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Guidance for 9FM0  \nFirst teaching from September 2017  \nContents  \nPaper 1 and Paper 2: Core Pure Mathematics....................................... 4  \nPaper 3 and Paper 4: Further Mathematics Options ........................... 20  \nPaper 3A: Further Pure Mathematics 1 .......................................................... 20  \nPaper 4A: Further Pure Mathematics 2 .......................................................... 25  \nPaper 3B: Further Statistics 1* .................................................................... 30  \nPaper 4B: Further Statistics 2 ...................................................................... 35  \nPaper 3C: Further Mechanics 1* ................................................................... 41  \nPaper 4C: Further Mechanics 2 .................................................................... 43  \nPaper 3D: Decision Mathematics 1* .............................................................. 48  \nPaper 4D: Decision Mathematics 2................................................................ 56  \nContent of this document is based on the accredited version of Pearson Edexcel Level 3 Advanced GCE in Further Mathematics (9FM0) and includes enhanced content guidance to accompany the specification document.  \nTo support the co-teaching of this qualification with the AS Mathematics qualification, common content has been highlighted in bold.  \nOur free support for the AS and A level Mathematics and Further Mathematics specifications can be found on the Pearson Edexcel Mathematics website ([quals.pearson.com/Alevelmaths2017](quals.pearson.com/Alevelmaths2017)) and on the Emporium ([www.edexcelmaths.com](www.edexcelmaths.com)).  \n\n| Updates to this document since the previous version (version 1) |  |\n| --- | --- |\n| Change(s) made | Page no. |\n| Correction to inequality symbols in section 3.1-changed to P(Y n ) = P(X r ) | 31 |\n\nPaper 1 and Paper 2: Core Pure Mathematics  \n\n| Topic | What students need to learn: |  |  |  |  |\n| --- | --- | --- | --- | --- | --- |\n|  | Content |  | Guidance |  | Enhanced content guidance |\n| 1\u003Cbr>Proof | 1.1 | Construct proofs using mathematical induction.\u003Cbr>Contexts include sums of series, divisibility and powers of matrices. | To include induction proofs for (i) summation of series\u003Cbr>n\u003Cbr>[e.g. show](e.g. show) 􀂦r3 = ~~1~~4 n2 (n + 1)2 r =1\u003Cbr>or\u003Cbr>n  n(n + 1)(n + 2)\u003Cbr>show rr (r + 1) = 3 |  | Students need to understand the concept of proof by induction and be able to apply it in a variety of contexts. Proof by induction in contexts other than those listed in the guidance may be set.\u003Cbr>For example:\u003Cbr>(i) Simple recurrence relations If un+1 = 6un − 5 with u1 = 6, prove that un = 5􀁵 6n−1 + 1\u003Cbr>(ii) Differentiation\u003Cbr>If y = 1x prove that dndxyn = (−1)n n!x − (n+1) |\n|  |  |  | (ii) [divisibility e.g. show](divisibility e.g. show 32n)[ 3](divisibility e.g. show 32n)[2](divisibility e.g. show 32n)[n](divisibility e.g. show 32n) +11 divisible by 4\u003Cbr>(iii) [matrix products e.g. show](matrix products e.g. show) | is |  |\n|  |  |  | 􀂧3 −4 􀂷n 􀂧2n + 1 −4n 􀂷􀂨 􀂸 = 􀂨 􀂸􀂩1 −1 􀂹 􀂩 n 1 − 2n 􀂹 |  |  |\n| 2\u003Cbr>Complex\u003Cbr>numbers | 2.1 | Solve any quadratic equation with real coefficients.\u003Cbr>Solve cubic or quartic equations with real coefficients. | Given sufficient information to deduce at least one root for cubics or at least one complex root or quadratic factor for quartics, for example:\u003Cbr>(i) f(z) = 2z3 + 5z2 + 7z + 10\u003Cbr>Given that z + 2 is a factor of f(z), use algebra to solve f(z) = 0 completely.\u003Cbr>(ii) g(x) = x4 –x3 + 6x2 + 14x – 20\u003Cbr>Given g(1) = 0 and g(–2) = 0, use algebra to solve g(x) = 0 completely. |  |  |\n\n\n| Topic | What students need to learn: |  |  |  |\n| --- | --- | --- | --- | --- |\n|  | Content |  | Guidance | Enhanced content guidance |\n| 2\u003Cbr>Complex\u003Cbr>numbers\u003Cbr>continued | 2.2 | Add, subtract, multiply and divide complex numbers in the form x ","cbCaiek1qfeLGlIl","https://ap.wps.com/l/cbCaiek1qfeLGlIl","pdf",1050600,63,"English","# Paper 1 and Paper 2: Core Pure Mathematics\n## Proof\n## Complex numbers\n# Paper 3 and Paper 4: Further Mathematics Options\n## Further Pure Mathematics 1\n## Further Pure Mathematics 2\n## Further Statistics 1\n## Further Statistics 2\n## Further Mechanics 1\n## Further Mechanics 2\n## Decision Mathematics 1\n## Decision Mathematics 2","[{\"question\":\"What is the purpose of this Enhanced Content Guidance for 9FM0?\",\"answer\":\"It accompanies the Further Mathematics specification document by providing enhanced content guidance aligned with the accredited 9FM0 specification.\"},{\"question\":\"How does the document support co-teaching with AS Mathematics?\",\"answer\":\"Common content shared with AS Mathematics is highlighted in bold to support co-teaching and consistent delivery.\"},{\"question\":\"What core topics are included in Paper 1 and Paper 2?\",\"answer\":\"Paper 1 and Paper 2 cover core pure mathematics topics such as proof (including mathematical induction) and complex numbers, including work on Argand diagrams and modulus-argument forms.\"}]","Pearson Edexcel Level 3 Advanced GCE in Further Mathematics (9FM0) - Enhanced Content Guidance for 9FM0 | PDF",1792466868,159]