KS3 Maths Progress Pi 3-year Scheme of Work Pi 1 Scheme of Work 2014 Programme of Study Unit description Pre-2014 sub-levels KS2 Reference

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1 T Ui Tachig hos 1 Aalysig ad displayig daa 11 dscib, ip ad copa obsvd disibios of a sigl vaiabl hogh: appopia ass of cal dcy (a, od, dia) cosc ad ip fqcy abls cosc ad ip ba chas cosc ad ip vical li (o ba) chas fo gopd daa K3 Mahs Pogss Pi 3-ya ch of Wok Pi 1 ch of Wok 2014 Poga of dy Ui dscipio P-2014 sb-lvls K2 Rfc Us a calclao ffcivly 3a Rps ad ip daa i abls, chas ad diagas 3c/3b Ya 3: aisics Exac daa ad ip disc ba chas 3a Ya 3: aisics Cosc o pap, ad sig ICT sipl ba gaphs ad ba-li gaphs 4c/ Fid 'os coo' fo a s of disc daa o gopd ba cha 3b/4c Exac daa ad ip fqcy abls Cosc o pap, ad sig ICT, fqcy diagas fo gopd disc daa Collc daa fo a sipl xpi ad cod i a sipl fqcy abl A 2 Calclaig 12 dsad ad s plac val fo igs od posiiv ad gaiv igs s h sybols =,, <, >,, s h fo opaios, icldig foal wi hods, wih posiiv ad gaiv igs s ig pows ad associad al oos (sqa, cb ad high) s a calclao ad oh chologis o calcla sls accaly ad h ip h appopialy Exac daa, ip ad daw coclsios fo li gaphs 4c/ Ya 4: aisics Fid h od fo ay ba cha Fid h odal class fo a sall s of gopd disc daa Fid h od ad ag of a s of daa. 3a/4c/ Calcla h dia of a s of daa Copa wo sipl disibios sig h ag, od ad dia Calcla h a fo a sall s of disc daa Ya 6: aisics Daw coclsios fo sipl saisics fo a sigl disibio Udsad ad apply h od i sipl calclaios (o backs) 3c/3b Ya 6: Addiio ad sbacio Apply h picipls of h coaiv, disibiv ad associaiv laws wih 3b/3a bs Add ad sbac sval bs, lookig fo sagis 3c/3b/3a Ya 3: Addiio ad sbacio olv sipl pobls sig idas of aio ad popoio ('o fo vy ad o i vy... ) 3a Ya 6: Raio ad popoio Dvlop calclao skills ivolvig gaiv b ip, sig chag, sqas ad sqa oo kys Cosolida h apid call of addiio ad sbacio facs ad posiiv ig 4c copls o 100 Us sadad col pocds o add ad sbac whol bs 4c Rcogis ad xd b sqcs fod by coig o o coig 3c/3b Ya 5: Addiio ad sbacio back Appoxia bfo cayig o a addiio o sbacio. 4c Ya 3: Addiio ad sbacio Rod posiiv whol bs o h as 10 3b Ya 4: Nb ad plac val Ya 5: Addiio ad sbacio Cosolida h apid call of liplicaio facs o Ya 4: Mliplicaio ad divisio Kow sqa bs, 1 1 p o / Ya 5: Mliplicaio ad divisio Chck a sl by cosidig if i is of h igh od of agid Mliply ad divid igs by 10 ad 100 ad 1000 ad xplai h ffc Ya 5: Mliplicaio ad divisio Divid a qaiy io wo pas i a giv aio wh aio is giv i wodd fo Ya 6: Raio ad popoio 3b/ Od posiiv ad gaiv igs i cox; show posiios o b lis 3 Expssios, fcios ad fola 11 Half- s s ad ip algbaic oaio: 3y i plac of y + y + y ad 3 y Fid ops of sipl fcios xpssd i wods sbsi ical vals io fola ad xpssios, icldig sciific fola Fid ops of sipl fcios i wods ad sybols dsad ad s h cocps ad vocablay of xpssios, qaios, iqaliis, s ad Dscib sipl fcios i wods facos Fid ops of o coplx fcios xpssd i wods iplify sipl lia algbaic xpssios by collcig lik s Cosc xpssios fo wodd dscipio, sig addiio ad sbacio 4c 4c 4 Gaphs 8 wok wih coodias i all fo qadas Cosc xpssios fo wodd dscipio, sig addiio, sbacio ad liplicaio bsi posiiv igs io sipl fola xpssd i wods Ya 6: Algba bsi igs io sipl fola xpssd i l sybols Ya 6: Algba Idify vaiabls ad s l sybols Ya 6: Algba Idify h kows i a fola ad a fcio Udsad h diffc bw a xpssio ad a fola ad h aig of h ky vocablay '' Div sipl fola xpssd i l sybols / Ip ifoaio fo a sipl al lif gaph, g pa (icldig Rad gaivs), x ad aifall; y coodia covsio i h gaphs fis qada - ic is ad ccis Ya 6: Posiio ad dicio Plo a co-odia i h fis qada Ya 6: Posiio ad dicio

2 5 Facos ad lipls 11 Kow ad dsad covios ad oaio sd fo 2-D co-odias i h Ya 6: Posiio ad dicio fis qada Rad x ad y co-odia i all fo qadas Ya 6: Posiio ad dicio Ga fis qada co-odias ha saisfy a sipl lia l; plo hs Ed of s s h cocps ad vocablay of pi bs s h cocps ad vocablay of facos (o divisos) Kow ad s h od of opaios (fo ls, o pows o backs) Ya 6: Addiio, sbacio, liplicaio ad divisio s h cocps ad vocablay of lipls s h cocps ad vocablay of coo facos Dvlop calclao skills ivolvig h s of cla kys ad all opaio kys 3c s h cocps ad vocablay of coo lipls Rcogis lipls of 2, 5, ad 10 ad 25 3a s h cocps ad vocablay of highs coo faco Exd wi hods o HTU U 4c Ya 4: Mliplicaio ad divisio s h cocps ad vocablay of lows coo lipl s covioal oaio fo h pioiy of opaios, icldig backs, pows, oos ad cipocals Udsad liplicaio as i applis o whol bs ad kow how o s s appoxiaio hogh odig o sia asws associaiv, coaivi ad disibiv laws. s a calclao ad oh chologis o calcla sls accaly ad h ip h Apply sipl ss of divisibiliy (2, 9, 10, 5) 3a appopialy Exd wi hods o HTU U Ya 5: Mliplicaio ad divisio Idify a las 2 facos of 2 digi bs wih 3 o 4 facos 3b Rod p o dow af divisio, dpdig o cox 3a Rcogis ad s lipls ad facos 4c Ya 5: Mliplicaio ad divisio Apply sipl ss of divisibiliy (3, 6, 4) 4c Fid coo facos ad pis Ya 5: Mliplicaio ad divisio Ya 6: Addiio, sbacio, liplicaio ad divisio Idify bs wih xacly 2 facos (pis) Rcogis ad s coo faco, highs coo faco ad lows coo lipl Apply sipl ss of divisibiliy (3, 6, 9, 4) 4c

3 p i g 6 Dcials ad ass 12 7 Agls ad lis 10 8 Masig ad shaps 11 dsad ad s plac val fo dcials dsad ad s plac val fo ass od dcials ad facios s h fo opaios, icldig foal wi hods, wih posiiv ad gaiv dcials od bs ad ass o a appopia dg of accacy [fo xapl, o a b of dcial placs o sigifica figs] s appoxiaio hogh odig o sia asws Choos siabl is o sia o as lgh, ass ad capaciy 3c/ Ya 6: Mas Rcod adigs ad sias fo scals o a siabl dg of accacy 3b/3a Rad ad ip scals o a ag of asig iss Daw ad as lis o h as illi (i ) 3a/4c Us dcial oaio fo hs ad hddhs 3b Ya 5: Nb facios Rcogis h laioship bw hddhs ad hs 3a Ya 5: Nb facios Kow wha ach digi pss i bs wih p o wo dcial placs 3a Ya 6: Facios Rad ad wi whol bs i figs ad wods 3a Od dcials (icldig i cox of ass) 4c Ya 5: Nb facios Udsad ad s dcial oaio ad plac val Ya 6: Facios Rad ad ip scals ivolvig dcials Copa dcials i diff coxs Ya 5: Nb facios Od ic is of as (.g. 1, 1 c, 1, 1 k o qival) 3a Cov bw lag ad sall whol b ic is / Ya 6: Mas Rcogis ad xd b sqcs by coig i dcials. 4c Us sadad col pocds o add ad sbac dcials wih p o wo placs Cosolida ad xd al hods of calclaio o icld dcials Rod posiiv whol bs o h as 10, 100 o c Rod dcials o o dcial plac o o h as whol b / Ya 6: Facios E ad ip bs o a calclao i diff coxs (dcials ad oy) E oy aos o calclao Rod dcials o wo dcial placs i cox of oy oly Ya 6: Facios Half- s dscib, skch ad daw sig covioal s ad oaios: pois, lis, paalll lis, Idify igh agls ad paalll lis 3c/4c Ya 3: Popis of shaps ppdicla lis, igh agls, gla polygos, ad oh polygos ha a flcivly ad oaioally Kow ad s lf ad igh, aiclockwis ad clockwis 3a syic Dscib agls as facios of fll s 1/4, 1/2, 3/4 3a Ya 5: Popis of shaps s h sadad covios fo labllig h sids ad agls of iagl ABC Kow ad s copass pois ad 90, 180, 270 3a apply h popis of agls a a poi apply h popis agls a a poi o a saigh li Idify ppdicla lis Ya 3: Popis of shaps Disigish bw ac ad obs agls 4c Ya 5: Popis of shaps Us a poaco o as ac agls o h as dg 4c Ya 5: Popis of shaps Us coc oaio fo labllig lis ad agls 4c/ Disigish bw ac, obs ad flx agls Ya 5: Popis of shaps Us a poaco o as obs agls o h as dg Ya 5: Popis of shaps Bgi o sia h siz of agls Us a poaco o daw ac agls o h as dg Ya 5: Popis of shaps Kow h s of agls o a saigh li Ya 6: Popis of shaps Kow h s of agls a od a poi Ya 6: Popis of shaps Ed of s calcla ad solv pobls ivolvig coposi shaps Choos siabl ic is o sia aa Ya 5: Mas daw ad as li sgs ad agls i goic figs Us is of as o sia ad solv pobls i vyday coxs div ad illsa popis of iagls, qadilaals, cicls, ad oh pla figs [fo xapl, ivolvig lgh, aa qal lghs ad agls] sig appopia lagag ad chologis Kow as of gla polygos 3c Classify iagls (isoscls, qilaal, scal) sig qal sids. 3c Ya 4: Popis of shaps Classify iagls (isoscls, qilaal, scal) sig qal agls 3b Ya 4: Popis of shaps Classify iagls (isoscls, qilaal, scal) sig lis of syy 3a Ya 4: Popis of shaps Rcogis popis of sqas ad cagls 3b/3a Udsad ad as pis of cagls ad gla polygos 3b Ya 5: Mas Calcla pis of cagls ad gla polygos 3a/4c Ya 5: Mas Fid h pi of a sqa/cagl by coig Calcla h pi ad aa of shaps ad fo cagls / Us h fola o calcla h aa of a sqa/cagl Ya 5: Mas Ya 6: Mas Idify sipl agl, sid ad syy popis of iagls Rcogis ad visalis h syy of a 2D shap li syy ad / Ya 4: Popis of shaps oaio syy Dscib flcio syy of ay iagl o qadilaal / Dscib li syy popis of gla polygos olv sipl goical pobls sig popis of iagls Fid h as of a sid giv h pi of sqas ad cagls

4 9 Facios, dcials ad pcags Tasfoaios 8 od dcials ad facios dfi pcag as b of pas p hdd kow ad s h ciia fo cogc of iagls idify popis of, ad dscib h sls of: aslaios idify popis of, ad dscib h sls of: oaios idify popis of, ad dscib h sls of: flcios Od facios wih coo doiaos o i facios sig diagas 3b Ya 6: Nb facios Us facio oaio o dscib pas of shaps. Ya 6: Nb facios Rcogis wh wo facios a qival wih a diaga 3b Ya 6: Nb facios Cacl a facio dow o is sipls fo 4c Chag a ipop facio o a ixd b Fid sipl facios of whol b qaiis 3b Ya 3: Nb facios Rla facios o divisio 3a Cosolda ad xd al hods of calclaio o icld facios Ya 6: Nb facios Cosolida ad xd al hods of calclaio o icld facios. (Addig ad sbacig facios wih coo doiaos) Ya 6: Nb facios Udsad a pcag as h b of pas p 100 4c Cov a pcag o a b of hddhs o hs Rcogis h qivalc of facios, dcials ad pcags Ya 6: Nb facios Fid sipl pcags of whol b qaiis Half- s Rcogis wh a shap will b af a flcio 3b Ya 6: Posiio ad dicio Rcogis ad visalis flcio i a io li Ya 6: Posiio ad dicio Udsad ad s lagag associad wih flcio Rcogis wh a shap will b af a aslaio 3a Ya 6: Posiio ad dicio Udsad ad s lagag associad wih aslaios 4c Rcogis ad visalis h asfoaio of a 2D shap; aslaio Ya 6: Posiio ad dicio Visalis wh a shap will b af a oaio Udsad oaios sig facio of, ad clockwis aiclockwis. Kow ad dsad h cog Bgi o dsad ha i cog shaps, cospodig sids ad agls a qal Ed of s Ed of ya s T Ui Tachig hos 1 Nb popis ad calclaios A Pi 2 ch of Wok 2014 Poga of dy Ui dscipio P-2014 sb-lvls 12 dsad ad s plac val fo igs Add ad sbac igs wih vayig bs of sigifica figs s h fo opaios, icldig foal wi hods, wih posiiv ad gaiv igs Udsad how o s backs i sipl calclaios s covioal oaio fo h pioiy of opaios, icldig backs, pows, oos ad cipocals Exd wi hods o TU x TU ad HTU x TU s aio oaio Add ad sbac gaiv igs fo posiiv ad gaiv igs dc a aio o sipls fo divid a giv qaiy io wo pas i a giv pa:pa aio Mliply by zo xpss h divisio of a qaiy io wo pas as a aio Mliply ad divid gaiv igs by a posiiv b dsad ha a liplicaiv laioship bw wo qaiis ca b xpssd as a aio o a Us aio oaio facio Rdc a aio o is sipls fo Rdc a h pa aio o is sipls fo by cacllig Fid qival aios olv sipl pobls sig aio xpssd i wods ad i aio oaio Rcogis h liks bw aio ad facioal oaio Us dic popoio i sipl coxs Us h iay hod o solv sipl wod pobls ivolvig aio 2 haps ad ass i 3D 11 div ad apply fola o calcla ad solv pobls ivolvig vol of cboids (icldig cbs) Kow ad s as of 3D shaps Idify 2D psaios of 3D shaps Idify ad co facs, dgs, vics Idify a pis ad kow i has a cosa coss scio Kow ad s goic popis of cboids ad shaps ad fo cboids Ddc popis of 3D shaps fo 2D psaios, icldig s, 3D skchs ad isoic dawigs Idify s of closd cbs ad cboids Idify s of 3D shaps gla ad igla polyhda Half- s 3 aisics 10 dscib, ip ad copa obsvd disibios of a sigl vaiabl hogh: appopia gaphical psaio ivolvig disc daa Us a l ad copass o cosc sipl s of 3D shaps Calcla h sfac aa of cbs Us s o calcla h sfac aa of sipl cboids Fid h vol of a cb ad cboid by coig cbs Kow h fola fo h vol of cb ad a cboid olv sipl pobls ivolvig is of as i h cox of lgh, aa ad capaciy Cov c 3 o lis Gop daa, wh appopia i qal class ivals / / / 4c/ / /

5 p i g psaio ivolvig disc daa cosc ad ip fqcy abls cosc ad ip ba chas cosc ad ip pi chas 4 Expssios ad qaios 10 cogis ad s laioships bw opaios icldig ivs opaios s ad ip algbaic oaio: backs sbsi ical vals io fola ad xpssios, icldig sciific fola dsad ad s h cocps ad vocablay of xpssios, qaios, iqaliis, s ad facos siplify ad aipla algbaic xpssios o aiai qivalc: collcig lik s siplify ad aipla algbaic xpssios o aiai qivalc: liplyig a sigl ov a back Ed of s 5 Dcial calclaios 10 dsad ad s plac val fo dcials od posiiv ad gaiv igs od dcials ad facios s h sybols =,, <, >,, s h fo opaios, icldig foal wi hods, wih posiiv ad gaiv dcials 6 Agls 10 daw ad as li sgs ad agls i goic figs s h sadad covios fo labllig h sids ad agls of iagl ABC apply h popis of agls a a poi apply h popis agls a a poi o a saigh li apply h popis vically opposi agls div ad s h s of agls i a iagl Half- s 7 Nb popis 10 s covioal oaio fo h pioiy of opaios, icldig backs, pows, oos ad cipocals s ig pows ad associad al oos (sqa, cb ad high) cogis pows of 2, 3, 4, 5 s h cocps ad vocablay of pi bs Us xpiaio o copl a daa collcio sh,.g. howig a dic o daa-loggig Us qsioai sposs o copl a daa collcio sh Ip daa fo copod ad copaaiv ba chas / Cosc a fqcy abl fo gopd disc daa ad daw a gaph Cosc copod ba gaphs Ip sipl pi chas Us aihic opaios wih algba iplify o coplx lia algbaic xpssios by collcig lik s,.g. x x, 2b 3a + Fid ops ad ips of sipl fcios xpssd i wods o sybols sig ivs opaios Cosc fcios (coplig a b achi) Udsad h diffc bw a xpssio ad a qaio ad h aig of h ky vocablay '' Udsad ad idify h kows i a qaio olv sipl lia qaios wih ig cofficis, of h fo ax = b o x +/ b = c,.g. 2x = 18, x + 7 = 12 o x 3 = 15 bsi solio back io qaio o chck i is coc Us disibiv law wih backs, wih bs Kow ha xpssios ca b wi i o ha o way,.g. 2 x x 7 = 2(3 + 7) Bgi o liply a posiiv ig ov a back coaiig lia s,.g. 4(x + 3) B abl o add dcials wih p o wo dcial placs, b wih vayig bs of dcial placs B abl o add o ha wo dcials wih p o wo dcial placs, b wih vayig bs of dcial placs B abl o sbac igs ad dcials wih p o wo dcial placs, b wih vayig bs of dcial placs B abl o add ad sbac o ha wo dcials wih p o wo dcial placs, b wih vayig bs of dcial placs ad sig a ix of opaios wihi h calclaio. Exd h possibl dcials ha ca b sd i al calclaios by sig halvig ad doblig sagis. Us al sagis fo liplicaio paiioig wo 2 digi bs wh o b iclds a dcial (boh bs hav wo sigifica figs) Mliply dcials wih wo placs by sigl-digi whol bs Mliply igs ad dcials icldig by dcials sch as 0.6 ad 0.06, 0. x 0. o 0. x 0.0h, 0.0h x 0. ad 0.0h x 0.0h Mally b abl o calcla h sqas of bs lss ha 16 liplid by a lipl of,.g. 0.2, 300, olv pobls ivolvig dcial bs /// Choos h coc opaio o s wh solvig dcial pobls /// Rod ad od dcials / Divid a qaiy io wo pas i a giv aio (whol bs), wh h asw is a dcial Us a poaco o as flx agls o h as dg Us coc oaio fo labllig iagls Us a poaco o daw flx agls o h as dg Calcla agls aod a poi Us a poaco o daw obs agls o h as dg Us a poaco o daw flx agls o as dg Idify iio ad xio agls i a shap Kow h s of agls i a iagl Calcla agls i a iagl Rcogis ad s vically opposi agls Us a l ad poaco o cosc a iagl giv wo sids ad h icldd agl (A) Us a l ad poaco o cosc a iagl giv wo agls ad h icldd sid (AA) Us l ad poaco o cosc sipl s of 3D shaps, sig sqas, cagls ad iagls,.g. sqa-basd pyaid, iagla pis Ivsiga iagls sig Pyhagoas' ho Kow sqa bs byod 10 x 10 Fid cospodig oos Us h sqa oo ad chag sig kys o a calclao

6 s h cocps ad vocablay of pi bs s h cocps ad vocablay of facos (o divisos) s h cocps ad vocablay of lipls s h cocps ad vocablay of coo facos s h cocps ad vocablay of coo lipls s h cocps ad vocablay of highs coo faco s h cocps ad vocablay of lows coo lipl s h cocps ad vocablay of pi facoisaio s podc oaio ad h iq facoisaio popy s covioal oaio fo h pioiy of opaios, icldig backs, pows, oos ad cipocals s ig pows ad associad al oos (sqa, cb ad high) cogis pows of 2, 3, 4, 5 s a calclao ad oh chologis o calcla sls accaly ad h ip h appopialy Ed of s 8 qcs 11 ga s of a sqc fo a -o- l ga s of a sqc fo a posiio-o- cogis aihic sqcs fid h h cogis goic sqcs ad appcia oh sqcs ha ais 9 Facios ad pcags 11 s h fo opaios, icldig foal wi hods, wih posiiv ad gaiv facios ip pcags ad pcag chags as a facio o a dcial xpss o qaiy as a pcag of aoh ip facios ad pcags as opaos Half- s 10 Pobabiliy 10 cod, dscib ad aalys h fqcy of ocos of sipl pobabiliy xpis ivolvig adoss, faiss, qally ad qally likly ocos s appopia lagag of pobabiliy s h 0-1 pobabiliy scal dsad ha pobabiliis of all possibl ocos s o 1 Exd al calclaios o sqas ad sqa oos Us a calclao fo cbs ad cb oos Us h od of opaios wih backs icldig i o coplx calclaios Us idx oaio fo sqas ad cbs ad fo posiiv ig pows of 10 Us idx oaio fo sall ig pows,.g = Fid LCM ad HCF fo liss of facos o lipls Fid h pi faco dcoposiio of a b lss ha 100 Fid h HCF o LCM of 2 bs lss ha 100 (sig pi faco dcoposiio) Kow all h sqas of bs lss ha 16 ad kow h sqa oo giv h sqa b. Chck by a ivs opaio (qsios oh ha fo ls,.g. sqa oos chckd wih sqaig) Wok wih calclaios wh h backs a sqad o sqa ood Esia sqa oos of o-sqa bs lss ha 100,.g. giv igs ha h oos li bw Ga s of sqcs aisig fo pacical coxs / Ga s of sipl sqcs sig -o- ls lik +3 o 2 Us h wods fii, ifii, ascdig ad dscdig o dscib sqcs Udsad h ifii a of a s of igs Ga s of a o coplx sqc sig -o- ls lik x 2 h +1 o 1 h x2 Ga s of lia sqcs sig -o- wih posiiv o gaiv igs Kow ha a aihic sqc is gad by a saig b a, h addig a cosa b, d Ga ad dscib sipl ig sqcs, sqa ad iagla bs Rcogis iagla bs Ga ad dscib ig sqcs sch as pows of 2 ad gowig cagls Rcogis goic sqcs ad appcia oh sqcs ha ais Fid a giv is posiio i h sqcs lik h b i 4x abl is 40 (o opaio o ) Fid a of a pacical sqc giv is posiio i h sqc Ga s of lia sqcs sig posiio-o- wih posiiv igs Bgi o s lia xpssios o dscib h h i a o-sp aihic sqc Us a diaga o copa wo o o sipl facios wih diff doiaos, ad o i facios Calcla facios of qaiis ad ass / Idify qival facios. Bgi o add ad sbac sipl facios ad hos wih sipl coo doiaos Exd h possibl facios ha ca b sd i al calclaios by sig halvig ad doblig sagis. Add facios by wiig wih a coo doiao, wh h doiaos a 12 o lss, wh h asw is lss ha 1 Udsad ha wh wo posiiv facios a addd h asw is lag ha ih of h oigial wo facios iplify facios by cacllig all coo facos Expss o b as a facio of aoh (halvs, qas, hids) Mliply a facio by a ig bac facios by wiig wih a coo doiao, wh h doiaos a lss ha 12 ad h fis facio is lag ha h scod Exd al hods of calclaio o icld pcags Calcla sipl pcags Us pcags o copa sipl popoios Expss o giv b as a pcag of aoh Us h vocablay of pobabiliy Us a pobabiliy scal wih wods Udsad ad s h pobabiliy scal fo 0 o 1 Idify all possibl ally xclsiv ocos of a sigl v Fid ad jsify pobabiliis basd o qally likly ocos i sipl coxs Kow ha if pobabiliy of v is p h pobabiliy of v o occig is 1 p

7 Ed of s Ed of ya s Idify all ally xclsiv ocos fo wo sccssiv vs wih wo ocos i ach v Esia pobabiliis basd o giv xpial daa Wh ipig sls of a xpi, s vocablay of pobabiliy Us xpiaio o copl a daa collcio sh.g. howig a dic o daa-loggig Us h lagag of pobabiliy o copa h choic of x/a wih y/a Pi 3 ch of Wok T Ui Tachig hos 2014 Poga of dy Ui dscipio P-2014 sb-lvls 1 Nb calclaios 10 s h fo opaios, icldig foal wi hods, wih posiiv ad gaiv ipop facios B abl o add ad sbac o ha wo igs wih vayig bs of ad ixd bs sigifica figs s covioal oaio fo h pioiy of opaios, icldig backs, pows, oos ad cipocals B abl o add ad sbac o ha wo dcials wih p o wo dcial s ig pows ad associad al oos (sqa, cb ad high) placs cogis pows of 2, 3, 4, 5 Cov bs sch as o 2.36 illio Us al sagis fo liplicaio - doblig ad halvig sagis Mliply 4-digi igs ad dcials by a sigl digi ig Mliply 3- o 4-digi igs by a 2-digi ig Divid 3-digi igs by a sigl digi ig wih aid Divid 3-digi by 2-digi igs o aid Divid dcials wih o o wo placs by sigl-digi igs Divid.p by a 2-digi b o giv.p Divid a ig o dcial wih 1 o 2 dp by a dcial b wih 1 d.p. Mliply gaiv igs by a gaiv b Divid gaiv igs by a posiiv o gaiv bs / Udsad h ifii a of h s of al bs (whol bs ad dcials h) Kow all h sqas of bs lss ha 16 ad giv h posiiv ad gaiv sqa oo of a sqa b Wok o cbs ad cb oos ally o wih a calclao / Us idx oaio fo sall ig pows, g p o 5 Esablish idx laws fo posiiv pows wh h asw is a posiiv pow Fid h pi faco dcoposiio of a b >100 Fid h HCF o LCM of 2 bs lss ha 100 sig pi faco dcoposiio Cobi laws of aihic fo backs wih al calclaios of sqas, /// cbs ad sqa oos B abl o wok wih dcials ad a calclao wih xpssios ha coai backs, sqas ad sqa oos as wll as h fo opaios B abl o sia asws o calclaios ivolvig 2 o o opaios 2 qcs ad qaios 11 s ad ip algbaic oaio: ab i plac of a b s ad ip algbaic oaio: 3y i plac of y + y + y ad 3 y Cosc xpssios fo wodd dscipio, sig all 4 basic opaios,.g. 30/x, x y, /2, 3 + 4, a + a + 3, a² s ad ip algbaic oaio: a² i plac of a a Kow ha liplicaio ad divisio a caid o bfo addiio ad ga s of a sqc fo a -o- l sbacio,.g. ab + cd, a b ad c d s b calclad bfo addig ga s of a sqc fo a posiio-o- cogis aihic sqcs iplify sipl xpssios i o ha o vaiabl, icldig posiivs ad gaivs, by collcig lik s fid h h Ga s of a lia sqc sig posiio-o -wih posiiv igs. A Ga s fo a coplx pacical cox (.g. axi cossigs fo a giv b of lis) Ga s of a lia sqc sig posiio-o- wih gaiv igs. Bgi o s lia xpssios o dscib h h i a wo-sp aihic sqc. (.g. h is o /2 5) Fid ops of o coplx fcios xpssd i wods (.g. add 6 h liply by 3) olv sipl wo-sp lia qaios wih ig cofficis, of h fo ax + b = c,.g. 3x + 7 = 25 Half- s 3 aisics 11 dscib, ip ad copa obsvd disibios of a sigl vaiabl hogh: appopia gaphical lc ad idify h daa lad o a pobl psaio ivolvig disc daa lc h ag of possibl hods ha cold b sd o collc his daa as dscib, ip ad copa obsvd disibios of a sigl vaiabl hogh: appopia gaphical piay o scoday daa psaio ivolvig coios ad gopd daa Discss h ag of possibl hods ha cold b sd o ivsiga a dscib, ip ad copa obsvd disibios of a sigl vaiabl hogh: appopia ass pobl,.g. qsioai, svy, odllig, daa loggig, c. of cal dcy (a, od, dia) lc appopia lvl of accacy of daa fo liid choics dscib, ip ad copa obsvd disibios of a sigl vaiabl hogh: appopia ass Fo a ag of sapl sizs idify h os ssibl asw of spad (ag, cosidaio of olis) Discss facos ha ay possibly affc h collcio of daa,.g. i, plac, cosc ad ip fqcy abls yp of popl askd, phasig of qsios cosc ad ip ba chas / /

8 4 Facios, dcials ad pcags cosc ad ip ba chas cosc ad ip pi chas cosc ad ip vical li (o ba) chas fo gopd daa cosc ad ip vical li (o ba) chas fo gopd ical daa Dscib sipl ahaical laioships bw wo vaiabls (bivaia daa) i obsvaioal ad xpial coxs Illsa sipl ahaical laioships bw wo vaiabls (bivaia daa) sig sca gaphs 12 wok ichagably wih iaig dcials ad hi cospodig facios (sch as 3.5 ad 7/2 o ad 3/8) ip pcags liplicaivly xpss o qaiy as a pcag of aoh copa wo qaiis sig pcags wok wih pcags ga ha 100% solv pobls ivolvig pcag chag: pcag icas solv pobls ivolvig pcag chag: dcas solv pobls ivolvig pcag chag: oigial val pobls solv pobls ivolvig pcag chag: sipl is i fiacial ahaics Ed of s 5 Goy i 2D ad 3D 10 div ad apply fola o calcla ad solv pobls ivolvig vol of cboids (icldig cbs) s scal diagas s aps div ad apply fola o calcla ad solv pobls ivolvig vol of cboids (icldig cbs) div ad s h sadad l ad copass coscios: ppdicla bisco of a li sg div ad s h sadad l ad copass coscios: coscig a ppdicla o a giv li fo/a a giv poi div ad s h sadad l ad copass coscios: biscig a giv agl cogis ad s h ppdicla disac fo a poi o a li as h shos disac o h li dscib, skch ad daw sig covioal s ad oaios: pois, lis, paalll lis, ppdicla lis, igh agls, gla polygos, ad oh polygos ha a flcivly ad oaioally syic dsad ad s h laioship bw paalll lis ad ala ad cospodig agls s h s of agls i a iagl o ddc h agl s i ay polygo div popis of gla polygos s h s of agls i a iagl o ddc h agl s i ay polygo div popis of gla polygos s h s of agls i a iagl o ddc h agl s i ay polygo Fid h od ad ag fo a fqcy abl Calcla h a fo a sipl fqcy abl Daw coclsios fo sipl saisics fo a sigl disibio Copa wo sipl disibios sig h ag ad h dia Copa wo sipl disibios sig h ag ad h a o ag ad od Copa wo disibios giv say saisics / Rcogis wh i is appopia o s a, dia, o od i o coplx cass Us wo-way abls / Cosc a sipl (o boday daa) fqcy abl wih giv qal class ivals fo coios daa Idify disc ad coios daa Dsig abls codig disc ad coios daa Fid h odal class of a s of coios daa Cosc o pap ad sig ICT sipl pi chas sig cagoical daa,.g. wo o h cagois Daw pi chas fo daa psd i a abl. Ip ad plo sca gaphs ad cogis aoalis Ip ad / o copa ba gaphs (wih cpl zos, diff scals) ad fqcy diagas wh daa is icopl / scals a icoc. Ip ad / o copa ba gaphs ad fqcy diagas which a isladig (wih fals oigis, diff scals c.) Choos ad jsify appopia diagas, gaphs ad chas, sig ICT as appopia, o illsa a sho po of a saisical qiy Idify fh lis of qiy fo ifoaio povidd fo a iiial qiy B abl o add ad sbac o ha wo dcials wih p o wo dcial placs, b wih vayig bs of dcial placs ad sig a ix of opaios wihi h calclaio Rcall kow facs icldig facio o dcial covsios Cov iaig dcials o facios / La facioal qivals o ky cig dcials,.g , , Ip odd off cig dcials displayd o a calclao as facios 2/3, 1/6, 1 2/3, 1 1/6 Kow h doiaos of sipl facios ha podc cig dcials, ad hos ha do o Us divisio o cov a facio o a dcial Add ad sbac sipl facios wih doiaos of ay siz Chck addiio o sbacio of facios wih a ivs calclaio Add ad sbac ixd b facios wiho coo doiaos / Add ad sbac p o 3 facios ixig boh addiio ad sbacio i h calclaio Ip divisio as a liplicaiv ivs; kow ha 1 dividd by 1/4 is h sa as 1 4 Udsad h ffc of liplyig a posiiv b by a facio lss ha 1 Mliply a facio by a facio Divid a ig by a facio Rcall qival facios, dcials ad pcag Us h qivalc of facios, dcials ad pcags o copa popoios (i.. copa a facio ad a pcag) Fid h oco of giv pcag icas o dcas / Idify ala agls Idify cospodig agls Explai how o fid h ss of h iio ad xio agls of qadilaals, pagos ad hxagos Us scals i aps ad plas Mak sipl dawigs, dosaig acca as of lgh ad agl (daw accaly fo a pla). Us saigh dg ad copasss o cosc h idpoi ad ppdicla bisco of a li sg Us saigh dg ad copasss o cosc h bisco of a agl Rcogis ad s h ppdicla disac fo a poi o a li as h shos disac o h li Visalis ad s a wid ag of 2D psaios of 3D objcs Aalys 3D shaps hogh ifoal 2D psaios Bgi o s plas ad lvaios. Fid vols of shaps ad fo cboids B abl o cocly idify h hypos Cay o a ivsigaio ladig o dsadig of Pyhagoas' ho

9 p i g 6 Algbaic ad al-lif gaphs 10 odl siaios o pocds by sig gaphs wok wih coodias i all fo qadas cogis, skch ad podc gaphs of lia fcios of o vaiabl wih appopia scalig, sig qaios i x ad y ad h Casia pla ip ahaical laioships boh algbaically ad gaphically dc a giv lia qaio i wo vaiabls o h sadad fo y = x + c calcla ad ip gadis ad icps of gaphs of sch lia qaios ically calcla ad ip gadis ad icps of gaphs of sch lia qaios gaphically Half- s 7 Mliplicaiv asoig 9 s sadad is of ass, lgh, i, oy ad oh ass, icldig wih dcial qaiis chag fly bw lad sadad is [fo xapl i, lgh, aa, vol/capaciy, ass] divid a giv qaiy io wo pas i a giv pa:whol aio la h lagag of aios ad h associad calclaios o h aihic of facios solv pobls ivolvig dic popoio solv popoio pobls icldig gaphical ad algbaic psaios s copod is sch as spd, i picig ad dsiy o solv pobls Ed of s 8 Algbaic ad goic fola 13 dsad ad s sadad ahaical fola aag fola o chag h sbjc odl siaios o pocds by aslaig h io algbaic xpssios o fola s algbaic hods o solv lia qaios div fola o calcla ad solv pobls ivolvig pi of iagls, paalllogas, apzia div ad apply fola o calcla ad solv pobls ivolvig aa of iagls, paalllogas, apzia calcla ad solv pobls ivolvig pis of cicls calcla ad solv pobls ivolvig aas of cicls calcla ad solv pobls ivolvig coposi shaps 9 Pobabiliy 9 cod, dscib ad aalys h fqcy of ocos of sipl pobabiliy xpis ivolvig adoss, faiss, qally ad qally likly ocos s appopia lagag of pobabiliy s h 0 1 pobabiliy scal dsad ha pobabiliis of all possibl ocos s o 1 ga hoical sapl spacs fo sigl ad cobid vs wih qally likly ad ally xclsiv ocos s sapl spacs fo sigl ad cobid vs o calcla hoical pobabiliis. 10 Polygos ad asfoaios 10 s scal facos idify ad cosc cog iagls Half- s Daw coclsios basd o h shap of li gaphs Ip ifoaio fo a al-lif gaph Plo a gaph of a sipl lia fcio i h fis qada Rcogis saigh-li gaphs paalll o x- o y-axs Expss sipl fcios i sybols,.g. y = x + 3 o daw gaph Ga fo qada coodia pais of sipl lia fcios Plo a sipl saigh-li gaph (disac i gaphs) Discss ad ip li gaphs ad gaphs of fcios fo a ag of socs Kow how o fid h idpoi of a li sg Fid h idpoi of a hoizoal (o vical) li AB, sig h coodias of hs pois Ip icp of al-lif gaphs Plo h gaphs of sipl lia fcios i h fo y = x + c i fo qadas Divid a qaiy io wo pas i a giv aio, wh aio giv i aio oaio Divid a qaiy io wo pas i a giv aio (whol bs), wh h asw is a dcial Divid a qaiy io o ha 2 pas i a giv aio Rdc a aio o is sipls fo, wh a aio is xpssd i diff is Udsad h laioship bw aio ad popoio Us liplicaiv asoig o solv a pobl Us h iay hod o solv sipl wod pobls ivolvig aio ad dic popoio olv bs by / i pic pobls Udsad ha a liplicaiv laioship bw wo qaiis ca b xpssd as a aio o a facio Rcogis wh vals a i dic popoio by fc o h gaph fo olv pobls ivolvig dic ad ivs popoio, icldig gaphical ad algbaic psaios Us is of as o calcla ad solv pobls i vyday coxs ivolvig lgh, aa, vol, ass, i ad agl Cov bw aa ass (.g. ² o c², c² o ², ad vic vsa) Kow ogh ic qivals of ipial ass i daily s (f, ils, pods, pis, gallos) Fid h as of a sid giv h pi of sqas ad cagls, wh o o o lghs a dcials bsi igs io fola xpssd i l sybols Div fola xpssd i l sybols bsi igs io fola (ivolvig backs ad o ha o opaio) xpssd i l sybols Us a fola o calcla h aa of iagls Calcla h pi ad aa of shaps ad fo cagls Udsad h diff ol of l sybols i fola ad fcios bsi posiiv ad gaiv igs io sipl fola Calcla aas of copod shaps ad fo cagls ad iagls Us a fola o calcla h aa of paalllogas bsi igs io fola o giv qaios ad solv Kow h as of pas of a cicl Us a fola o calcla h cicfc of a cicl Us a fola o calcla h aa of a cicl Chag h sbjc of a o-sp fola Apply pobabiliis fo xpial daa o a diff xpi i sipl siaios Idify all ally xclsiv ocos fo wo sccssiv vs wih h ocos i ach v. Idify codiios fo a fai ga fo a sall s of sipl opios Us wo-way abls fo disc daa. Copl ad collc pobabiliis Us h lagag of pobabiliy o copa h choic of x/a wih x/b Apply pobabiliis fo xpial daa o a diff xpi i applyig o wo sp ocos Fid h pobabiliy fo wo-way abls Idify dpd ad idpd vs Wok o h pobabiliy of wo idpd vs Daw ad s diagas o ps ocos of wo idpd vs ad calcla pobabiliis olv sipl goical pobls sig popis of iagls

10 idify ad cosc cog iagls cosc siila shaps by lag wiho coodia gids cosc siila shaps by lag coodia gids apply agl facs, iagl cogc, siilaiy ad popis of qadilaals o div sls abo agls ad sids Ed of s Ed of ya s Udsad ad s h lagag associad wih oaios Tasla a shap o a coodia gid Roa a shap o a coodia gid Rflc a shap o a coodia gid Kow ha i cog shaps, cospodig sids ad agls a qal olv sipl goical pobls showig asoig Tasfo 2D shaps by sipl cobiaios of oaios, flcios ad oaios Plo pois o a gid a idify slig goic shaps acoss all fo qadas olv goic pobls sig sid ad agl popis of qilaal ad isoscls iagls olv goic pobls sig sid ad agl popis of qilaal, isoscls ad igh-agld iagls Classify qadilaals by hi goic popis Us h lagag ad oaio associad wih lag Kow ha aslaios, oaios ad flcios psv lgh ad agl Elag 2D shaps, giv a c of lag ad a posiiv whol-b scal faco

11 T Ui Til Tachig hos 2014 Poga of sdy Ui dscipio P-2014 sb-lvls K2 Rfc 1 Aalysig ad displayig daa 11 dscib, ip ad copa obsvd disibios of a sigl vaiabl hogh: appopia ass Fid h od, dia, a ad ag fo a s of daa 4c,,, Ya 6: Daa of cal dcy (a, od, dia) ad Copa ss of daa sig hi ags ad avags,, appopia ass of spad (ag, cosidaio of olis) Rad ad daw ally chas, abls, chas ad li gaphs, icldig fo gopd cosc ad ip vical li (o ba) chas fo gopd ad gopd daa daa 4c,,,,, Ya 4: Daa Us ICT o ps daa ad cosc chas 4c,,, 2 Nb skills 12 s covioal oaio fo h pioiy of opaios od bs ad ass o a appopia dg of accacy Kow ad s h pioiy of opaios ad laws of aihic,, Ya 6: Addiio, sbacio, liplicaio ad divisio cogis ad s laioships bw opaios icldig ivs opaios s h fo opaios, icldig foal wi hods, wih posiiv ad gaiv igs Rod whol b ad dcials 4c, Ya 4: Dcials ad facios; Nb, plac val ad odig od posiiv ad gaiv igs Chck asws sig vaios hods 4c,, Ya 3: Addiio ad sbacio s h cocps ad vocablay of pi bs, facos [o divisos] ad pi bs Us wi hods o add, sbac, liply ad divid whol bs 4c,,,, Ya 5: Mliplicaio ad divisio s ig pows ad associad al oos (sqa, cb) s appoxiaio hogh odig o sia asws A 3 Expssios, fcios ad fola 4 Dcials ad ass K3 Mahs Pogss Tha 3-ya ch of Wok Tha Ya 1 ch of Wok Us posiiv ad gaiv igs,,,, Ya 6: Mass Rcogis ad s facos, lipls ad pi bs 4c,,,, Ya 6: Addiio, sbacio, liplicaio ad divisio Kow sqa bs ad hi cospodig sqa oos Us idx oaio fo sqas, cbs ad posiiv ig pows of 10 Half- s sbsi ical vals io fola ad xpssios, icldig sciific fola Dscib ad fid ops of sipl fcios 4c,, siplify ad aipla algbaic xpssios o aiai qivalc: collcig lik s, liplyig a iplify xpssios by collcig lik s,,, Ya 6: Algba ov a back Wi xpssios,, Ya 6: Algba s ad ip algbaic oaio: 3y i plac of y + y + y ad 3 y bsi io fola,,, odl siaios o pocds by aslaig h io algbaic xpssios o fola Wi fola,, dsad ad s plac val fo dcials Od ad od dcials,,, Ya 5: Dcials ad facios od dcials ad facios Us ass ad covsios,,,, Ya 6: Mass s h sybols =,, <, >,, Rad scals ad plo coodias,,, Ya 4: Posiio ad dicio dsad ad s plac val fo ass Calcla wih dcials,,, Ya 5: Dcials ad facios wok wih coodias i all fo qadas s h fo opaios, icldig foal wi hods, wih posiiv ad gaiv dcials Wok o pi ad aa 4c,,,,, Ya 5: Mass div fola o calcla ad solv pobls ivolvig pi ad aa of paalllogas,, p i g 5 Facios 10 od dcials ad facios s h sybols =,, <, >,, s h fo opaios, icldig foal wi hods, wih posiiv ad gaiv facios dfi pcag as b of pas p hdd ip a pcag as a facio o a dcial ip facios ad pcags as opaos 6 Pobabiliy 9 s appopia lagag of pobabiliy s h 0 1 pobabiliy scal dsad ha pobabiliis of all possibl ocos s o 1 cod, dscib ad aalys h fqcy of ocos of sipl pobabiliy xpis ivolvig adoss, faiss, qally ad qally likly ocos Ed of s Copa facios,, Ya 6: Facios iplify facios Ya 6: Facios Calcla wih facios (addiio, sbacio ad facios of aos),,, Ya 6: Facios Wok wih qival facios, dcials ad pcags 4c,,, Ya 6: Facios Fid pcags of aos 4c,,, Ya 6: Raio ad popoio Us h vocablay of pobabiliy Udsad ad s h pobabiliy scal fo 0 o 1 Calcla pobabiliy basd o qally likly ocos Calcla h pobabiliy of a v o happig Calcla xpial pobabiliy Half- s 7 Raio ad popoio 10 solv pobls ivolvig dic popoio olv pobls ivolvig dic popoio,, s aio oaio Udsad ad s aios,,,, Ya 6: Raio ad popoio dc a aio o sipls fo Us facios o copa popoios, divid a giv qaiy io wo pas i a giv pa:pa aio Us pcags o copa popoios, s scal facos dsad ha a liplicaiv laioship bw wo qaiis ca b xpssd as a aio o a facio xpss h divisio of a qaiy io wo pas as a aio 8 Lis ad agls 11 s h sadad covios fo labllig h sids ad agls of iagl ABC daw ad as li sgs ad agls i goic figs apply h popis agls a a poi ad o a saigh li apply h popis vically opposi agls div ad s h s of agls i a iagl s h s of agls i a iagl o ddc h agl s i ay polygo s kow sls o obai sipl poofs,,,,, Ed of s Idify ad labl agls ad lis 4c,, Ya 6: Popis of shaps Us popis of 2-D shaps Ya 3: Popis of shaps Ya 5: Popis of shaps Esia, as ad daw agls,,, Ya 5: Popis of shaps Daw iagls accaly,, olv pobls ivolvig agls,,,, Ya 6: Popis of shaps Udsad popis, agl facs ad pobls ivolvig qadilaals,, Ya 6: Popis of shaps

12 9 qcs ad gaphs 10 ga s of a sqc fo a -o- l ga s of a sqc fo a posiio-o- cogis aihic sqcs fid h h cogis goic sqcs ad appcia oh sqcs ha ais wok wih coodias i all fo qadas podc gaphs of lia fcios ip ahaical laioships boh algbaically ad gaphically 10 Tasfoaios 10 div popis of gla polygos idify popis of, ad dscib h sls of: aslaios idify popis of, ad dscib h sls of: oaios idify popis of, ad dscib h sls of: flcios Ga ad dscib sipl ad o coplx sqcs icldig h 4c,,,,,, Idify ad plo coodias i all fo qadas,,, Ya 6: Posiio ad dicio Rcogis ad plo saigh li gaphs,, Mak liks bw gaphs, sqcs ad fcios Half- s Dscib cogc, Fid lags ad scal facos, Idify li ad oaioal syy,, Dscib flcios,, Dscib oaios,, Dscib aslaios Cobi asfoaios,, Ed of s Ed of ya s

13 Tha Ya 2 ch of Wok T Ui Til Tachig hos 2014 Poga of sdy Ui dscipio P-2014 sb-lvls 1 Nb 11 s h cocps ad vocablay of coo facos Divid.p by a wo digi b o giv.p s h cocps ad vocablay of coo lipls s h cocps ad vocablay of highs coo faco Add ad sbac igs posiiv ad gaiv bs (wih vayig bs of sigifica figs ) s h cocps ad vocablay of lows coo lipl Fid h HCF o LCM of 2 bs lss ha 100 s h cocps ad vocablay of pi facoisaio Esia sqa oos of o sqa bs lss ha 100 s h fo opaios, icldig foal wi hods, wih posiiv ad gaiv igs Mliply ad divid igs - posiiv ad gaiv bs s covioal oaio fo h pioiy of opaios, icldig backs, pows, oos ad cipocals s ig pows ad associad al oos (sqa, cb ad high) Calcla sqas, cbs ad cb oos cogis pows of 2, 3, 4, 5 Add, sbac, liply ad divid igs. Exd o h disibiv law a(b + c) Fid h pi faco dcoposiio of a b Us h fcio kys fo pows ad facios Cobi laws of aihic fo backs wih al calclaios of cbs oos ad sqa oos 2 Aa ad vol 11 div ad apply fola o calcla ad solv pobls ivolvig aa of iagls, paalllogas, Calcla sfac aas of cbs ad cboids,, apzia Calcla aas of iagls, paalllogas, apzia,, div ad apply fola o calcla ad solv pobls ivolvig vol of cboids (icldig cbs) Calcla aas of copod shaps calcla ad solv pobls ivolvig coposi shaps Calcla h vol of shaps ad fo cboids chag fly bw lad sadad is [fo xapl i, lgh, aa, vol/capaciy, ass] olv vol pobls Cov bw ic ad ipial ass, ad c 3 ad lis.,, Calcla h sfac aa of shaps ad fo cboids Half- s 3 aisics, gaphs ad chas 12 dscib, ip ad copa obsvd disibios of a sigl vaiabl hogh: appopia gaphical Calcla h a fo a sipl fqcy abl, ad sig a assd a, psaio ivolvig disc daa Ip ad cosc pi chas,, dscib, ip ad copa obsvd disibios of a sigl vaiabl hogh: appopia gaphical Us coplx wo way abls psaio ivolvig coios ad gopd daa Ip sca gaphs, daw lis of bs fi ad s colaio,, dscib, ip ad copa obsvd disibios of a sigl vaiabl hogh: appopia ass of spad (ag, cosidaio of olis) Fid h odal class of a s of coios daa dscib, ip ad copa obsvd disibios of a sigl vaiabl hogh: appopia ass Us s ad laf diagas o fid od, dia, a, ag of cal dcy (a, od, dia) Idify isladig gaphs ad saisics cosc ad ip fqcy abls cosc ad ip ba chas cosc ad ip pi chas Illsa sipl ahaical laioships bw wo vaiabls (bivaia daa) sig sca gaphs 4 Expssios ad qaios 11 s ad ip algbaic oaio: ab i plac of a b s ad ip algbaic oaio: a 2 i plac of a a s ad ip algbaic oaio: a 3 i plac of a a a s ad ip algbaic oaio: cofficis wi as facios ah ha as dcials s ad ip algbaic oaio: backs dsad ad s h cocps ad vocablay of xpssios, qaios, iqaliis, s ad facos siplify ad aipla algbaic xpssios o aiai qivalc: collcig lik s siplify ad aipla algbaic xpssios o aiai qivalc: akig o coo facos s algbaic hods o solv lia qaios i o vaiabl (icldig all fos ha qi aag) olv sipl lia qaios wih ig cofficis, Cosc ad solv lia qaios,, bsi igs io fola ad solv fo issig vals o- sp qaios iplify sipl xpssios ivolvig pows, Mliply a sigl ov a back Us h disibiv law o ak o ical coo facos p i g Ed of s 5 Ral-lif gaphs 10 odl siaios o pocds by sig gaphs ip ahaical laioships boh algbaically ad gaphically fid appoxia solios o coxal pobls fo giv gaphs of a vaiy of fcios: icldig pic-wis lia gaphs 6 Dcials ad aio 10 s h fo opaios, icldig foal wi hods, wih posiiv ad gaiv dcials od bs ad ass o a appopia dg of accacy [fo xapl, o a b of dcial placs o sigifica figs] s aio oaio dc a aio o sipls fo divid a giv qaiy io wo pas i a giv pa:pa aio divid a giv qaiy io wo pas i a giv pa:whol aio xpss h divisio of a qaiy io wo pas as a aio dsad ha a liplicaiv laioship bw wo qaiis ca b xpssd as a aio o a facio Daw ad ip li gaphs Ip ifoaio fo a coplx al-lif gaph, ad vals ad discss ds Daw, s ad ip covsio gaphs Daw ad s gaphs o solv disac i pobls Plo h gaphs of a fcio divd fo a al-lif pobl Discss ad ip lia ad o-lia gaphs fo a ag of socs Us gaphs o solv disac i pobls Discss ad ip al-lif gaphs Mliply ad divid igs ad dcials wih p o wo dcial placs / Divid a qaiy i o ha wo pas i a giv aio, icldig dcial vals / Od posiiv ad gaiv bs, icldig dcials, as a lis Mliply o divid ay b by 0.1 ad 0.01 iplify a aio xpssd i dcials Rod bs o a appopia dg of accacy Us sadad col pocds o add ad sbac igs ad dcials of ay siz Mliply ad divid by dcials Us > o < cocly bw wo gaiv dcials

14 Half- s 7 Lis ad agls 10 div ad illsa popis of iagls, qadilaals, cicls, ad oh pla figs [fo xapl, qal lghs ad agls] sig appopia lagag ad chologis dsad ad s h laioship bw paalll lis ad ala ad cospodig agls s h s of agls i a iagl o ddc h agl s i ay polygo apply agl facs, iagl cogc, siilaiy ad popis of qadilaals o div sls abo agls ad sids Ed of s 8 Calclaig wih facios 10 s h fo opaios, icldig foal wi hods, wih posiiv ad gaiv facios s h fo opaios, icldig foal wi hods, wih posiiv ad gaiv ipop facios ad ixd bs wok ichagably wih iaig dcials ad hi cospodig facios (sch as 3.5 ad 7/2 o ad 3/8) s sadad is of ass, lgh, i, oy ad oh ass, icldig wih dcial qaiis Classify qadilaals by hi goic popis Udsad a poof ha h s of h agls of a iagl is 180 ad of a qadilaal is 360 olv goic pobls sig sid ad agl popis of iagls ad spcial / qadilaals Idify ala agls ad cospodig agls Calcla h iio ad xio agls of gla ad igla polygos / olv pobls ivolvig agls by sig p qaios ad solvig h olv goical pobls showig asoig / Add ad sbac facios wih ay siz doiao Mliply igs ad facios by a facio Us facios ad dcials wihi calclaios icldig backs Fid h cipocal of a b Divid igs ad facios by a facio Calcla wih ixd bs / / // 9 aigh-li gaphs Pcags, dcials ad facios 10 cogis, skch ad podc gaphs of lia fcios of o vaiabl wih appopia scalig, sig qaios i x ad y ad h Casia pla dc a giv lia qaio i wo vaiabls o h sadad fo y = x + c calcla ad ip gadis ad icps of gaphs of sch lia qaios ically calcla ad ip gadis ad icps of gaphs of sch lia qaios gaphically calcla ad ip gadis ad icps of gaphs of sch lia qaios algbaically solv pobls ivolvig dic popoio solv popoio pobls icldig gaphical ad algbaic psaios xpss o qaiy as a pcag of aoh copa wo qaiis sig pcags wok wih pcags ga ha 100% ip pcags liplicaivly Half- s Ed of s Ed of ya s Fid gadis of lis Plo h gaphs of lia fcios Fid idpois of li sgs Wi h qaios of saigh li gaphs i h fo y = x + c Idify ad dscib xapls of dic popoio olv pobls ivolvig dic popoio Od facios by covig h o dcials o qival facios. Fid qival facios, dcials ad pcags. Expss o b as a pcag of aoh Wok o a pcag icas o dcas olv pcag pobls / /

15 Tha Ya 3 ch of Wok T Ui Til Tachig hos 2014 Poga of sdy Ui dscipio P-2014 sb-lvls 1 Idics ad sadad fo 10 disigish bw xac psaios of oos ad hi dcial appoxiaios Esablish idx laws fo posiiv pows wh h asw is a posiiv pow ip bs i sadad fo A 10 1 A < 10, wh is a posiiv o gaiv ig o zo Udsad which pa of a xpssio is aisd o a pow copa bs i sadad fo A 10 1 A < 10, wh is a posiiv o gaiv ig o zo B abl o siplify xpssios coaiig pows olv wod pobls sig sqa oos ad cb oos Kow h pfixs associad wih 10 12, 10 9, 10 6, 10 3, 10-2, 10-3, 10-6, 10-9, Kow ha ay b o h pow of zo is 1 Mak ad jsify sias ad appoxiaios of calclaios ivolvig o ha wo opaios ad BIDMA Udsad h od i which o calcla xpssios ha coai pows ad backs Apply h idx laws fo liplicaio ad divisio of ig pows / Wi ad od bs i sadad idx fo / 2 Expssios ad fola 11 s ad ip algbaic oaio: a 2 b i plac of a a b bsi igs io sipl xpssios ivolvig sall pows s ad ip algbaic oaio: b/a i plac of a b Div coplx algbaic xpssios ad fola siplify ad aipla algbaic xpssios o aiai qivalc: xpadig podcs of wo o iplify xpssios ivolvig backs ad pows o bioials Apply h idx laws icldig gaiv pow asws / dsad ad s sadad ahaical fola Us h disibiv law o ak o sigl algbaic facos aag fola o chag h sbjc bsi igs io fola o giv qaios ad solv / A Mliply o backs ad collc lik s Chag h sbjc of a fola Cay o algbaic facio calclaios Half- s 3 Dalig wih daa 11 dscib, ip ad copa obsvd disibios of a sigl vaiabl hogh: appopia gaphical lc h ag of possibl hods ha cold b sd o collc piay daa psaio ivolvig disc daa Di siabl sapl siz ad dg of accacy dd / dscib, ip ad copa obsvd disibios of a sigl vaiabl hogh: appopia gaphical Dsig ad s a daa collcio sh fo coios gopd daa psaio ivolvig coios ad gopd daa Discss facos ha ay affc h collcio of daa / dscib, ip ad copa obsvd disibios of a sigl vaiabl hogh: appopia ass Dsig abls codig disc ad coios daa of cal dcy (a, od, dia) dscib, ip ad copa obsvd disibios of a sigl vaiabl hogh: appopia ass Idify ky fas of daa ss dscibd i ih li gaphs o sca gaphs of spad (ag, cosidaio of olis) cosc ad ip fqcy abls icldig xcpios ad colaio Fo a sall choic of opios idify ways o dc bias i a sapl Illsa sipl ahaical laioships bw wo vaiabls (bivaia daa) sig sca gaphs Fid h odal class of a lag s of daa Us a li of bs fi, daw by y, o sia h issig val i a wo vaiabl daa s Cosc ad s fqcy polygos o copa ss of daa Calcla sia of a fo lag ss of gopd daa 4 Mliplicaiv asoig 11 s copod is sch as spd, i picig ad dsiy o solv pobls Elag 2D shaps, giv a c of lag ad a posiiv whol b wok wih pcags ga ha 100% cosc siila shaps by lag wiho coodia gids scal faco Fid h c of lag by dawig lis o a gid cosc siila shaps by lag coodia gids Rod bs o a giv b of sigifica figs ip ahaical laioships boh algbaically ad goically olv 'oigial val' pobls sig ivs opaio Elag 2D shaps, giv a facioal scal faco olv pobls sig copod ass olv pobls sig cosa as ad lad fola Calcla pcag chag, sig h fola acal chag / oigial ao 100 wh fola is calld Ed of s 5 Coscios 10 s scal diagas Idify ala ad cospodig agls o h sa diaga s aps Aalys 3D shaps hogh coss-scios, plas ad lvaios / div ad s h sadad l ad copass coscios: ppdicla bisco of a li sg Us ad ip aps ad scal dawigs / div ad s h sadad l ad copass coscios: coscig a ppdicla o a giv li Us saigh dg ad copass o cosc h id-poi ad ppdicla fo/a a giv poi bisco of a li sg div ad s h sadad l ad copass coscios: biscig a giv agl Us saigh dg ad copass o cosc h bisco of a agl cogis ad s h ppdicla disac fo a poi o a li as h shos disac o h li dscib, skch ad daw sig covioal s ad oaios: pois, lis, paalll lis, Us saigh dg ad copass o cosc a iagl, giv h sids () ppdicla lis, igh agls, gla polygos, ad oh polygos ha a flcivly ad oaioally Us saigh dg ad copass o cosc h ppdicla fo a poi o a syic s h popis of facs, sfacs, dgs ad vics of cbs, cboids, piss, cylids ad li sg Us saigh dg ad copass o cosc h ppdicla fo a poi o a pyaids o solv pobls i 3-D s h popis of sfacs of cos ad sphs o solv pobls i 3-D li sg Us saigh dg ad copass o cosc a iagl, giv igh agl, hypos ad sid (RH) Cosc s of iagla pis, pyaid ad wdg shap sig o RH fo h iagla scios Daw ad ip loci // 6 Eqaios, iqaliis ad 11 s ad ip algbaic oaio: cofficis wi as facios ah ha as dcials Udsad h diffc bw xpssio, qaio, fcio ad fola popoioaliy s ad ip algbaic oaio: backs sbsi ical vals io fola ad xpssios, icldig sciific fola Cosc ad solv qaios of h fo (ax +/ b)/c = (dx +/ )/f {o of c o f shold b 1} dsad ad s h cocps ad vocablay of xpssios, qaios, iqaliis, s ad facos Fid a posiiv sqa oo as a solio of a qaio ivolvig x²

16 p i g 7 Cicls, Pyhagoas ad piss facos siplify ad aipla algbaic xpssios o aiai qivalc: collcig lik s siplify ad aipla algbaic xpssios o aiai qivalc: liplyig a sigl ov a back siplify ad aipla algbaic xpssios o aiai qivalc: akig o coo facos siplify ad aipla algbaic xpssios o aiai qivalc: xpadig podcs of wo o o bioials Half- s 10 calcla possibl os slig fo siaig, xpssd sig iqaliy oaio a < x b calcla ad solv pobls ivolvig pis of cicls calcla ad solv pobls ivolvig aas of cicls s Pyhagoas Tho o solv pobls ivolvig igh-agld iagls Ed of s 8 qcs ad gaphs 12 odl siaios o pocds by sig gaphs cogis, skch ad podc gaphs of qadaic fcios of o vaiabl wih appopia scalig, sig qaios i x ad y ad h Casia pla dc a giv lia qaio i wo vaiabls o h sadad fo y = x + c calcla ad ip gadis ad icps of gaphs of sch lia qaios ically calcla ad ip gadis ad icps of gaphs of sch lia qaios gaphically calcla ad ip gadis ad icps of gaphs of sch lia qaios algbaically s lia gaphs o sia vals of y fo giv vals of x ad vic vsa ad o fid appoxia solios of silaos lia qaios s qadaic gaphs o sia vals of y fo giv vals of x ad vic vsa ad o fid appoxia solios of silaos lia qaios fid appoxia solios o coxal pobls fo giv gaphs of a vaiy of fcios: icldig pic-wis lia gaphs fid appoxia solios o coxal pobls fo giv gaphs of a vaiy of fcios: xpoial gaphs 9 Pobabiliy 10 fid appoxia solios o coxal pobls fo giv gaphs of a vaiy of fcios: cipocal a ss ad ios / iscios of ss sysaically, sig abls ad gids a ss ad ios / iscios of ss sysaically, sig V diagas ga hoical sapl spacs fo sigl ad cobid vs wih qally likly ad ally xclsiv ocos s sapl spacs fo sigl ad cobid vs o calcla hoical pobabiliis. Dscib sipl ahaical laioships bw wo vaiabls (bivaia daa) i obsvaioal ad xpial coxs Half- s 10 Copaig shaps 9 kow ad s h ciia fo cogc of iagls div ad illsa popis of iagls, qadilaals, cicls, ad oh pla figs [fo xapl, qal lghs ad agls] sig appopia lagag ad chologis Kow ad dsad h aig of a idiy ad s h idiy sig Cosc ad solv qaios of h fo a(bx +/ c) = d(x +/ f) wh gaiv sigs a aywh i h qaio. {a o d a bigg ha 1}.g. 3( 2x 1) = 4x + 1 Mliply boh sids of a iqaliy by a gaiv b olv sipl lia iqaliis i o vaiabl ad ps h solio o a b li.g. 6 < 2 = 4 o 9 < = 7 Udsad h sps qid o solv a pai of silaos qaios of h fo ax + y = b, y = ax Us sysaic ial ad ipov o fid h appoxia solio o o dcial plac of qaios sch as x³ = 29 Cosc ad solv qaios ha ivolv liplyig o backs by a gaiv b ad collcig lik s Fid a kow wh i is o h sbjc of h fola ad wh a qaio s b solvd olv o coplx lia iqaliis i o vaiabl ad ps h solio o a b li.g <11 ad 2 1 >1 Udsad h sps qid o solv a pai of silaos, wh hy a solvd by addiio. Eqaios a of h fo ax + y = b, x y = c Us sysaic ial ad ipov o fid h appoxia solio o o dcial plac of qaios sch as x³ + x = 50 Kow h as of pas of a cicl Us h fola fo h cicfc of a cicl Rod o a appopia b of dcial placs af calclaios Us h fola fo h cicfc, giv h cicfc, o calcla h adis o dia Us h fola fo aa of a cicl, giv h adis o dia Us h fola fo aa of a cicl, giv aa, o calcla h adis o dia Kow h fola fo Pyhagoas' ho ad how o sbsi i vals fo a diaga Us ad apply Pyhagoas' ho o solv pobls Calcla h sfac aa ad vol of igh piss (icldig cylid), Calcla sipl o ivals, sch as +/ 10% Idify ad calcla pp ad low bods, Us iqaliy oaio a < x b Bgi o s foal algba o dscib h h i a aihic sqc Ga s of a lia sqc sig posiio-o- l Ga h x i a qadaic sqc Rcogis goic sqcs ad appcia oh sqcs ha ais Classify sqcs as lia, goic ad qadaic Calcla ad ip gadi sig y = x + c Fid ad ip h y-icp fo y = x + c Plo gaphs of qadaic fcios by had ad sig ICT Rcogis ha ay li paalll o a giv li will hav h sa gadi dc a giv lia qaio i wo vaiabls o h sadad fo y = x + c Idify h solio of silaos qaios o a gaph Us gaphs o solv disac-i pobls, Cosc a abl of vals, icldig gaiv vals of x fo a fcio sch as y = ax 3 Calcla pobabiliis fo wo-way abls wih o ha wo cols / ows ach way Us h lagag of pobabiliy o copa h choic of x/a wih x/b Us h lagag of pobabiliy o copa h choic of x/a wih y/b Calcla h pobabiliy of a cobiaio of vs o sigl issig vs of a s of ally xclsiv vs sig s of ocos is o Calcla sias of pobabiliy fo xpis o svy sls Us xpial pobabiliis o pdic ocos Idify all ally xclsiv ocos fo wo sccssiv vs Copa xpial ad hoical pobabiliis Ea ss ad cobiaios of ss sysaically, sig abla, gid ad V diagas Idify codiios fo a fai ga Us P(A ad B) = P(A) P(B) fo wo idpd vs Copl ad s diagas o calcla pobabiliis 8b, Us cog shaps o hlp yo solv pobls abo iagls ad qadilaals, ad xplai all yo asoig