Mathematics. toughest areas of the 2017 exam papers. Edexcel GCSE (9-1) Higher. guided exam support on the top 10 toughest

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1 toughest res of the 07 em ppers Edecel GSE (9-) Mthemtics Higher guided em support on the top 0 toughest res of the 07 Higher tier ppers from

2 Top 0 Edecel GSE Mths Higher tier 07 Help our students ctch up, keep up nd mke epected progress with our Trget intervention workooks for Edecel GSE (9-) Mthemtics. Using dt from Resultslus, this ooklet presents the top 0 toughest res of the 07 Edecel GSE (9 ) Mths Higher tier em ppers. Our unique intervention pproch gives students step--step guidnce on overcoming the rriers holding them ck t ech grde rnge. This ooklet: l To find out more visit: l l l delivers specific guidnce in n ccessile formt for ou to work through with our students provides full worked-through em questions tken from the 07 series, with commentr developed from the mrk scheme nd eminer report supports students in the res the found most chllenging in the 07 ems identifies how erson s Trget intervention series cn help improve these skills nd ppl them in future ems. The Top 0 Topics ISN: ISN: ISN: Using the sine nd cosine rule.... Solving qudrtic equtions.... Eqution of circle ircle theorems...0. Grdients nd intercepts of liner functions.... Relting rtios to frctions nd to liner functions ISN: ISN: ISN: sic congruence criteri for tringles (SSS, SS, S, RHS) Multiplictive resoning Trnsltions nd reflections of function Vectors...

3 Using the sine nd cosine rule c G know nd ppl the sine rule sin sin sin, nd cosine rule Using the sine nd cosine rules to find ngles To find ngles, use the sine rule with ngles on top sin sin sin _ c + c c cos, to find unknown lengths nd ngles or sustitute into the cosine rule nd solve to find ngle.? 07 emintion questions per (Non-clcultor) Most students who scored elow grde 9 in this pper did not gin n mrks for this question. sed on the performnce of cndidtes in 07, this ws the hrdest skill nd question cross the Higher tier ppers. The digrm shows hegon EF. 0 method mrk for rerrnging the cosine rule for cos Q. EF nd nde Ere re congruent congruent prllelogrms prllelogrms where cm. cm. EF the point point on on F F nd nd Q Q is is the point point on on such tht tht 0 0 cm. isis the Q Giventht thtngle ngle 0, 0, _ Given ( ). prove tht cos Q 00 prove tht cos Q method mrk for sustituting Q for. ccurc mrk for conclusion (with ll working shown). + cos 0 Lel the ngle to mtch the formul. ( ) (to d.p.) Lel the ngle to e found () s. Lel nd the sides, nd c. Find ngle Q, correct to d.p. 7.7 cm Q, so ou cn sustitute our vlue for into Q..7 cm 70 R cm sin sin c 9 cm Hint Use the Y method in Q. 0 cm Z Use the cosine rule to find ngle. 0 cm X 8 cm [ mrks] sin _ Find ngle Y, to the nerest degree. Q ( + cos 0) _ ( ) _ 00 0 Hint cm cm c Hence find ngle. cm. cm Hint cos is negtive. 8.8 cm.9 cm 0. cm Em-stle question 8 cos Q 7 cos cos _ Q cos Q + cm cos _ 8 Mn students lost mrks ecuse the could not recll the vlue of cos 0. _ cos Q c 7 cm 8 cos lot of students hd troule rememering nd using ngle rules. The cosine rule is given s + c c cos. cm Use the sine rule to find sin. cos 0 cm + c c cos 7 cm You know the two sides tht include the ngle, so use the cosine rule. Lel the ngle ou wnt. method mrk for finding either or Q using the cosine rule. cm Find ngle, correct to d.p. ccurc mrk for stting the vlue of cos 0. This pge from the Trget Grde 7 lger nd Shpe Workook will help ou prctise prolems using the cosine rule nd the sine rule. You m not e given the sine nd? cosine rules in the em, so tr to rememer them. The digrm shows tringle EF. Edecel GSE (9-) Mthemtics - Higher Find. ( mrks).9 cm For more prctice, including worked emples, see Unit in the: - ctivelern igitl Service. Find E. ( mrks) F Reflect.9 cm E 7. cm igrm NOT ccurtel drwn In Q, when did ou use the cosine rule? When did ou use the sine rule? Unit 8 Trigonometr in non-right-ngled tringles Trget Grde 7 lger nd Shpe Workook

4 Solving qudrtic equtions 8 solve qudrtic equtions lgericll fctorising; find pproimte solutions using grph Solving liner nd non-liner simultneous equtions lgericll pir of liner nd qudrtic or circle simultneous equtions hve two possile solutions providing the stright line intersects the curve or circle. Solve these simultneous equtions. + nd 9 + nd emintion questions per (lcultor) 0 The digrm shows prt of the grph of +. The verge score for this question ws 0.0 mrks, mening lmost ll students found this chllenging. Most students did not know how to derive the stright line eqution from the informtion provided. Sustitute the liner epression for into the qudrtic eqution. + 9 Rerrnge so the right-hnd side is 0. 0 drwing suitle stright line, use our grph to find estimtes for the solutions of 0. Fctorise nd solve the eqution. ( + )( The solution to this question is the crossing points of the given grph nd stright line derived from the second eqution. Write down ech solution pir. So the solutions re, 0 nd ( ( ) )+ + Solutions to 0 re solutions to rewhen when eqution of stright line line is + + eqution of stright is grphs cross crosstt nd.. nd grphs, Rerrnge the liner eqution to mke the suject method mrk for deriving the eqution of the stright line + )0 ) 0, giving Either ( + ) 0, giving or ( Sustitute ech vlue of into the liner eqution to find the corresponding vlue of. When, ( ) + 0, ( )+ When t 0, Most students were unle to derive the stright line eqution, which ment the could not drw the grph nd find the solutions. This pge from Trget Grde 9 lger Workook will guide ou through sustitution nd rerrngement to help ou etter mnipulte qudrtic equtions. Sustitute the liner epression for into the circle eqution. + ( + ) ccurc mrk for two solutions red from the grph, one etween 0. nd 0. nd the other etween. nd.. Simplif nd rerrnge the eqution so the right-hnd side is Solve the qudrtic eqution. ( + )( )0 Either ( + ) 0, giving or ( [ mrks] ) 0, giving Sustitute ech vlue of into the liner eqution to find the corresponding vlue of. When, ( ) + When Edecel GSE (9-) Mthemtics - Higher ( ) + So the solutions re, nd For more prctice, including worked emples, see Unit in the: - ctivelern igitl Service., Unit Simultneous equtions, Trget Grde 9 lger Workook

5 Most students scored less thn mrk on this question, suggesting the were unfmilir with Finding equtions of rdii nd tngents the required method. This pge from the Trget Grde 9 lger The tngent is perpendiculr to the rdius. techniques, Shpe nd When line hs grdient m, the grdient of line perpendiculr to it is m Sttistics Workook will give ou some guided prctice on similr question. Eqution of circle recognise nd use the eqution of circle with centre t the origin; find the eqution of tngent to circle t given point The eqution of this circle is emintion questions per (clcultor) L is the circle with eqution +. is point on L. method mrk for finding the grdient of O. Find n eqution of the tngent to L t the point. Grdient GrdientofofOO 7 _ 7 _ 7 _ Grdientofoftngent tngent Grdient method mrk mrk for finding the grdient of the tngent. 7 _ _ 7 ccurc mrk for the eqution of the tngent. The grdient of norml is the negtive reciprocl of the grdient of its tngent. [ mrks] Sustitute in the points nd the grdient to find the eqution of the line. Edecel GSE (9-) Mthemtics - Higher For more prctice, including worked emples, see Unit in the: - ctivelern igitl Service. 8 Find the grdient of the rdius, O. Grdient of rdius _ Use m + c ( +c 7 ) _ + _ c 8 7 _ c Mn students lost mrks stopping fter 7 finding the grdients. You need to give the _ + _ full eqution _ (, ) O +c Eqution of rdius O is _ Find the grdient of the tngent t. Grdient of tngent is _ Use m + c _ + c Sustitute (, ) to find c. _ +c 9 + _ c Eqution of tngent is 9 _ + chnge in Grdient _ chnge in In m + c, c is the -intercept. -intercept is 0, so c 0. Eqution of of tngent Eqution tngent 7 _ the tngent to the circle t the point (, ). The circle hs centre t 0, so the grdient of O is _ 7 _ 0 chnge in _ chnge in _ 0 the rdius Most students were not comfortle strting this question. Some students gined mrks for finding the grdient of the norml nd the tngent, ut did not give the finl eqution. Find the eqution of Tngent nd rdius re perpendiculr. Grdient of perpendiculr m For n eqution in the form + c, multipl oth sides nd rerrnge: 9 For this circle, find i the grdient of the rdius ii the eqution of the rdius t point (, ) (, ) Grdient of O O Eqution of O: m + c Trget Grde 7 lger nd Shpe Workook Unit 9 ircles

6 ircle theorems G0 ppl nd prove the stndrd circle theorems concerning ngles, rdii, tngents nd chords, nd use them to prove relted results Fmilirising ourself with circle theorems will mke questions like this much more mngele. You cn use this pge from Trget Grde 7 lger nd Shpe Workook to get strted. It m lso e helpful to prctise questions out similr nd congruent shpes. Mke sure ou re comfortle with the definition of ech. ngles in the sme segment ngles in the sme segment re equl. 0 Find the sizes of the ngles mrked with letters. d c 07 emintion questions per (lcultor) The mjorit of students missed the first mrk in this question. Some students correctl identified E nd E s equivlent ut generll students did not seem confident with circle theorems.,, nd re four points on the circumference of circle. communiction mrk for identifing second pir of equl ngles with correct reson, or three pirs of ngles with no resons. ngles in the sme segment re c E nd E re stright lines. rove tht tringle E nd tringle E re similr. You must give resons for ech stge of our working. ngles t circumference Write the reson. legs of oth ngles strt t the sme point chord divides circle into two segments Write in smols. Find the sizes of the ngles lelled with letters. 0 c 0 z nglese nde reequl, equl, ecuseverticll verticll End Ere ngles ecuse opposite nglesre reequl. equl. opposite ngles End Ere nde reequl, equl, ecusengles ngles the nglese ngles ecuse ttthe circumference equl. circumferencesutended sutended on on the the sme rc re equl.. 0 Mn students confused similrit nd congruence. Tringles re similr if ll three pirs of ngles re the sme. communiction mrk for identifing one pir of equl ngles with correct reson, or two ngles with no resons. Identif the ngles in the sme segment. Find the sizes of ngles r nd s. 70 Hint Find r first, then turn the digrm upside down. r ngles ecuse in in thethe End Ere nde reequl, equl, ecusengles ngles nglese sme equl. sme segment segment re re equl. s 0 communiction mrk for identifing third pir of equl ngles with correct reson. [ mrks] Em-stle question The three mrks re given for identifing the three ngles, ou don t hve to eplin wh this mkes the tringles similr. Find the size of ngle. Give resons for ech stge of our working. 0 0 E Edecel GSE (9-) Mthemtics - Higher For more prctice, including worked emples, see Unit in the: - ctivelern igitl Service. 0 ( mrks) Reflect oes it help to write ngles on the digrm s ou find them? Unit ircle theorems Trget Grde 9 lger techniques, Shpe nd Sttistics Workook

7 Grdients nd intercepts of liner functions 0 identif nd interpret grdients nd intercepts of liner functions grphicll nd lgericll The grdient of the tngent t n point on speed time grph gives the ccelertion t tht point. 8 Speed (m/s) escrie full wht our nswer to prt represents. 0 0 method mrk for drwing tngent to the curve. On the grph, drw tngent to the curve t the point when t The tngent should e stright line with grdient equl to tht of the curve t the point given. ccurc mrk for method to clculte the grdient. chnge in speed Grdient _ chnge in t,,,, chnge in _ chnge in Find two points on the tngent nd clculte the grdient. 8 Time, t (seconds) 0 The tngent to curve t given point is the stright line tht touches the curve t tht point. For emple, tngent to the curve t seconds fter the strt of the rce, Lei ws. Tngents do not need to pss through the origin. 0 is the point on the grph of + where lculte n estimte for the grdient of the grph t the point. ccurc mrk for grdient etween. nd.. lculte n estimte for the grdient of the grph when t Worked em question t. m/s. Wht does the grdient of the tngent t n point on speed time grph represent? Em-stle question The grph shows informtion out the distnce, d metres, of cclist t seconds fter setting off. Work out n estimte for the grdient when t [ mrks] s this is n estimte, there re rnge of correct nswers. istnce, d (metres) Lei runs in rce. The grph shows her speed, in metres per second, t seconds fter the strt of the rce. Students tht gined grde 8 or ove generll chieved most of the mrks on this question. Students who chieved no mrks used chord insted of tngent, or drew their tngent through the origin. 0 The digrm shows prt of the grph of +. Grdient The grdient of the tngent t n point on distnce time grph gives the speed t tht point. 07 emintion questions per (lcultor) Use this pge from the Trget Grde 9 lger Workook to prctise drwing tngents. The pge lso contins some questions out using grdients in contet ( mrks) 0 Time, t (seconds) Write n interprettion of this grdient. Edecel GSE (9-) Mthemtics - Higher For more prctice, including worked emples, see Unit 9 in the: - ctivelern igitl Service. ( mrk) Reflect Wht would negtive grdient on speed time grph represent? Unit 8 re-clculus Trget Grde 9 lger Workook

8 Relting rtios to frctions nd to liner functions R8 relte rtios to frctions nd to liner functions ividing line in given rtio Right-ngled tringles on the sme sloping line re similr. E nd re similr. 07 emintion questions per (Non-clcultor) Ver few students chieved more thn of the ville mrks, even those otining grde 7 or ove overll. White shpes nd lck shpes re used in gme. is the point (0, ) nd is the point (, ). oint divides the line in the rtio :. Find the coordintes of. (0, ) Some of the shpes re circles. process mrk for finding frction, rtio or numer of white circles. process mrk for finding frction, rtio or numer of lck circles. ccurc mrk for the correct nswer (or equivlent). The rtio of the numer of white shpes to the numer of lck shpes is :7 Write the rtio :. : The rtio of the numer of white circles to the numer of white squres is : The rtio of the numer of lck circles to the numer of lck squres is : white : lck lck : :77 7 lck white, white, lck 0 0 You cn use three methods to nswer this question: convert the rtios to frctions (s shown), multipl to find equivlent rtios, or choose hpotheticl totl numer of shpes. white circles circle : squre : : circles circles 9 ( _) lck circles circle : squre : : circles circles 7 7 ( ) circles + ( ) ( 8 (0, ) 9 (0, ) ), ) Sides re in the sme rtio so _ ( M is the point (0, 0) nd N is the point (0, ). oint X divides the line MN in the rtio :. Find the coordintes of X. X N (0, ) Hint rw the tringles. M (0, 0) Em-stle question [ mrks] is the line joining (, ) nd (, 9). Find the coordintes of, which divides in the rtio :. (, ) Edecel GSE (9-) Mthemtics - Higher, (, ) (8, 9) For more prctice, including worked emples, see Unit nd Unit 0 in the: - ctivelern igitl Service. s ou re looking for the frction of shpes tht re white N circulr, ou multipl the frctions. s ou re looking for shpes tht re white circles OR lck circles ou need to dd the frctions. Write s frction of. Use similr tringles. 8 Work out the coordintes of. Work out wht frction of ll the shpes re circles. process mrk for first step using n of the three methods. Write in the distnces in the nd directions. (, ) rw two similr tringles. ll the other shpes re squres. E Students were uncomfortle converting rtios to frctions. This pge from Trget Grde 9 lgeric techniques, Shpe nd Sttistics Workook provides some guided prctice on converting rtios to frctions in contet. (, 9) Reflect ( mrks) When is the midpoint of line, wht is the rtio :? Unit Tringles Trget Grde 9 lgeric techniques, Shpe nd Sttistics Workook

9 7 sic congruence criteri for tringles (SSS, SS, S, RHS) The prolems from this pge of the Trget Grde 7 lger eciding if shpes re congruent or similr nd Shpe Workook m look different to the one on the previous pge, ut fmilirising ourself with Two tringles re congruent when one (or more) of these conditions is true: congruence nd similrit will SSS (ll three sides equl) mke questions like the one SS (two sides nd the included ngle re equl) opposite more pprochle. S or S or S (two ngles nd corresponding side re equl) G use the sic congruence criteri for tringles (SSS, SS, S, RHS)! #$%&''()*+,-)'-'+&.-+&$/(+.+&$)*0-%7 89-:'-0%;-'&/&'$.&();(&).%<! #$#use the sic congruence criteri for tringles (SSS, SS, S, RHS) 07 emintion questions per (Non-clcultor) >?!-:$@&)$.&(),-%.&()%$;-+?() E' $0',0$.(+7 communiction mrk for. communiction mrk for. is qudrilterl. RHS (right ngle, hpotenuse nd one other side re equl). Students tht gined grde 7 or ove tpicll chieved mrk for this question. Mn students hd not understood tht this ws question out congruence in tringles. Which tringle is congruent to? Which tringle is similr to? rove tht. communiction mrk for pointing out the shred side. Tringles re congruent congruent s Tringles re sthe thestisf stisfcriteri criteriof ofside sidengle side ngle(ss). side (SS). congruent. s tringles tringles nd nd re re congruent. [ mrks] communiction mrk for eplining tht the tringles re congruent nd the lines re n equl length. To prove tht, show tht the tringles nd re congruent. Some students lost mrks ecuse the used the wrong tringles. 0 cm cm S 0 0 cm SS Rotte. 9 cm 9 cm cm cm 70 0 cm cm 9 cm Find the scle fctor for one pir of corresponding sides. 9 scle fctor 9 scle fctor. heck this scle fctor works for the other corresponding sides. 0. is similr to. Rememer to nswer the originl question if the tringles re congruent then. Two sides nd n ngle re equivlent, so the tringles re congruent. Show tht the tringles in ech pir re congruent. Stte the reson. cm c Edecel GSE (9-) Mthemtics - Higher 0 cm 8 For more prctice, including worked emples, see Unit in the: - ctivelern igitl Service. 0 cm 0 cm cm 70 cm 70 9 cm Sketch the tringles with mtching ngles in the sme position. olour corresponding sides. cm 0 For similrit, look for tringle with the sme ngles ut different side lengths is congruent to. Write one or more resons. S or SS The dshes show tht the mrked lines re the sme length. ngle ngle. cm For congruence, look for tringle with the sme side lengths tht trnsltes, rottes or reflects to fit ectl on to.. Worked em question cm cm 0 cm 8 7 cm 7 cm 8 cm cm Unit ongruence nd similrit cm d 0. cm 8 cm cm cm 0. cm 8 cm Trget Grde 7 lger nd Shpe Workook

10 8 Multiplictive resoning R epress multiplictive reltionship etween two quntities s rtio or frction ividing line in given rtio Right-ngled tringles on the sme sloping line re similr. E nd re similr. E 07 emintion questions per (lcultor) process mrk for eginning method to equte the two rtios. The points,, nd lie in order on stright line. : : Mn students were unle to strt this question. Some could identif the multiplier drwing digrm or using equivlent frctions. is the point (0, ) nd is the point (, ). oint divides the line in the rtio :. Find the coordintes of. (0, ) Work out : :. Write in the distnces in the nd directions. Write the rtio :. : You m find it useful to drw lelled digrm. Find Find s multiplier 8 use use s multiplier You could lso convert the rtio prts to frctions ( _). 8 ( 8 (0, ) ( : ) : 7 7 [ mrks] (0, ) ), ) Sides re in the sme rtio so _ M is the point (0, 0) nd N is the point (0, ). oint X divides the line MN in the rtio :. Find the coordintes of X. N (0, ) Hint rw the tringles. Em-stle question is the line joining (, ) nd (, 9). Find the coordintes of, which divides in the rtio :. (, ) Edecel GSE (9-) Mthemtics - Higher For more prctice, including worked emples, see Units nd in the: - ctivelern igitl Service. 9 M (0, 0) : : : : 8 ( X ccurc mrk for the correct rtio., (, ) (8, 9) ( : ) : process mrk for complete process to find the rtio. Write s frction of. Use similr tringles. 8 Work out the coordintes of. (, ) rw two similr tringles. : 7 : In the em question students struggled to recognise the reltionship etween the two rtios nd mn did not ttempt to nswer it t ll. This pge from Trget Grde 9 lgeric Techniques, Shpe nd Sttistics will help ou strt the prolem showing ou how to pproch rtios on line. (, 9) Reflect ( mrks) When is the midpoint of line, wht is the rtio :? Unit Tringles Trget Grde 9 lgeric Techniques, Shpe nd Sttistic

11 9 Trnsltions nd reflections of function Edecel specifiction points!#$%&'(%)*+&'%&,$-.(-/)*+&'+.%.0&/)*+& sketch trnsltions nd reflections of given function recognise nd use the eqution of circle with the centre t the origin,-/-('-/*.*/%)*+&+*&)'!#$%$&'()*+$),-.&/-)0.&$-.$,(/(*)0.&$$-$0(.$.*)0. $!7$%$,(*.0&($-.$&($)+($(8-)0.$$-$*0,*/($90)+$)+($*(.),($ $ -)$)+($, emintion questions per (lcultor) 78-%9*&%)*+&:0-')*+&' ; <%-$>?%(/0(%)+$@ 0 The eqution of circle is +. method mrk for centre of (, 0) or circle with rdius of, or intersections t either (, 0) or (7, 0). The circle is trnslted the vector to give circle. rwing grphs of circles The grph of + r is circle, centre the origin, rdius r. rw the grph of + 8 Write down r from the eqution. Find r. significnt numer of students did not ttempt this question, even though the could hve strted with drwing circle. Most students who gined t lest mrks went on to chieve grde 8 or 9 overll. + r + 8 r Lel with coordintes, the centre of circle nd n points of intersection with the -is. 0 8 O 8 0 (7, (7, 0) 0) method mrks for two of: centre of (, 0) or circle with rdius of, or intersections t either (, 0) or (7, 0). common error ws to mke the trnsltion long the -is. 8 0 rw the grph of + ircle, rdius, centre O rw the grph of + 0. For more prctice, including worked emples, see Units nd 9 in the: - ctivelern igitl Service. 0 rw the grph of + 9 Edecel GSE (9-) Mthemtics - Higher Use compsses to drw circle, centre O, through the points. r [ mrks] method mrks nd ccurc mrk for ll of: centre of (, 0) or circle with rdius of, or intersections t either (, 0) or (7, 0) Mrk where the grph crosses the es. When 0, 8, ±9 When 0, 8, ±9 r (, (, ( 0) 0) So the circle hs rdius 9 nd centre (0, 0). 0 8 rw sketch of circle. (, 0) (, 0) This is the eqution of circle, centre (0, 0). r9 This pge from Trget Grde 9 lgeric techniques, shpe nd sttistics demonstrtes how to drw circle nd find the rdius, which is ke step in this em question. You could lso use Trget Grde 9 lger Workook, which gives some guided prctice on trnsforming grphs. Hint Round r to deciml plce. Lel the intercepts on the es. O O + 0 Trget Grde 9 lgeric techniques, shpe nd sttistics O Unit 9 ircles 9

12 Get ck on trck 0 Vectors G descrie trnsltions s vectors G ppl ddition sutrction of vectors, multipliction of! #nd $%&'()*# vectors sclr, nd digrmmtic nd column representtions +,%-&%.#*/%&00&'0(#/(0'* # of vectors; use vectors to construct geometric rguments nd proofs!#$ %$&'()*+,'$-*./(0.-+/($.($$')-*($ $!$ %$.0$.&&+-+/$./&$(7,-*.)-+/$8$')-*(9$:70-+0+).-+/$8$ $ ')-*($,$.$().0.*9$./&$&+.;*.::.-+)$./&$)07:/$*'*'('/-.-+/($ $ 8$')-*(<$7('$')-*($-$)/(-*7)-$;':'-*+)$.*;7:'/-($./&$*8( $ 07 emintion questions per (Non-clcultor)!#%-70'0(#89%*'0(*# : #;/%)#! #<( >&.&9.'()?# process mrk for first step to solve the prolem. 9 rolem-solve! O Students generll gined the first mrk for this question ut hd troule following through to solution. correct eqution or rtio using k. With O nd in terms of c, ou cn simplif to find k. ccurc mrk for the ndo c O nd XX isis the. the midpoint of the line. O line so so tht tht O O!: kk!:. O is stright line : :. Given tht X c Given M Edecel GSE (9-) Mthemtics - Higher For more prctice, including worked emples, see Unit 8 in the: - ctivelern igitl Service. ( mrk) Find M in terms of. ( mrk) Lel the digrm with the informtion given. Visulising the prolem cn mke it esier to understnd, nd sometimes ou get mrks for showing wht ou know! c X c OX + X O Keep n ee on the signs throughout our working. Vectors chnge sign when going + c + c c the opposite direction, for emple c O ut O. O : k : c : c : Those who got this fr lost the finl _ : mrk leving the nswer s _ : kk + correct nswer. M is the midpoint of O. OM Find O in terms of. O O O is prllelogrm. O nd O. Epress in terms of nd. ( mrk) Epress O in terms of nd. O prllelogrm. O is is prllelogrm. OX process mrk for Y X find the vlue find vlue of of k. k. Em-stle questions process mrk for correct sttement using. OXY is tringle. OX nd OY Write the vector X Y in terms of nd. X This pge from Trget Grde Shpe nd Sttistics Workook fetures some questions similr to the one opposite. Once ou hve finished this pge, tr the Em question gin, using n lterntive method to the one shown. ( mrk) is tringle. is point on., nd. Find the vector, in terms of. ( mrk) Find the vector, in terms of nd. ( mrks) [ mrks] Now tht ou hve completed this unit, how confident do ou feel? Understnd nd use vector nottion dd nd sutrct vectors Trget Grde Shpe nd Sttistics Workook Find multiples of vectors Unit Vectors 7

13 Your net steps ownlod free mteril Visit our wesite to downlod full smple chpters of our Trget Grde,, 7 nd 9 Workooks: Tlk to us Request n ppointment to discuss the est pckge for our school: Order online Order online using code 8OTHR to get the schools price of.9* ech: *UK schools price of.9. RR.99. EUK X0 erson Eduction Ltd is committed to reducing its impct on the environment using responsil sourced nd reccled pper.