9795 FURTHER MATHEMATICS
|
|
- Cory Barton
- 5 years ago
- Views:
Transcription
1 UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS Pre-U Certificate MARK SCHEME for the Ma/June question paper for the guidance of teachers 9795 FURTHER MATHEMATICS 9795/ Paper (Further Pure Mathematics), maximum raw mark This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners meeting before marking began, which would have considered the acceptabilit of alternative answers. Mark schemes must be read in conjunction with the question papers and the report on the examination. Cambridge will not enter into discussions or correspondence in connection with these mark schemes. Cambridge is publishing the mark schemes for the Ma/June question papers for most IGCSE, Pre-U, GCE Advanced Level and Advanced Subsidiar Level sllabuses and some Ordinar Level sllabuses.
2 Page Mark Scheme: Teachers version Sllabus Paper Pre-U Ma/June 9795 n ( r r + ) r r + r n n r r n Splitting summation and use of given results r n n + )(n + ) n( n + ) + n st for Σr ; nd for Σr & Σ n B B 6 ( n n + ) legitimatel A [] ( A k ( + cosθ ) dθ including squaring attempt; ignore limits and k ( + sin θ ) dθ for use of the double-angle formula OR integration of cosθ as k sin θ or k cos θ B π / θ cos θ ft (constants onl) in the integration; MUST be separate terms A π + A [] d (i) (sinh x) (sinh x) d. cosh x OR sinh x cosh x + A A [] (ii) d +. B Sep g. Vars. in (i) s answer x + d A But x sinh t so + t sinh (t ) + C condone missing + C A ALT. Set t sinhθ, t dt coshθ dθ Full substn. t coshθ dt dθ A + t.dθ θ sinh (t ) A + sinh θ ALT. Set t tanθ, t dt sec θ dθ Full substn. t sec θ dt dθ A + t sec θ.dθ + tan θ ln secθ + tanθ ln t + + t A [] Universit of Cambridge International Examinations
3 Page Mark Scheme: Teachers version Sllabus Paper Pre-U Ma/June 9795 (i) x + x +.x x + ( ) Creating a quadratic in x For real x, ( ) Considering the discriminant Creating a quadratic inequalit For real x, (6 + )( ) Factorising/solving a -term quadratic 6 cso NB lack of inequalit earlier with unjustified correct answer loses onl the rd M mark A [5] (ii) substd. back (x x + ) x [ ] A substd. back 6 (x + 6x + 9) x [ 6 6 ] A Allow alternative approach via calculus: d x x + Solving quadratic to find values of x ( x + ) Then A A each pair of correct (x, ) coordinates [] 5 (i) cosα sinα (a) sinα cosα cos β sin β (b) sin β cos β B B [] (ii) cosφ sinφ sinφ cosθ cosφ cosθ Multn. of reflection matrices. Correct order. cos φ cosθ + sinφ cosφ sinφ cosθ sinφ cosθ cosφ cosφ cosθ + sinφ cos( φ θ ) sin( φ θ ) sin( φ θ ) cos( φ θ ) giving a Rotation (about O) Use of the addition formulae; correctl done through (φ θ ) acw [or (θ φ ) cw] A A Those who get the initial matrices in the wrong order, can get 5/6, losing onl that M mark [6] Universit of Cambridge International Examinations
4 Page Mark Scheme: Teachers version Sllabus Paper Pre-U Ma/June (i) Possible orders are,,,, 6 & B B Lagrange s Theorem, the order of an element divides the order of the group (since the order of an element the order of the subgroup generated b that element) B [] (ii) E.g. xx. x xx. x b x. x. x.. b x. x. ( ) [b ] x. (x ) x. e b M s for first, correct uses of different conditions; the A for the rd condition used to clinch the result. SPECIAL CASE Allow / for those who correctl argue the converse A [] (iii) Proving G not abelian: [e.g. b xx but x e] G not cclic OR establishing a contradiction B B [] 7 (i) cosθ + i (c + is) Use of de Moivre s Theorem c + c.is + 6c.i s + c.i s + i s Binomial expansion attempted cosθ c 6c s + s and c s cs Equating Re & Im parts sin θ c s cs tanθ cos θ c 6c s + s t t Dividing throughout b c to get 6t + t legitimatel A [5] (ii) t tanθ B 5 9 ( ) + 9 π + tan 9 9 tan 9 Noting that this is tan( tan ) so that tan 5 5 π + tan 9 A A [] Universit of Cambridge International Examinations
5 Page 5 Mark Scheme: Teachers version Sllabus Paper Pre-U Ma/June (i) Subst g. x, f() and f () into (*) f () 5 A [] x (ii) { x f ( x) + xf ( x) } + {( x ) f ( x) + f ( x) } f ( x) e Product Rule used twice; at least one bracket correct A Subst g. x, f () and f () 5 into this f () ft their f () A [] (iii) f(x) f() + f ()(x ) + f ()(x ) + 6 f ()(x ) + Use of the Talor series + (x ) + 5 (x ) (x ) + st two terms cao; nd two terms ft (i) & (ii) s answers A A [] (iv) Subst g. x. f(.). to d.p. cso (i.e. exactl this answer) A [] 9 (i) d + x is a Bernouilli (differential) equation u du d B Then d + x d du becomes 9x u 9x AG A [] (ii) Method IF is e x ue x 9xe x x xe e x Use of parts A (x + )e x + C A Gen. Soln. is u x + + Ce x ft B x + + Ce ft B x Using x, to find C C 7 or x x + + 7e A [9] Universit of Cambridge International Examinations
6 Page 6 Mark Scheme: Teachers version Sllabus Paper Pre-U Ma/June 9795 Method Aux. Eqn. m u C Ae x is the Comp. Fn. A For Part. Intgl. tr u P ax + b, u P a Subst g. u P ax + b and u P a into the d.e. and comparing terms a ax b 9x a, b i.e. u P x + A Gen. Soln. is u x + Ae x ft PI + CF provided PI has no arbitrar constants and CF has one B x + + Ae ft B x Using x, to find A A 7 or x x + + 7e A [9] (i) + λ Subst g. + λ into plane equation; i.e. + 6λ OR an point on line (since given ) + λ + λ 6 k + 6λ k + 6λ + 8 λ λ 6 A [] (ii) + m Working with vector 6m. m + m Subst g. into the plane equation: + 6m 6 k m Solving a linear equation in m: + m + 6m + 9m 9 6 m Q (6, 6, ) B A Sh. Dist. is m 6 or PQ Alternate methods that find onl Sh. Dist. but not Q can score A onl A [5] Universit of Cambridge International Examinations
7 Page 7 Mark Scheme: Teachers version Sllabus Paper Pre-U Ma/June 9795 (iii) Finding points in the plane: e.g. A(,, ), B(,, 8), C(,, ) Then vectors in (// to) plane: e.g. AB, 6 OR B B for an two vectors in the plane 9 AC 5, 5 6 BC 5 Vector product of an two of these to get normal to plane: (an non-zero multiple) 9 A d 9 (an position vector) 9 e.g. 9 x 9 + z 9 cao (or an correct equivalent form) ALTERNATE SOLUTION A [6] ax + b + cz d contains + λ + λ + 6λ and... so a + aλ + bλ b + c + 6cλ d and a + b c d B Then a b + c d and a + b + 6c (λ terms) i.e. equating terms Eliminating (e.g.) c from st two eqns. 9a + b Choosing a, b 9 c and d 9 i.e. x 9 + z 9 cao A [6] Universit of Cambridge International Examinations
8 Page 8 Mark Scheme: Teachers version Sllabus Paper Pre-U Ma/June 9795 or A (i) w ( ) + ( + ) arg(w) tan 5 tan ( + ) π (ii) (a) z (, π ), (, π ), (, or π ) π A [] w ; arg(w) 5, π These method marks can be earned for just the first root 9 9 z ( ), (, π ), (, π ) 6 6 A marks for the nd & rd roots: 6 r e^(iθ) forms equall acceptable A A [] (b) z, z, z the roots of z.z +.z w z z z w ( ) + i( + ) ALT. Multipling the roots together in an form (c) Three points in approx. correct places A [] All equall spaced around a circle, centre O, radius (Explained that equilateral) ( π ) l sin 6 or b the Cosine Rule (d) k exp{ i. π} or exp{ i. π} or exp{ i. π} B A A [5] [] Universit of Cambridge International Examinations
9 Page 9 Mark Scheme: Teachers version Sllabus Paper Pre-U Ma/June 9795 (i) I n x n x 6 + x Correct splitting and use of parts ( 6 + x ) x n. / / n ( 6 + x ) ( n ) x A n 5 x n 6 + x 6 + x Method to get nd integral of correct form n ( ) n n.5 { 6 I } n + I n [i.e. reverting to I s in nd integral ft] I n n.5 6(n ) I n (n ) I n Collecting up I n s (n + ) I n 5 n 6(n ) I n AG A [6] (ii) (a) Spiral (with r increasing) B From O to just short of θ π B [] (b) r θ dr dθ θ and dr 8 6 r + θ + θ A 6 dθ θ ( ) I L 6 + θ Now ( + x ) A / 6 I 6 B 5 I or and ( 6 ) 7 Use of given reduction formula so that L or 6 or awrt.7 ft onl from suitable k I 6 A NB The last marks can be earned b integrating in a variet was [7] Universit of Cambridge International Examinations
10 Page Mark Scheme: Teachers version Sllabus Paper Pre-U Ma/June 9795 Base-line case: for n 5, 579 R contains a string of (5 ) 7 s B 579 R , 579 R , etc. or form of st & last digits B Assume that, for some k 5, 579 R k Induction hpothesis (k ) 7 s Then, for n k +, 579 R k + 579(R k + ) Give the M mark for the ke observation that R k + R k + or k + R k, even if not subsequentl used (k ) 7 s (k + ) 7 s which contains a string of (k + ) 7 s, as required. Proof follows b induction (usual round-up). A E [6] Universit of Cambridge International Examinations
Paper 1 Further Pure Mathematics For Examination from 2016 SPECIMEN MARK SCHEME 3 hours MAXIMUM MARK: 120
Cabridge International Exainations Cabridge Pre-U Certificate www.xtreepapers.co FURTHER MATHEMATICS (PRINCIPAL) 9795/ Paper Further Pure Matheatics For Exaination fro SPECIMEN MARK SCHEME hours MAXIMUM
More information0606 ADDITIONAL MATHEMATICS
CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME for the October/November 0 series 0606 ADDITIONAL MATHEMATICS 0606/ Paper, maimum raw
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 informationCambridge Assessment International Education Cambridge International General Certificate of Secondary Education. Published
Cambridge Assessment International Education Cambridge International General Certificate of Secondary Education ADDITIONAL MATHEMATICS 0606/ Paper 07 MARK SCHEME Maximum Mark: 80 Published This mark scheme
More informationMark Scheme (Results) Summer 2009
Mark (Results) Summer 009 GCE GCE Mathematics (6668/0) June 009 6668 Further Pure Mathematics FP (new) Mark Q (a) = rr ( + ) r ( r+ ) r ( r+ ) B aef () (b) n n r = r = = rr ( + ) r r+ = + +...... + + n
More information0606 ADDITIONAL MATHEMATICS
CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME for the May/June 5 series 66 ADDITIONAL MATHEMATICS 66/ Paper, maximum raw mark 8 This
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 information0606 ADDITIONAL MATHEMATICS
CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME for the March 06 series 0606 ADDITIONAL MATHEMATICS 0606/ Paper, maimum raw mark 80 This
More informationMARK SCHEME for the May/June 2011 question paper for the guidance of teachers 0580 MATHEMATICS
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 0 question paper for the guidance of teachers 0580 MATHEMATICS 0580/4
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 information0606 ADDITIONAL MATHEMATICS
CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the October/November 0 series 0606 ADDITIONAL MATHEMATICS 0606/ Paper, maximum raw mark 80
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 informationA-LEVEL Mathematics. Further Pure 2 MFP2 Mark scheme June Version/Stage: Final
A-LEVEL Mathematics Further Pure MFP Mark scheme 660 June 04 Version/Stage: Final Mark schemes are prepared by the Lead Assessment Writer and considered, together with the relevant questions, by a panel
More informationCambridge International Examinations Cambridge International General Certificate of Secondary Education. Published
Cambridge International Examinations Cambridge International General Certificate of Secondary Education ADDITIONAL MATHEMATICS 0606/ Paper March 07 MARK SCHEME Maximum Mark: 80 Published This mark scheme
More information9794 MATHEMATICS. 9794/03 Paper 3 (Applications of Mathematics), maximum raw mark 80
CAMBRIDGE INTERNATIONAL EXAMINATIONS Pre-U Certificate MARK SCHEME for the May/June 013 series 9794 MATHEMATICS 9794/03 Paper 3 (Applications of Mathematics), maximum raw mark 80 This mark scheme is published
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 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 informationCambridge Assessment International Education Cambridge Pre-U Certificate. Published
Cambridge Assessment International Education Cambridge Pre-U Certificate MATHEMATICS 979/0 Paper Pure Mathematics MARK SCHEME Maimum Mark: 80 Published This mark scheme is published as an aid to teachers
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
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 information4024 MATHEMATICS 4024/02 Paper 2, maximum raw mark 100
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Level www.xtremepapers.com MARK SCHEME for the May/June 009 question paper for the guidance of teachers 404 MATHEMATICS 404/0 Paper, maimum
More informationMARK SCHEME for the October/November 2014 series 0580 MATHEMATICS
CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International General Certificate of Secondary Education MARK SCHEME for the October/November 04 series 0580 MATHEMATICS 0580/4 Paper 4 Extended, maximum
More information0580 MATHEMATICS. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers.
CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 0 series 0580 MATHEMATICS 0580/4 Paper 4 (Extended), maximum raw mark 0 This mark
More informationMark Scheme (Results) June GCE Further Pure FP3 (6669) Paper 1
Mark (Results) June 0 GCE Further Pure FP (6669) Paper Edexcel is one of the leading examining and awarding bodies in the UK and throughout the world. We provide a wide range of qualifications including
More informationThe number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 72.
ADVANCED GCE UNIT MATHEMATICS (MEI) Applications of Advanced Mathematics (C) Paper A TUESDAY 3 JANUARY 007 Additional materials: Answer booklet (8 pages) Graph paper MEI Examination Formulae and Tables
More informationADDITIONAL MATHEMATICS 4037/12 Paper 1 October/November 2016 MARK SCHEME Maximum Mark: 80. Published
Cambridge International Eaminations Cambridge Ordinary Level ADDITIONAL MATHEMATICS 07/ Paper October/November 06 MARK SCHEME Maimum Mark: 80 Published This mark scheme is published as an aid to teachers
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 informationFP3 mark schemes from old P4, P5, P6 and FP1, FP2, FP3 papers (back to June 2002)
FP mark schemes from old P, P5, P6 and FP, FP, FP papers (back to June ) Please note that the following pages contain mark schemes for questions from past papers. Where a question reference is marked with
More informationFP2 Mark Schemes from old P4, P5, P6 and FP1, FP2, FP3 papers (back to June 2002)
FP Mark Schemes from old P, P5, P6 and FP, FP, FP papers (back to June 00) Please note that the following pages contain mark schemes for questions from past papers. The standard of the mark schemes is
More information0580 MATHEMATICS 0580/31 Paper 31 (Core), maximum raw mark 104
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 00 question paper for the guidance of teachers 0580 MATHEMATICS
More informationabc Mathematics Further Pure General Certificate of Education SPECIMEN UNITS AND MARK SCHEMES
abc General Certificate of Education Mathematics Further Pure SPECIMEN UNITS AND MARK SCHEMES ADVANCED SUBSIDIARY MATHEMATICS (56) ADVANCED SUBSIDIARY PURE MATHEMATICS (566) ADVANCED SUBSIDIARY FURTHER
More informationMARK SCHEME for the October/November 2012 series 0580 MATHEMATICS
CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the October/November 01 series 0580 MATHEMATICS 0580/4 Paper 4 (Extended), maximum raw mark
More informationCambridge International Examinations Cambridge International General Certificate of Secondary Education. Published
Cambridge International Eaminations Cambridge International General Certificate of Secondary Education ADDITIONAL MATHEMATICS 0606/ Paper October/November 06 MARK SCHEME Maimum Mark: 80 Published This
More informationMARK SCHEME for the October/November 2012 series 0580 MATHEMATICS
CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the October/November 0 series 0580 MATHEMATICS 0580/4 Paper 4 (Extended), maximum raw mark
More informationMARK SCHEME for the May/June 2012 question paper for the guidance of teachers 0580 MATHEMATICS
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 0 question paper for the guidance of teachers 0580 MATHEMATICS 0580/4
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 informationVersion 1.0. General Certificate of Education (A-level) June 2012 MFP3. Mathematics. (Specification 6360) Further Pure 3.
Version.0 General Certificate of Education (A-level) June 0 Mathematics MFP (Specification 660) Further Pure Mark Scheme Mark schemes are prepared by the Principal Examiner and considered, together with
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 informationMARK SCHEME for the May/June 2012 question paper for the guidance of teachers 0580 MATHEMATICS. 0580/33 Paper 3 (Core), maximum raw mark 104
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 202 question paper for the guidance of teachers 0580 MATHEMATICS
More informationADDITIONAL MATHEMATICS 4037/23 Paper 2 October/November 2016 MARK SCHEME Maximum Mark: 80. Published
Cambridge International Examinations Cambridge Ordinary Level ADDITIONAL MATHEMATICS 407/ Paper October/November 016 MARK SCHEME Maximum Mark: 80 Published This mark scheme is published as an aid to teachers
More informationCambridge International Examinations Cambridge International General Certificate of Secondary Education. Published
Cambridge International Eaminations Cambridge International General Certificate of Secondary Education ADDITIONAL MATHEMATICS 0606/ Paper March 07 MARK SCHEME Maimum Mark: 80 Published This mark scheme
More informationCambridge International Examinations Cambridge International General Certificate of Secondary Education. Published
Cambridge International Eaminations Cambridge International General Certificate of Secondary Education ADDITIONAL MATHEMATICS 0606/ Paper May/June 07 MARK SCHEME Maimum Mark: 80 Published This mark scheme
More information0606 ADDITIONAL MATHEMATICS
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the June 004 question papers 0606 ADDITIONAL MATHEMATICS 0606/01 Paper 1, maximum
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 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 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 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 information9231 FURTHER MATHEMATICS
CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Level MARK SCHEME for the May/June 201 series 921 FURTHER MATHEMATICS 921/21 Paper 2, maximum raw mark 100 This mark scheme is published as an aid to teachers
More informationCambridge International Examinations Cambridge International General Certificate of Secondary Education
Cambridge International Eaminations Cambridge International General Certificate of Secondary Education ADDITIONAL MATHEMATICS 0606/ Paper May/June 07 MARK SCHEME Maimum Mark: 80 Published This mark scheme
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 informationA-LEVEL Mathematics. MFP2 Further Pure 2 Mark scheme June Version: 1.0 Final
A-LEVEL Mathematics MFP Further Pure Mark scheme 660 June 0 Version:.0 Final Mark schemes are prepared by the Lead Assessment Writer and considered, together with the relevant questions, by a panel of
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 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 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 information0580 and 0581 MATHEMATICS
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 007 question paper 0580 and 0581 MATHEMATICS 0580/04 and 0581/04
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. 9709/12 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 informationCambridge International Examinations Cambridge International General Certificate of Secondary Education. Published
Cambridge International Examinations Cambridge International General Certificate of Secondary Education ADDITIONAL MATHEMATICS 0606/ Paper October/November 06 MARK SCHEME Maximum Mark: 80 Published This
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 information0607 CAMBRIDGE INTERNATIONAL MATHEMATICS
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 0 question paper for the guidance of teachers 0607 CAMBRIDGE INTERNATIONAL
More informationGCE Mathematics. Mark Scheme for June Unit 4727: Further Pure Mathematics 3. Advanced GCE. Oxford Cambridge and RSA Examinations
GCE Mathematics Unit 477: Further Pure Mathematics 3 Advanced GCE Mark Scheme for June 04 Oxford Cambridge and RSA Examinations OCR (Oxford Cambridge and RSA) is a leading UK awarding body, providing a
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 informationCambridge Assessment International Education Cambridge Ordinary Level. Published
Cambridge Assessment International Education Cambridge Ordinary Level ADDITIONAL MATHEMATICS 407/ Paper 07 MARK SCHEME Maimum Mark: 80 Published This mark scheme is published as an aid to teachers and
More informationCambridge International Examinations Cambridge International General Certificate of Secondary Education. Published
Cambridge International Examinations Cambridge International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL MATHEMATICS 007/4 Paper 4 Paper 4 (Extended) October/November 0 MARK SCHEME
More informationMark Scheme. Mathematics General Certificate of Education examination - June series. MFP3 Further Pure 3
Version.0: 0606 abc General Certificate of Education Mathematics 660 MFP Further Pure Mark Scheme 006 examination - June series Mark schemes are prepared by the Principal Examiner and considered, together
More informationMARK SCHEME for the May/June 2012 question paper for the guidance of teachers 0580 MATHEMATICS
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 0 question paper for the guidance of teachers 0580 MATHEMATICS 0580/4
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 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 informationMark Scheme Summer 2009
Mark Summer 009 GCE Core Mathematics C (666) Edecel is one of the leading eamining and awarding bodies in the UK and throughout the world. We provide a wide range of qualifications including academic,
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 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 information0580 MATHEMATICS. 0580/43 Paper 4 (Extended), maximum raw mark 130
CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MARK SCHEME for the May/June 04 series 0580 MATHEMATICS 0580/4 Paper 4 (Extended), maximum raw mark 0 This
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. 9709/11 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 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 informationVersion 1.0. General Certificate of Education (A-level) January 2011 MFP2. Mathematics. (Specification 6360) Further Pure 2.
Version.0 General Certificate of Education (A-level) January 0 Mathematics MFP (Specification 660) Further Pure Mark Scheme Mark schemes are prepared by the Principal Eaminer and considered, together with
More information4024 MATHEMATICS (SYLLABUS D)
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Level MARK SCHEME for the May/June 2010 question paper for the guidance of teachers 4024 MATHEMATICS (SYLLABUS D) 4024/22 Paper 22, maimum
More informationCondensed. Mathematics. General Certificate of Education Advanced Level Examination January Unit Further Pure 3.
General Certificate of Education Advanced Level Examination January 0 Mathematics MFP Unit Further Pure Monday January 0 9.00 am to 0.0 am For this paper you must have: the blue AQA booklet of formulae
More informationCondensed. Mathematics. General Certificate of Education Advanced Subsidiary Examination January Unit Pure Core 2.
General Certificate of Education Advanced Subsidiary Examination January 0 Mathematics MPC Unit Pure Core Monday January 0 9.00 am to 0.0 am For this paper you must have: the blue AQA booklet of formulae
More informationA-LEVEL Mathematics. MPC4 Pure Core 4 Mark scheme June Version: 1.0 Final
A-LEVEL Mathematics MPC4 Pure Core 4 Mark scheme 660 June 06 Version:.0 Final Mark schemes are prepared by the Lead Assessment Writer and considered, together with the relevant questions, by a panel of
More informationVersion: abc. General Certificate of Education. Mathematics MPC4 Pure Core 4. Mark Scheme examination - June series
Version:.0 0608 abc General Certificate of Education Mathematics 660 MPC4 Pure Core 4 Mark Scheme 008 examination - June series Mark schemes are prepared by the Principal Examiner and considered, together
More informationCambridge Assessment International Education Cambridge Ordinary Level. Published
Cambridge Assessment International Education Cambridge Ordinary Level ADDITIONAL MATHEMATICS 4037/ Paper 07 MARK SCHEME Maimum Mark: 80 Published This mark scheme is published as an aid to teachers and
More informationMark Scheme (Results) January 2008
Mark Scheme (Results) January 008 GCE GCE Mathematics (6664/01) Edecel Limited. Registered in England and Wales No. 4496750 Registered Office: One90 High Holborn, London WC1V 7BH January 008 6664 Core
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 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 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 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 MATHEMATICS 9709/1 Paper 1 May/June 016 MARK SCHEME Maximum Mark: 75 Published This mark scheme is published
More informationMARK SCHEME for the May/June 2011 question paper for the guidance of teachers 9794 MATHEMATICS
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS Pre-U Certificate MARK SCHEME for the May/June 0 question paper for the guince of teachers 9794 MATHEMATICS 9794/0 Paper (Pure Mathematics and Mechanics),
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 informationMark Scheme (Results) Summer Pearson Edexcel GCE In Further Pure Mathematics FP2 (6668/01)
Mark Scheme (Results) Summer 017 Pearson Edexcel GCE In Further Pure Mathematics FP (6668/01) Edexcel and BTEC Qualifications Edexcel and BTEC qualifications are awarded by Pearson, the UK s largest awarding
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 informationMark Scheme (Results) January 2007
Mark Scheme (Results) January 007 GCE GCE Mathematics Core Mathematics C (666) Edexcel Limited. Registered in England and Wales No. 96750 Registered Office: One90 High Holborn, London WCV 7BH January 007
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 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 informationVersion 1.0: abc. General Certificate of Education. Mathematics MFP2 Further Pure 2. Mark Scheme examination June series
Version.0: 0608 abc General Certificate of Education Mathematics 6360 MFP Further Pure Mark Scheme 008 examination June series Mark schemes are prepared by the Principal Examiner and considered, together
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 information4024 MATHEMATICS (SYLLABUS D)
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Ordinary Level MARK SCHEME for the May/June 00 question paper for the guidance of teachers 404 MATHEMATICS (SYLLABUS D) 404/ Paper, maximum raw mark
More informationPMT. Version 1.0: abc. General Certificate of Education. Mathematics MPC3 Pure Core 3. Mark Scheme examination - June series
Version.0: 0608 abc General Certificate of Education Mathematics 660 MPC Pure Core Mark Scheme 008 eamination - June series MPC - AQA GCE Mark Scheme 008 June series Mark schemes are prepared by the Principal
More information