501 Algebra Questions 2nd Edition - SF Bay Area, CA

1 501 Algebra Questions501 Algebra Questions2nd EditionNEW YORK Copyright 2006 LearningExpress, rights reserved under International and Pan-American Copyright in the United States by LearningExpress, LLC, New of Congress Cataloging-in-Publication Data:501 Algebra Questions . 2nd ed. of: 501 Algebra Questions / [William Recco]. 1st ed. 1-57685-552-X1. Algebra Problems, exercises, etc. I. Recco, William. 501 algebraquestions. II. LearningExpress (Organization). III. Title: Five hundred onealgebra Questions . IV. Title: Five hundred and one Algebra 2006512 dc222006040834 Printed in the United States of America98765432 1 Second EditionISBN 1-57685-552-XFor more information or to place an order, contact LearningExpress at:55 Broadway8th FloorNew York, NY 10006Or visit us LearningExpress Skill Builder in Focus Writing Teamiscomprised of experts in test preparation, as well as educators and teachers who specialize in language arts and Skill Builder in Focus Writing TeamBrigit DermottFreelance WriterEnglish Tutor, New York CaresNew York, New YorkSandy GadeProject EditorLearningExpressNew York, New YorkKerry McLeanProject EditorMath TutorShirley, New YorkWilliam Recco Middle School Math Teacher, Grade 8 New York Shoreham/Wading River School DistrictMath TutorSt.

2 James, New YorkColleen SchultzMiddle School Math Teacher, Grade 8 Vestal Central School DistrictMath TutorVestal, New YorkIntroductionix1 Working with Integers12 Working with Algebraic Expressions123 Combining Like Terms244 Solving Basic Equations415 Solving Multi-Step Equations496 Solving Equations with Variables on Both Sides of an Equation587 Using Formulas to Solve Equations728 Graphing Linear Equations819 Solving Inequalities11010 Graphing Inequalities11911 Graphing Systems of Linear Equations and Inequalities14212 Solving Systems of Equations Algebraically17213 Working with Exponents186 Contents14 Multiplying Polynomials19415 Factoring Polynomials20616 Using Factoring21517 Solving Quadratic Equations22918 Simplifying Radicals24219 Solving Radical Equations25020 Solving Equations with the Quadratic Formula261viiiContentsThis book is designed to provide you with review and practice for algebrasuccess!

3 It is not intended to teach common Algebra topics. Instead, it provides501 problems so you can flex your muscles and practice a variety of mathe-matical and algebraic skills. 501 Algebra Questionsis designed for many audi-ences. It s for anyone who has ever taken a course in Algebra and needs torefresh and revive forgotten skills. It can be used to supplement current instruc-tion in a math class. Or, it can be used by teachers and tutors who need to rein-force student skills. If, at some point, you feel you need further explanationabout some of the Algebra topics highlighted in this book, you can find them inthe LearningExpress publication Algebra Success in 20 Minutes a to Use This BookFirst, look at the table of contents to see the types of Algebra topics covered inthis book. The book is organized into 20 chapters with a variety of arithmetic, Algebra , and word problems. The structure follows a common sequence of con-cepts introduced in basic Algebra courses.

4 You may want to follow the sequence,as each succeeding chapter builds on skills taught in previous chapters. But ifIntroductionyour skills are just rusty, or if you are using this book to supplement topics you arecurrently learning, you may want to jump around from topic to are arranged using the same method. Each chapter has an introductiondescribing the mathematical concepts covered in the chapter. Second, there arehelpful tips on how to practice the problems in each chapter. Last, you are pre-sented with a variety of problems that generally range from easier to more difficultproblems and their answer explanations. In many books, you are given one modelproblem and then asked to do many problems following that model. In this book,every problem has a complete step-by-step explanation for the solutions. If you findyourself getting stuck solving a problem, you can look at the answer explanation anduse it to help you understand the problem-solving you are solving problems, it is important to be as organized and sequential inyour written steps as possible.

5 The purpose of drills and practice is to make you pro-ficient at solving problems. Like an athlete preparing for the next season or a musi-cian warming up for a concert, you become skillful with practice. If, aftercompleting all the problems in a section, you feel that you need more practice, dothe problems over. It s not the answer that matters most it s the process and thereasoning skills that you want to will probably want to have a calculator handy as you work through some ofthe sections. It s always a good idea to use it to check your calculations. If you havedifficulty factoring numbers, the multiplication chart on the next page may helpyou. If you are unfamiliar with prime numbers, use the list on the next page so youwon t waste time trying to factor numbers that can t be factored. And don t forgetto keep lots of scrap paper on a CommitmentSuccess does not come without effort. Make the commitment to improve your alge-bra skills.

6 Work for understanding. Whyyou do a math operation is as importantas howyou do it. If you truly want to be successful, make a commitment to spendthe time you need to do a good job. You can do it! When you achieve Algebra suc-cess, you have laid the foundation for future challenges and success. So sharpenyour pencil and practice!x501 Algebra QuestionsxiMultiplication Table 2345678910111224681012 14161820222436 9 12151821242730333648 1216202428323640444851015202530354045505 5606121824303642485460667271421283542495 6637077848162432404856647280889691827364 5546372819099108102030405060708090100 110 120112233445566778899110 121 1321224364860728496108 120 132 144 Commonly Used Prime Numbers235711131719232931374143475359616 7717379838997101103107109113127131137139 1491511571631671731791811911931971992112 2322722923323924125125726326927127728128 3293307311313317331337347349353359367373 3793833893974014094194214314334394434494 5746146346747948749149950350952152354154 7557563569571577587593599601607613617619 6316416436476536596616736776836917017097 1972773373974375175776176977378779780981 1821823827829839853857859863877881883887 9079119199299379419479539679719779839919 971,009 1,013501 Algebra Questions501 Algebra QuestionsFor some people.

7 It is helpful to try to simplify expressions containingsigned numbers as much as possible. When you find signed numbers withaddition and subtraction operations, you can simplify the task by changingall subtraction to addition. Subtracting a number is the same as adding itsopposite. For example, subtracting a three is the same as adding a negativethree. Or subtracting a negative 14 is the same as adding a positive 14. Asyou go through the step-by-step answer explanations, you will begin to seehow this process of using only addition can help simplify your understand-ing of operations with signed numbers. As you begin to gain confidence,you may be able to eliminate some of the steps by doing them in your headand not having to write them down. After all, that s the point of practice!You work at the problems until the process becomes automatic. Then youown that process and you are ready to use it in other Tips for Working with Integerssection that follows gives yousome simple rules to follow as you solve problems with integers.

8 Refer tothem each time you do a problem until you don t need to look at s when you can consider them will also want to review the rules for Order of Operations withnumerical expressions. You can use a memory device called a mnemonicto help you remember a set of instructions. Try remembering the wordPEMDAS. This nonsense word helps you remember to:1 Working with IntegersPdo operations inside ParenthesesEevaluate terms with ExponentsM Ddo Multiplicationand Divisionin order from left to rightA SAddand Subtractterms in order from left to rightTips for Working with IntegersAdditionSigned numbers the same? Find the SUM and use the same sign. Signed num-bers different? Find the DIFFERENCE and use the sign of the larger num-ber. (The larger number is the one whose value without a positive or negativesign is greatest.)Addition is commutative. That is, you can add numbers in any order andthe result is the same.

9 As an example, 3 +5 = 5 +3, or 2 + 1 = 1 + the operation sign to addition, change the sign of the number fol-lowing the operation, then follow the rules for the same? Multiply or divide and give the result a positivesign. Signsdifferent? Multiply or divide and give the result a is commutative. You can multiply terms in any order and theresult will be the same. For example: (2 5 7) = (2 7 5) = (5 2 7) = (5 7 2) and so the following + 52. 18 + 20 163. 15 + + 4 2 + 97. 25 3 + 15 58. 5 9 8 + 3 711. 15 + 5 + 112501 Algebra Questions312.(49 7) (48 4) + 7 14 + 514. (5 3) + (12 4)15.( 18 2) (6 3) + (64 16) ( 4)218.(3 5)3+ (18 6) + (11 + 8)320.(32+ 6) ( 24 8) scuba diver descends 80 feet, rises 25 feet, descends 12 feet, and thenrises 52 feet where he will do a safety stop for five minutes beforesurfacing. At what depth did he do his safety stop? digital thermometer records the daily high and low temperatures.

10 Thehigh for the day was +5 C. The low was 12 C. What was the differencebetween the day s high and low temperatures? checkbook balance sheet shows an initial balance for the month of $ the month, checks were written in the amounts of $25, $82, $213,and $97. Deposits were made into the account in the amounts of $84 and$116. What was the balance at the end of the month? gambler begins playing a slot machine with $10 in quarters in her coinbucket. She plays 15 quarters before winning a jackpot of 50 quarters. Shethen plays 20 more quarters in the same machine before walking many quarters does she now have in her coin bucket? glider is towed to an altitude of 2,000 feet above the ground beforebeing released by the tow plane. The glider loses 450 feet of altitudebefore finding an updraft that lifts it 1,750 feet. What is the glider saltitude now?501 Algebra QuestionsAnswersNumerical expressions in parentheses like this [ ] are operations performed on only part of the originalexpression.