Unit Circle
CHAPTER 10
DIFFERENTIAL AND INTEGRAL CALCULUS
Limits and Continuity of Functions
Continuity of Functions
Average Rate of Change
Instantaneous Rate of Change
Rules for Finding First Derivatives
Rules for Finding Second Derivatives
Applications of First and Second Derivatives to a Graph
Antiderivatives
Definite Integral
CHAPTER 11
MEASUREMENT IN GEOMETRY
Perimeters and Areas of Twodimensional Figures
Threedimensional Figures
Using Calculus for Areas between Curves and Arc Length
CHAPTER 12
AXIOMS, PROPERTIES, AND THEOREMS OF EUCLIDEAN GEOMETRY
Properties of Points, Line Segments, Rays, Angles, Planes, and Distances
Properties of Sides and Angles of Triangles
Theorems Concerning Congruent and Similar Triangles
Properties of Quadrilaterals
Similarity for Threedimensional Figures
Geometric Constructions Using a Compass and a Straightedge
CHAPTER 13
APPLICATIONS OF EUCLIDEAN GEOMETRY TO CIRCLES
AND COMPOSITE FIGURES
Properties of Lines and Angles Related to Circles
Areas of Circles and Portions of Circles
Properties of Regular Polygons
Perimeters and Areas of Composite Figures
Crosssections and Nets of Threedimensional Figures
Geometric Constructions Related to Circles
CHAPTER 14
COORDINATE, TRANSFORMATIONAL, AND VECTOR GEOMETRY
Transformations and their Properties
Concepts and Properties of Slope, Midpoint, and Distance in the Coordinate Plane
Equations and Properties of Conic Sections Geometric Properties of Matrices and Vectors
CHAPTER 15
GRAPHICAL AND NUMERICAL TECHNIQUES TO ANALYZE DATA
Measurement Scales for Data
Various Displays to Represent Data
Measures of Central Tendency and Dispersion
Linear Transformation of Data
Summary of Formulas
CHAPTER 16
PROBABILITY CONCEPTS AND APPLICATIONS
Sample Spaces Categories of Probability Permutations and Combinations
Application of Probability to Permutations and Combinations
Application of Probability to Geometric Figures
CHAPTER 17
PROBABILITY DISTRIBUTIONS, SAMPLING, AND STATISTICAL INFERENCE
Probability Distribution
Binomial Distribution
Hypothesis Testing
Regression Analysis
CHAPTER 18
MATHEMATICAL REASONING AND PROBLEM SOLVING
Indirect Proof
Deductive Reasoning
Inductive Reasoning Counterexamples
CHAPTER 19
COMMUNICATING MATHEMATICAL CONCEPTS
Application to Biology
Application to Engineering
Business and Finance
Leisure and Entertainment
Connections to Mathematics
CHAPTER 20
INSTRUCTION AND ASSESSMENT
Mathematical Instruction: Then and Now
Assessment
PRACTICE TEST 1
TExES Mathematics 135 Practice Test 1
Answer Key Practice Test 1
Practice Test 1 Progress Chart
Detailed Solutions
PRACTICE TEST 2
TExES Mathematics 135 Practice Test 2
Answer Key Practice Test 2
Practice Test 2 Progress Chart
Detailed Solutions
INDEX
INSTALLING REA’S TestWare®
Customer Reviews
Most Helpful Customer Reviews
I purchased this book one month before taking the test. I did a chapter a day (there are 20) and then the two practice test going over everything. It was freaking hard as heck. This book was really good at giving examples and if you are a self sufficient type, then understanding it will not be a problem for you. I took the test, passed on the first try. This book went above and beyond what was on the actual test. I felt overly ready which is better than not at all. I had not taken a math class for nearly 6 years when I began to read this book. Take your time, do not stress and all things will fall into place. I reccomend this book if you want to be prepared and then some.

This book was ok. When I worked through page 8, I already noticed simple errors. The book was detailed in most part but the chapters may have needed better arrangements, to follow suit of build on information.
I emailed the publisher of the book about the mistakes, they emailed me back on a full page of corrections. I then found a few more errors, that they never got back to me on... not even to let me know if I was wrong.
The book went over the principle of caluclations,working the problems, but needed to spend extensive time on using the concepts to understand the problems yours may have when calculating.(ex. foiling (a+b)^2 does not equal a^2 +b^2)
I went completely through the book and did pass my Texes with a 250 on first try, but I think it was more luck and skills on my end than the book helping.
