TECHNICAL MATHEMATICS

Transcription

1 Ntiol Curriculu Stteet NCS Curriculu Assesset Polic Stteet GRADES 0

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3 CURRICULUM AND ASSESSMENT POLICY STATEMENT CAPS GRADES 0 CAPS

4 DISCLAIMER I view striget tie requireets ecoutered b Deprtet Bsic Eductio to effect ecessr editoril chges d lout djustets to Curriculu d Assesset Polic Stteets d suppleetr polic docuets, possible errors hve occurred i sid docuets plced o ficil deprtetl website If editoril, lout, cotet, teriolog or forule icosistecies re detected, user is kidl requested to brig this to ttetio Deprtet Bsic Eductio E-il: cpscoets@dbegovz or f Deprtet Bsic Eductio Strube Street Privte Bg X895 Pretori 000 South Afric Tel: F: Plei Street Privte Bg X90 Cpe Tow 8000 South Afric Tel: F: Website: 04 Deprtet Bsic Eductio ISBN: Desig d Lout b: Prited b: Goveret Pritig Works CURRICULUM AND ASSESSMENT POLICY STATEMENT CAPS

5 FOREWORD BY THE MINISTER Our tiol curriculu is culitio our efforts over period sevetee ers to trsfor curriculu bequed to us b prid Fro strt deocrc we hve built our curriculu o vlues tht ispired our Costitutio Act The Preble to Costitutio sttes tht is Costitutio re to: hel divisios pst d estblish societ bsed o deocrtic vlues, socil justice d fudetl hu rights; iprove qulit life ll citizes d free potetil ech perso; l foudtios for deocrtic d ope societ i which goveret is bsed o will people d ever citize is equll protected b lw; d build uited d deocrtic South Afric ble to tke its rightful plce s sovereig stte i fil tios Eductio d curriculu hve iportt role to pl i relig se is I 997 we itroduced outcoes-bsed eductio to overcoe curriculr divisios pst, but eperiece ipleettio propted review i 000 This led to first curriculu revisio: Revised Ntiol Curriculu Stteet Grdes R-9 d Ntiol Curriculu Stteet Grdes 0-00 Ogoig ipleettio chlleges resulted i or review i 009 d we revised Revised Ntiol Curriculu Stteet 00 to produce this docuet Fro 0 two 00 curricul, for Grdes R-9 d Grdes 0- respectivel, re cobied i gle docuet d will sipl be kow s Ntiol Curriculu Stteet Grdes R- The Ntiol Curriculu Stteet for Grdes R- builds o previous curriculu but lso updtes it d is to provide clerer specifictio wht is to be tught d lert o ter-b-ter bsis The Ntiol Curriculu Stteet Grdes R- ccordigl replces Subject Stteets, Lerig Progre Guidelies d Subject Assesset Guidelies with b Curriculu d Assesset Polic Stteets CAPS for ll pproved subjects listed i this docuet; Ntiol polic pertiig to progre d prootio requireets Ntiol Curriculu Stteet Grdes R ; d c Ntiol Protocol for Assesset Grdes R MRS ANGIE MOTSHEKGA, MP MINISTER OF BASIC EDUCATION CAPS

6 CONTENTS SECTION : INTRODUCTION TO THE CURRICULUM AND ASSESSMENT POLICY STATEMENTS FOR GRADE 0-6 Bckgroud 6 Overview 6 Geerl Ais South Afric Curriculu 7 4 Tie Alloctio 8 4 Foudtio Phse 8 4 Iteredite Phse 8 4 Seior Phse 9 44 Grdes 0 9 SECTION : FET INTRODUCTION 0 Wht is Techicl Mtics? 0 Specific Ais Techicl Mtics 0 Specific Skills 4 Focus Cotet Ares 5 Weightig Cotet Ares SECTION : FET CONTENT SPECIFICATION AND CLARIFICATION Specifictio Cotet to show Progressio Overview topics 4 Cotet Clrifictio with techig guidelies 9 Alloctio Techig Tie 0 Sequecig d Pcig Topics Topic lloctio per ter d clrifictio 4 SECTION 4: FET ASSESSMENT GUIDELINES 46 4 Itroductio 46 4 Iforl or Dil Assesset 47 4 Forl Assesset 47 4 CURRICULUM AND ASSESSMENT POLICY STATEMENT CAPS

7 44 Progre Assesset Recordig d Reportig Modertio Assesset 5 47 Geerl 5 47 Ntiol polic pertiig to progre d prootio requireets Ntiol Curriculu Stteet Grdes R ; d 5 47 The polic docuet, Ntiol Protocol for Assesset Grdes R 5 CAPS 5

8 SECTION INTRODUCTION TO THE CURRICULUM AND ASSESSMENT POLICY STATEMENTS FOR TECHNICAL MATHEMATICS GRADE 0 - Bckgroud The Ntiol Curriculu Stteet Grdes R NCS stipultes polic o curriculu d ssesset i schoolig sector To iprove its ipleettio, Ntiol Curriculu Stteet ws eded, with edets coig ito effect i Jur 0 A gle coprehesive Ntiol Curriculu d Assesset Polic Stteet ws developed for ech subject to replce old Subject Stteets, Lerig Progre Guidelies d Subject Assesset Guidelies i Grdes R The eded Ntiol Curriculu d Assesset Polic Stteets Jur 0 replce Ntiol Curriculu Stteets Grdes R 9 00 d Ntiol Curriculu Stteets Grdes Overview The Ntiol Curriculu Stteet Grdes R Jur 0 represets polic stteet for lerig d techig i South Afric schools d coprises followig: Ntiol Curriculu d Assesset Polic stteets for ech pproved school subject s listed i polic docuet, d Ntiol polic pertiig to progre d prootio requireets Ntiol Curriculu Stteet Grdes R, which replces followig polic docuets: i ii Ntiol Seior Certificte: A qulifictio t Level 4 o Ntiol Qulifictios Frework NQF; d A ddedu to polic docuet, Ntiol Seior Certificte: A qulifictio t Level 4 o Ntiol Qulifictios Frework NQF, for lerers with specil eeds, published i Goveret Gzette, No9466 Deceber 006 b c d The Ntiol Curriculu Stteet Grdes R Jur 0 should be red i cojuctio with Ntiol Protocol for Assesset Grde R, which replces polic docuet, A ddedu to polic docuet, Ntiol Seior Certificte: A qulifictio t Level 4 o Ntiol Qulifictios Frework NQF, for Ntiol Protocol for Assesset Grde R, published i Goveret Gzette, No 9467 Deceber 006 The Subject Stteets, Lerig Progre Guidelies d Subject Assesset Guidelies for Grdes R 9 d Grdes 0 hve bee repeled d replced b Ntiol Curriculu d Assesset Polic Stteets for Grdes R Jur 0 The sectios o Curriculu d Assesset Polic s discussed i Chpters, d 4 this docuet costitute ors d stdrds Ntiol Curriculu Stteet Grdes R Therefore, i ters sectio 6A South Afric Schools Act, 996 Act No , this fors bsis o which Miister Bsic Eductio will deterie iiu outcoes d stdrds, s well s processes d procedures for ssesset lerer chieveet, tht will ppl i public d idepedet schools 6 CURRICULUM AND ASSESSMENT POLICY STATEMENT CAPS

9 Geerl Ais South Afric Curriculu b The Ntiol Curriculu Stteet Grdes R spells out wht is regrded s kowledge, skills d vlues worth lerig It will esure tht childre cquire d ppl kowledge d skills i ws tht re eigful to ir ow lives I this regrd, curriculu prootes ide groudig kowledge i locl cotets, while beig sesitive to globl ipertives The Ntiol Curriculu Stteet Grdes R serves purposes : equippig lerers, irrespective ir socio-ecooic bckgroud, rce, geder, phsicl bilit or itellectul bilit, with kowledge, skills d vlues ecessr for self-fulfilet, d eigful prticiptio i societ s citizes free coutr; providig ccess to higher eductio; fcilittig trsitio lerers fro eductio istitutios to workplce; d providig eploers with sufficiet prile lerer s copetecies c The Ntiol Curriculu Stteet Grdes R is bsed o followig priciples: socil trsfortio: esurig tht eductiol iblces pst re redressed, d tht equl eductiol opportuities re provided for ll sectios our popultio; ctive d criticl lerig: ecourgig ctive d criticl pproch to lerig, rr th rote d ucriticl lerig give truths; high kowledge d high skills: specifig iiu stdrds kowledge d skills to be chieved t ech grde settig high, chievble stdrds i ll subjects; progressio: showig progressio fro siple to cople i cotet d cotet ech grde; hu rights, iclusivit, eviroetl d socil justice: ifug priciples d prctices socil d eviroetl justice d hu rights s defied i Costitutio Republic South Afric The Ntiol Curriculu Stteet Grdes 0 Geerl is sesitive to issues diversit such s povert, iequlit, rce, geder, lguge, ge, disbilit d or fctors vlue idigeous kowledge sstes: ckowledgig rich histor d heritge this coutr s iportt cotributors to urturig vlues cotied i Costitutio; d credibilit, qulit d efficiec: providig eductio tht is coprble i qulit, bredth d depth to those or coutries d The Ntiol Curriculu Stteet Grdes R is to produce lerers tht re ble to: idetif d solve probles d ke decisios ug criticl d cretive thikig; work effectivel s idividuls d with ors s ebers te; orgise d ge selves d ir ctivities resposibl d efficietl; collect, lse, orgise d evlute ifortio criticll; couicte effectivel ug visul, sbolic d/or lguge skills i vrious odes; use sciece d techolog effectivel d criticll showig resposibilit towrds eviroet d helth ors; d deostrte uderstdig world s set relted sstes b recogig tht proble solvig cotets do ot eist i isoltio CAPS 7

10 e Iclusivit should be cetrl prt orgistio, plig d techig t ech school This c ol occur if ll techers hve cpcit to recogise d ddress brriers to lerig, d to pl for diversit The ke to gig iclusivit is to esure tht brriers re idetified d ddressed b ll relevt support structures withi school couit, icludig techers, district-bsed support tes, istitutiol-level support tes, prets d Specil Schools s resource cetres To ddress brriers i clssroo, techers should eplo vrious curriculu differetitio strtegies such s those cotied i Deprtet Bsic Eductio s Guidelies for Iclusive Techig d Lerig 00 4 Tie Alloctio 4 Foudtio Phse The istructiol tie for ech subject i Foudtio Phse is idicted i tble below: Subject i Lguges FAL d HL ii Mtics iii Life Skills Begiig Kowledge Cretive Arts Phsicl Eductio Persol d Socil Well-beig Tie lloctio per week hours b c d Totl istructiol tie for Grdes R, d is hours d for Grde is 5 hours To Lguges 0 hours re llocted i Grdes R d hours i Grde A iu 8 hours d iiu 7 hours re llocted to Hoe Lguge d iiu hours d iu hours to First Additiol Lguge i Grdes R I Grde iu 8 hours d iiu 7 hours re llocted to Hoe Lguge d iiu hours d iu 4 hours to First Additiol Lguge To Life Skills Begiig Kowledge hour is llocted i Grdes R d hours re llocted for Grde s idicted b hours i brckets 4 Iteredite Phse The tble below shows subjects d istructiol ties llocted to ech i Iteredite Phse Subject i Hoe Lguge ii First Additiol Lguge iii Mtics iv Sciece d Techolog v Socil Scieces vi Life Skills vii Cretive Arts viii Phsicl Eductio i Religious Studies Tie lloctio per week hours CURRICULUM AND ASSESSMENT POLICY STATEMENT CAPS

11 4 Seior Phse The istructiol tie for ech subject i Seior Phse is llocted s follows: Subject i Hoe Lguge ii First Additiol Lguge iii Mtics iv Nturl Scieces v Socil Scieces vi Techolog vii Ecooic Mgeet Scieces viii Life Oriettio i Arts d Culture Tie lloctio per week hours Grdes 0 The istructiol tie for ech subject i Grdes 0 is llocted s follows: Subject i Hoe Lguge ii First Additiol Lguge iii Mtics iv Techicl Mtics v Mticl Literc vi Life Oriettio vii Three Electives Tie lloctio per week hours h The llocted tie per week be utilised ol for iiu uber required NCS subjects s specified bove, d ot be used for dditiol subjects dded to list iiu subjects Should lerer wish to fer dditiol subjects, dditiol tie hs to be llocted i order to fer se subjects CAPS 9

12 Sectio Curriculu d Assesset Polic Stteet CAPS FET Itroductio I Sectio, Furr Eductio d Triig FET Phse Techicl Mtics CAPS provides techers with defiitio Techicl Mtics, specific is, specific skills focus cotet res, d weightig cotet res Wht is Techicl Mtics? Mtics is uiversl sciece lguge tht kes use sbols d ottios for describig uericl, geoetric d grphicl reltioships It is hu ctivit tht ivolves observig, represetig d ivestigtig ptters d qulittive reltioships i phsicl d socil pheoe d betwee ticl objects selves It helps to develop etl processes tht ehce logicl d criticl thikig, ccurc d proble solvig tht will cotribute i decisio-kig Mticl proble solvig ebles us to uderstd world phsicl, socil d ecooic roud us, d, ost ll, teches us to thik cretivel The i Techicl Mtics is to ppl Sciece Mtics to Techicl field where ephsis is o APPLICATION dot o bstrct ides Specific Ais Techicl Mtics To ppl ticl priciples To develop fluec i coputtio skills with usge clcultors Mticl odellig is iportt focl poit curriculu Rel life techicl probles should be icorported ito ll sectios wheever pproprite Eples used should be relistic d ot cotrived Cotetul probles should iclude issues reltig to helth, socil, ecooic, culturl, scietific, politicl d eviroetl issues wheever possible 4 To provide opportuit to develop i lerers bilit to be ethodicl, to geerlize d to be skilful users Sciece Mtics 5 To be ble to uderstd d work with uber sste 6 To proote ccessibilit Mticl cotet to ll lerers This could be chieved b cterig for lerers with differet eeds, eg TECHNICAL NEEDS 7 To develop proble-solvig d cogitive skills Techig should ot be liited to how but should rr feture whe d wh proble tpes 8 To provide lerers t Techicl schools ltertive d vlue ddig substitute to Mticl Literc 9 To support d susti techicl subjects t Techicl schools 0 Techicl Mtics c ol be tke b lerers ferig Techicl subject echicl, civil d electricl egieerig To provide voctiol route liged with epecttios lbour i order to esure direct ccess to lerership/ ppreticeship 0 CURRICULUM AND ASSESSMENT POLICY STATEMENT CAPS

13 To crete opportuit for lerers to furr ir studies t FET Colleges t etrce level N-4 d thus cretig ltertive route to ccess or HEIs Specific Skills To develop essetil ticl skills lerer should: develop correct use lguge Mtics; use ticl process skills to idetif d solve probles use sptil skills d properties shpes d objects to idetif, pose d solve probles cretivel d criticll; prticipte s resposible citizes i techicl eviroet locll, s well s i tiol d globl couities; d couicte ppropritel b ug descriptios i words, grphs, sbols, tbles d digrs 4 Focus Cotet Ares Techicl Mtics i FET Phse covers te i cotet res Ech cotet re cotributes towrds cquisitio specific skills The tble below shows i topics i FET Phse Nuber sste Fuctios d grphs Fice, growth d dec 4 Algebr 5 Differetil Clculus 6 Euclide Geoetr 7 Mesurtio 8 Circles, gles d gulr oveet 9 Alticl Geoetr 0 Trigooetr Mi topics for Techicl Mtics: 5 Weightig Cotet Ares The weightig Techicl Mtics cotet res serves two prir purposes: firstl weightig gives guidce o out tie eeded to ddress dequtel cotet withi ech cotet re; secodl weightig gives guidce o spred cotet i eitio especill ed er sutive ssesset CAPS

14 Weightig Cotet Ares Descriptio Grde 0 Grde Grde PAPER Algebr Epressios, equtios d iequlities icludig ture roots i Grdes & 60 ± 90 ± 50 ± Fuctios & Grphs ecludig trig fuctios 5 ± 45 ± 5 ± Fice, growth d dec 5 ± 5 ± 5 ± Differetil Clculus d Itegrtio 50 ± TOTAL PAPER : Descriptio Grde 0 Grde Grde Alticl Geoetr 5 ± 5 ± 5 ± Trigooetr icludig trig fuctios 40 ± 50 ± 50 ± Euclide Geoetr 0 ± 40 ± 40 ± Mesurtio, circles, gles d gulr oveet 5 ± 5 ± 5 ± TOTAL Techicl Mtics i FET The subject Techicl Mtics i Furr Eductio d Triig Phse fors lik betwee Seior Phse d Higher Eductio bd All lerers psg through this phse cquire fuctioig kowledge Techicl Mtics tht epowers to ke sese ir Techicl field stud d ir plce i societ It esures ccess to eteded stud techicl ticl scieces d vriet techicl creer pths I FET Phse, lerers should be eposed to techicl ticl eperieces tht give opportuities to develop ir ticl resoig d cretive skills i preprtio for ore pplied tics i HEIs or i-job triig CURRICULUM AND ASSESSMENT POLICY STATEMENT CAPS

15 Sectio Curriculu d Assesset Polic Stteet CAPS FET Cotet Specifictio d Clrifictio Itroductio Sectio provides techers with: Specifictio cotet to show progressio Clrifictio cotet with techig guidelies Alloctio tie Specifictio Cotet to show Progressio The specifictio cotet shows progressio i ters cocepts d skills fro Grde 0 to for ech cotet re However, i certi topics cocepts d skills re siilr i two or three successive grdes The clrifictio cotet gives guidelies o how progressio should be ddressed i se cses The specifictio cotet should refore be red i cojuctio with clrifictio cotet CAPS

16 Overview topics Overview topics NUMBER SYSTEM NUMBER SYSTEM Grde Grde 0 0 Grde Grde Grde Grde Idetif rtiol ubers ubers d covert d covert Tke ote tht ubers eist eist or or th th those those o There re There ubers re ubers or th or those th studied those teritig or recurrig decils ito ito o rel uber rel uber lie, lie, so-clled so-clled o-rel o-rel ubers It i erlier studied grdes i clled erlier igir grdes ubers clled igir, It is for where,, b Z d b 0 ubers is possible It It is to possible squre to certi squre o-rel certi orel obti ubers egtive d rel obti ubers egtive s rel swers ubers Add, subtrct, divide, ultipl d ubers d d cople ubers ubers d cople ubers b b b Uderstd tht tht siple siple surds surds re ot re ot s swers Add, subtrct, divide, ultipl d siplif siplif rtiol rtiol igir igir ubers ubers d cople d ubers cople ubers Bir ubers ubers should should be be kow kow Solve equtios ivolvig cople Solve equtios ubers ivolvig cople ubers FUNCTIONS FUNCTIONS Work with reltioships betwee vribles Eted Grde 0 work o reltioships Itroduce ore forl defiitio i ters uericl, grphicl, verbl d Work with reltioships betwee vribles i Eted betwee Grde vribles 0 work i o ters reltioships uericl, Itroduce fuctio ore d forl eted defiitio Grde work o sbolic represettios fuctios ters uericl, grphicl, verbl d d betwee vribles i ters uericl, fuctio d eted Grde work o covert fleibl sbolic betwee represettios se represettios fuctios d grphicl, grphicl, verbl verbl d d sbolic sbolic represettios represettios reltioships reltioships betwee betwee vribles vribles i ters i ters tbles, covert grphs, fleibl words d betwee forule se fuctios fuctios d d covert covert fleibl fleibl betwee betwee se se uericl, uericl, grphicl, grphicl, verbl verbl d d sbolic sbolic represettios tbles, grphs, words d forule represettios fuctios d covert Iclude represettios lier d tbles, soe grphs, qudrtic words poloil d represettios tbles, grphs, words d represettios fuctios d covert fleibl betwee se represettios fuctios, forule epoetil fuctios d soe forule Iclude lier d qudrtic poloil fuctios, fleibl betwee se represettios tbles, grphs, words d forule rtiol fuctios epoetil fuctios dsoe rtiol fuctios tbles, grphs, words d forule Iclude lier, qudrtic d soe cubic poloil fuctios, epoetil d soe rtiol fuctios Iclude lier, qudrtic d soe cubic poloil fuctios, epoetil d soe Geerte s grphs s ecessr, iitill b rtiol Revise fuctios work studied i erlier grdes Geerte es s poit-b-poit grphs s plottig, ecessr, to ke iitill d test Revise work studied i erlier grdes b cojectures es poit-b-poit d hece geerlise plottig, to ke effects d preter test cojectures which results d hece i horizotl geerlise shift d tht effects which results preter i horizotl which stretch results i d/or reflectio horizotl bout shift -is d tht which results i horizotl stretch d/or reflectio bout - is Iclude lier d qudrtic poloil fuctios, epoetil fuctios d soe rtiol fuctios Iclude lier d soe qudrtic poloil fuctios, epoetil fuctios d soe rtiol fuctios Geerte s grphs s ecessr, iitill b es poit-b-poit plottig, to geerlise ke d test cojectures effect d preter hece which results geerlise i verticl effect shift d preter tht which which results i results verticl i verticl stretch shift d/or tht reflectio which results bout i -is verticl stretch d/or reflectio bout -is Geerte s grphs s ecessr, iitill b es poit-b-poit plottig, to ke d test cojectures d hece 4 CURRICULUM AND ASSESSMENT POLICY STATEMENT CAPS Proble solvig d grph work ivolvig prescribed fuctios Proble solvig d grph work ivolvig prescribed fuctios Averge grdiet betwee two poits Proble solvig d grph work ivolvig prescribed fuctios Proble solvig d grph work ivolvig prescribed fuctios Proble solvig d grph work ivolvig prescribed fuctios Averge grdiet betwee two poits Proble solvig d grph work ivolvig prescribed fuctios Pge 7 59

17 S FINANCE, GROWTH AND DECAY Use Use siple siple d d copoud copoud growth/dec growth/dec Streg Streg Grde work Grde work Use siple d copoud forule A P i d A P i growth forule to solve Use siple d copoud growth/dec probles forule A P i icludig iterest, d A P i hire purchse, to solve probles forule A P i d A P i to solve ifltio, icludig popultio probles iterest, growth icludig hire purchse, d iterest, or rel ifltio, hire life purchse, popultio probles icludig iterest, hire purchse, probles growth d ifltio, or rel popultio life probles growth d or rel life ifltio, popultio growth d or rel life probles probles The effect differet periods copoudig Criticll lse differet lo optios growth d dec The iplictios icludig effective fluctutig d foreig The effect differet periods copoudig The effect differet periods copoudig growth Criticll lse differet lo optios oil iterest echge rtes rtes growth d dec icludig effective d d dec icludig effective d oil iterest oil iterest rtes rtes FINANCE, GROWTH AND DECAY FINANCE, GROWTH AND DECAY Use siple d d copoud growth growth forule forule A P i d A P i to solve probles probles icludig icludig iterest, iterest, hire purchse, hire purchse, ifltio, ifltio, popultio popultio growth d growth or d rel or life rel life probles CAPS C The iplictios fluctutig foreig echge The iplictios rtes fluctutig foreig echge rtes 4 ALGEBRA 4 ALGEBRA Siplif epressios ug lws 4 ALGEBRA Appl lws epoets to epressios ivolvig Appl lw logrith to solve rel Siplif epoets epressios for itegrl ug epoets lws rtiol Appl epoets lws epoets to epressios Appl lw life probles logrith to solve rel life epoets for itegrl epoets ivolvig rtiol Siplif epoets epressios ug lws probles Appl lws epoets to epressios A b Estblish betwee which two itegers b Add, subtrct, b Estblish betwee which two itegers b Add, subtrct, epoets ultipl ultipl for d itegrl d divide divide siple epoets siple surds ivolvig rtiol epoets p give siple surd lies give siple surd lies c surds Deostrte b Estblish uderstdig betwee which two itegers defiitio b Add, subtrct, ultipl d divide siple c c Roud Roud rel rel ubers ubers to pproprite to pproprite c Deostrte logrith give d uderstdig siple lws surd eeded lies to solve rel life surds degree degree ccurc ccurc to to give give uber uber probles defiitio c Roud logrith rel ubers d to lws pproprite c Deostrte uderstdig decil digits decil digits eeded to solve degree rel life ccurc probles to give uber defiitio logrith d lws d Revise scietific ottio decil digits eeded to solve rel life probles d Revise scietific ottio Mipulte lgebric epressios b: Revise fctoristio fro Grde 0 Tke ote d uderstd Mipulte lgebric epressios b: Revise fctoristio fro Grde 0 ultiplig bioil b trioil; Tke ote d uderstd Reider d Reider Fctor Theores ultiplig bioil b trioil; Mipulte lgebric epressios b: d Fctor Revise Theores fctoristio for poloils fro Grde up 0 for poloils up to third fctorig coo fctor revisio; fctorig coo fctor revisio; ultiplig bioil b trioil; to third degree degree pros pros Reider fctorig fctorig b groupig b groupig i pirs; i pirs; fctorig coo fctor revisio; Reider d d Fctor Fctor ores ores will ot will ot be fctorig fctorig trioils; trioils; fctorig b groupig i pirs; be eied eied fctorig differece differece two squres two squres fctorig trioils; Fctorise third-degree Fctorise poloils third-degree revisio; fctorig differece two squres icludig eples which require revisio; poloils icludig eples fctorig differece d sus two revisio; fctorig differece d sus Fctor Theore which require Fctor cubes; d fctorig differece d sus two two cubes; d Theore siplifig, ddig, subtrctig, cubes; d siplifig, ddig, subtrctig, ultiplig d divisio lgebric siplifig, ddig, subtrctig, ultiplig d divisio lgebric frctios with uertors d ultiplig d divisio lgebric frctios with uertors d deoitors liited to poloils frctios with uertors d deoitors liited to poloils covered i fctoristio deoitors liited to poloils covered i fctoristio covered i fctoristio Pge

18 Deterie ture roots d coditios for which roots re rel, o-rel, equl, uequl, rtiol d irrtiol Deterie ture roots d coditios for which roots re rel, o-rel, equl, uequl, rtiol d irrtiol Solve: Solve: qudrtic equtios b fctoristio d b ug qudrtic forul; qudrtic equtios b fctoristio d b ug qudrtic forul; equtios i two ukows, oe which is 4 ALGEBRA Solve: Solve: lier equtios; lier equtios; qudrtic equtios b fctoristio; lier equtios or qudrtic, i two lgebricll ukows, oe or which is lier grphicll or qudrtic, lgebricll or grphicll literl equtios chgig subject epoetil forul; equtios cceptig tht qudrtic equtios b fctoristio; literl equtios chgig subject forul; Eplore Eplore ture roots ture through roots through vlue vlue b 4 c lws epoetil epoets hold equtios for rel cceptig epoets d solutios tht re lws ot ecessril epoets itegrl hold for or eve rel rtiol; epoets d solutios re ot lier iequlities ecessril i itegrl oe vrible or eve d rtiol; illustrte lier solutio iequlities grphicll; i oe vrible d d lier equtios illustrte i two solutio vribles grphicll; d lier equtios i two vribles siulteousl lgebricll d grphicll siulteousl lgebricll d grphicll 5 DIFFERENTIAL CALCULUS AND INTEGRATION 5 DIFFERENTIAL CALCULUS AND INTEGRATION A ituitive uderstdig A ituitive uderstdig cocept cocept liit b Differetitio specified fuctios fro first priciples liit b Differetitio specified fuctios fro first priciples c Use specified rules differetitio c Use specified rules differetitio d The equtios tgets to grphs fuctios e The bilit to sketch grphs cubic f Prcticl probles fuctios ivolvig optiistio d The equtios tgets to grphs e The bilit to sketch grphs cubic f Prcticl probles ivolvig optiistio d rtes chge icludig clculus otio d rtes chge icludig clculus otio 6 CURRICULUM AND ASSESSMENT POLICY STATEMENT CAPS g Bsic itegrtio g Bsic itegrtio 6 EUCLIDEAN GEOMETRY Revise cocept siilrit d proportiolit b Appl proportiolit i trigles c Appl id-poit ore Ivestigte ores geoetr circles ssuig results fro erlier grdes, toger with oe or result cocerig tgets d rdii circles b Solve circle geoetr probles, providig resos for stteets whe required Revise bsic results estblished i erlier grdes b Ivestigte d for cojectures bout properties specil trigles sclee, isosceles, equilterl d right-gled trigle d qudrilterls Pge 9 59

19 Revise cocept siilrit d proportiolit b Appl proportiolit i trigles Ivestigte ores geoetr circles ssuig results fro erlier grdes, toger with oe or result cocerig tgets d rdii circles 6 EUCLIDEAN GEOMETRY Revise bsic results estblished i erlier grdes c Ivestigte ltertive but equivlet b Ivestigte d for cojectures bout defiitios vrious polgos icludig properties specil trigles sclee, isosceles, equilterl sclee, isosceles, d right-gled equilterl trigle d rightgled d qudrilterls trigle, kite, prllelogr, CAPS c Appl id-poit ore b Solve circle geoetr probles, providig resos for stteets whe required c Ivestigte ltertive but equivlet defiitios vrious polgos icludig sclee, isosceles, equilterl d right-gled trigle, kite, prllelogr, rectgle, rhobus, squre d trpeziu rectgle, rhobus, squre d trpeziu d Applictio ore Pthgors 7 MENSURATION Coversio uits, squre uits d cubic Solve probles ivolvig volue d Revise work studied i erlier Grdes uits d Applictio ore Pthgors surfce re solids studied i erlier 7 MENSURATION grdes d cobitios those objects Coversio uits, squre uits d cubic uits to for Solve ore cople probles shped ivolvig solids volue d surfce Revise work studied i erlier Grdes b Deterie re irregulr figure ug Mid-ordite Rule re solids studied i erlier grdes d cobitios those objects to for ore cople shped solids 8 CIRCLES, ANGLES AND ANGULAR MOVEMENT b Deterie re irregulr figure ug Defie rdi Mid-ordite Rule Agles d rcs 8 CIRCLES, Covertig ANGLES degrees AND ANGULAR to rdis d MOVEMENT vice Degrees d rdis vers Defie rdi Sectors d Agles segets d rcs Covertig degrees to rdis d vice vers Agulr d Degrees circuferetil d rdis velocit Sectors d segets 9 ANALYTICAL GEOMETRY Agulr d circuferetil velocit 9 ANALYTICAL GEOMETRY Represet Represet geoetric geoetric figures figures i Crtesi i Crtesi coorditordite co- Use Crtesi Use co-ordite Crtesi co-ordite sste to sste to deterie: Use two-diesiol Use two-diesiol Crtesi co-ordite Crtesi co- sste, sste, d derive d derive d ppl, d for ppl, for two deterie: equtio lie through two give sste to deterie: ordite sste to deterie: two poits ; d ; forul for clcultig: equtio poits; lie through two give equtio circle equtio with cetre circle t with clcultig: distce betwee two poits; poits; equtio lie through oe poit d origi cetre cetre is 0;0; t origi cetre is distce betwee two poits; equtio lie through oe poit equtio tget to circle t grdiet lie seget joiig prllel or perpediculr to give lie; d 0;0; grdiet lie seget joiig d prllel or perpediculr to give give poit o circle; d poits; gle iclitio lie equtio tget to poits; lie; d poit/s itersectio circle t circle give d poit o co-ordites id-poit lie co-ordites id-poit gle iclitio lie stright lie circle; d seget joiig poits; d lie seget joiig poits; d poit/s itersectio circle equtio equtio stright stright lie joiig lie joiig two d stright lie two poits poits 7 Pge 0 59

20 8 CURRICULUM AND ASSESSMENT POLICY STATEMENT CAPS 0 TRIGONOMETRY Defiitios trigooetric fuctios 0 TRIGONOMETRY Defiitios trigooetric fuctios, d gled i right t trigles Tke ote tht re re specil es for reciprocls trigooetric fuctios ec ; sec d t cot c Eted defiitios, d t to 60 0 d clculte trigooetric rtios d Siplifictio trigooetric epressios/equtios b kig use clcultor d Solve siple trigooetric equtios for gles betwee 0 0 d 90 0 Use idetities: t,, t sec, d cot ec b Reductio forule, 80 d 60 c Deterie solutios trigooetric equtios for 60 0 d Appl e, ie d re rules pros se rules will ot be eied Appl trigooetric erlier grdes to pro side equls to right h Solve probles i two diesios b ug bove trigooetric fuctios d b costructig d iterpretig geoetric d trigooetric odels Solve probles i two diesios b ug e, ie d re rule Solve probles i two b costructig d iter d trigooetric odel uericl distces/leg Drw grphs, d t The effects preters o grphs defied b k, k d k t The effects p o grphs p, p d t p Oe preter should be tested t give tie if eiig horizotl shift Revise work studied i e Rottig vectors e d ie curves ol, Pge 59 0 TRIGONOMETRY Defiitios trigooetric fuctios, d gled i right t trigles Tke ote tht re re specil es for reciprocls trigooetric fuctios ec ; sec d t cot c Eted defiitios, d t to 60 0 d clculte trigooetric rtios d Siplifictio trigooetric epressios/equtios b kig use clcultor d Solve siple trigooetric equtios for gles betwee 0 0 d 90 0 Use idetities: t,, t sec, d cot ec b Reductio forule, 80 d 60 c Deterie solutios trigooetric equtios for 60 0 d Appl e, ie d re rules pros se rules will ot be eied Appl trigooetric idetities studied i erlier grdes to prove tht left hd side equls to right hd side Solve probles i two diesios b ug bove trigooetric fuctios d b costructig d iterpretig geoetric d trigooetric odels Solve probles i two diesios b ug e, ie d re rule Solve probles i two d three diesios b costructig d iterpretig geoetric d trigooetric odels Ol gles d uericl distces/legths should be used Drw grphs, d t The effects preters o grphs defied b k, k d k t The effects p o grphs p, p d t p Oe preter should be tested t give tie if eiig horizotl shift Revise work studied i erlier grdes Rottig vectors e d ie curves ol d Pge 59 0 TRIGONOMETRY Defiitios trigooetric fuctios, d gled i right t trigles Tke ote tht re re specil es for reciprocls trigooetric fuctios ec ; sec d t cot c Eted defiitios, d t to 60 0 d clculte trigooetric rtios d Siplifictio trigooetric epressios/equtios b kig use clcultor d Solve siple trigooetric equtios for gles betwee 0 0 d 90 0 Use idetities: t,, t sec, d cot ec b Reductio forule, 80 d 60 c Deterie solutios trigooetric equtios for 60 0 d Appl e, ie d re rules pros se rules will ot be eied Appl trigooetric idetities studied i erlier grdes to prove tht left hd side equls to right hd side Solve probles i two diesios b ug bove trigooetric fuctios d b costructig d iterpretig geoetric d trigooetric odels Solve probles i two diesios b ug e, ie d re rule Solve probles i two d three diesios b costructig d iterpretig geoetric d trigooetric odels Ol gles d uericl distces/legths should be used Drw grphs, d t The effects preters o grphs defied b k, k d k t The effects p o grphs p, p d t p Oe preter should be tested t give tie if eiig horizotl shift Revise work studied i erlier grdes Rottig vectors e d ie curves ol trigles Tke ote tht re re specil es for reciprocls trigooetric fuctios 0 TRIGONOMETRY Defiitios trigooetric fuctios, d gled i right t trigles Tke ote tht re re specil es for reciprocls trigooetric fuctios ec ; sec d t cot c Eted defiitios, d t to 60 0 d clculte trigooetric rtios d Siplifictio trigooetric epressios/equtios b kig use clcultor d Solve siple trigooetric equtios for gles betwee 0 0 d 90 0 Use idetities: t,, t sec, d cot ec b Reductio forule, 80 d 60 c Deterie solutios trigooetric equtios for 60 0 d Appl e, ie d re rules pros se rules will ot be eied Appl trigooetric idetities stu erlier grdes to prove tht left h side equls to right hd side Solve probles i two diesios b ug bove trigooetric fuctios d b costructig d iterpretig geoetric d trigooetric odels Solve probles i two diesios b ug e, ie d re rule Solve probles i two d three die b costructig d iterpretig geo d trigooetric odels Ol gles uericl distces/legths should be Drw grphs, d t The effects preters o grphs defied b k, k d k t The effects p o grphs p, p d t p Oe preter should be tested t give tie if eiig horizotl shift Revise work studied i erlier grdes Rottig vectors e d ie curves ol Pge 59 TRIGONOMETRY Defiitios trigooetric fuctios, d gled i right t trigles Tke ote tht re re specil es for reciprocls trigooetric fuctios ec ; sec d t cot c Eted defiitios, d t to 60 0 d clculte trigooetric rtios d Siplifictio trigooetric epressios/equtios b kig use clcultor d Solve siple trigooetric equtios for gles betwee 0 0 d 90 0 Use idetities: t,, t sec, d cot ec b Reductio forule, 80 d 60 c Deterie solutios trigooetric equtios for 60 0 d Appl e, ie d re rules pros se rules will ot be eied Appl trigooetric idetities studied i erlier grdes to prove tht left hd side equls to right hd side Solve probles i two diesios b ug bove trigooetric fuctios d b costructig d iterpretig geoetric d trigooetric odels Solve probles i two diesios b ug e, ie d re rule Solve probles i two d three diesios b costructig d iterpretig geoetric d trigooetric odels Ol gles d uericl distces/legths should be used Drw grphs, d t The effects preters o grphs defied b k, k d k t The effects p o grphs p, p d t p Oe preter should be tested t give tie if eiig horizotl shift Revise work studied i erlier grdes Rottig vectors e d ie curves ol d Pge 59 0 TRIGONOMETRY Defiitios trigooetric fuctios, d gled i right t trigles Tke ote tht re re specil es for reciprocls trigooetric fuctios ec ; sec d t cot c Eted defiitios, d t to 60 0 d clculte trigooetric rtios d Siplifictio trigooetric epressios/equtios b kig use clcultor d Solve siple trigooetric equtios for gles betwee 0 0 d 90 0 Use idetities: t,, t sec, d cot ec b Reductio forule, 80 d 60 c Deterie solutios trigooetric equtios for 60 0 d Appl e, ie d re rules pros se rules will ot be eied Appl trigooetric idetities studied i erlier grdes to prove tht left hd side equls to right hd side Solve probles i two diesios b ug bove trigooetric fuctios d b costructig d iterpretig geoetric d trigooetric odels Solve probles i two diesios b ug e, ie d re rule Solve probles i two d three diesios b costructig d iterpretig geoetric d trigooetric odels Ol gles d uericl distces/legths should be used Drw grphs, d t The effects preters o grphs defied b k, k d k t The effects p o grphs p, p d t p Oe preter should be tested t give tie if eiig horizotl shift Revise work studied i erlier grdes Rottig vectors e d ie curves ol b Eted defiitios Pge 59 0 TRIGONOMETRY Defiitios trigooetric fuctios, d gled i right t trigles Tke ote tht re re specil es for reciprocls trigooetric fuctios ec ; sec d t cot c Eted defiitios, d t to 60 0 d clculte trigooetric rtios d Siplifictio trigooetric epressios/equtios b kig use clcultor d Solve siple trigooetric equtios for gles betwee 0 0 d 90 0 Use idetities: t,, t sec, d cot ec b Reductio forule, 80 d 60 c Deterie solutios trigooetric equtios for 60 0 d Appl e, ie d re rules pros se rules will ot be eied Appl trigooetric idetities studied i erlier grdes to prove tht left hd side equls to right hd side Solve probles i two diesios b ug bove trigooetric fuctios d b costructig d iterpretig geoetric d trigooetric odels Solve probles i two diesios b ug e, ie d re rule Solve probles i two d three diesios b costructig d iterpretig geoetric d trigooetric odels Ol gles d uericl distces/legths should be used Drw grphs, d t The effects preters o grphs defied b k, k d k t The effects p o grphs p, p d t p Oe preter should be tested t give tie if eiig horizotl shift Revise work studied i erlier grdes Rottig vectors e d ie curves ol, Pge 59 0 TRIGONOMETRY Defiitios trigooetric fuctios, d gled i right t trigles Tke ote tht re re specil es for reciprocls trigooetric fuctios ec ; sec d t cot c Eted defiitios, d t to 60 0 d clculte trigooetric rtios d Siplifictio trigooetric epressios/equtios b kig use clcultor d Solve siple trigooetric equtios for gles betwee 0 0 d 90 0 Use idetities: t,, t sec, d cot ec b Reductio forule, 80 d 60 c Deterie solutios trigooetric equtios for 60 0 d Appl e, ie d re rules pros se rules will ot be eied Appl trigooetric idetities studied i erlier grdes to prove tht left hd side equls to right hd side Solve probles i two diesios b ug bove trigooetric fuctios d b costructig d iterpretig geoetric d trigooetric odels Solve probles i two diesios b ug e, ie d re rule Solve probles i two d three diesios b costructig d iterpretig geoetric d trigooetric odels Ol gles d uericl distces/legths should be used Drw grphs, d t The effects preters o grphs defied b k, k d k t The effects p o grphs p, p d t p Oe preter should be tested t give tie if eiig horizotl shift Revise work studied i erlier grdes Rottig vectors e d ie curves ol d 0 TRIGONOMETRY Defiitios trigooetric fuctios, d gled i right t trigles Tke ote tht re re specil es for reciprocls trigooetric fuctios ec ; sec d t cot c Eted defiitios, d t to 60 0 d clculte trigooetric rtios d Siplifictio trigooetric epressios/equtios b kig use clcultor d Solve siple trigooetric equtios for gles betwee 0 0 d 90 0 Use idetities: t,, t sec, d cot ec b Reductio forule, 80 d 60 c Deterie solutios trigooetric equtios for 60 0 d Appl e, ie d re rules pros se rules will ot be eied Appl trigooetric ide erlier grdes to prove side equls to right h Solve probles i two diesios b ug bove trigooetric fuctios d b costructig d iterpretig geoetric d trigooetric odels Solve probles i two diesios b ug e, ie d re rule Solve probles i two d t b costructig d iterpre d trigooetric odels O uericl distces/legths Drw grphs, d t The effects preters o grphs defied b k, k d k t The effects p o grphs p, p d t p Oe preter should be tested t give tie if eiig horizotl shift Revise work studied i erlie Rottig vectors e d ie curves ol to Pge 59 0 TRIGONOMETRY Defiitios trigooetric fuctios, d gled i right t trigles Tke ote tht re re specil es for reciprocls trigooetric fuctios ec ; sec d t cot c Eted defiitios, d t to 60 0 d clculte trigooetric rtios d Siplifictio trigooetric epressios/equtios b kig use clcultor d Solve siple trigooetric equtios for gles betwee 0 0 d 90 0 Use idetities: t,, t sec, d cot ec b Reductio forule, 80 d 60 c Deterie solutios trigooetric equtios for 60 0 d Appl e, ie d re rules pros se rules will ot be eied Appl trigooetric idetities studied i erlier grdes to prove tht left hd side equls to right hd side Solve probles i two diesios b ug bove trigooetric fuctios d b costructig d iterpretig geoetric d trigooetric odels Solve probles i two diesios b ug e, ie d re rule Solve probles i two d three diesios b costructig d iterpretig geoetric d trigooetric odels Ol gles d uericl distces/legths should be used Drw grphs, d t The effects preters o grphs defied b k, k d k t The effects p o grphs p, p d t p Oe preter should be tested t give tie if eiig horizotl shift Revise work studied i erlier grdes Rottig vectors e d ie curves ol d clculte trigooetric rtios c Siplifictio trigooetric epressios/ equtios b kig use clcultor d Solve siple trigooetric equtios for gles betwee 0 0 d 90 0 Use idetities: Pge 59 0 TRIGONOMETRY Defiitios trigooetric fuctios, d gled i right t trigles Tke ote tht re re specil es for reciprocls trigooetric fuctios ec ; sec d t cot c Eted defiitios, d t to 60 0 d clculte trigooetric rtios d Siplifictio trigooetric epressios/equtios b kig use clcultor d Solve siple trigooetric equtios for gles betwee 0 0 d 90 0 Use idetities: t,, t sec, d cot ec b Reductio forule, 80 d 60 c Deterie solutios trigooetric equtios for 60 0 d Appl e, ie d re rules pros se rules will ot be eied Appl trigooetric idetities studied i erlier grdes to prove tht left hd side equls to right hd side Solve probles i two diesios b ug bove trigooetric fuctios d b costructig d iterpretig geoetric d trigooetric odels Solve probles i two diesios b ug e, ie d re rule Solve probles i two d three diesios b costructig d iterpretig geoetric d trigooetric odels Ol gles d uericl distces/legths should be used Drw grphs, d t The effects preters o grphs defied b k, k d k t The effects p o grphs p, p d t p Oe preter should be tested t give tie if eiig horizotl shift Revise work studied i erlier grdes Rottig vectors e d ie curves ol, Pge 59 0 TRIGONOMETRY Defiitios trigooetric fuctios, d gled i right t trigles Tke ote tht re re specil es for reciprocls trigooetric fuctios ec ; sec d t cot c Eted defiitios, d t to 60 0 d clculte trigooetric rtios d Siplifictio trigooetric epressios/equtios b kig use clcultor d Solve siple trigooetric equtios for gles betwee 0 0 d 90 0 Use idetities: t,, t sec, d cot ec b Reductio forule, 80 d 60 c Deterie solutios trigooetric equtios for 60 0 d Appl e, ie d re rules pros se rules will ot be eied Appl trigooetric idetities studied i erlier grdes to prove tht left hd side equls to right hd side Solve probles i two diesios b ug bove trigooetric fuctios d b costructig d iterpretig geoetric d trigooetric odels Solve probles i two diesios b ug e, ie d re rule Solve probles i two d three diesios b costructig d iterpretig geoetric d trigooetric odels Ol gles d uericl distces/legths should be used Drw grphs, d t The effects preters o grphs defied b k, k d k t The effects p o grphs p, p d t p Oe preter should be tested t give tie if eiig horizotl shift Revise work studied i erlier grdes Rottig vectors e d ie curves ol, Pge 59 0 TRIGONOMETRY Defiitios trigooetric fuctios, d gled i right t trigles Tke ote tht re re specil es for reciprocls trigooetric fuctios ec ; sec d t cot c Eted defiitios, d t to 60 0 d clculte trigooetric rtios d Siplifictio trigooetric epressios/equtios b kig use clcultor d Solve siple trigooetric equtios for gles betwee 0 0 d 90 0 Use idetities: t,, t sec, d cot ec b Reductio forule, 80 d 60 c Deterie solutios trigooetric equtios for 60 0 d Appl e, ie d re rules pros se rules will ot be eied Appl trigooetric idetities studied i erlier grdes to prove tht left hd side equls to right hd side Solve probles i two diesios b ug bove trigooetric fuctios d b costructig d iterpretig geoetric d trigooetric odels Solve probles i two diesios b ug e, ie d re rule Solve probles i two d three diesios b costructig d iterpretig geoetric d trigooetric odels Ol gles d uericl distces/legths should be used Drw grphs, d t The effects preters o grphs defied b k, k d k t The effects p o grphs p, p d t p Oe preter should be tested t give tie if eiig horizotl shift Revise work studied i erlier grdes Rottig vectors e d ie curves ol, d 0 TRIGONOMETRY Defiitios trigooetric fuctios, d gled i right t trigles Tke ote tht re re specil es for reciprocls trigooetric fuctios ec ; sec d t cot c Eted defiitios, d t to 60 0 d clculte trigooetric rtios d Siplifictio trigooetric epressios/equtios b kig use clcultor d Solve siple trigooetric equtios for gles betwee 0 0 d 90 0 Use idetities: t,, t sec, d cot ec b Reductio forule, 80 d 60 c Deterie solutios trigooetric equtios for 60 0 d Appl e, ie d re rules pros se rules will ot be eied Appl trigooetric idetities studied i erlier grdes to prove tht left hd side equls to right hd side Solve probles i two diesios b ug bove trigooetric fuctios d b costructig d iterpretig geoetric d trigooetric odels Solve probles i two diesios b ug e, ie d re rule Solve probles i two d three diesios b costructig d iterpretig geoetric d trigooetric odels Ol gles d uericl distces/legths should be used Drw grphs, d t The effects preters o grphs defied b k, k d k t The effects p o grphs p, p d t p Oe preter should be tested t give tie if eiig horizotl shift Revise work studied i erlier grdes Rottig vectors e d ie curves ol b Reductio forule, Pge 59 0 TRIGONOMETRY Defiitios trigooetric fuctios, d gled i right t trigles Tke ote tht re re specil es for reciprocls trigooetric fuctios ec ; sec d t cot c Eted defiitios, d t to 60 0 d clculte trigooetric rtios d Siplifictio trigooetric epressios/equtios b kig use clcultor d Solve siple trigooetric equtios for gles betwee 0 0 d 90 0 Use idetities: t,, t sec, d cot ec b Reductio forule, 80 d 60 c Deterie solutios trigooetric equtios for 60 0 d Appl e, ie d re rules pros se rules will ot be eied Appl trigooetric idetities studied i erlier grdes to prove tht left hd side equls to right hd side Solve probles i two diesios b ug bove trigooetric fuctios d b costructig d iterpretig geoetric d trigooetric odels Solve probles i two diesios b ug e, ie d re rule Solve probles i two d three diesios b costructig d iterpretig geoetric d trigooetric odels Ol gles d uericl distces/legths should be used Drw grphs, d t The effects preters o grphs defied b k, k d k t The effects p o grphs p, p d t p Oe preter should be tested t give tie if eiig horizotl shift Revise work studied i erlier grdes Rottig vectors e d ie curves ol d 0 TRIGONOMETRY Defiitios trigooetric fuctios, d gled i right t trigles Tke ote tht re re specil es for reciprocls trigooetric fuctios ec ; sec d t cot c Eted defiitios, d t to 60 0 d clculte trigooetric rtios d Siplifictio trigooetric epressios/equtios b kig use clcultor d Solve siple trigooetric equtios for gles betwee 0 0 d 90 0 Use idetities: t,, t sec, d cot ec b Reductio forule, 80 d 60 c Deterie solutios trigooetric equtios for 60 0 d Appl e, ie d re rules pros se rules will ot be eied Appl trigooetric i erlier grdes to prov side equls to right h Solve probles i two diesios b ug bove trigooetric fuctios d b costructig d iterpretig geoetric d trigooetric odels Solve probles i two diesios b ug e, ie d re rule Solve probles i two d b costructig d iterp d trigooetric odels uericl distces/legt Drw grphs, d t The effects preters o grphs defied b k, k d k t The effects p o grphs p, p d t p Oe preter should be tested t give tie if eiig horizotl shift Revise work studied i er Rottig vectors e d ie curves ol c Deterie solutios trigooetric equtios for Pge 59 0 TRIGONOMETRY Defiitios trigooetric fuctios, d gled i right t trigles Tke ote tht re re specil es for reciprocls trigooetric fuctios ec ; sec d t cot c Eted defiitios, d t to 60 0 d clculte trigooetric rtios d Siplifictio trigooetric epressios/equtios b kig use clcultor d Solve siple trigooetric equtios for gles betwee 0 0 d 90 0 Use idetities: t,, t sec, d cot ec b Reductio forule, 80 d 60 c Deterie solutios trigooetric equtios for 60 0 d Appl e, ie d re rules pros se rules will ot be eied Appl trigooetric idetities studied i erlier grdes to prove tht left hd side equls to right hd side Solve probles i two diesios b ug bove trigooetric fuctios d b costructig d iterpretig geoetric d trigooetric odels Solve probles i two diesios b ug e, ie d re rule Solve probles i two d three diesios b costructig d iterpretig geoetric d trigooetric odels Ol gles d uericl distces/legths should be used Drw grphs, d t The effects preters o grphs defied b k, k d k t The effects p o grphs p, p d t p Oe preter should be tested t give tie if eiig horizotl shift Revise work studied i erlier grdes Rottig vectors e d ie curves ol d Appl e, ie d re rules pros se rules will ot be eied Appl trigooetric idetities studied i erlier grdes to prove tht left hd side equls to right hd side Solve probles i two diesios b ug bove trigooetric fuctios d b costructig d iterpretig geoetric d trigooetric odels Solve probles i two diesios b ug e, ie d re rule Solve probles i two d three diesios b costructig d iterpretig geoetric d trigooetric odels Ol gles d uericl distces/legths should be used Drw grphs Pge 59 0 TRIGONOMETRY Defiitios trigooetric fuctios, d gled i right t trigles Tke ote tht re re specil es for reciprocls trigooetric fuctios ec ; sec d t cot c Eted defiitios, d t to 60 0 d clculte trigooetric rtios d Siplifictio trigooetric epressios/equtios b kig use clcultor d Solve siple trigooetric equtios for gles betwee 0 0 d 90 0 Use idetities: t,, t sec, d cot ec b Reductio forule, 80 d 60 c Deterie solutios trigooetric equtios for 60 0 d Appl e, ie d re rules pros se rules will ot be eied Appl trigooetric idetities studied i erlier grdes to prove tht left hd side equls to right hd side Solve probles i two diesios b ug bove trigooetric fuctios d b costructig d iterpretig geoetric d trigooetric odels Solve probles i two diesios b ug e, ie d re rule Solve probles i two d three diesios b costructig d iterpretig geoetric d trigooetric odels Ol gles d uericl distces/legths should be used Drw grphs, d t The effects preters o grphs defied b k, k d k t The effects p o grphs p, p d t p Oe preter should be tested t give tie if eiig horizotl shift Revise work studied i erlier grdes Rottig vectors e d ie curves ol, Pge 59 0 TRIGONOMETRY Defiitios trigooetric fuctios, d gled i right t trigles Tke ote tht re re specil es for reciprocls trigooetric fuctios ec ; sec d t cot c Eted defiitios, d t to 60 0 d clculte trigooetric rtios d Siplifictio trigooetric epressios/equtios b kig use clcultor d Solve siple trigooetric equtios for gles betwee 0 0 d 90 0 Use idetities: t,, t sec, d cot ec b Reductio forule, 80 d 60 c Deterie solutios trigooetric equtios for 60 0 d Appl e, ie d re rules pros se rules will ot be eied Appl trigooetric idetities studied i erlier grdes to prove tht left hd side equls to right hd side Solve probles i two diesios b ug bove trigooetric fuctios d b costructig d iterpretig geoetric d trigooetric odels Solve probles i two diesios b ug e, ie d re rule Solve probles i two d three diesios b costructig d iterpretig geoetric d trigooetric odels Ol gles d uericl distces/legths should be used Drw grphs, d t The effects preters o grphs defied b k, k d k t The effects p o grphs p, p d t p Oe preter should be tested t give tie if eiig horizotl shift Revise work studied i erlier grdes Rottig vectors e d ie curves ol d 0 TRIGONOMETRY Defiitios trigooetric fuctios, d gled i right t trigles Tke ote tht re re specil es for reciprocls trigooetric fuctios ec ; sec d t cot c Eted defiitios, d t to 60 0 d clculte trigooetric rtios d Siplifictio trigooetric epressios/equtios b kig use clcultor d Solve siple trigooetric equtios for gles betwee 0 0 d 90 0 Use idetities: t,, t sec, d cot ec b Reductio forule, 80 d 60 c Deterie solutios trigooetric equtios for 60 0 d Appl e, ie d re rules pros se rules will ot be eied Appl trigooet erlier grdes to p side equls to righ Solve probles i two diesios b ug bove trigooetric fuctios d b costructig d iterpretig geoetric d trigooetric odels Solve probles i two diesios b ug e, ie d re rule Solve probles i two b costructig d i d trigooetric od uericl distces/le Drw grphs, d t The effects preters o grphs defied b k, k d k t The effects p o grphs p, p d t p Oe preter should be tested t give tie if eiig horizotl shift Revise work studied i Rottig vectors e d ie curves ol The effects preters o grphs defied b Pge 59 0 TRIGONOMETRY Defiitios trigooetric fuctios, d gled i right t trigles Tke ote tht re re specil es for reciprocls trigooetric fuctios ec ; sec d t cot c Eted defiitios, d t to 60 0 d clculte trigooetric rtios d Siplifictio trigooetric epressios/equtios b kig use clcultor d Solve siple trigooetric equtios for gles betwee 0 0 d 90 0 Use idetities: t,, t sec, d cot ec b Reductio forule, 80 d 60 c Deterie solutios trigooetric equtios for 60 0 d Appl e, ie d re rules pros se rules will ot be eied Appl trigooetric idetities studied i erlier grdes to prove tht left hd side equls to right hd side Solve probles i two diesios b ug bove trigooetric fuctios d b costructig d iterpretig geoetric d trigooetric odels Solve probles i two diesios b ug e, ie d re rule Solve probles i two d three diesios b costructig d iterpretig geoetric d trigooetric odels Ol gles d uericl distces/legths should be used Drw grphs, d t The effects preters o grphs defied b k, k d k t The effects p o grphs p, p d t p Oe preter should be tested t give tie if eiig horizotl shift Revise work studied i erlier grdes Rottig vectors e d ie curves ol, Pge 59 0 TRIGONOMETRY Defiitios trigooetric fuctios, d gled i right t trigles Tke ote tht re re specil es for reciprocls trigooetric fuctios ec ; sec d t cot c Eted defiitios, d t to 60 0 d clculte trigooetric rtios d Siplifictio trigooetric epressios/equtios b kig use clcultor d Solve siple trigooetric equtios for gles betwee 0 0 d 90 0 Use idetities: t,, t sec, d cot ec b Reductio forule, 80 d 60 c Deterie solutios trigooetric equtios for 60 0 d Appl e, ie d re rules pros se rules will ot be eied Appl trigooetric idetities studied i erlier grdes to prove tht left hd side equls to right hd side Solve probles i two diesios b ug bove trigooetric fuctios d b costructig d iterpretig geoetric d trigooetric odels Solve probles i two diesios b ug e, ie d re rule Solve probles i two d three diesios b costructig d iterpretig geoetric d trigooetric odels Ol gles d uericl distces/legths should be used Drw grphs, d t The effects preters o grphs defied b k, k d k t The effects p o grphs p, p d t p Oe preter should be tested t give tie if eiig horizotl shift Revise work studied i erlier grdes Rottig vectors e d ie curves ol d 0 TRIGONOMETRY Defiitios trigooetric fuctios, d gled i right t trigles Tke ote tht re re specil es for reciprocls trigooetric fuctios ec ; sec d t cot c Eted defiitios, d t to 60 0 d clculte trigooetric rtios d Siplifictio trigooetric epressios/equtios b kig use clcultor d Solve siple trigooetric equtios for gles betwee 0 0 d 90 0 Use idetities: t,, t sec, d cot ec b Reductio forule, 80 d 60 c Deterie solutios trigooetric equtios for 60 0 d Appl e, ie d re rules pros se rules will ot be eied Appl trigooet erlier grdes to p side equls to righ Solve probles i two diesios b ug bove trigooetric fuctios d b costructig d iterpretig geoetric d trigooetric odels Solve probles i two diesios b ug e, ie d re rule Solve probles i two b costructig d it d trigooetric od uericl distces/le Drw grphs, d t The effects preters o grphs defied b k, k d k t The effects p o grphs p, p d t p Oe preter should be tested t give tie if eiig horizotl shift Revise work studied i Rottig vectors e d ie curves ol The effects Pge 59 0 TRIGONOMETRY Defiitios trigooetric fuctios, d gled i right t trigles Tke ote tht re re specil es for reciprocls trigooetric fuctios ec ; sec d t cot c Eted defiitios, d t to 60 0 d clculte trigooetric rtios d Siplifictio trigooetric epressios/equtios b kig use clcultor d Solve siple trigooetric equtios for gles betwee 0 0 d 90 0 Use idetities: t,, t sec, d cot ec b Reductio forule, 80 d 60 c Deterie solutios trigooetric equtios for 60 0 d Appl e, ie d re rules pros se rules will ot be eied Appl trigooetric idetities studied i erlier grdes to prove tht left hd side equls to right hd side Solve probles i two diesios b ug bove trigooetric fuctios d b costructig d iterpretig geoetric d trigooetric odels Solve probles i two diesios b ug e, ie d re rule Solve probles i two d three diesios b costructig d iterpretig geoetric d trigooetric odels Ol gles d uericl distces/legths should be used Drw grphs, d t The effects preters o grphs defied b k, k d k t The effects p o grphs p, p d t p Oe preter should be tested t give tie if eiig horizotl shift Revise work studied i erlier grdes Rottig vectors e d ie curves ol o grphs 0 TRIGONOMETRY Defiitios trigooetric fuctios, d gled i right t trigles Tke ote tht re re specil es for reciprocls trigooetric fuctios ec ; sec d t cot c Eted defiitios, d t to 60 0 d clculte trigooetric rtios d Siplifictio trigooetric epressios/equtios b kig use clcultor d Solve siple trigooetric equtios for gles betwee 0 0 d 90 0 Use idetities: t,, t sec, d cot ec b Reductio forule, 80 d 60 c Deterie solutios trigooetric equtios for 60 0 d Appl e, ie d re rules pros se rules will ot be eied Appl trigooetric id erlier grdes to prove side equls to right h Solve probles i two diesios b ug bove trigooetric fuctios d b costructig d iterpretig geoetric d trigooetric odels Solve probles i two diesios b ug e, ie d re rule Solve probles i two d b costructig d iterpr d trigooetric odels uericl distces/legth Drw grphs, d t The effects preters o grphs defied b k, k d k t The effects p o grphs p, p d t p Oe preter should be tested t give tie if eiig horizotl shift Revise work studied i erl Rottig vectors e d ie curves ol, Pge 59 Defiitios trigooetric fuctios, d gled i right t trigles Tke ote tht re re specil es for reciprocls trigooetric fuctios ec ; sec d t cot c Eted defiitios, d t to 60 0 d clculte trigooetric rtios d Siplifictio trigooetric epressios/equtios b kig use clcultor d Solve siple trigooetric equtios for gles betwee 0 0 d 90 0 Use idetities: t,, t sec, d cot ec b Reductio forule, 80 d 60 c Deterie solutios trigooetric equtios for 60 0 d Appl e, ie d re rules pros se rules will ot be eied Appl trigooetric idetities studied i erlier grdes to prove tht left hd side equls to right hd side Solve probles i two diesios b ug bove trigooetric fuctios d b costructig d iterpretig geoetric d trigooetric odels Solve probles i two diesios b ug e, ie d re rule Solve probles i two d three diesios b costructig d iterpretig geoetric d trigooetric odels Ol gles d uericl distces/legths should be used Drw grphs, d t The effects preters o grphs defied b k, k d k t The effects p o grphs p, p d t p Oe preter should be tested t give tie if eiig horizotl shift Revise work studied i erlier grdes Rottig vectors e d ie curves ol d Pge 59 Defiitios trigooetric fuctios, d gled i right t trigles Tke ote tht re re specil es for reciprocls trigooetric fuctios ec ; sec d t cot c Eted defiitios, d t to 60 0 d clculte trigooetric rtios d Siplifictio trigooetric epressios/equtios b kig use clcultor d Solve siple trigooetric equtios for gles betwee 0 0 d 90 0 Use idetities: t,, t sec, d cot ec b Reductio forule, 80 d 60 c Deterie solutios trigooetric equtios for 60 0 d Appl e, ie d re rules pros se rules will ot be eied Appl trigooetric idetities studied i erlier grdes to prove tht left hd side equls to right hd side Solve probles i two diesios b ug bove trigooetric fuctios d b costructig d iterpretig geoetric d trigooetric odels Solve probles i two diesios b ug e, ie d re rule Solve probles i two d three diesios b costructig d iterpretig geoetric d trigooetric odels Ol gles d uericl distces/legths should be used Drw grphs, d t The effects preters o grphs defied b k, k d k t The effects p o grphs p, p d t p Oe preter should be tested t give tie if eiig horizotl shift Revise work studied i erlier grdes Rottig vectors e d ie curves ol Oe preter should be tested t give tie if eiig horizotl shift Revise work studied i erlier grdes Rottig vectors e d ie curves ol