PRAXIS II: Mathematics Content Knowledge (0061/5061) w/Online Practice Tests, 2nd Ed.


REA's Test Prep for PRAXIS II Mathematics Content Knowledge (0061/5061)
with Online Practice Tests Gets You Certified and in the Classroom!

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 ...

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REA's Test Prep for PRAXIS II Mathematics Content Knowledge (0061/5061)
with Online Practice Tests Gets You Certified and in the Classroom!

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 PRAXIS II Mathematics Content Knowledge (0061/5061) exam doesn't just help you get certified to teach, it helps you build your career!

Our PRAXIS II test prep is designed to help teacher candidates master the information on the Mathematics Content Knowledge (0061/5061) exam. It's perfect for college students, teachers, and career-changing professionals who are looking to become Middle School math teachers.

Written by education experts and fully aligned with the latest test specifications, our in-depth review guides you through all the content topics tested on the PRAXIS: algebra and number theory, measurement, geometry, trigonometry, functions, calculus, data analysis and statistics, probability, matrix algebra, and discrete mathematics.

A diagnostic exam and two full-length practice exams based on actual PRAXIS questions are available in the book and online. Each practice test is balanced to include every type of question, subject area, and skill tested on the exam. Our practice tests replicate the PRAXIS question format, allowing you to assess your skills and gauge your test-readiness.

All three tests come with instant scoring, diagnostic feedback, and detailed explanations of answers. REA's Study Center gives you 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 includes detailed feedback on every question. We don't just say which answers are right-we explain why the other answer choices are wrong-so test-takers will be prepared on test day. Our detailed answers help you identify your strengths and weaknesses while building your skills. Comes complete with a customized study schedule and REA's test-taking strategies and tips.

This test prep is a must-have for anyone who wants to become a math teacher!

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: 9780738610528
  • Publisher: Research & Education Association
  • Publication date: 11/19/2012
  • Series: PRAXIS Teacher Certification Test Prep
  • Edition description: Second
  • Edition number: 2
  • Pages: 464
  • Sales rank: 234,707
  • Product dimensions: 8.40 (w) x 10.80 (h) x 1.20 (d)

Meet the Author

Mel H. Friedman, M.S., 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.

Sandra Rush has a B.A. in mathematics from Temple University and an M.A. in ionospheric physics from UCLA. Her career has been focused on education, serving as a mathematics and physics instructor at the secondary school and college levels in Massachusetts and Colorado. Her interest in education has extended beyond the classroom to the publishing field, including writing and editing preparation manuals for standardized tests for all ages as well as one-on-one tutoring and coaching.

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Read an Excerpt

Congratulations! By taking the PRAXIS II Mathematics Content Knowledge 0061/5061 test, you’re on your way to a rewarding career as a mathematics teacher. Our book and the online tools that come with it, give you everything you need to succeed on this important exam, bringing you one step closer to being certified to teach. Our PRAXIS test prep package includes:

• A complete overview of the PRAXIS II Mathematics Content Knowledge test

• A comprehensive review of every content category tested

• Three full-length practice tests with online diagnostic tools to help you personalize your prep

There are many different ways to prepare for the PRAXIS II Mathematics Content Knowledge 0061/5061 test. What’s best for you depends on how much time you have to study and how comfortable you are with the subject matter. To score your highest, you need a study system that can be customized to fit you: your schedule, your learning style, and your current level of knowledge.

Let our experts help put you on the path to success and get you ready for the PRAXIS exam.

How to Use This Book

About the Review
The review chapters in this book are designed to help you sharpen the basic skills you need to approach the PRAXIS II Mathematics Content Knowledge 0061/5061test. This book contains a thorough review of the material tested in each of the content categories as detailed in the Test at-a-Glance published by ETS.

Keep in mind that your schooling has taught you most of what you need to know to answer the questions on the test. The education classes you took should have provided you with the know-how to make important decisions about situations you will face as a teacher. Our review is designed to help you fit the information you have acquired into specific domain components. Studying your class notes and textbooks together with our review will give you an excellent foundation for passing the exam.

About the REA Study Center
The best way to personalize your study plan is to get feedback on what you know and what you don’t know. At the online REA Study Center, we give you three full-length practice tests with detailed score reports that pinpoint your strengths and weaknesses.

Before you review with the book, go to the REA Study Center and take Practice Test 1 as a diagnostic test. Armed with your score reports, you can personalize your study plan. Review the parts of the book where you’re weakest and focus your study on the areas where you need the most review.

After reviewing with the book, take Practice Tests 2 and 3 at the REA Study Center to ensure that you have mastered the material and are ready for test day.

If you are studying and don’t have Internet access, you can take the printed tests in the book. These are the same practice tests offered at the REA Study Center, but without the added benefits of timed testing conditions and diagnostic score reports.

An Overview of the Test

What’s on the Test?
The PRAXIS II Mathematics Content Knowledge exam is designed to assess the mathematical knowledge and competencies for a beginning secondary school teacher. The exam addresses five main content categories and five process categories.

The content categories were designed to measure the ability to integrate knowledge of mathematics and may involve more than one competency, as well as competencies from more than one content area.

In addition to content categories, the test contains process categories. Entry-level mathematics teachers must demonstrate that they have an understanding of the various ways in which math content knowledge is acquired and used. The process categories test and assess this ability, and one or more may be applied to any of the content topics in the test.

There are 50 multiple-choice questions on the PRAXIS Mathematics test, and each contains four response options, (A) through (D). You are given two hours to complete the test, so be aware of the amount of time you are spending on each question. Using the online practice tests will help you pace your time evenly, efficiently, and productively.

Format of the Test
The PRAXIS II Mathematics Content Knowledge 0061/5061 exam is offered in paper- and computer-based formats. The test is made up of multiple-choice questions which are designed to assess your knowledge of the domains and related skills mentioned previously and reviewed in this book. In general, the multiple-choice questions are intended to make you think logically. You are expected in most cases to demonstrate more than an ability to recall factual information; you may be asked to think critically about the information, analyze it, consider it carefully, compare it with knowledge you have, or make a judgment about it.

Answering the multiple-choice questions is straightforward. You must mark your choice on a separate answer sheet or, if you are taking the computer-based version of the test, directly below each test item. You should have plenty of time in which to complete the test, so speed is not important.

However, be aware of the amount of time you are spending on each question; maintaining a steady pace when answering the questions will ensure that you complete the whole test.

When Should the Test be Taken?
Traditionally, teacher preparation programs determine when their candidates take the various tests required for teacher certification. These programs will also clear you to take the examinations and make final recommendations for certification to the certifiying authority of your particular state. For those seeking certification right out of school, the test is generally taken just before graduation. If you are planning to become a teacher of secondary school mathematics you must take and pass this test.

The PRAXIS II Mathematics Content Knowledge 0061/5061 exam is administered six times a year at locations throughout the country. The usual testing day is Saturday, but the test may be taken on an alternate day if a conflict, such as a religious obligation, exists.

The PRAXIS Registration Bulletin offers detailed information about test dates and locations, as well as registration information and instructions on how to arrange testing accommodations for those with special needs. The registration bulletin is available at

Is There a Registration Fee?
Yes, you must pay a registration fee to take the PRAXIS Mathematics exam. If you are using the registration form, all fees must be paid in full by personal check, cashier’s check, or money order. All payments must be made in U.S. dollars. Cash will not be accepted. If you are registering via the Internet or phone during the emergency registration period, payment must be made by VISA or MasterCard.

A Note About Graphing Calculators
Graphing calculators are required for the PRAXIS Mathematics test, so one should be used during your practice tests in this book. On test day, bring your graphing calculator to the testing site as one will not be provided. ETS states that the calculator should be able to:

1. produce a graph of a function within an arbitrary viewing window.

2. find the zeros of a function.

3. compute the derivative of a function numerically.

4. compute definite integrals numerically.

Calculator memories need not be cleared. No calculators with typewriter-type QWERTY keyboards and electronic writing pads are allowed. Please see the ETS website for further details on the types of calculating devices that are prohibited.

Scoring the Exam
Keep in mind that examinees are not penalized for wrong answers. A question answered correctly is worth one raw point, and your total raw score is the number of questions answered correctly on the full test. Passing scores vary from state to state, and test-takers should check with their state board of education for their state’s requirements.

How many correctly answered questions equal a passing grade? According to ETS, there is no way to predict this. There are several editions of each test, and each edition contains different questions. The questions on one edition may be slightly more difficult (or easier) than those on another edition. To make all editions of a test comparable, the conversion tables adjust for difficulty among editions. There is no way to predict which edition of the test you will take.

When and Will I Receive My Score Report?
Test scores will be mailed approximately four weeks after test day to those who you designated to receive them. There is a fee for each additional score report requested.

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Table of Contents

Chapter 1
How to Use This Book
An Overview of the Test
Scoring the Exam
6-Week Study Plan
Test-Taking Tips
The Day of the Test

Chapter 2
Number Theory and Algebra
Number Theory
The Real Number System and Its Subsystems
Real Number Properties
Complex Numbers
Factors, Multiples, and Primes
Odd and Even Numbers
Ratio, Proportion, Variation, and Mean
Radical Expressions
Mean, Median, and Mode
Solving Linear Equations
Linear Inequalities with One Variable
Absolute Value
Linear Equations with Two Variables
Linear Inequalities with Two Variables
Systems of Linear Equations
Systems of Inequalities
Rational Expressions
Solving Quadratic Equations

Chapter 3
Measurement, Geometry, and Trigonometry
Measurement Units
Conversion of Units
Unit Conversion
Accuracy and Percent of Error
Successive Approximation, Bounds, and Limits
Properties of Sides and Angles of Triangles
Right Triangles
Theorems Concerning Congruent and Similar Triangles
Parallel Lines
Area of a Regular Polygon
Three-Dimensional Figures
Surface Area and Volume of Three-Dimensional Figures
Similarity for Three-Dimensional Figures
Transformations in the Coordinate Plane
Right Triangle Trigonometry
Inverse Trigonometric Relations
Defining Trigonometric Functions
Graphing the Trigonometric Functions
Trigonometric Identities and Formulas
Rectangular and Polar Coordinates

Chapter 4
Functions and Calculus
Introduction to Functions
Domain and Range
Composition and Inverse
Quadratic Functions
Polynomial Functions
Exponential Functions
Logarithmic Functions
Limits of Functions
Rate of Change
Instantaneous Rate of Change
First Derivatives
Second Derivative
Applications of First and Second Derivatives to a Graph
Antiderivatives: Integrals
Fundamental Theorem of Calculus
Definite Integrals
Geometric Series

Chapter 5
Data Analysis, Statistics, and Probability
Data Analysis
Sampling and Experimentation
Overview of Methods of Data Collection
Planning and Conducting Surveys
Types of Sampling Methods
Displays to Represent Quantitative Data
Qualitative Data Descriptors
Quantitative Data Descriptors
Normal Distributions
Using Samples to Estimate Populations
Confidence Intervals
Alpha Values
Statistical Significance
Correlation of Bivariate Data
Sample Spaces
Compound Events
Addition Rule of Probability
Expected Value
Empirical Probability

Chapter 6
Matrix Algebra and Discrete Mathematics
Matrix Algebra
Four Basic Number Properties
Geometric Properties of Matrices and Vectors
Discrete Mathematics
Permutations and Combinations
Fundamental Counting Principle
Arithmetic Sequences and Series
Geometric Sequences and Series
Binary Relations

Answer Key
Detailed Explanations of Answers

Answer Key
Detailed Explanations of Answers

Answer Key
Detailed Explanations of Answers

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