Nme: Bd: Algebr II Pcker Collegite Istitute 008-009 Fil Exm Review Project We ve lered lot this yer. To prepre you for the fil exm, ech of you will be resposible for cretig study guide d study questios for few topics we ve studied this yer. Istructios for the study guide re below. I will collect d sc ech study guide, d pss this collective study guide o to you. If you do good job, you will be givig your collegues the gift of gret study guide. If you do bd job, you will be well ot relly be doig your collegues y fvors. Sice the work we ve doe o the eight-stdrd fuctios d their trsformtios, expoetil equtios, d logrithms hs bee so recet, I m ot icludig them for this study guide project. You will hve to review those o your ow. You c mke your study guide your ow. However, ech study guide should iclude the followig: 1. A expltio of the topics beig covered. You wt to use words d grphs d x-y tbles, etc., to expli to your udiece wht your topic is. You should ssume your udiece hs slightly less uderstdig of Algebr II th you do.. A listig of the relevt pges i the textbook (if pplicble) for your topic. If there re prticulr problems i the textbook which would provide good prctice, you should hve list of those problems.. A listig of ll the SmrtBords (if they exist) for your topic so studets kow where to go o the course coferece for more iformtio. 4. Exmple problems: t lest (but likely more) two exmple problems, whose solutios you hve worked out i detil expliig every step. 5. Prctice problems: At lest (but likely more) two prctice problems, for your collegues to work o. You will hve to hve solutios writte out o seprte pge, for studets to check their swers. Besides these study guides, the bsolute best resources you c use to study re (i order): Your old ssessmets The Qurter Test Study Guide Worksheets we ve doe i clss SmrtBords / clss otes The textbook Hds dow, the bsolute best resources you c use to study re your old ssessmets. If you c do those, you will be fie o the fil exm. 1
Poits / 5 / 10 / / 5 / 10 / 10 BONUS RUBRIC Expecttio You use proper mthemticl termiology d lguge i your writte expltio of your topic. You hve provided comprehesive overview o your topic, focusig o illumitig the cocepts to your clssmtes. Comprehesive mes you hve covered ll spects of your topic. You hve used grphs, tbles, chrts, umber lies, d/or pictures to illustrte your topic (if pplicble). You hve creted your grphs either usig your virtul TI, http://grphsketch.com/, or some other grphig progrm. You hve VERY NEATLY writte out (or typed) the equtios. You hve chose pproprite exmple d prctice problems. Approprite mes tht the problems re similr to oes we hve see o ssessmets or i clss ot too esy d ot too hrd. Your solutios to the exmple d prctice problems re comprehesive. Comprehesive mes tht the solutios re well-explied so tht everyoe c follow them. Your solutios hve o mistkes i them. This is of criticl importce, becuse your collegues will be usig these problems s their study guide. Ech mistke will result i sigifict poit reductio. You c er up to 5 bous poits for the followig: Icludig dditiol prctice problems d solutios for your topic Fidig d icludig the URLs for videos expliig your topic (YouTube!) Doig goig beyod the cll of duty job with your study guide Comig up with relly cretive/good dditiol problems (e.g. multiple choice, true flse, expli this sttemet) Typig up your work i MS Word, usig equtio editor to write your equtios (You cot er over 100% for this project.) Uit 1: Number Lies, Itervls, d Sets Set ottio (uio, itersectio, subset) Lier iequlities grph o umber lie Compoud iequlities Usig set d itervl ottio to write solutios to lier d compoud iequlities Absolute vlue iequlities Uit II: Algebric Mipultio: Rtiol Expressios d Expoets Fctorig qudrtic d cubic expressios Polyomil multiplictio d divisio (icludig sythetic divisio) Rtiol expressio dditio, subtrctio, multiplictio, d divisio Solvig rtiol equtios (wtchig out for dividig by zero!) Review of bsic expoet rules d simplifictio
Uit III: Rdicl Equtios SAMPLE Review properties of rdicls (iteger expoets) SAMPLE Simplifyig rdicls d rtiolizig the deomitor SAMPLE Solvig rdicl equtios Uit IV: Fuctios d Reltios Circles Wht is fuctio? (Icludig the defiitio of fuctio d fuctio ottio; the verticl lie test; idepedet d depedet vribles) Compositio of fuctios Fidig the domi d rge of fuctio visully (give grph, wht is the domi d rge); expressig the domi d rge i itervl ottio. Fidig the domi of fuctio lgebriclly (o dividig by zero, o egtives uder the squre root sig); expressig the domi d rge i itervl ottio Evlutig piecewise fuctio from () its equtio or (b) its grphs Icresig/decresig itervls for fuctios; reltive mxim/miim (visully d o clcultor) Mx/mi word problems (e.g. mximizig re d miimizig cost) Uit V: Lier Fuctios Equtios of verticl d horizotl lies Grphig lies (d their itersectios) Fidig prllel d perpediculr lies Systems of Equtios (grphig, substitutio, elimiitio) Lier regressios Uit VI: Qudrtics & Iequlities Complex umbers (dditio, subtrctio, multiplictio, divisio) Powers of i Completig the squre (vertex form); fidig the vertex Qudrtic formul d discrimit; fidig the zeros (rel, complex) Grphig qudrtics (1,, 5, ) Lier & Qudrtic Iequlities (umber lie) Lier & Qudrtic Iequlities (coordite ple) Qudrtic-lier systems
Smple Study Guide for: RADICALS AND RADICAL EQUATIONS NOTE: I m ot icludig prctice problems for this study guide. Relevt Resources: Textbook Sectios: R.6 (pges 8-47) d.5 (pges 7-9) Textbook Problems: R.6 #11-18, 5-8, 45-48, 51-58, 65-74, 89-9.5 #5-6, 40-60 Video o Simplifyig Rdicls: http://www.youtube.com/wtch?v=odqgv0vakg Video o Solvig Rdicl Equtios: http://www.youtube.com/wtch?v=ly8vbslf-4m Smrtbord: 008-10-14, 008-10-16, 008-10-17, 008-10-, 008-10-4 I previous yers, we ve lered bout squre roots. We kow 5 represets the umber tht whe multiplied by itself gives us 5. Whe we eter 5 o our clcultors, we get pproximtely.4 (d whe we multiply.4 by.4, we get pproximtely 5). For my study guide, I m goig to expli to you how we c hve more th squre roots. We c hve cube roots, fourth roots, d eve th roots. We will lso ler how to solve simple equtios ivolvig rdicls. First off, I m goig to remid you of some ottio: 1/ = Ay umber rised to the 1/ power is simply the squre root of tht umber! It my ot mke sese why b c b c this is true immeditely, but rememberig the expoet rule = + will help us. Expltio of ottio: We kow tht 5 represets the umber, tht whe multiplied by itself, gives us 5. I other words: 5 5 = 5. However, let me write just oe more thig usig tht expoet rule: 1/ 1/ 1 5 5 = 5. From this it is cler tht 1/ 5 = 5. The sme rgumet follows whe I sy 5 represets the umber whe multiplied by itself three times gives us 5 (i other words: 5 5 5 = 5 ). Similrly, we c sy: = 1/ DANGER!: There is oe importt poit you must kow bout rdicls. You c ever hve egtive umber uder eve root, but you c hve egtive umber uder odd root. Why? Becuse if you hd 4, you d eed (rel) umber tht whe multiplied by itself, give you 4. But o (rel) umber whe multiplied by itself c give you egtive umber! So tht does t mke sese. However if you hd 8, you d eed umber tht whe multiplied by itself three times, gives you 8. Clerly tht umber is. 4
Simplifyig Rdicls To simplify rdicls, you should use fctor tree. If you hve th root, you eed fctors of umber to leve the rdicl. SAMPLE PROBLEM 1: Simplify 500 5 100 Rdicl Rules Sice there re two 10s, this simplifies to 10 5. SAMPLE PROBLEM : Simplify 100 Without doig the fctor tree, I foud the fctors of 100 to be *****5*5 Sice there re three s, I c simplify this to 150 The rules for rdicls re the sme s the rules you kow for squre roots: 1. b = b (multiplictio).. b b = where 0 = m m/ Rtiolizig the Deomitor b (divisio) Sometimes whe there re squre roots i the deomitor, we wt to remove them. This is reltively simple if we hve somethig like: 7 5 10 10. All we hve to do is multiply the expressio by (just 1!): SAMPLE PROBLEM : = i = However, if there you re fced with somethig like:, you cot use the sme method! We lered + 1 tht you c multiply the expressio by the cojugte of the deomitor: 1 SAMPLE PROBLEM 4: 1 ( 1) = i = = = + 1 + 1 1 + 1 1 5
Solvig Rdicl Equtios A rdicl equtio is simply equtio with rdicl i it. We mily solved equtios with squre roots i them. The simplest form of rdicl equtio is somethig like: SAMPLE PROBLEM 5: x = 7 We see just by lookig t it tht the solutio is x = 49 to get tht swer: ( x ) = ( 7), so x = 49. We might hve other roots, though, like: SAMPLE PROBLEM 6:( x 1) = ( ) x 1 = x 1 = 8 x = 7. We lso kow tht we could squre both sides The fil d most rduous of these types of equtios look like x + 5 + 5 = x. To solve these, there re certi steps: STEP 1: Get the rdicl loe o oe side of the equl sig: x + 5 = x 5 STEP : Squre both sides d simplify: x + 5 = ( x 5) x + 5 = x 10x + 5 STEP : Get ll terms o oe side of the equl sig: 0 = x 1x + 0 STEP 4: Solve the qudrtic equtio (by fctorig or qudrtic formul): 0 = ( x 10)( x ) So x = 10 d x = STEP 5: Test both solutios by pluggig them bck ito the origil equtio! x = 10 : 5 + 5 = 10 x = : 9 + 5 So the oly solutio is x = 10 6