Scheme of Work
Cambridge International AS & A Level Mathematics 9709/06 Probability & Statistics !S" #or e$amination %rom 07 Contents Introd'ction((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((( Introd'ction(((((((((((((((((((((((((((((((((((((((((((((((( ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((( (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((( ) ( *e+resentation o% data(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((( data(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((( (((((((((((((((((((((((((((((((((((((((((((( , ( Perm'tations and combinations(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((( combinations(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((( (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((( 7 )( Probability(((((((((((((((((((((((((((((((((((((((((((((((( Probability((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((( ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((( (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((( .( iscrete random variables(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((( variables((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((( ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((( ((( 0 ,( he normal distrib'tion(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((( distrib'tion((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((
Cambridge International AS & A Level Mathematics !9709" 1 %rom 07
Scheme o% 2or3
Introduction his scheme o% 4or3 +rovides ideas abo't ho4 to constr'ct and deliver a co'rse( It has been bro3en do4n into di%%erent 'nits o% the three s'b5ect areas o% P're Mathematics !'nits P P and P)" Mechanics !'nits M and M" and Probability & Statistics !'nits S and S"( #or each 'nit there are s'ggested teaching activities and learning reso'rces to 'se in the classroom %or all o% the syllab's learning ob5ectives( his scheme o% 4or3 li3e any other is meant to be a g'ideline o%%ering advice ti+s and ideas( It can never be com+lete b't ho+e%'lly +rovides teachers 4ith a basis to +lan their lessons( It covers the minim'm re'ired %or the Cambridge International AS & A Level co'rse b't also adds enhancement and develo+ment ideas( It does not ta3e into acco'nt that di%%erent schools ta3e di%%erent amo'nts o% time to cover the Cambridge International AS & A Level co'rse( he mathematical content o% Probability & Statistics in the syllab's is detailed in the tables belo4( he order in 4hich to+ics are listed is not intended to im+ly anything abo't the order in 4hich they might be ta'ght( Recommended prior knowledge 8no4ledge o% the content o% Cambridge Level / Cambridge I:CS;< Mathematics is ass'med( Candidates 4ill be e$+ected to be %amiliar 4ith scienti%ic notation %or the e$+ression o% com+o'nd 'nits e(g( , m s 1 %or , metres +er second( As 4ell as demonstrating s3ill in the a++ro+riate techni'es candidates 4ill be e$+ected to a++ly their 3no4ledge in the sol'tion o% +roblems( Individ'al 'estions set may involve ideas and methods %rom more than one section o% the relevant content list( Outline S'ggestions %or inde+endent st'dy (I) and %ormative assessment (F) are indicated 4here a++ro+riate 4ithin this scheme o% 4or3( he activities in the scheme o% 4or3 are only s'ggestions and there are many other 'se%'l activities to be %o'nd in the materials re%erred to in the learning reso'rce list( ++ort'nities %or di%%erentiation are indicated as basic/consolidation and challenging/extension( here is the +otential %or di%%erentiation by reso'rce length gro'+ing e$+ected level o% o'tcome and degree o% s'++ort by the teacher thro'gho't the scheme o% 4or3( imings %or activities and %eedbac3 are le%t to the 5'dgment o% the teacher according to the level o% the learners and si=e o% the class( Length o% time allocated to a tas3 is another +ossible area %or di%%erentiation( Teacher support eacher S'++ort !http://teachers.cie.org.uk" is a sec're online reso'rce ban3 and comm'nity %or'm %or Cambridge teachers 4here yo' can do4nload s+ecimen and +ast 'estion +a+ers mar3 schemes and other reso'rces( 2e also o%%er online and %ace>to>%ace training? details o% %orthcoming training o++ort'nities are +osted online(
@( 60
Cambridge International AS & A Level Mathematics !9709" 1 %rom 07
Scheme o% 2or3
his scheme o% 4or3 is available as P# and an editable version in Microso%t 2ord %ormat? both are available on eacher S'++ort at http://teachers.cie.org.uk( I% yo' are 'nable to 'se Microso%t 2ord yo' can do4nload +en %%ice %ree o% charge %rom 444(o+eno%%ice(org( Resources he '+>to>date reso'rce list %or this syllab's incl'ding te$tboo3s endorsed by Cambridge is listed at 444(cie(org('3 Endorsed textbooks have been 4ritten to be closely aligned to the syllab's they s'++ort and have been thro'gh a detailed 'ality ass'rance +rocess( As s'ch all te$tboo3s endorsed by Cambridge %or this syllab's are the ideal reso'rce to be 'sed alongside this scheme o% 4or3 as they cover each learning ob5ective( ebsites and !ideos his scheme o% 4or3 incl'des 4ebsite lin3s +roviding direct access to internet reso'rces( Cambridge International ;$aminations is not res+onsible %or the acc'racy or content o% in%ormation contained in these sites( he incl'sion o% a lin3 to an e$ternal 4ebsite sho'ld not be 'nderstood to be an endorsement o% that 4ebsite or the siteBs o4ners !or their +rod'cts/services"( he 4ebsite +ages re%erenced in this scheme o% 4or3 4ere selected 4hen the scheme o% 4or3 4as +rod'ced( ther as+ects o% the sites 4ere not chec3ed and only the +artic'lar reso'rces are recommended(
@( 60
)
Cambridge International AS & A Level Mathematics !9709" 1 %rom 07
Scheme o% 2or3
"# Representation o$ data %earning ob&ecti!es
'uggested teaching acti!ities
Select a s'itable 4ay o% +resenting ra4 statistical data and disc'ss advantages and/or disadvantages that +artic'lar re+resentations may have(
2hen 4or3ing 4ith learners on 'estions that re'ire them to dra4 statistical diagrams it 4o'ld be good +ractice %or yo' to disc'ss 4ith them 4hy that +artic'lar diagram 4as chosen( #or e$am+le in these past papers 9709/6) D'ne . 'estion 4hy 4ere bac3>to>bac3 stem and lea% diagrams chosenE 9709/6 D'ne . 'estion 6 4hy 4as a histogram chosenE As an e$tension activity learners co'ld read the %ollo4ing interesting article %rom the Fniversity o% Leicester( It covers s'itable 4ays to +resent ra4 data +artic'larly %oc'sing on ho4 to +resent data 4hen 4riting re+orts( htt+//444(le(ac('3/o%%ices/ld/reso'rces/n'merical>data/n'merical>data
Constr'ct and inter+ret stem>and>lea% diagrams bo$>and>4his3er +lots histograms and c'm'lative %re'ency gra+hs(
o' co'ld sho4 learners the %ollo4ing video lin3s in class +a'sing the video %or learners to com+lete each tas3 or they co'ld 'se the videos as an inde+endent revision or consolidation reso'rce( Constr'cting and inter+reting stem and lea% diagrams %rom ;$amSol'tions( htt+s//444(yo't'be(com/4atchEvG*P;D5LHD3+. Introd'ction to histograms %rom ;$amSol'tions htt+s//444(yo't'be(com/4atchEvGC.iagtcA Jo$ and 2his3er +lots e$+lained !Marty Jrandl" yo'>t'be cli+ htt+s//444(yo't'be(com/4atchEvG6),;r=*9K=c C'm'lative %re'ency 1 +lotting htt+s//444(yo't'be(com/4atchEvGK9a55Jam*Pc ast papers (I)(F) *eading a histogram( 9709/6 ovember 0) 'estion . Constr'cting a histogram( 9709/6 D'ne 0. 'estion 6 !ii" Constr'cting a stem>and>lea% diagram( 9709/6 ovember 0 'estion . C'm'lative %re'ency/bo$ and 4his3er( 9709/6) ovember 0 'estion ,
@( 60
.
Cambridge International AS & A Level Mathematics !9709" 1 %rom 07
@( 60
Scheme o% 2or3
,
Cambridge International AS & A Level Mathematics !9709" 1 %rom 07
Scheme o% 2or3
%earning ob&ecti!es
'uggested teaching acti!ities
Fnderstand and 'se di%%erent meas'res o% central tendency !mean median mode" and variation !range inter'artile range standard deviation" e(g( in com+aring and contrasting(
o' co'ld sho4 learners the %ollo4ing video lin3s in class +a'sing the video %or learners to com+lete each tas3 or they co'ld 'se the videos as an inde+endent revision or consolidation reso'rce( A general introd'ction to meas'res o% central tendency htt+s//444(3hanacademy(org/math/+robability/descri+tive>statistics/centralHtendency/v/statistics>intro>mean>median> and>mode Com+aring di%%erent meas'res o% central tendency 4ith a disc'ssion o% 4hich may be the best to 'se in certain sit'ations htt+s//444(3hanacademy(org/math/+robability/descri+tive>statistics/centralHtendency/v/com+aring>distrib'tion>means htt+s//444(3hanacademy(org/math/+robability/descri+tive>statistics/centralHtendency/v/e$+loring>mean>and>median> mod'le :eneral introd'ction to meas'res o% dis+ersion htt+s//444(yo't'be(com/4atchEvG;.Ad0Nn*c
Fse a c'm'lative %re'ency gra+h to estimate the median val'e the 'artiles and the inter'artile range o% a set o% data(
o' co'ld ma3e a card matching activity %or this to+ic involving cards 4ith c'm'lative %re'ency diagrams on them %or learners to match to the corres+onding bo$ and 4his3er +lots( (F)
Calc'late the mean and standard deviation o% a set o% data !incl'ding gro'+ed data" either %rom the data itsel% or %rom given totals s'ch as 2 2 Σ x and Σ x , or Σ( x – a) and Σ( x – a) .
e$tboo3s 4ill have many e$am+les o% 'estions that learners can 'se %or calc'lation +ractice(
ast paper 'estion on c'm'lative %re'ency and bo$ and 4his3er +lots 9709/6) ovember 0 'estion ,
ast papers (I)(F) Calc'lating mean and standard deviation 9709/6 ovember 0) 'estion . 9709/6 D'ne 0. 'estion 6!iii"
*# ermutations and combinations
@( 60
6
Cambridge International AS & A Level Mathematics !9709" 1 %rom 07
Scheme o% 2or3
%earning ob&ecti!es
'uggested teaching acti!ities
Fnderstand the terms +erm'tation and combination and solve sim+le +roblems involving selections(
o hel+ learners 'nderstand the terms +erm'tation and combination yo' co'ld 'se these t4o video cli+s as a 4hole class activity +a'sing the video at +artic'lar +oints to as3 direct 'estions( (F) Alternatively learners co'ld 4atch the videos individ'ally %or revision or consolidation( Perm'tations incl'ding notations 'sed and the %orm'la are e$+lained in the 8han Academy yo'>t'be cli+ htt+s//444(yo't'be(com/4atchEvGKNK27K%A his video e$+lains combinations and incl'des an e$+lanation o% the di%%erence bet4een +erm'tations and combinations htt+s//444(yo't'be(com/4atchEvGbC$Mhnc*7PF
Solve +roblems abo't arrangements o% ob5ects in a line incl'ding those involving >re+etition !e(g( the n'mber o% 4ays o% arranging the letters o% the 4ord O;;L;SS" >restriction !e(g( the n'mber o% 4ays several +eo+le can stand in a line i% +artic'lar +eo+le m'st 1 or m'st not 1 stand ne$t to each other"(
ast papers (I)(F) 9709/6 ovember 0) 'estion 6 9709/6 ovember 0 'estion 7 9709/6) ovember 0 'estion . N'estions and 4or3ed e$am+les are on the Maths is #'n 4ebsite htt+//444(mathsis%'n(com/combinatorics/combinations>+erm'tations(html
+# robabilit, %earning ob&ecti!es
'uggested teaching acti!ities
;val'ate +robabilities in sim+le cases by means o% en'meration o% e'i+robable elementary events !e(g( %or the total score 4hen t4o %air dice are thro4n" or by calc'lation 'sing +erm'tations or
o' can +er%orm e$+eriments in class enabling learners to 4or3 o't e$+erimental +robabilities and com+are them 4ith theoretical +robabilities( !e(g( roll a die 0 times and see ho4 many times it lands on each %ace( *e+eat the e$+eriment by rolling the die 600 times( *e+eat 4ith a Obiased die? can learners 4or3 o't ho4 it is biasedE" Probability O3its are 4idely available %rom ed'cational s'++liers and o%ten have biased dice and sam+le bottles in them that can ma3e e$+eriments 'ic3er to +er%orm(
@( 60
7
Cambridge International AS & A Level Mathematics !9709" 1 %rom 07
%earning ob&ecti!es
Scheme o% 2or3
'uggested teaching acti!ities
combinations( o' co'ld as3 sim+le +robability 'estions as a starter activity 4ith learners 4riting their ans4ers on mini> 4hiteboards( (F) Some e$am+les o% +ractical activities and e$am+les o% eval'ating +robabilities in sim+le cases are at htt+//444(cimt(+lymo'th(ac('3/+ro5ects/me+res/alevel/statsHch(+d% An e$tension activity !balls in a bo$" involving +robabilities and tree diagrams is at htt+//444(s,)0,),0)(4ebsitehome(co('3/msv/msv>)(html o' co'ld 'se the %ollo4ing video lin3s as interactive reso'rces in class and yo' co'ld +a'se the videos %or direct 'estioning and %or learners to com+lete tas3s inde+endently( Alternatively learners co'ld 'se the video inde+endently as a revision or consolidation reso'rce( Jasic +robability e'ally +robable events and e$+erimental +robability are e$+lained in the 8han Academy yo'>t'be cli+ htt+s//444(yo't'be(com/4atchEvG'=3c>@o3 o' can %ind e$am+les o% calc'lating +robabilities 'sing combinations on the 8han Academy yo'>t'be cli+ htt+s//444(yo't'be(com/4atchEvGK%cyrMbI here is a 'se%'l collection o% arsia 5igsa4s available %or %ree do4nload %rom http://www.mrbartonmaths.com/jigsaw.htm ( :o to ata and Statistical o+ics then OProbability rees to %ind one that 4ill hel+ learners to +ractise calc'lating +robabilities %rom tree diagrams( !o' may need to do4nload the %ree arsia so%t4are %irst"( An interactive !consolidation" reso'rce on com+leting a +robability tree diagram is here htt+//444(do'is(net/Ii4s/+robabilityHtree(html Fse addition and m'lti+lication o% +robabilities as a++ro+riate in sim+le cases(
o' can %ind an e$+lanation o% the addition r'le %or +robability on the 8han Academy yo'>t'be cli+ htt+s//444(yo't'be(com/4atchEvGN;'*6>cF As a lesson starter activity yo' co'ld as3 learners sim+le 'estions involving addition and m'lti+lication o% +robabilities and they co'ld ans4er on mini>4hiteboards( (F)
@( 60
-
Cambridge International AS & A Level Mathematics !9709" 1 %rom 07
Scheme o% 2or3
%earning ob&ecti!es
'uggested teaching acti!ities
Fnderstand the meaning o% e$cl'sive and inde+endent events and calc'late and 'se conditional +robabilities in sim+le cases e(g( sit'ations that can be re+resented by means o% a tree diagram(
o' co'ld sho4 learners the %ollo4ing video cli+s as a 4hole class or they co'ld 4atch them inde+endently(I% yo' +rod'ce a set o% 'estions covering 3ey +oints % rom the videos learners co'ld ans4er them either 4hile 4atching or a%ter4ards( (F) his 8han Academy yo'>t'be cli+ e$+lains ho4 to 'se tree diagrams to 4or3 o't +robabilities htt+s//444(yo't'be(com/4atchEvG6;H@nboMJhe %orm'la %or conditional +robabilities is e$+lained 'sing both @enn diagrams and tree diagrams on this yo'>t'be cli+ htt+s//444(yo't'be(com/4atchEvGh0,@8K5@;
his is an interesting +roblem involving inde+endent events and real data( o' may 4ish to 'se it as an e$tension activity htt+//s)(ama=ona4s(com/ill'strativemathematics/ill'strationH+d%s/000/000/9,0/original/ill'strativeHmathematicsH9,0( +d%E)907,0-9 o' co'ld as3 learners sim+le +robability 'estions involving conditional +robabilities as a lesson starter activity 4ith learners 4riting their ans4ers on mini>4hiteboards( (F) ast papers (I)(F) 9709/6 ovember 0) 'estion 9709/6 ovember 0) 'estion 7!iii"!iv"
-# .iscrete random !ariables
@( 60
9
Cambridge International AS & A Level Mathematics !9709" 1 %rom 07
Scheme o% 2or3
%earning ob&ecti!es
'uggested teaching acti!ities
Constr'ct a +robability distrib'tion table relating to a given sit'ation involving a discrete random variable X and calc'late ;! X " and @ar! X "(
o' co'ld ma3e a matching card activity consisting o% a set o% cards sho4ing +robability distrib'tion tables %or learners to match 4ith the corres+onding ;!K" and @ar!K"( (F)
Fse %orm'lae %or +robabilities %or the binomial distrib'tion and recognise +ractical sit'ations 4here the binomial distrib'tion is a s'itable model !the notation J!n p" is incl'ded"(
A Jinostat is very 'se%'l %or calc'lating binomial +robabilities and deriving the %orm'la( Jalls are dro++ed into the binostat and learners can calc'late the +robability o% a ball getting into each slot( o' co'ld sho4 the video cli+ belo4 as a demonstration o% this htt+s//444(yo't'be(com/4atchEvGNy,-).ls
ast papers (I)(F) 9709/6 ovember 0) 'estion 7 !ii" 9709/6 ovember 0 'estion 9709/6 D'ne 0. N' .
o' co'ld 'se the %ollo4ing video lin3s as interactive reso'rces in class and yo' co'ld +a'se the videos %or direct 'estioning and %or learners to com+lete tas3s inde+endently( Alternatively learners co'ld 'se the video inde+endently as a revision or consolidation reso'rce( o' 4ill %ind an e$+lanation o% the +ro+erties o% a Jinomial istrib'tion and the notation 'sed in the ;$amSol'tions yo'>t'be cli+ htt+s//444(yo't'be(com/4atchEvGa0=@yKN he %orm'la is e$+lained %rom a tree diagram on the cli+ htt+s//444(yo't'be(com/4atchEvG>Fc*>;r*@c ast papers (I)(F) 9709/6 D'ne 0. 'estion
Fse %orm'lae %or the e$+ectation and variance o% the binomial distrib'tion(
o' co'ld 'se the %ollo4ing video lin3s as interactive reso'rces in class +a'sing the video %or direct 'estioning and %or learners to com+lete tas3s inde+endently( Alternatively learners co'ld 'se the video inde+endently as a revision or consolidation reso'rce( he %orm'lae are given and e$+lained and e$am+les 'sing them are in the ;$amSol'tions yo'>t'be cli+ htt+s//444(yo't'be(com/4atchEvG=;yLaSt-#I As an e$tension !challenging" activity learners co'ld consider the +roo% o% the %orm'lae( See the lin3 here htt+//444(s,)0,),0)(4ebsitehome(co('3/msv/msv>.0(html
@( 60
0
Cambridge International AS & A Level Mathematics !9709" 1 %rom 07
Scheme o% 2or3
# The normal distribution
@( 60
Cambridge International AS & A Level Mathematics !9709" 1 %rom 07
%earning ob&ecti!es
Scheme o% 2or3
'uggested teaching acti!ities
Fnderstand the 'se o% a normal o' co'ld 'se the %ollo4ing video lin3s as interactive reso'rces in class +a'sing the videos %or direct 'estioning and distrib'tion to model a contin'o's random %or learners to com+lete tas3s inde+endently or yo' co'ld ma3e a set o% 3ey 'estions to accom+any the videos( (F) variable and 'se normal distrib'tion Alternatively learners co'ld 'se the videos inde+endently as a revision or consolidation reso'rce( tables( he OStandard ormal istrib'tion is e$+lained in the O+oysermath yo'>t'be cli+ htt+s//444(yo't'be(com/4atchE vGcd)v@M,vand in the Oho4ststs yo'>t'be cli+ htt+s//444(yo't'be(com/4atchEvG$gNhe%#KrM his video e$+lains ho4 to %ind +robabilities 'sing tables htt+s//444(yo't'be(com/4atchEvG'$43$.s7F!ote that statistical tables can vary( Learners sho'ld be %amiliar 4ith the tables given in the Cambridge International ;$aminations M#9 List o% %orm'lae and tables o% the normal distrib'tion(" here are some 'se%'l Oarsia 5igsa4s to hel+ learners to +ractise vario's calc'lations connected 4ith the normal distrib'tion( ou can do4nload them %ree %rom htt+//444(mrbartonmaths(com/5igsa4(htmi% yo' clic3 on arsia A++lied o+ics then Statistics normal distrib'tion( !o' may need to do4nload the arsia so%t4are %rom htt+//444(mmlso%t(com/inde$(+h+/+rod'cts/tarsia" ast papers (I)(F) 9709/6 ovember 0) 'estion Solve +roblems concerning a variable X 4here X ~ !QR" incl'ding >%inding the val'e o% P! X T x " or a related +robability given the val'es o% x, μ, σ >%inding a relationshi+ bet4een x, μ, and σ given the val'e o% P! X T x " or a related +robability(
his ;$amSol'tion yo'>t'be cli+ +resents a method %or solving a +roblem involving %inding the mean and standard deviation htt+s//444(yo't'be(com/4atchEvGCs'IN>%sF
*ecall conditions 'nder 4hich the normal distrib'tion can be 'sed as an a++ro$imation to the binomial distrib'tion
o' co'ld 'se the %ollo4ing video lin3s as interactive reso'rces in class +a'sing the videos %or direct 'estioning and %or learners to com+lete tas3s inde+endently or yo' co'ld ma3e a set o% 3ey 'estions to accom+any the videos( (F) Alternatively learners co'ld 'se the videos inde+endently as a revision or consolidation reso'rce(
@( 60
Some e$am+les 4ith s'++ort and hints are available here htt+//onlinestatboo3(com//normalHdistrib'tion/ch6He$ercises(html ast papers (I)(F) 9709/6 ovember 0 'estion )
Cambridge International AS & A Level Mathematics !9709" 1 %rom 07
@( 60
Scheme o% 2or3
)
U Cambridge International ;$aminations 06 @ersion ( F+dated 0(0)(6
Cambridge International ;$aminations ills *oad Cambridge CJ ;F Fnited 8ingdom tel V.. ) ,,),,. %a$ V.. ) ,,),,email in%oWcie(org('3 444(cie(org('3
