Table Of Content

Marcy, PRD, Gl Creative Publications , Maroy, MA, ‘The Authors: Steve Marcy and vanis Marcy Santa Monica: Malou Unitied Scnaot District Limited Reproduction Permission: Permission to duplicate these materials linited to the teacher for whom they are purchased, Reproduction for an ertre school or schoo! district is unlawful and strictly prohibited, Tho authors wish ta thank Mr, Beb Fine and Mr. Torry Groen for their helptul suggestions, and especially a! aur former students in Santa Manica wha workud with there puzzles as they were beng developed Faited by Lyn Savage ‘Cover by Nimbus Design 1983, 1289, 1996 Creative Publicatiors, Two Prudential Plaza, Suite 1:7 Ch cago. IL 60601 = Printed in U.S.A. ISBN: 0-26488-791 X 11.99 NOTES FROM THE AUTHORS. ALGEBRA V/ITH1 P12242Z! n aBinde* «. dosignod to provide practice wh skis ard conegpls ‘aught “re. year algetia courses, Tre sara le an esters on. and coneualian ofa FRE ALGESRA VATH PIZZAZ7! aries, alse publi od by Create Pus cations wre believe that mestery of algebra aks ae connapts renuires boh geas each ng and. great seal 9 practing. Our nal ist aroide pizz'e cies rat make fig prastoe mote eFective, We ‘uae red obi ta these acivies tree snaracetisin rar ncrense the eFectenoss of pracice, 1. KNOWLEDGE OF RESULTS Yan as devions ave useu in Iva puzeles Ic vel etude walle Ine ansivure wa corel Fopeback occurs imesialoly ator ta stalent W>'ks each exoisp. or example, iit pavietlaranexor gro: m the d0¢9 oF eerambled arsaor Ist tha sizer hr ow = neo-ect Ibor se can bran Ir again wr ask or Fel. Adalinal‘eacback ane rvintorcenteat occurs vinen Ine eludert finds a puzac solar ‘hat & approansto. Wo rsa ‘cund trl slacants ‘really approcate ara benoft irom tg immeaa:e hrawlodge ot roauls 2. CONTROL OF EXERCISE VARIATION AND DIFFICULTY ‘Toe parzlas mir eaer major top re carly soquentad se that cach ana buos on while ‘and consepre proviousty covered. Each puzzle “causes ena specie obclive. The secuence of exere ee win each puzzle cacignod to gude sbadams in ncrenanll. slep-by-elep faaricn towara mastory ef the abjcctivn, Exarases ral pat eutorariady om i's Fnotomertal cove-opme i, of Fal require en aorenary insight. avi nal buen ud, Or the othr hand, to wrorcices proves urough eately and chalerge te sid fhe ster interest and a vopi2s0at tre kl e* canes lary. Our geal is sludcnt success, Tati, ater a reasonable per ca of expiration ard examples studons wil beable “odo the exorcioos land rereby actreve tho ahyectve a respectable lever 3. A MOTIVATING GOAL FOR THE STUDENT “The puzales ape des reo 90 hl stuvents wil conen.ct a okt cr uneoramble fre anger to file in the aracess of checking Tho & answers. The ime onetales. a ar incentive ‘secause he audorts oot gel the puch lice unt they compere the xeraises. While ‘algobra sud nts eometias doorythesojokos as ‘dumb’ ar ever "very cam," ou npr os hs buen thal eidenls ally teak Pawar fe solvirg te puzzles and that they ‘doer ay the oki ane res, n wa Le, ng vaity ane. nevcy of prococures fr seine ‘hu puzzles ie p eapliro shunt eros. Dy kecoing seramb ec answer Vets shor arc Procedures simp, we nave Wiad Lo mir mize the te epert cn Fnoing answers cx ding biter purtle-ruch ares. In adnan Ia i830 elles io aka he putes efectve, we vs uc lo make trem eauy o use. Tha objet va or each puzac glen Bot 8: tne bovam et the uz: w vag ard in he Lal 8c! conten, Fa nigger pie onsions ard spentie abet ccmresane to hore in widely sed llgebia tunbouss, Nearly avory plzale requros rupicairg arly one page. Fina y bucauee Fa puzzles are 2ol-corracng, shay ar elmnato te teak el rerting aesign” ert ‘We hope tha: you wil ind the weauh-ng ef slgeb-n, al you stunems the ‘earning of algebra, le lout ard more in with sete puzzles. Save are aris Mi TABLE OF CONTENTS AND OBJECTIVES BOOK A INTRODUCTION TO ALGEBRA Evaluate varisble expressions. Apply rules for erder of operations: evaiuaie variable expressions Simplify ar evaluate expressions with grouping symbols Recognize applicstons of the commutative and asscciative axioms Use the aistributive axiom to mattiply of factor expressions. Simplify expressions by combining Ike terms (all positive terms) Simplify expressions containing parertaeses {al. positive terms} Evaluate expressions containing exponents |. Determine if a glen vafue s a solution of an open sentence. i, Translate English phrases imo algeoraic expression OPERATIONS WITH INTEGERS Ade integers represented by arrows on a number line Add integer a Use spposite and absolute values of intege:s... Use several integers; solve word problems involving addon of Integers Multialy integers... . — Multialy integers {including factors with exponents). ‘Add or mutiply integers (review! ‘Subtract integers Divice integers. ‘Add, muliiply. or divide integers (review! Perform all four operations wilh inegers (review) VARIABLES, EXPRESSIONS, AND FORMULAS ‘Simplify expressions by combining ike terms. ‘Simplify and then evaluate expressions. Simpy expressions covtaining parentheses ‘Simplify expressions that require ading ot subtractirg a nomial ‘Sly and evahote expressions cortaicing parentheses Evaluate formulas. SOLVING EQUATIONS AND WORD PROBLEMS Solve equations of the form x-+ a ~ b (terms n each equatens are added) ‘Solve equations cf the jorm x~ @-= b (terms are aoded or subtracted] ‘Solve word problems sing equations ike those on pages 28-29 ‘Solve equations of the form ax ~ b, where ais an imeger or unit fraction faalutions are integers) 2. Solve equations of the form ax ~ b, where a's an integer oF unit fraction {solutions are not necessarily integers)... . f. Solve equations of the form ax 6, where ais an iteger or iraction 9. Solve equavions of the form ax + b= 6 where ais an integer {solutions are integers) h, Solve equatons of the form ax 1 b=, where ais an integer (solutions are not necessary integers). Solve aquaticns of the form ax~ = ¢, where ais ar integer or unit fraction. Solve word problems using eq satans fk» those an page 36 Solve equations of the form ax + b = 6, where ais an integer oF fraction Solve word problems using equations ke those on pags 38 Salve equations containing parentheses. sve. Solve equations having tve variable in both sides . Solve equations containing parentheses and having the variable in both sides SOLVING WORD PROBLEMS: Solve word problems invelving two numbers . Solve world probems involving wo of three numbers Solve word problems involving pet Mete un Solve word problems involving perimeter tmare chailenging problems}. Salve word problems involving consecutive integers - Solve word problems using equations lke those on pages 41-42 Solve word problems lke these on page 48 (more challenging problems) Solve word problenis involving ages Salve word problems invling ages iors changing problems Solve assorted werd problems (reve; DDITIONAL PRACTICE FOR SELECTED OBJECTIVES A a, Additional practice for Cbjective 2-k (page 21). ,Additionay practice for Objective 4h (page 85} c. ry e eagcrte Adgitional practice for Objeciive 4-# (page 38) Additional practice for Objective 4-0 [page 42) Adlitionat practioe for Objective 5-b [page 44 TEST OF GENIUS SOLUTIONS TABLE OF CONTENTS AND OBJECTIVES BOOK B POLYNOMIALS: a. Wrte or evauuate exponential expressions ee) ._Smekiy pebmarat oy cerbinng the ems . — 60 © Add polynomials i. 84 Subtract polynomials... sss onnsunsssnnn ne va se 62 fe. Muttiply monomials.... nnn win : co 5 Find powers af a monomer so 64 9. Add, subtract, or muliply mononars (review)... : 85 fh, Muttpty or tnd powers of snonomials (review) eB i. Add, subtract. multiply, er find powers of monamials (eviews 6? ji Multiply 4 polynoria! by a monamal 68 k Muttiply palynornials 68 | Solve word pioblams invalving area {quadratic terms cancal) 70 MORE WORK WITH FORMULAS AND WORD PROBLEMS a b Evaluate lomulas. nA Solve a formula for a given variable (formulas have ne variables in the denominator) 7 Solve word problems involving money. 2 Solve word problems invelvng wnitorm mation 74 Solve word problems invalving uniiorm mation (r1ora challenging problems) .......75 FACTORING POLYNOMIALS a b 6 4 e f Q h Divide monomials 76 Ovid a polynomial by a maririal 7 Find a missing factor of a moron 78 Identity factors of a monomial 7a Factor a polynamial as the product ofits graatest monomial factar and anather ppol nomial (polynomials in one variate} ... 20 Factor a palynomual as the proguct ofits greatest mienorial factor ard anther polynomial ‘polyneraials in one or wo var'ables} at Mustiply binomials meataly 2-88 Simplty products of the form (a ~ bia Oh factor differences oF squares, a4 Find squares of binomials; recognize twnornial squares as Find squares oj bnomiais; tacior tiromial squares, a6 Factor completely @ polyriamal that has as a factor a difference of squares ara trinomial square. Factor tinomals of the torm x” + bx + 6 whera cis positive Factor tiramals of the form x° + bx + 6, whera cis negative a Factor trinomials of the form x° + 9x-+ 6, where Cis positive or negative (review)... 90 Factor trinamials of the form av’ — by + c, where als a positive integer ‘reate: than + oni 91-92 Factor trinomists usirg the methods on preceding pages (raview) Factor polynomtiais completely {excludes factonng by grauping). Factor a palynorial whose terms corcain a ecmman binomia! factor Facter polyncrriats by grouping Factar poiynerria's completely tincludes faciering by grouping) Factor polynomials cumplotely {po.ynomials with tactors of the farm aK + bay + ey4) os Factor polynomials complataly {review ofall iynes on preceding pages)... 4, SOLVING EQUATIONS AND WORD PROBLEMS BY FACTORING Solve equations when ane side is in factored form and the other side is 0. Sulve quadratic equations by factoring ‘equations in standard form Solve quadratic equations by factoring {equations in standard fori Solve pa ynomial equatiors of degree ‘hree or four by ‘acloring Salve wore problems involving squares of nunbers ar consecutive integers Solve word problems involving area, 5. SIMPLIFYING ALGEBRAIC FRACTIONS b « Simplify algebraic fractions both numerater and denaininator walten in descending order of exponents with first coefficient posilive} ‘Simplify algabraie fractions (numerator aud‘or denorrinator not written in ascending orcar of axgoncnts with fret caetficant positive} ‘Simplify algabraic fractions (numerator end denominator contain monomial factors} ‘Simply algabraic fractions (raviaw of procading threa pagas) Multiply algebraic fractions. Multiply algebraic fractions imare chalanging exercises) Divide algebra’ fractions... ‘Simpily products and quotients involving three algebraic fractions 6. VOCABULARY REVIEW Demonstrate knowledge of basic vocabulary used in lirs-semester algebra.. 7. TEST OF GENIUS 8. SOLUTIONS. 116 288 TABLE OF CONTENTS AND OBJECTIVES BOOK C COMBINING ALGEBRAIC FRACTIONS a. Add algebraic fractions with like denominators. ssi onnnonncinen eel E tb. Add aigsbra‘e fractions with unlike maomial deneminators. excluding unlike powers} : ne Add algebraic fractions with unlike moramial denominators (including unlike powers} vo sev ee NG d. Add algebraic fractions with polynomial denaminatars san. en 120 ©. Subtract algebraic fractiens, . denen BT {Simply mised expressions nd 22 POLYNOMIAL DIVISION 8. wide a polynomial by a binomial b. Divide a polynomial by a binomial (more challenging exarses) APPLYING ALGEBRAIC FRACTIONS a. Express a ratia ar rate in simplest form 128 b. Solve word oroblems invoWing ratios. 128 €. Solve propartons 107 4. Solve ward prablems using proportions 128 ©. Solve equations with fractional coetticients ~ 128 {Solve word problems using equations like Srase on page 129 ve wesosewecvess-o190 9. Solve fractional equations (solving a quadratic equation is notrequited) ...2....131 h. Solve fractional equations (solving a quadratic equation may be required) es... 132 i. Find @ percant of a number 133 i. Find a percent ot a number; find what percent one number is of anther: or ‘ind a number given a percent of the number on 134-436 k. Solve ward problems invoiving percents " vin ene Solve word problems invoiving tha percent ot increase or decrease inva quantity 137 MORE WORK WITH FORMULAS AND WORD PROBLEMS a. Sclve a formula for a given letter (formulas may have variables inthe denominator) ees . can 498 2. Sclve word problams involving investments. ss. 2139 © Sclva word problems involving investments (more Bhalenging DrObIEMMS| en 1 AD 4. Sclve ward problems involving dry mixtures ri 2. Solve word problems involving liquid mixtures. 142 1 Solve word problems involving work meas LINEAR EQUATIONS iN TWO VARIABLES AND GRAPHING a. Locate a point in a coardinate plans given its ccordinates.. - 14a b. Determine whether a gran orderad pair is a solution of an equation in twa variables. . 145 vi Find ordered pairs that satify a linear equation ana use them fo graph tha equatian iequations are so'ved for ys 146 147 4. Solve an equation far yin terms of x. 148 . Find ordered pas that satisly a linear equation and use them to graph the equation (equations are not solved for #3, 149 {Find the x-intercept and the y-intercept of tha graph of a inear aquation and use them ta graph the squatior 150-181 9. Find the slope ofa line given twa points on the line (using the graph 152 hf. Find the slope of a line given two poins on the line (net using the graph i. Find an equator of a ine given two nctats on the line (using the graph. J. Graph a tne given its equator in slope-intercapt form k.Find the slope and y-intarcapt of a line, given its equation |. Graph a line given its equatior (excludes vertical lines} m. Graph a line giver. ‘ts equatior [incudes vertical lines} 1. Find an equation ot a line give7 tha sicpe and one paint on tha kine ©. Find ar equatior. of a ling giver two points on tha ling (not using "he graph} SYSTEMS OF LINEAR EQUATIONS IN TWO VARIABLES a, Solve systems of equations by graphing. . 181-182 0. Solve systems of equations by the subs1ution snethod..... 183 ©. Solve systems of equations by the addition method no ‘Multiplication fs reqUiEED) vec nue eo Ne 4d. Salve systams of equattons by the addition method | (mulipication by - 1 may be raquirea) BB 2. Solve word oroblems using systems of equations like those on pages 103-165... 66 1. Solve systems of equations us ng multiplication wit. the addition method (equations are in standard form). AGT g. Solve systems of equations using multiplication with the addition method (equations are not necessayily in standard form}... 168 h. Solve word problems using systems of equations like those 99 page 67 wa. wu 189 SOLVING WORD PROBLEMS USING SYSTEMS OF EQUATIONS a. Solve word problems involving wniferm motion in a currant 170 b, Solve word problems involving ages ral & Soma word problems involving the digits of a numbar 172 1d, Soive assorted word problams (more challenging problems} - 173 TEST OF GENIUS so sn sneccunnnecmcnen 174 SOLUTIONS oe 238 TABLE OF CONTENTS AND OBJECTIVES BOOK D FUNCTIONS AND THEIA GRAPHS Determne whether ar not a relation is functor Find values of a funct'an; find the range ot a function for a given domain Deseribe how real warla iuntiona, relationships can ba represented by graphs, using concepts such as slope, domain, range, and inital cancitions. 177 ‘Scetch the graph ot a function using knowledge of real-norld relationships. ‘Graph quadratic functions and compare them te a linear ‘ynetion Find the constant af variation and write a1 aquation expressing direct var ation Graph ecuations expressing direct variation Solve ward problems involving diract variavan Find the constant of variation and write an equation expressing inve’se variation Graph equations expressing ‘nverse variation Solve word prabiems involving inverse variation: Solve ward problems involving direct or inverse variation as a square Write a formula expressing joint andar combined variation: INEQUALITIES a b d Identify the graph of the solution set af an inequality Solve inequalities of the form ax — b> ¢, where ais an integer ‘Solve nequalities af the ‘orm ax — bc, whore ais an intagar ar fraction ‘Solve inequalities containing parentheses andior having the variable in both sides. Identity she graph the union or imersection of two sets expressed ‘as inequalities 193. Identify the graph ol the solution sat of a combined inequality Solve equat'ons and inequalitias involving absolute value Graph lirear nequalitos in two variables finequalities arc so'ved for Graph linear incqualitis in two variables {inaqualitios are not necessarily solved far p 198-1 Solve systems of Inear inequalities in hwo variablas by graphing RATIONAL AND IRRATIONAL NUMBERS; RADICAL EXPRESSIONS a b, 6 4 Exp’ess a fraction a8 a repeating of terminating decimal: express 3 repeating dec ma as a fraction in lonest terms... Find the square rocts of numbers and expressions that have raticnal square roots Demonstrate understanding ot basic corcepts and vocabulary rélared to Lie ‘set of real nuribers. ‘Simplify square icots of numbars that have perfect scuare factors Find the length of a side of a right triangle using the Pythagurean property Solve word problems using the Pythagorean property 175 176 178 178 189 181 192 189 194 185 186 187 188 188 199 19° 192 194 195 196 197 198 200 201 202 208 204 205 206