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FTCE Mathematics 6-12 w/CD-ROM 2nd edition


REA’s FTCE Mathematics Grades 6-12 Test Prep with TestWare CD

Gets You Certified and in the Classroom!

Updated Second Edition!

Nationwide, more than 5 million teachers will be needed over the next decade, and all must take appropriate tests to be licensed. REA gets you ready for your teaching career with our outstanding library of Teacher ...

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REA’s FTCE Mathematics Grades 6-12 Test Prep with TestWare CD

Gets You Certified and in the Classroom!

Updated Second Edition!

Nationwide, more than 5 million teachers will be needed over the next decade, and all must take appropriate tests to be licensed. REA gets you ready for your teaching career with our outstanding library of Teacher Certification test preps!

Scoring well on the FTCE Mathematics Grades 6-12 exam doesn’t just help you get certified to teach in Florida, it helps you build your career.

Our popular FTCE test prep was designed to help you master the information on the Mathematics Grades 6-12 exam. This test prep is perfect for college students, prospective teachers, and career-changing professionals who are seeking certification as mathematics teachers.

Written by education experts, our complete study package contains an in-depth review of all the competencies tested on the official FTCE exam, including algebra, functions, and geometry through reasoning, mathematical connections, instruction, and assessment.

Two full-length, multiple-choice practice tests in the book simulate the actual FTCE exam. Each practice test is balanced to include every type of question, subject area, and skill tested on the exam. Our practice tests replicate the FTCE question format, allowing you to assess your skills and gauge your test-readiness.

This TestWare edition features both of the book’s practice tests on CD in a timed format with instant scoring, diagnostic feedback, and on-screen detailed explanations of answers. Our TestWare CD offers the most powerful scoring and diagnostic tools available today. Automatic scoring and instant reports help you zero in on the topics and types of questions that give you trouble now, so you’ll succeed when it counts!

Every practice exam comes with detailed feedback on every question. We don’t just say which answers are right—we explain why the other answer choices are wrong—so you’ll be prepared on test day. Our detailed explanations of answers help you identify your strengths and weaknesses while building your skills. This complete test prep package comes with a customized study schedule and REA’s test-taking strategies and tips.

This test prep is a must-have for teacher certification candidates in Florida!

REA books and software have proven to be the extra support teacher candidates need to pass their challenging tests for licensure. Our comprehensive test preps are teacher-recommended and written by experts in the field.

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Product Details

  • ISBN-13: 9780738609621
  • Publisher: Research & Education Association
  • Publication date: 8/15/2011
  • Series: FTCE Teacher Certification Test Prep
  • Edition description: Second
  • Edition number: 2
  • Pages: 348
  • Sales rank: 293,416
  • Product dimensions: 8.20 (w) x 10.70 (h) x 1.10 (d)

Meet the Author

Mel H. Friedman, M.S., is REA’s Lead Mathematics Editor. He has a diversified background in mathematics and has developed test items for Educational Testing Service. His teaching experience is at both the high school and college levels.

Catherine Capuzzi Feuerstein, M.A., earned a master’s degree in mathematics at Boston University before teaching high school mathematics for six years in Westfield, New Jersey. She co-authored the third edition of University of Chicago School Mathematics Project’s Transition Mathematics and Geometry textbooks. Working for the last three years as a freelance mathematics content developer, she developed effective curriculum and assessment materials for various companies across the nation, including Kaplan, Inc.

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Read an Excerpt

About This Book & TestWare®

REA’s FTCE Mathematics 6–12 (026) Test is a comprehensive guide designed to assist you in preparing to take the FTCE required for teaching mathematics in grades 6–12. To enhance your chances of success in this important step toward your career as a teacher in Florida schools, this test guide, along with REA’s exclusive TestWare® CD, offers these features:

• An accurate and complete overview of the FTCE Mathematics Grade 6–12 (026).

• All of the important information and its representation on the exam.

• A comprehensive review of every competency.

• Sample questions in the actual test format.

• Tips and strategies for successfully completing standardized tests.

• Diagnostic tools to identify areas of strength and weakness.

• Half-length diagnostic test to help pinpoint strengths and weaknesses.

• Full-length practice test based on the most recently administered FTCE.

• True-to-format practice materials calibrated to the appropriate levels of difficulty.

• Detailed explanations for each question on the diagnostic and practice tests, enabling you to identify correct answers and understand why they are correct and, just as important, why the other answers are incorrect.

This guide draws from many resources. The editors considered the most recent test administrations and professional standards. They also researched information from the Florida Department of Education, professional journals, textbooks, and educators in the field. This guide includes the best test preparation materials based on the latest information available.

Format of the Test

The FTCE Mathematics 6–12 addresses 15 main areas of competency identified by the Florida Department of Education as foundational to effective teaching. Divided between the 15 competencies are 118 skill areas that you will be questioned about to assess your mastery of Mathematics 6–12. Individual test items require a variety of different thinking levels, ranging from simple recall to evaluation and problem solving.

The competencies are broad statements written in a way to reflect the information that an entry-level educator needs in order to be a truly effective teacher. The competencies themselves will not be discussed in the actual FTCE test, only the skills.

All the questions on the FTCE are in multiple-choice format. Each question will have four options, lettered A through D, from which to choose. You should have plenty of time in which to complete the FTCE, but be aware of the amount of time you are spending on each question so that you allow yourself time to complete the test. Although speed is not very important, a steady pace should be maintained when answering the questions. Using the practice tests will help you prepare for this task.

Computer-Based Testing

The FTCE is offered only on computer at flexible times and locations throughout the year. Minimal computer and typing skills are required to complete the computer-based tests. You need to be comfortable with a Windows environment, using a mouse (including clicking, double-clicking, dragging, and scrolling), and typing at a rate that will allow you to complete the assignment in the allotted time (approximately 30 words per minute). In the FTCE Mathematics Grades 6–12 computer-based test, you will complete the test by selecting answers on-screen to 80 multiple-choice questions.

Who Administers the Test?

The Florida Department of Education develops this test and it is administered by Pearson Education’s Evaluation Systems group. Visit the FTCE website at Subject area knowledge tested on the Mathematics 6–12 examination of the FTCE was identified and validated by committees of content specialists from the state of Florida. Public school teachers made up the majority of the committee members, but the committees also included district supervisors and college faculty. Selection of committee members was based on recommendations by professional associations, experts, and teachers’ unions. Development of the appropriate content and difficulty levels of the exam involved literature review, teacher interviews, beta tests, and professional judgment.

When Should the FTCE Be Taken?

Florida law requires that teachers demonstrate mastery of basic skills, professional knowledge, and content area of specialization. If you’ve graduated from a Florida state-approved teacher preparation program and made the decision to teach Mathematics 6–12, you need to begin the process by applying for a Florida Temporary Certificate in that subject. The Bureau of Educator Certification will only evaluate your eligibility in the subject/s you request on your application form. The Temporary Certificate is valid for three school years, which allows you time to complete the certification tests while teaching full-time.

For high school grads and out-of-state educators, the Bureau of Educator Certification will provide you with official information about which test(s) to take to complete requirements for the Professional Certificate. During registration you can request special accommodations. To receive information on upcoming administrations of the FTCE you should consult the FTCE Registration Bulletin, which can be obtained by contacting:

FTCE/FELE Customer Service
Evaluation Systems
P.O. Box 660
Amherst, MA 01004-9018
Telephone: (413) 256-2893
8:00 a.m.–6:00 p.m. Eastern time, Monday–Friday

The FTCE Registration Bulletin also includes information regarding test retakes and score reports.

Is There a Registration Fee?
You can register online at any time as there are no deadlines for the computer-based registration. But to hold a desired date, it is wise to register early, as seating is limited. To register online use the following web address:

You must be ready to pay for the test with a credit card when you register.

Can I Retake the Test?
If you do not achieve a passing grade on the FTCE, don’t panic. The test can be taken again after 31 days, so you can seriously work on improving your score in preparation for your next FTCE. A score on the FTCE that does not match your expectations does not mean you should change your plans about teaching.

How to Use This Book & TestWare®

How Do I Begin Studying?

1. Review the organization of this test preparation guide.

2. To best utilize your study time, follow our FTCE Independent Study Schedule. The schedule is based on a seven-week program, but can be condensed to four weeks if necessary.

3. Take the diagnostic test on CD-ROM, and score it according to directions.

4. Review the format of the FTCE.

5. Review the test-taking advice and suggestions presented later in this chapter.

6. Pay attention to the information about competencies and skills, content, and topics on the test.

7. Spend time reviewing topics that stand out as needing more study.

8. Take the Practice Test on CD-ROM, review the explanations to your answers carefully, study the competencies that your scores indicate need further review.

9. Follow the suggestions at the end of this chapter for the day before and the day of the test.

10. If time allows, retake the practice test printed in the book.

Note: Scientific calculators may be used during this test, so use one during the practice tests in this book. However, do not bring one on test day—calculators are provided by the testing center for the exam.

When Should I Start Studying?

It is never too early to start studying for the FTCE. 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, since it does not allow you the time to think about the content, review the competencies and the practice test. It is important, however, to review the material one last time the night before the test administration.

Studying for the Test

It is very important for you to choose the time and place for studying that works best for you. Some individuals may set aside a certain number of hours every morning to study, while others may choose to study at night before going to sleep. Other people may study during the day, while waiting in line, or even while eating lunch. Only you can determine when and where your study time will be most effective. Be consistent and use your time wisely. Work out a study routine and stick to it.

When you take the diagnostic test and the practice test, simulate the conditions of the actual test as closely as possible. Turn your television and radio off, and sit down at a quiet table free from distraction. As you complete each test, score your test and thoroughly review the explanations to the questions you answered incorrectly; however, do not review too much at any one time. Concentrate on one problem area at a time by reviewing the question and explanation, and by studying our review until you are confident that you have mastered the material. Keep track of your scores. By doing so, you will be able to gauge your progress and discover general weaknesses in particular sections. Give extra attention to the reviews that cover your areas of difficulty, as this will build your skills in those areas.

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Table of Contents


Chapter 1

About This Book and TestWare
About the Test
Format of the Test
How to Use This Book and TestWare
Studying for the Test
Study Schedule
Scoring the Test
The Day of the Test

Diagnostic Test

Answer Sheet
Diagnostic Test
Answer Key
Competency Chart
Diagnostic Test: Answer Explanations

Chapter 2

Competency 1: Knowledge of Algebra
Linear Equations
Linear Inequalities
Absolute Value
Systems of Linear Equations and Inequalities
Radical Expressions
Factoring Polynomials and Quadratic Equations
Graphs of Quadratic Equations and Inequalities
Solving Radical Equations
Rational Expressions
Ratio, Proportion, and Variation

Chapter 3

Competency 2: Knowledge of Functions
Definition of a Function
Introduction to Functions
Special Functions
Composition and Inverse Properties of Functions
Zeros of a Polynomial Function
Transformations of Functions

Chapter 4

Competency 3: Knowledge of Geometry from a Synthetic Perspective
Basic Definitions
Right Triangles
Parallel Lines
Measurement, Perimeter, and Area
Three-Dimensional Figures

Chapter 5

Competency 4: Knowledge of Geometry from an Algebraic Perspective
Distance and Midpoint
Conic Sections
Transformations in the Coordinate Plane

Chapter 6

Competency 5: Knowledge of Trigonometry
Right Triangle Trigonometry
Defining Trigonometric Functions
Graphing the Trigonometric Functions
Law of Sines and Law of Cosines

Chapter 7

Competency 6: Knowledge of Statistics
Graphical Displays of Univariate Data
Summarizing Distributions of Univariate Data
Exploring Bivariate Data
Sampling and Experimentation
Planning and Conducting Surveys

Chapter 8

Competency 7: 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 9

Competency 8: Knowledge of Discrete Mathematics
Sequences and Series
Permutations and Combinations

Chapter 10

Competency 9: Knowledge of Calculus
Limits and Continuity of Functions
Continuity of Functions
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
Rules for Related Rates
Volume Disks and Washers

Chapter 11

Competency 10: Knowledge of Number Sense and Mathematical Structure
Real Number System and Its Subsystems
Complex Numbers
Inverse Operations
Scientific Notation

Chapter 12

Competency 11: Knowledge of Mathematics as Communication
The Language of Mathematics
Beyond Words

Chapter 13

Competency 12: Knowledge of Mathematics as Reasoning
Logical Arguments
Mathematical Proof

Chapter 14

Competency 13: Knowledge of Mathematical Connections
Equivalent Representations
Relationships Between Topics
Arithmetic Operators

Chapter 15

Competency 14: Knowledge of Mathematical Instruction
Problem-Solving Strategies
Teaching Tools

Chapter 16

Competency 15: Knowledge of Assessment
Student Errors

Practice test

Answer Sheet
Practice Test
Answer Key
Competency Chart
Detailed Explanations of Answers


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