Collect data from a simple experiment and record in a simple frequency table

Transcription

1 K3 Mahs Pogss Pi 3-ya ch of Wok Pi 1 ch of Wok T Ui Tachig hos Poga of dy 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 Ui dscipio Us a calclao ffcivly Rps ad ip daa i abls, chas ad diagas Exac daa ad ip disc ba chas Cosc o pap, ad sig ICT sipl ba gaphs ad ba-li gaphs Fid 'os coo' fo a s of disc daa o gopd ba cha 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 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 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. 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 Daw coclsios fo sipl saisics fo a sigl disibio Udsad ad apply h od i sipl calclaios (o backs) Apply h picipls of h coaiv, disibiv ad associaiv laws wih bs Add ad sbac sval bs, lookig fo sagis olv sipl pobls sig idas of aio ad popoio ('o fo vy ad o i vy... ) 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 copls o 100 A Us sadad col pocds o add ad sbac whol bs Rcogis ad xd b sqcs fod by coig o o coig back Appoxia bfo cayig o a addiio o sbacio. Rod posiiv whol bs o h as 10 Cosolida h apid call of liplicaio facs o Kow sqa bs, 1 1 p o 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 Divid a qaiy io wo pas i a giv aio wh aio is giv i wodd fo 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 sbsi ical vals io fola ad xpssios, icldig sciific fola dsad ad s h cocps ad vocablay of xpssios, qaios, iqaliis, s ad facos Fid ops of sipl fcios xpssd i wods Fid ops of sipl fcios i wods ad sybols Dscib sipl fcios i wods 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 Cosc xpssios fo wodd dscipio, sig addiio, sbacio ad liplicaio bsi posiiv igs io sipl fola xpssd i wods bsi igs io sipl fola xpssd i l sybols Idify vaiabls ad s l sybols 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 4 Gaphs 8 wok wih coodias i all fo qadas Ip ifoaio fo a sipl al lif gaph, g pa (icldig gaivs), aifall; covsio gaphs - ic is ad ccis 4a Rad x ad y coodia i h fis qada Plo a co-odia i h fis qada Kow ad dsad covios ad oaio sd fo 2-D co-odias i h fis qada Rad x ad y co-odia i all fo qadas

2 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) 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 covioal oaio fo h pioiy of opaios, icldig backs, pows, oos ad cipocals s appoxiaio hogh odig o sia asws s a calclao ad oh chologis o calcla sls accaly ad h ip h appopialy 5 Facos ad lipls 11 Kow ad s h od of opaios (fo ls, o pows o backs) Dvlop calclao skills ivolvig h s of cla kys ad all opaio kys Rcogis lipls of 2, 5, ad 10 ad 25 Exd wi hods o HTU U Udsad liplicaio as i applis o whol bs ad kow how o s associaiv, coaivi ad disibiv laws. Apply sipl ss of divisibiliy (2, 9, 10, 5) Exd wi hods o HTU U Idify a las 2 facos of 2 digi bs wih 3 o 4 facos Rod p o dow af divisio, dpdig o cox Rcogis ad s lipls ad facos Apply sipl ss of divisibiliy (3, 6, 4) Fid coo facos ad pis Idify bs wih xacly 2 facos (pis) Rcogis ad s coo faco, highs coo faco ad lows coo lipl p i g 6 Dcials ad ass 12 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 Apply sipl ss of divisibiliy (3, 6, 9, 4) Choos siabl is o sia o as lgh, ass ad capaciy Rcod adigs ad sias fo scals o a siabl dg of accacy Rad ad ip scals o a ag of asig iss Daw ad as lis o h as illi (i ) Us dcial oaio fo hs ad hddhs Rcogis h laioship bw hddhs ad hs Kow wha ach digi pss i bs wih p o wo dcial placs Rad ad wi whol bs i figs ad wods Od dcials (icldig i cox of ass) Udsad ad s dcial oaio ad plac val Rad ad ip scals ivolvig dcials Copa dcials i diff coxs Od ic is of as (.g. 1, 1 c, 1, 1 k o qival) Cov bw lag ad sall whol b ic is Rcogis ad xd b sqcs by coig i dcials. 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 1000 Rod dcials o o dcial plac o o h as whol b 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 7 Agls ad lis 10 8 Masig ad shaps 11 Half- s 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 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 Ed of s calcla ad solv pobls ivolvig coposi shaps daw ad as li sgs ad agls i goic figs div ad illsa popis of iagls, qadilaals, cicls, ad oh pla figs [fo xapl, qal lghs ad agls] sig appopia lagag ad chologis Idify igh agls ad paalll lis Kow ad s lf ad igh, aiclockwis ad clockwis Dscib agls as facios of fll s 1/4, 1/2, 3/4 Kow ad s copass pois ad 90, 180, 270 Idify ppdicla lis Disigish bw ac ad obs agls Us a poaco o as ac agls o h as dg Us coc oaio fo labllig lis ad agls Disigish bw ac, obs ad flx agls Us a poaco o as obs agls o h as dg Bgi o sia h siz of agls Us a poaco o daw ac agls o h as dg Kow h s of agls o a saigh li Kow h s of agls a od a poi Choos siabl ic is o sia aa Us is of as o sia ad solv pobls i vyday coxs ivolvig lgh, aa Kow as of gla polygos Classify iagls (isoscls, qilaal, scal) sig qal sids.

3 Classify iagls (isoscls, qilaal, scal) sig qal agls Classify iagls (isoscls, qilaal, scal) sig lis of syy Rcogis popis of sqas ad cagls Udsad ad as pis of cagls ad gla polygos Calcla pis of cagls ad gla polygos 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 Idify sipl agl, sid ad syy popis of iagls Rcogis ad visalis h syy of a 2D shap li syy ad oaio syy 9 Facios, dcials ad pcags 11 od dcials ad facios dfi pcag as b of pas p hdd 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 Od facios wih coo doiaos o i facios sig diagas Us facio oaio o dscib pas of shaps. Rcogis wh wo facios a qival wih a diaga Cacl a facio dow o is sipls fo Chag a ipop facio o a ixd b Fid sipl facios of whol b qaiis Rla facios o divisio Cosolda ad xd al hods of calclaio o icld facios Cosolida ad xd al hods of calclaio o icld facios. (Addig ad sbacig facios wih coo doiaos) Udsad a pcag as h b of pas p 100 Cov a pcag o a b of hddhs o hs Rcogis h qivalc of facios, dcials ad pcags Fid sipl pcags of whol b qaiis 10 Tasfoaios 8 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 Half- s Rcogis wh a shap will b af a flcio Rcogis ad visalis flcio i a io li Udsad ad s lagag associad wih flcio Rcogis wh a shap will b af a aslaio Udsad ad s lagag associad wih aslaios Rcogis ad visalis h asfoaio of a 2D shap; aslaio 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 Pi 2 ch of Wok T Ui Tachig hos Poga of dy 1 Nb popis ad 12 dsad ad s plac val fo igs calclaios s h fo opaios, icldig foal wi hods, wih posiiv ad gaiv igs s covioal oaio fo h pioiy of opaios, icldig backs, pows, oos ad cipocals s aio oaio dc a aio o sipls fo divid a giv qaiy io wo pas i a giv pa:pa 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 Ui dscipio Add ad sbac igs wih vayig bs of sigifica figs Udsad how o s backs i sipl calclaios Exd wi hods o TU x TU ad HTU x TU Add ad sbac gaiv igs fo posiiv ad gaiv igs Mliply by zo Mliply ad divid gaiv igs by a posiiv b Us aio oaio 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

4 A 2 haps ad ass i 3D 11 div ad apply fola o calcla ad solv pobls ivolvig vol of cboids (icldig cbs) Half- s 3 aisics 10 dscib, ip ad copa obsvd disibios of a sigl vaiabl hogh: appopia gaphical psaio ivolvig disc daa cosc ad ip fqcy abls cosc ad ip ba chas cosc ad ip pi chas 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 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 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 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 Ip sipl pi chas Us aihic opaios wih algba iplify o coplx lia algbaic xpssios by collcig lik s,.g. x x, 2b 3a + 6b 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) 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 Ed of s 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 p i g 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 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

5 Ivsiga iagls sig Pyhagoas' ho 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 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 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 Ed of s 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 Ed of s Ed of ya s Kow sqa bs byod 10 x 10 Fid cospodig oos Us h sqa oo ad chag sig kys o a calclao 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 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

6 T Ui Tachig hos 1 Nb calclaios 10 Poga of dy s h fo opaios, icldig foal wi hods, wih posiiv ad gaiv ipop facios ad ixd 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) cogis pows of 2, 3, 4, 5 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 s ad ip algbaic oaio: a ² i plac of a a ga s of a sqc fo a -o- l ga s of a sqc fo a posiio-o- cogis aihic sqcs fid h h Ui dscipio B abl o add ad sbac o ha wo igs wih vayig bs of sigifica figs B abl o add ad sbac o ha wo dcials wih p o wo dcial placs 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 Cosc xpssios fo wodd dscipio, sig all 4 basic opaios,.g. 30/x, x y, /2, 3 + 4, a + a + 3, a² Kow ha liplicaio ad divisio a caid o bfo addiio ad sbacio,.g. ab + cd, a b ad c d s b calclad bfo addig iplify sipl xpssios i o ha o vaiabl, icldig posiivs ad gaivs, by collcig lik s Ga s of a lia sqc sig posiio-o -wih posiiv igs. 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 A Half- s 3 aisics 11 dscib, ip ad copa obsvd disibios of a sigl vaiabl hogh: appopia gaphical psaio ivolvig disc daa dscib, ip ad copa obsvd disibios of a sigl vaiabl hogh: appopia gaphical psaio ivolvig coios ad gopd daa dscib, ip ad copa obsvd disibios of a sigl vaiabl hogh: appopia ass of cal dcy (a, od, dia) dscib, ip ad copa obsvd disibios of a sigl vaiabl hogh: appopia ass of spad (ag, cosidaio of olis) cosc ad ip fqcy abls cosc ad ip ba chas cosc ad ip pi chas 4 Facios, dcials ad pcags 12 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 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% lc ad idify h daa lad o a pobl lc h ag of possibl hods ha cold b sd o collc his daa as piay o scoday daa Discss h ag of possibl hods ha cold b sd o ivsiga a pobl,.g. qsioai, svy, odllig, daa loggig, c. lc appopia lvl of accacy of daa fo liid choics Fo a ag of sapl sizs idify h os ssibl asw Discss facos ha ay possibly affc h collcio of daa,.g. i, plac, yp of popl askd, phasig of qsios 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

7 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 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 p i g s h s of agls i a iagl o ddc h agl s i ay polygo 6 Algbaic ad al-lif gaphs 10 odl siaios o pocds by sig gaphs wok wih coodias i all fo qadas Daw coclsios basd o h shap of li gaphs Ip ifoaio fo a al-lif gaph cogis, skch ad podc gaphs of lia fcios of o vaiabl wih appopia scalig, sig qaios i x ad y Plo a gaph of a sipl lia fcio i h fis qada ad h Casia pla ip ahaical laioships boh algbaically ad gaphically Rcogis saigh-li gaphs paalll o x - o y -axs 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 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 Half- s 7 Mliplicaiv asoig 9 8 Algbaic ad goic fola 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 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 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

8 calcla ad solv pobls ivolvig aas of cicls calcla ad solv pobls ivolvig coposi shaps 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 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. 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 Half- s 10 Polygos ad asfoaios 10 s scal facos 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 olv sipl goical pobls sig popis of iagls 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