9231 FURTHER MATHEMATICS
|
|
- Oliver Walker
- 5 years ago
- Views:
Transcription
1 CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advaced Level MARK SCHEME for the October/vember series 9 FURTHER MATHEMATICS 9/ Paper, maximum raw mark This mark scheme is published as a aid to teachers ad cadidates, to idicate the requiremets of the examiatio. It shows the basis o which Examiers were istructed to award marks. It does ot idicate the details of the discussios that took place at a Examiers meetig before markig bega, which would have cosidered the acceptability of alterative aswers. Mark schemes should be read i cojuctio with the questio paper ad the Pricipal Examier Report for Teachers. Cambridge will ot eter ito discussios about these mark schemes. Cambridge is publishig the mark schemes for the October/vember series for most IGCSE, GCE Advaced Level ad Advaced Subsidiary Level compoets ad some Ordiary Level compoets.
2 Page Mark Scheme Syllabus Paper GCE A LEVEL October/vember 9 Mark Scheme tes are of the followig three types: M A B Method mark, awarded for a valid method applied to the problem. Method marks are ot lost for umerical errors, algebraic slips or errors i uits. However, it is ot usually sufficiet for a cadidate just to idicate a itetio of usig some method or just to quote a formula; the formula or idea must be applied to the specific problem i had, e.g. by substitutig the relevat quatities ito the formula. Correct applicatio of a formula without the formula beig quoted obviously ears the M mark ad i some cases a M mark ca be implied from a correct aswer. Accuracy mark, awarded for a correct aswer or itermediate step correctly obtaied. Accuracy marks caot be give uless the associated method mark is eared (or implied). Mark for a correct result or statemet idepedet of method marks. Whe a part of a questio has two or more "method" steps, the M marks are geerally idepedet uless the scheme specifically says otherwise; ad similarly whe there are several B marks allocated. The otatio DM or DB (or dep*) is used to idicate that a particular M or B mark is depedet o a earlier M or B (asterisked) mark i the scheme. Whe two or more steps are ru together by the cadidate, the earlier marks are implied ad full credit is give. The symbol implies that the A or B mark idicated is allowed for work correctly followig o from previously icorrect results. Otherwise, A or B marks are give for correct work oly. A ad B marks are ot give for fortuitously "correct" aswers or results obtaied from icorrect workig. te: B or A meas that the cadidate ca ear or. B// meas that the cadidate ca ear aythig from to. The marks idicated i the scheme may ot be subdivided. If there is geuie doubt whether a cadidate has eared a mark, allow the cadidate the beefit of the doubt. Uless otherwise idicated, marks oce gaied caot subsequetly be lost, e.g. wrog workig followig a correct form of aswer is igored. Wrog or missig uits i a aswer should ot lead to the loss of a mark uless the scheme specifically idicates otherwise. For a umerical aswer, allow the A or B mark if a value is obtaied which is correct to s.f., or which would be correct to s.f. if rouded ( d.p. i the case of a agle). As stated above, a A or B mark is ot give if a correct umerical aswer arises fortuitously from icorrect workig. For Mechaics questios, allow A or B marks for correct aswers which arise from takig g equal to 9.8 or 9.8 istead of. Cambridge Iteratioal Examiatios
3 Page Mark Scheme Syllabus Paper GCE A LEVEL October/vember 9 The followig abbreviatios may be used i a mark scheme or used o the scripts: AEF AG BOD CAO CWO ISW MR PA SOS SR Ay Equivalet Form (of aswer is equally acceptable) Aswer Give o the questio paper (so extra checkig is eeded to esure that the detailed workig leadig to the result is valid) Beefit of Doubt (allowed whe the validity of a solutio may ot be absolutely clear) Correct Aswer Oly (emphasisig that o "follow through" from a previous error is allowed) Correct Workig Oly ofte writte by a fortuitous' aswer Igore Subsequet Workig Misread Premature Approximatio (resultig i basically correct work that is isufficietly accurate) See Other Solutio (the cadidate makes a better attempt at the same questio) Special Rulig (detailig the mark to be give for a specific wrog solutio, or a case where some stadard markig practice is to be varied i the light of a particular circumstace) Pealties MR PA A pealty of MR is deducted from A or B marks whe the data of a questio or part questio are geuiely misread ad the object ad difficulty of the questio remai ualtered. I this case all A ad B marks the become "follow through " marks. MR is ot applied whe the cadidate misreads his ow figures this is regarded as a error i accuracy. A MR pealty may be applied i particular cases if agreed at the coordiatio meetig. This is deducted from A or B marks i the case of premature approximatio. The PA pealty is usually discussed at the meetig. Cambridge Iteratioal Examiatios
4 Page Mark Scheme Syllabus Paper GCE A LEVEL October/vember 9 Commetary Solutio Part Use of: Use of: Obtais result. + r ( + )( + ) ( + )( + ) ( + )( + ) ( + ) 8 + ( + )(7 + (AG) ( ) ) M M A A [] Sets determiat. Factorises, or completes square. States result. a a a + 8a (a )( a + ) a or (Or by row operatios.) MA M A [] Propositio. Proves base case. States iductive hypothesis. Proves iductive step. States coclusio. H N : S N ( N + )! S H is true.!! H k : Assume S k is true. ( k + )! k + ( k + )! ( k + ) + ( k + ) S k + + ( k + )! ( k + )! ( k + )! S k + H k H k+. ( k + )! (By PMI H is) true for all positive itegers N. B B M A A 5 [5] Fids vector product. Fids area of triagle. AB AB AC AC i j k Area of triagle ABC B MA MA Fids legth of perpedicular. + + d d A [] Cambridge Iteratioal Examiatios
5 Page 5 Mark Scheme Syllabus Paper GCE A LEVEL October/vember 9 Commetary Solutio Part 5 Sketches graph. Correct shape ad orietatio. Passig through (,) ad (,) B B Uses area of sector formula. Uses double agle formula Itegrates. Area ( + cosθ ) dθ ( + cosθ + cos θ )dθ ( + cosθ + cos θ ) dθ M M Obtais result. [ θ + siθ + si θ ] 5 + A A [] Differetiates. ds Obtais dt x& t y& t t + ( y& ) t + t t + t + ( x &) t t B MA Uses surface area formula about y-axis. 5 S xds t t + dt ( t t) dt t + t + t + + MA MA 7 [7] 7 ( + + ) ( + + ) + + α β γ αβ βγ γα α β γ αβ Either Required equatio is x x + x + c α a + + c c 5 8 c (AG) Or α + β + γ αβγ ( α + β + γ )( α + β + γ αβ βγ γα) (or some other appropriate idetity, e.g. ( α + β + γ ) α + β + γ + ( α + β + γ )( αβ + βγ + γα) αβγ )... αβγ x x + x + (AG) ( x + )( x )( x ) x,,. MA M M A (M) (MA) A MA [8] Cambridge Iteratioal Examiatios
6 Page Mark Scheme Syllabus Paper GCE A LEVEL October/vember 9 Commetary Solutio Part 8 Re-write. Obtais result. Use of Bi. Thm. Takes imagiary part ad uses de M. Applies iitial result. + z cos θ + i si θ cos θ cos θ cos θ + isi θ (AG) z z z z ( + ) z Im( ) siθ si θ... si θ But ( + z ) cos θ θ i e MA A M M MA B Equates imagiary parts to obtai result. siθ si θ... si θ cos θ si θ A [9] 9 States vertical asymptote. Vertical asymptote is x. B Divides ad states oblique asymptote. oblique asymptote is y x. M A Rearrages as quadratic i x. xy y x x + x ( y + ) x + ( + y) B Uses discrimiat to obtai coditio stated. For real x, B AC ( y + ) ( + y)... ( y )( y + )) y or y o poits for < y < (AG) M A A Differetiates, puts ad obtais x-values. y ( x ) x or (Or uses y ad to obtai x-values.) M States statioary poits. Statioary poits are (, ) ad (,) AA Sketch. Oe mark for each brach correctly placed. BB [] Cambridge Iteratioal Examiatios
7 Page 7 Mark Scheme Syllabus Paper GCE A LEVEL October/vember 9 Commetary Solutio Part Differetiates implicitly. dy Equates to dx zero. x + y y y + xy dy y x dx y BB M Obtais relatioship. Substitutes for y. Obtais x ad y. y x xy + y xy y xy y x ( y ) x x x x ad y ( x ) A M AA Differetiates Uses y. Idetifies maximum. x + y y + y( y ) y + xy + y x x y (x y ) y x( x ) y max B BB M A 8 (Other watertight methods for showig a maximum accepted.) [] Cambridge Iteratioal Examiatios
8 Page 8 Mark Scheme Syllabus Paper GCE A LEVEL October/vember 9 Commetary Solutio Part Verifies result. Correct parts. Itegrates by parts. d ( x dx x ) ) + c ( x x I ( x dx. x( x ) ) ( x) x( x dx ) B M Substitutes limits. Obtais reductio formula. x. ( x ) + ( ) x. ( x ) x ( x )( x ) dx I I + ) I ( ) I (AG) ( dx MA M A 5 Uses substitutio correctly. Uses double agle formula. Itegrates correctly. Uses reductio formula correctly. x si u dx cosudu Limits: x u x u ( x ) dx I cos udu (cos u + ) du si u + u I (AG) M A M MA MA 5 [] Cambridge Iteratioal Examiatios
9 Page 9 Mark Scheme Syllabus Paper GCE A LEVEL October/vember 9 Cambridge Iteratioal Examiatios Commetary Solutio Part EITHER Use of these results. Fids missig eigevalues of A. Fids missig eigevector of A. Calculates eigevectors of B Uses iitial result to fid eigevalues of C.( mark for oe correct value, marks for all three.) Fids P ad D. Ae λe ad e Be µ e e Ae e A ABe λµ µλ µ µ λ λ λ k j i ~ µ µ µ C has eigevalues: ) ( ) ( P (OE) 9 D M A B B MA B B B B,, B MA 8 []
10 Page Mark Scheme Syllabus Paper GCE A LEVEL October/vember 9 Commetary Solutio Part OR Fids complemetary fuctio. m + m + m ± i t x e ( Acos t + B si t) M A Fids particular itegral. x p cos t + qsi t x& p si t + q cos t & x p cos t q si t M ( 9 p + q)cost + (9q p)si t 75cost p q MA A Fids geeral solutio. Uses iitial coditios.. Obtais solutio. x e -t ( Acost + Bsi t) + cost + si t x 5 whe t 5 A + A t x& e ( Acost + Bsit) t + e ( Asit + Bcost) sit + 8cost x& whe t B B x t e (cos t si t) + cos t + si t A B M A A 7 Obtais limit. As t, e -t x cost + si t x 5 cos t + si t 5cost ta 5 5 (AG) M MA [] Cambridge Iteratioal Examiatios
9231 FURTHER MATHEMATICS
CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advaced Level www.xtremepapers.com MARK SCHEME for the October/vember series 9 FURTHER MATHEMATICS 9/ Paper, maximum raw mark This mark scheme is published as a
More informationwww.olieexamhelp.com www.olieexamhelp.com CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advaced Level MARK SCHEME for the October/vember series 9 FURTHER MATHEMATICS 9/ Paper, maximum raw mark This mark scheme
More information9231 FURTHER MATHEMATICS
CMRIDGE INTERNTIONL EXMINTIONS Cambridge Iteratioal dvaced Level MRK SCHEME for the May/Jue series 9 FURTHER MTHEMTICS 9/ Paper (Paper ), maimum raw mark This mark scheme is published as a aid to teachers
More information9795 FURTHER MATHEMATICS
CAMBRIDGE INTERNATIONAL EXAMINATIONS Pre-U Certificate MARK SCHEME for the May/Jue series 9795 FURTHER MATHEMATICS 9795/ Paper (Further Pure Mathematics, maximum raw mark This mark scheme is published
More informationVersion 1.0: abc. General Certificate of Education. Mathematics MFP2 Further Pure 2. Mark Scheme examination - January series
Versio.0: 008 abc Geeral Certificate of Educatio Mathematics 660 MFP Further Pure Mark Scheme 008 examiatio - Jauary series Mark schemes are prepared by the Pricipal Examier ad cosidered, together with
More informationMARK SCHEME for the October/November 2012 series 9709 MATHEMATICS. 9709/13 Paper 1, maximum raw mark 75
AMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the October/November 2012 series 9709 MATHEMATICS 9709/13 Paper 1, maximum raw mark 75 This mark
More informationN14/5/MATHL/HP1/ENG/TZ0/XX/M MARKSCHEME. November 2014 MATHEMATICS. Higher Level. Paper pages
N4/5/MATHL/HP/ENG/TZ0/XX/M MARKSCHEME November 04 MATHEMATICS Higher Level Paper 0 pages N4/5/MATHL/HP/ENG/TZ0/XX/M This markscheme is the property of the Iteratioal Baccalaureate ad must ot be reproduced
More informationMARK SCHEME for the May/June 2012 question paper for the guidance of teachers 9709 MATHEMATICS. 9709/11 Paper 1, maximum raw mark 75
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the May/June 0 question paper for the guidance of teachers 9709 MATHEMATICS 9709/
More informationThis document consists of 15 printed pages.
Cambridge International Examinations Cambridge International Advanced Level FURTHER MATHEMATICS 93/ Paper MARK SCHEME Maximum Mark: 00 Published This mark scheme is published as an aid to teachers and
More informationMarkscheme May 2015 Calculus Higher level Paper 3
M5/5/MATHL/HP3/ENG/TZ0/SE/M Markscheme May 05 Calculus Higher level Paper 3 pages M5/5/MATHL/HP3/ENG/TZ0/SE/M This markscheme is the property of the Iteratioal Baccalaureate ad must ot be reproduced or
More informationwww.onlineeamhelp.com www.onlineeamhelp.com UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Level MARK SCHEME for the May/June question paper for the guidance of teachers FURTHER MATHEMATICS
More information9231 FURTHER MATHEMATICS 9231/01 Paper 1, maximum raw mark 100
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Level MARK SCHEME for the October/November 9 question paper for the guidance of teachers 931 FURTHER MATHEMATICS 931/1 Paper 1, maximum raw
More informationCambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level. Published
Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level MATHEMATICS 9709/11 Paper 1 May/June 016 MARK SCHEME Maximum Mark: 75 Published This mark scheme is published
More information4755 Mark Scheme June Question Answer Marks Guidance M1* Attempt to find M or 108M -1 M 108 M1 A1 [6] M1 A1
4755 Mark Scheme Jue 05 * Attempt to fid M or 08M - M 08 8 4 * Divide by their determiat,, at some stage Correct determiat, (A0 for det M= 08 stated, all other OR 08 8 4 5 8 7 5 x, y,oe 8 7 4xy 8xy dep*
More informationMARK SCHEME for the May/June 2012 question paper for the guidance of teachers 9709 MATHEMATICS. 9709/41 Paper 4, maximum raw mark 50
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the May/June 2012 question paper for the guidance of teachers 9709 MATHEMATICS 9709/41
More information9709 MATHEMATICS. 9709/32 Paper 3, maximum raw mark 75
CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Level MARK SCHEME for the May/June 0 series 9709 MATHEMATICS 9709/3 Paper 3, maximum raw mark 75 This mark scheme is published as an aid to teachers and
More information9709 MATHEMATICS. 9709/31 Paper 3, maximum raw mark 75
CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Level MARK SCHEME for the May/June 0 series 9709 MATHEMATICS 9709/ Paper, maximum raw mark 75 This mark scheme is published as an aid to teachers and candidates,
More informationMARK SCHEME for the October/November 2012 series 9709 MATHEMATICS. 9709/11 Paper 1, maximum raw mark 75
CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the October/November 2012 series 9709 MATHEMATICS 9709/11 Paper 1, maximum raw mark 75 This mark
More information9709 MATHEMATICS 9709/31 Paper 31, maximum raw mark 75
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the October/November 009 question paper for the guidance of teachers 9709 MATHEMATICS
More informationCambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level MATHEMATICS 9709/1 Paper 1 May/June 016 MARK SCHEME Maximum Mark: 75 Published This mark scheme is published
More informationMARK SCHEME for the October/November 2013 series 9709 MATHEMATICS. 9709/33 Paper 3, maximum raw mark 75
www.onlineexamhelp.com www.onlineexamhelp.com CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Level MARK SCHEME for the October/November 03 series 9709 MATHEMATICS 9709/33 Paper 3, maximum raw mark 75
More information9709 MATHEMATICS. 9709/42 Paper 4 (Mechanics), maximum raw mark 50
CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International Advanced Subsidiary and Advanced Level MARK SCHEME for the March 016 series 9709 MATHEMATICS 9709/4 Paper 4 (Mechanics), maximum raw mark 50
More information9709 MATHEMATICS. 9709/33 Paper 3, maximum raw mark 75
CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Level MARK SCHEME for the May/June 04 series 9709 MATHEMATICS 9709/ Paper, maximum raw mark 75 This mark scheme is published as an aid to teachers and
More information9709 MATHEMATICS. 9709/12 Paper 1, maximum raw mark 75
CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the May/June 01 series 9709 MATHEMATICS 9709/1 Paper 1, maximum raw mark 7 This mark scheme is
More information9709 MATHEMATICS. 9709/42 Paper 4, maximum raw mark 50
CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the May/June 2013 series 9709 MATHEMATICS 9709/42 Paper 4, maximum raw mark 50 This mark scheme
More information9709 MATHEMATICS 8719 HIGHER MATHEMATICS
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary and Advanced Level MARK SCHEME for the June 005 question paper 9709 MATHEMATICS 8719 HIGHER MATHEMATICS 9709/03, 8719/03 Paper
More information9709 MATHEMATICS. 9709/13 Paper 1, maximum raw mark 75
CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the May/June 0 series 9709 MATHEMATICS 9709/ Paper, maximum raw mark 75 This mark scheme is published
More information9709 MATHEMATICS. 9709/11 Paper 1, maximum raw mark 75
CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the May/June 0 series 9709 MATHEMATICS 9709/ Paper, maimum raw mark 75 This mark scheme is published
More informationMARK SCHEME for the October/November 2014 series 9709 MATHEMATICS. 9709/13 Paper 1, maximum raw mark 75
CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International Advanced Subsidiary and Advanced Level MARK SCHEME for the October/November 04 series 9709 MATHEMATICS 9709/ Paper, maximum raw mark 75 This
More informationCambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level. Published
Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level MATHEMATICS 909/1 Paper 1 May/June 01 MARK SCHEME Maximum Mark: 5 Published This mark scheme is published
More informationMARK SCHEME for the October/November 2014 series 9709 MATHEMATICS. 9709/72 Paper 7, maximum raw mark 50
CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International Advanced Level MARK SCHEME for the October/November 014 series 9709 MATHEMATICS 9709/7 Paper 7, maximum raw mark 50 This mark scheme is published
More information4037 ADDITIONAL MATHEMATICS
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Level MARK SCHEME for the May/June 0 question paper for the guidance of teachers 407 ADDITIONAL MATHEMATICS 407/ Paper, maximum raw mark
More information9709 MATHEMATICS. 9709/31 Paper 3 (Paper 3), maximum raw mark 75
CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International Advanced Level MARK SCHEME for the May/June 015 series 9709 MATHEMATICS 9709/31 Paper 3 (Paper 3), maximum raw mark 75 This mark scheme is published
More information9709 MATHEMATICS. 9709/32 Paper 3 (Pure Mathematics), maximum raw mark 75
CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International Advanced Subsidiary and Advanced Level MARK SCHEME for the March 06 series 9709 MATHEMATICS 9709/3 Paper 3 (Pure Mathematics), maximum raw mark
More informationwww.onlineexamhelp.com www.onlineexamhelp.com UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Level MARK SCHEME for the May/June 010 question paper for the guidance of teachers 931 FURTHER
More informationMARK SCHEME for the October/November 2012 series 9709 MATHEMATICS. 9709/61 Paper 6, maximum raw mark 50
CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the October/November 2012 series 9709 MATHEMATICS 9709/61 Paper 6, maximum raw mark 50 This mark
More informationCambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level. Published
Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level MATHEMATICS 9709/1 Paper 1 October/November 016 MARK SCHEME Maximum Mark: 75 Published This mark scheme
More informationMARK SCHEME for the May/June 2012 question paper for the guidance of teachers 9709 MATHEMATICS. 9709/43 Paper 4, maximum raw mark 50
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the May/June 2012 question paper for the guidance of teachers 9709 MATHEMATICS 9709/43
More informationAS Further Mathematics
AS Further Mathematics Paper Mark scheme Specime Versio. Mark schemes are prepared by the Lead Assessmet Writer ad cosidered, together with the relevat questios, by a pael of subject teachers. This mark
More informationMARK SCHEME for the October/November 2015 series 9709 MATHEMATICS. 9709/12 Paper 1, maximum raw mark 75
CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International Advanced Subsidiary and Advanced Level MARK SCHEME for the October/November 05 series 9709 MATHEMATICS 9709/ Paper, maimum raw mark 75 This
More informationMARK SCHEME for the October/November 2010 question paper for the guidance of teachers 9709 MATHEMATICS. 9709/11 Paper 1, maximum raw mark 75
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the October/November 00 question paper for the guidance of teachers 70 MATHEMATICS
More informationMARK SCHEME for the October/November 2012 series 9709 MATHEMATICS. 9709/33 Paper 3, maximum raw mark 75
CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Level MARK SCHEME for the October/November 0 series 9709 MATHEMATICS 9709/ Paper, maximum raw mark 75 This mark scheme is published as an aid to teachers
More informationCambridge International Examinations Cambridge International Advanced Subsidiary Level. Published
Cambridge International Eaminations Cambridge International Advanced Subsidiary Level MATHEMATICS 9709/ Paper October/November 06 MARK SCHEME Maimum Mark: 50 Published This mark scheme is published as
More informationFURTHER MATHEMATICS 9231/13 Paper 1 October/November 2016 MARK SCHEME Maximum Mark: 100. Published
Cambridge International Examinations Cambridge International Advanced Level FURTHER MATHEMATICS 9/ Paper October/November 6 MARK SCHEME Maximum Mark: Published This mark scheme is published as an aid to
More informationMark Scheme (Results) January International GCSE Further Pure Mathematics (4PM0/01)
Mark Scheme (Results) Jauary 013 Iteratioal GCSE Further Pure Mathematics (4PM0/01) Edexcel ad BTEC Qualificatios Edexcel ad BTEC qualificatios come from Pearso, the world s leadig learig compay. We provide
More informationMARK SCHEME for the October/November 2012 series 9709 MATHEMATICS. 9709/73 Paper 7, maximum raw mark 50
CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Level MARK SCHEME for the October/November 01 series 9709 MATHEMATICS 9709/73 Paper 7, maximum raw mark 50 This mark scheme is published as an aid to teachers
More information4037 ADDITIONAL MATHEMATICS
CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Level MARK SCHEME for the October/November 202 series 07 ADDITIONAL MATHEMATICS 07/22 Paper 2, maimum raw mark 80 This mark scheme is published as an aid
More information9709 MATHEMATICS. 9709/12 Paper 1, maximum raw mark 75
CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the May/June 04 series 9709 MATHEMATICS 9709/ Paper, maximum raw mark 75 This mark scheme is published
More information9709 MATHEMATICS 9709/11 Paper 11, maximum raw mark 75
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the October/November 2009 question paper for the guidance of teachers 9709 MATHEMATICS
More informationThis document consists of 9 printed pages.
Cambridge International Examinations Cambridge International Advanced Level MATHEMATICS 9709/ Paper MARK SCHEME Maximum Mark: 75 Published This mark scheme is published as an aid to teachers and candidates,
More informationMARK SCHEME for the May/June 2012 question paper for the guidance of teachers 9709 MATHEMATICS. 9709/61 Paper 6, maximum raw mark 50
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the May/June 2012 question paper for the guidance of teachers 9709 MATHEMATICS 9709/61
More information0606 ADDITIONAL MATHEMATICS 0606/02 Paper 2, maximum raw mark 80
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 009 question paper for the guidance of teachers 0606 ADDITIONAL
More informationMARK SCHEME for the October/November 2011 question paper for the guidance of teachers 9709 MATHEMATICS. 9709/32 Paper 3, maximum raw mark 75
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the October/November 0 question paper for the guidance of teachers 9709 MATHEMATICS
More information4037 ADDITIONAL MATHEMATICS
CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Level MARK SCHEME for the October/November 0 series 4037 ADDITIONAL MATHEMATICS 4037/ Paper, maximum raw mark 80 This mark scheme is published as an aid
More informationCambridge Assessment International Education Cambridge International Advanced Level. Published
Cambridge Assessment International Education Cambridge International Advanced Level MATHEMATICS 9709/ Paper 07 MARK SCHEME Maximum Mark: 7 Published This mark scheme is published as an aid to teachers
More informationMARK SCHEME for the October/November 2013 series 9709 MATHEMATICS. 9709/11 Paper 1, maximum raw mark 75
CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the October/November 013 series 9709 MATHEMATICS 9709/11 Paper 1, maximum raw mark 75 This mark
More informationM06/5/MATHL/HP2/ENG/TZ0/XX MATHEMATICS HIGHER LEVEL PAPER 2. Thursday 4 May 2006 (morning) 2 hours INSTRUCTIONS TO CANDIDATES
IB MATHEMATICS HIGHER LEVEL PAPER DIPLOMA PROGRAMME PROGRAMME DU DIPLÔME DU BI PROGRAMA DEL DIPLOMA DEL BI 06705 Thursday 4 May 006 (morig) hours INSTRUCTIONS TO CANDIDATES Do ot ope this examiatio paper
More information9231 FURTHER MATHEMATICS
CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the October/November 2012 series 9231 FURTHER MATHEMATICS 9231/21 Paper 2, maximum raw mark 100
More information9709 MATHEMATICS. 9709/62 Paper 6, maximum raw mark 50
CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level www.xtremepapers.com MARK SCHEME for the May/June 2013 series 9709 MATHEMATICS 9709/62 Paper 6, maximum raw mark
More informationMARK SCHEME for the May/June 2011 question paper for the guidance of teachers 9709 MATHEMATICS. 9709/12 Paper 1, maximum raw mark 75
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the May/June 0 question paper for the guidance of teachers 9709 MATHEMATICS 9709/
More informationCambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level. Published
Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level MATHEMATICS 9709/42 Paper 4 MARK SCHEME Maximum Mark: 50 Published This mark scheme is published as an
More informationThis document consists of 11 printed pages.
Cambridge International Examinations Cambridge International Advanced Level MATHEMATICS 9709/3 Paper 3 Pure Mathematics March 017 MARK SCHEME Maximum Mark: 75 Published This mark scheme is published as
More informationCambridge Assessment International Education Cambridge International Advanced Subsidiary and Advanced Level
Cambridge Assessment International Education Cambridge International Advanced Subsidiary and Advanced Level MATHEMATICS 9709/1 Paper 1 017 MARK SCHEME Maximum Mark: 75 Published This mark scheme is published
More informationMARK SCHEME for the October/November 2007 question paper 9709 MATHEMATICS. 9709/06 Paper 6, maximum raw mark 50
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the October/November 007 question paper 9709 MATHEMATICS 9709/06 Paper 6, maximum
More information9709 MATHEMATICS. 9709/62 Paper 6 (paper 6), maximum raw mark 50
CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International Advanced Subsidiary and Advanced Level MARK SCHEME for the May/June 2015 series 9709 MATHEMATICS 9709/62 Paper 6 (paper 6), maximum raw mark
More informationMARK SCHEME for the November 2004 question paper 9709 MATHEMATICS 8719 HIGHER MATHEMATICS
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary and Advanced Level MARK SCHEME for the November 004 question paper 9709 MATHEMATICS 879 HIGHER MATHEMATICS 9709/03, 879/03 Paper
More informationCambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level
Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level MATHEMATICS 9709/04 Paper 4 For examination from 2017 MARK SCHEME Maximum Mark: 50 Specimen This document
More informationMEI STRUCTURED MATHEMATICS FURTHER CONCEPTS FOR ADVANCED MATHEMATICS, FP1. Practice Paper FP1-C
MEI Mathematics i Educatio ad Idustry MEI STRUCTURED MATHEMATICS FURTHER CONCEPTS FOR ADVANCED MATHEMATICS, FP Practice Paper FP-C Additioal materials: Aswer booklet/paper Graph paper MEI Examiatio formulae
More information9709 MATHEMATICS. 9709/62 Paper 6, maximum raw mark 50
CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the May/June 2014 series 9709 MATHEMATICS 9709/62 Paper 6, maximum raw mark 50 This mark scheme
More informationMark Scheme (Results) Summer GCE Further Pure Mathematics 3 (6669/01)
Mark (Results) Summer GCE Further Pure Mathematics (6669/) Edexcel ad BTEC Qualificatios Edexcel ad BTEC qualificatios come from Pearso, the world s leadig learig compay. We provide a wide rage of qualificatios
More information9709 MATHEMATICS 9709/41 Paper 41, maximum raw mark 50
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the October/November 2009 question paper for the guidance of teachers 9709 MATHEMATICS
More informationThis document consists of 9 printed pages.
Cambridge International Examinations Cambridge International Advanced Level MATHEMATICS 9709/72 Paper 7 MARK SCHEME Maximum Mark: 50 Published This mark scheme is published as an aid to teachers and candidates,
More information9231 FURTHER MATHEMATICS
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Level MARK SCHEME for the October/November 2011 question paper for the guidance of teachers 9231 FURTHER MATHEMATICS 9231/21 Paper 2, maximum
More informationCambridge Assessment International Education Cambridge International Advanced Level. Published
Cambridge Assessment International Education Cambridge International Advanced Level MATHEMATICS 9709/71 Paper 7 MARK SCHEME Maximum Mark: 50 Published This mark scheme is published as an aid to teachers
More information9231 FURTHER MATHEMATICS
CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Level MARK SCHEME for the October/November 2013 series 9231 FURTHER MATHEMATICS 9231/23 Paper 2, maximum raw mark 100 This mark scheme is published as
More informationCambridge Assessment International Education Cambridge International Advanced Level. Published
Cambridge Assessment International Education Cambridge International Advanced Level MATHEMATICS 9709/5 Paper 5 MARK SCHEME Maximum Mark: 50 Published This mark scheme is published as an aid to teachers
More informationIYGB. Special Extension Paper E. Time: 3 hours 30 minutes. Created by T. Madas. Created by T. Madas
YGB Special Extesio Paper E Time: 3 hours 30 miutes Cadidates may NOT use ay calculator. formatio for Cadidates This practice paper follows the Advaced Level Mathematics Core ad the Advaced Level Further
More information9231 FURTHER MATHEMATICS
CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International Advanced Level MARK SCHEME for the May/June 5 series 9 FURTHER MATHEMATICS 9/ Paper (Paper ), maimum raw mark This mark scheme is published
More information9231 FURTHER MATHEMATICS
CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Level MARK SCHEME for the October/November 2012 series 9231 FURTHER MATHEMATICS 9231/23 Paper 2, maximum raw mark 100 This mark scheme is published as
More informationGCE. Mathematics. Mark Scheme for January Advanced GCE Unit 4727: Further Pure Mathematics 3. physicsandmathstutor.com
GCE Mathematics Advaced GCE Uit 77: Further Pure Mathematics Mark Scheme for Jauary 0 Oford Cambridge ad RSA Eamiatios OCR (Oford Cambridge ad RSA) is a leadig UK awardig body, providig a wide rage of
More information(5x 7) is. 63(5x 7) 42(5x 7) 50(5x 7) BUSINESS MATHEMATICS (Three hours and a quarter)
BUSINESS MATHEMATICS (Three hours ad a quarter) (The first 5 miutes of the examiatio are for readig the paper oly. Cadidate must NOT start writig durig this time). ------------------------------------------------------------------------------------------------------------------------
More informationWELSH JOINT EDUCATION COMMITTEE 3.00 CYD-BWYLLGOR ADDYSG CYMRU MARKING SCHEMES JANUARY 2007 MATHEMATICS
MS WELSH JOINT EDUCATION COMMITTEE.00 CYD-BWYLLGOR ADDYSG CYMRU Geeral Certificate of Educatio Advaced Subsidiary/Advaced Tystysgrif Addysg Gyffrediol Uwch Gyfraol/Uwch MARKING SCHEMES JANUARY 007 MATHEMATICS
More informationCondensed. Mathematics. General Certificate of Education Advanced Level Examination January Unit Further Pure 4.
Geeral Certificate of Educatio Advaced Level Examiatio Jauary 0 Mathematics MFP4 Uit Further Pure 4 Friday Jauary 0 9.00 am to 0.30 am For this paper you must have: the blue AQA booklet of formulae ad
More informationThis document consists of 8 printed pages.
Cambridge International Examinations Cambridge International Advanced Level MATHEMATICS 9709/73 Paper 7 MARK SCHEME Maximum Mark: 50 Published This mark scheme is published as an aid to teachers and candidates,
More informationCambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level. Published
Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level MATHEMATICS 9709/63 Paper 6 October/November 2016 MARK SCHEME Maximum Mark: 50 Published This mark scheme
More information9231 FURTHER MATHEMATICS
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Level MARK SCHEME for the May/June 2008 question paper 9231 FURTHER MATHEMATICS 9231/02 Paper 2, maximum raw mark 100 This mark scheme is
More information4037 ADDITIONAL MATHEMATICS
CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Level MARK SCHEME for the October/November 0 series 40 ADDITIONAL MATHEMATICS 40/ Paper, maimum raw mark 80 This mark scheme is published as an aid to
More informationFurther Concepts for Advanced Mathematics (FP1) MONDAY 2 JUNE 2008
ADVANCED SUBSIDIARY GCE 4755/0 MATHEMATICS (MEI) Further Cocepts for Advaced Mathematics (FP) MONDAY JUNE 008 Additioal materials: Aswer Booklet (8 pages) Graph paper MEI Examiatio Formulae ad Tables (MF)
More informationCambridge Assessment International Education Cambridge International Advanced Subsidiary and Advanced Level. Published
Cambridge Assessment International Education Cambridge International Advanced Subsidiary and Advanced Level MATHEMATICS 9709/41 Paper 4 MARK SCHEME Maximum Mark: 50 Published This mark scheme is published
More informationwww.onlineexamhelp.com www.onlineexamhelp.com UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Level MARK SCHEME for the May/June 2011 question paper for the guidance of teachers 9231 FURTHER
More informationCambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level. Published
Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level MATHEMATICS 9709/62 Paper 6 MARK SCHEME Maximum Mark: 50 Published This mark scheme is published as an
More information9231 FURTHER MATHEMATICS
CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International Advanced Level MARK SCHEME for the October/November series 9 FURTHER MATHEMATICS 9/ Paper, maimum raw mar This mar scheme is published as an
More information0606 ADDITIONAL MATHEMATICS
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the June 005 question paper 0606 ADDITIONAL MATHEMATICS 0606/01 Paper 1, maximum
More informationM1 for method for S xy. M1 for method for at least one of S xx or S yy. A1 for at least one of S xy, S xx, S yy correct. M1 for structure of r
Questio 1 (i) EITHER: 1 S xy = xy x y = 198.56 1 19.8 140.4 =.44 x x = 1411.66 1 19.8 = 15.657 1 S xx = y y = 1417.88 1 140.4 = 9.869 14 Sxy -.44 r = = SxxSyy 15.6579.869 = 0.76 1 S yy = 14 14 M1 for method
More informationFurther Methods for Advanced Mathematics (FP2) WEDNESDAY 9 JANUARY 2008
ADVANCED GCE 7/ MATHEMATICS (MEI) Furter Metods for Advaced Matematics (F) WEDNESDAY 9 JANUARY 8 Additioal materials: Aswer Booklet (8 pages) Grap paper MEI Eamiatio Formulae ad Tables (MF) Afteroo Time:
More informationMARK SCHEME for the October/November 2012 series 9709 MATHEMATICS. 9709/12 Paper 1, maximum raw mark 75
CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the October/November 01 series 9709 MATHEMATICS 9709/1 Paper 1, maimum raw mar 75 This mar scheme
More informationNUMERICAL METHODS FOR SOLVING EQUATIONS
Mathematics Revisio Guides Numerical Methods for Solvig Equatios Page 1 of 11 M.K. HOME TUITION Mathematics Revisio Guides Level: GCSE Higher Tier NUMERICAL METHODS FOR SOLVING EQUATIONS Versio:. Date:
More informationNational Quali cations SPECIMEN ONLY
AH Natioal Quali catios SPECIMEN ONLY SQ/AH/0 Mathematics Date Not applicable Duratio hours Total s 00 Attempt ALL questios. You may use a calculator. Full credit will be give oly to solutios which cotai
More informationCambridge Assessment International Education Cambridge International Advanced Level. Published
Cambridge Assessment International Education Cambridge International Advanced Level MATHEMATICS 9709/51 Paper 5 MARK SCHEME Maximum Mark: 50 Published This mark scheme is published as an aid to teachers
More information