Gary M. Rubenstein - Regents Algebra I Power Pack Revised Edition

Copyright 2021, 2020, 2018, 2017, 2015 by Kaplan, Inc., d/b/a Barrons Educational Series

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• Published by Kaplan, Inc., d/b/a Barrons Educational Series
• 750 Third Avenue
• New York, NY 10017
• www.barronseduc.com

ISBN: 978-1-5062-7762-2

10 9 8 7 6 5 4 3 2 1

Kaplan, Inc., d/b/a Barrons Educational Series print books are available at special quantity discounts to use for sales promotions, employee premiums, or educational purposes. For more information or to purchase books, please call the Simon & Schuster special sales department at 866-506-1949.

Copyright 2021, 2020, 2018, 2017, 2015 by Kaplan, Inc., d/b/a Barrons Educational Series

All rights reserved under International and Pan-American Copyright Conventions. By payment of the required fees, you have been granted the non-exclusive, non-transferable right to access and read the text of this eBook on screen. No part of this text may be reproduced, transmitted, downloaded, decompiled, reverse engineered, or stored in or introduced into any information storage and retrieval system, in any form or by any means, whether electronic or mechanical, now known or hereinafter invented, without the express written permission of the publisher.

• Published by Kaplan, Inc., d/b/a Barrons Educational Series
• 750 Third Avenue
• New York, NY 10017
• www.barronseduc.com

ISBN: 978-1-5062-7198-9

10 9 8 7 6 5 4 3 2 1

Kaplan, Inc., d/b/a Barrons Educational Series print books are available at special quantity discounts to use for sales promotions, employee premiums, or educational purposes. For more information or to purchase books, please call the Simon & Schuster special sales department at 866-506-1949.

Gary Rubinstein has been teaching math for 25 years. He is a three-time recipient of the Math for America Master Teacher Fellowship. Gary lives with his wife Erica and his two children, Sarah and Sam. He has a YouTube channel at nymathteacher where students can find extra test tips and strategies for learning Algebra I.

To Erica, Sarah, and Sam

In June of 2014, New York State adopted a more difficult Algebra I course based on the Common Core curriculum and changed the Regents exam to reflect this new course. On the new Algebra I Regents exam, students are expected not only to solve algebra problems and answer algebra-related questions but also to explain their reasoning . This is a major shift in the testing of algebra concepts, so a thorough review is even more critical for success.

This book will introduce you to the concepts covered throughout the Algebra I Regents course as well as to the different types of problems you will encounter on the Regents exam at the end of the year.

Students and teachers alike can use this book as a resource for preparing for the Algebra I Regents exam.

Students will find this book to be a great study tool because it contains a review of all Algebra I concepts, useful examples, and practice problems of varying difficulty that can be practiced throughout the school year to reinforce what they are learning in class. The most ideal way to prepare for the Algebra Regents exam is to work through the practice problems in the review sections and then the recently administered Regents exams at the end of the book.

Teachers can use this book as a tool to help structure an Algebra I course that will culminate with the Regents exam. The topics in the book are arranged by priority, so the sections in the beginning of the book are the ones from which more of the questions on the Regents exam are drawn. There are 60 sections in the book, spread out over 14 chapters, dedicated to all topics for Algebra I, each with practice exercises and solutions.

Becoming familiar with the specific types of questions on the Algebra I Regents exam is crucial to performing well on this test. There are questions in which the math may be fairly easy but the way in which the question is asked makes the question seem much more difficult. For example, the question Find all zeros of the function f(x) = 2x + 6 is a fancy way of asking the much simpler sounding Solve for x if 2x + 6 = 0. Knowing exactly what the questions are asking is a big part of success on this test .

Algebra has been around for thousands of years, and its basic concepts have never changed. So fundamentally, the algebra curriculum today is not very different from the algebra taught in schools two years ago, ten years ago, or twenty years ago. But the exam that follows this Common Core-based course, with more complicated ways of asking questions and presenting problems, requires a specifically presented study plan thats more important than ever.

Gary Rubinstein

Algebra has a collection of tools that, when used appropriately, can be used to solve equations. These tools have names like the addition property of equality. Knowing the names and how to use these properties enables you to not only solve equations but also explain the logic behind your reasoning

Algebra is what you are doing when you solve equations for unknown variables. The most basic type of algebra problem is something like

Of all the possible numbers that can be substituted into the variable x, the only one that makes the equation true is the number 4. Any other number would make the equation false. Another way of saying this is that the number 4 satisfies the equation x 1 = 3 while other numbers do not satisfy that equation. All the numbers that satisfy an equation form the solution set of the equation. In this example, since only one number satisfies the equation, the solution set is just the set with the number 4 in it, or {4}.

If the equation is simple enough to solve the equation for the unknown variable x, you might be able to just see the answer, like in the x 1 = 3 example. But for more involved equations, you will use the properties of algebra.

For an equation like, x 1 = 3 the way to solve this equation with algebra is to eliminate the 1 from the left-hand side of the equation. You do this by adding 1 to each side of the equation.

It is the addition property of equality that lets you add something to both sides of an equation to create a new equation that has the same solution set as the original equation.