Mark Scheme (Results) January International GCSE Further Pure Mathematics (4PM0/02)

Transcription

1 Mark (Resuls) January 0 Inernaional GCSE Furher Pure Mahemaics (PM0/0)

2 Edexcel and BTEC Qualificaions Edexcel and BTEC qualificaions come from Pearson, he world s leading learning company. We provide a wide range of qualificaions including academic, vocaional, occupaional and specific programmes for employers. For furher informaion visi our qualificaions websies a or for our BTEC qualificaions. Alernaively, you can ge in ouch wih us using he deails on our conac us page a If you have any subjec specific quesions abou his specificaion ha require he help of a subjec specialis, you can speak direcly o he subjec eam a Pearson. Their conac deails can be found on his link: You can also use our online Ask he Exper service a You will need an Edexcel username and password o access his service. Our websie subjec pages hold useful resources, suppor maerial and live feeds from our subjec advisors giving you access o a poral of informaion. If you have any subjec specific quesions abou his specificaion ha require he help of a subjec specialis, you may find our Ask The Exper service helpful. Pearson: helping people progress, everywhere Our aim is o help everyone progress in heir lives hrough educaion. We believe in every kind of learning, for all kinds of people, wherever hey are in he world. We ve been involved in educaion for over 50 years, and by working across 70 counries, in 00 languages, we have buil an inernaional repuaion for our commimen o high sandards and raising achievemen hrough innovaion in educaion. Find ou more abou how we can help you and your sudens a: January 0 Publicaions Code UG0507 All he maerial in his publicaion is copyrigh Pearson Educaion Ld 0

3 General Marking Guidance All candidaes mus receive he same reamen. Examiners mus mark he firs candidae in exacly he same way as hey mark he las. Mark schemes should be applied posiively. Candidaes mus be rewarded for wha hey have shown hey can do raher han penalised for omissions. Examiners should mark according o he mark scheme no according o heir percepion of where he grade boundaries may lie. There is no ceiling on achievemen. All marks on he mark scheme should be used appropriaely. All he marks on he mark scheme are designed o be awarded. Examiners should always award full marks if deserved, i.e. if he answer maches he mark scheme. Examiners should also be prepared o award zero marks if he candidae s response is no worhy of credi according o he mark scheme. Where some judgemen is required, mark schemes will provide he principles by which marks will be awarded and exemplificaion may be limied. When examiners are in doub regarding he applicaion of he mark scheme o a candidae s response, he eam leader mus be consuled. Crossed ou work should be marked UNLESS he candidae has replaced i wih an alernaive response. Types of mark o M marks: mehod marks o A marks: accuracy marks. Can only be awarded if he relevan mehod mark(s) has (have) been gained. o B marks: uncondiional accuracy marks (independen of M marks) Abbreviaions o cao correc answer only o f follow hrough o isw ignore subsequen working o SC - special case o oe or equivalen (and appropriae) o dep dependen o indep independen o eeoo each error or omission No working If no working is shown hen correc answers may score full marks If no working is shown hen incorrec (even hough nearly correc) answers score no marks. Wih working

4 If here is a wrong answer indicaed always check he working and award any marks appropriae from he mark scheme. If i is clear from he working ha he correc answer has been obained from incorrec working, award 0 marks. Any case of suspeced misread which does no significanly simplify he quesion loses wo A (or B) marks on ha quesion, bu can gain all he M marks. Mark all work on follow hrough bu ener A0 (or B0) for he firs wo A or B marks gained. If working is crossed ou and sill legible, hen i should be given any appropriae marks, as long as i has no been replaced by alernaive work. If here are muliple aemps shown, hen all aemps should be marked and he highes score on a single aemp should be awarded. Follow hrough marks Follow hrough marks which involve a single sage calculaion can be awarded wihou working since you can check he answer yourself, bu if ambiguous do no award. Follow hrough marks which involve more han one sage of calculaion can only be awarded on sigh of he relevan working, even if i appears obvious ha here is only one way you could ge he answer given. Ignoring subsequen work I is appropriae o ignore subsequen work when he addiional work does no change he answer in a way ha is inappropriae for he quesion: eg. incorrec cancelling of a fracion ha would oherwise be correc. I is no appropriae o ignore subsequen work when he addiional work essenially shows ha he candidae did no undersand he demand of he quesion. Linear equaions Full marks can be gained if he soluion alone is given, or oherwise unambiguously indicaed in working (wihou conradicion elsewhere). Where he correc soluion only is shown subsiued, bu no idenified as he soluion, he accuracy mark is los bu any mehod marks can be awarded. Pars of quesions Unless allowed by he mark scheme, he marks allocaed o one par of he quesion CANNOT be awarded in anoher

5 June 0 PM0 Furher Pure Mahemaics Mark Quesion. (a) sinθ MA 6 sinθ θ 0.8 A () M (b) Area of secor r θ 6 θ (.6... ) Shaded area secor π,.8 M,A () [6] (a) an ( A B) ( ) ( ) sin A+ B sin Acos B+ cos Asin B + cos A + B cos Acos B sin Asin B M by cos Acos B M an A + an B an A anb A () (b) (i) an05 an ( 60 5) an 60 + an an 60 an 5 or see explicily an 60 and an 5 an 60 an 5 + an 60 an 5 + (ii) an5 an ( 60 5) MA MA () [7] 5

6 Quesion x + x x + + x!! (a) ( ) ( ) () ( ) ( ) M x + x x A,,0 () (b) x < x < B () f x kx + x + x x 8 (c) ( ) ( ) 5 k 5k 5 + k x + x + x 8 6 M MA () (d) 5 k 5 5, k 8 M,A () []. (a) sin5x+ 5xcos5x MAA () (b) x ( x ) ( x) ( x ) x e e 6 MAA () [6] 6

7 Quesion cos A cos A sin A, sin A sin A M,M 5(a) ( ) cos sin sin cos A A A A A () (b) cos sin sin ( cos ) A A A A k B () (c) 6 ( ) π 0 Volume π sin x dx M π 6 π ( cos x) d x M 0 π x sin x π 6 0 MAf (on k) π π sin π 6 M.... A (6) [0] 6 (a) V 5x h B ( ) A 5x + 5xh+ xh 5 6 h A 0x + x 0x + * MA () 5x x x (b) da dx 0 6 x x M da 6 0 0x M dx x (c) x A d A 0 + 7x dx M d A x.6 > 0 dx min MA (6) x.6 6 A MA () (using x. also gives.) [] 7

8 Quesion 7 (a) y x 6 ( y ) ( x ) MA y+ x 8 A () (b) ( ) 8 x x 8 M x x+ 0 ( x )( x ) 0 M equal roos angen A () (c) x, y BB () (d) grad g grad normal B Equaion normal : y ( x ) M y x+ 6 (oe ineger coeffs only) A () [] 8

9 Quesion 8 uuur uuur uuur (a) (i) AB OB OA b a uuuur uuur uuur (ii) OM OA + AB ( a+b) MA MA uuuur uuur uuuur + a+ b a b a 5 0 (iii) PM PA AM ( ) uuur uuuur uuur (b) OP + λpm OX MA (6) M a+ λ b a µ b 5 0 A λ 5 0 λ 6 µ λ M uuur OX b A () (c) area OAM area OAB area OAB area OAX M area OAM area OAX area OAX M 6 raio :6 A () []

10 Quesion (a) ar ar 768 MA 8 r 6 r ± A () (b) ar 8 a B () (c) r S (( ) ), 5787 B MA,A () (d) r B () (e) T.87 MA () (f) T MA ( ( ) ) n 0.00 > M.8 > n n.8 > Solve by logs or rial and error M greaes n is 5 A (5) [6] 0

11 Quesion 0 (a) 5 log x x x MA () log 6y+ 6y+ 5 5, (b) ( ) 5 y M,MA () 6 (c) log + log 5 + log 5 log 5 log + log M (change base) ( ) + ( ) log 5log 0 log 5log + 0 A ( log )( log ) 0 ( )( ) log log 0 M log log MA log log A (mus be posiive) (6) []

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