AS Further Mathematics - Edexcel
ASFurtherMathematicsSpecificationPearson Edexcel Level 3 Advanced Subsidiary GCE in Further Mathematics (8FM0)First teaching from September 2017First certification from 2018Issue 3
Summary of Pearson Edexcel Level 3 AdvancedSubsidiary GCE in Further Mathematics SpecificationIssue 3 changesSummary of changes made between previous issue and this current issuePagenumberInformation on ‘Content and assessment overview’ – Range of areas of knowledge,skills and understanding corrected4Information on ‘Content and assessment overview’ – Routes that can be taughtalongside the Pearson Edexcel Level 3 Advanced Subsidiary in Mathematicsqualification changed from E to F4Paper 1: Core Pure Mathematics, Section 4.3 – Plus sign in equation changed to equalssign12Paper 1: Core Pure Mathematics, Section 6.2 – Vectors changed to bold12Paper 2: Further Mathematics Options, Further Pure Mathematics 1, Section 4.1 –Correction made to Numerical methods formula15Paper 2: Further Mathematics Options, Further Pure Mathematics 2, Section 1.2 –Variable italicised16Paper 2: Further Mathematics Options, Further Pure Mathematics 2, Section 5.2 – n inequation changed to 117Paper 2: Further Mathematics Options, Further Pure Mathematics 2, Section 5.3 – n inequation changed to 117Paper 2: Further Mathematics Options, Further Mechanics 1, Section 2.1 – Furtherguidance added23Paper 2: Further Mathematics Options, Further Mechanics 2, Section 3.1 – Text in theguidance changed to clarify level of calculus required24Candidate malpractice – How to report candidate malpractice updated39Staff/centre malpractice – How to report staff/centre malpractice updated39Appendix 1: Formulae, Mechanics, Kinematics – Equation corrected49Earlier issues show previous changes.If you need further information on these changes or what they mean, contact us via our website s.html.
Contents1Introduction2Why choose Edexcel AS Level Further Mathematics?2Supporting you in planning and implementing this qualification3Qualification at a glance426Subject content and assessment informationPaper 1: Core Pure Mathematics9Paper 2: Further Mathematics Options14Assessment Objectives31337Administration and general informationEntries37Access arrangements, reasonable adjustments, special consideration andmalpractice37Student recruitment and progression40Appendix 1: Formulae43Appendix 2: Notation50Appendix 3: Use of calculators58Appendix 4: Assessment objectives59Appendix 5: The context for the development of this qualification61Appendix 6: Transferable skills63Appendix 7: Level 3 Extended Project qualification64Appendix 8: Codes66Appendix 9: Entry codes for optional routes67
1 IntroductionWhy choose Edexcel AS Level Further Mathematics?We have listened to feedback from all parts of the mathematics subject community, includinghigher education. We have used this opportunity of curriculum change to redesign aqualification that reflects the demands of a wide variety of end users as well as retainingmany of the features that have contributed to the increasing popularity of GCE Mathematicsin recent years.We will provide: Simple, intuitive specifications that enable co-teaching and parallel delivery. Increasedpressure on teaching time means that it’s important you can cover the content of differentspecifications together. Our specifications are designed to help you co-teach A and ASLevel, as well as deliver Maths and Further Maths in parallel. Clear, familiar, accessible exams with specified content in each paper. Our newexam papers will deliver everything you’d expect from us as the leading awarding body formaths. They’ll take the most straightforward and logical approach to meet thegovernment’s requirements. You and your students will know which topics are covered ineach paper so there are no surprises. They’ll use the same clear design that you’ve told usmakes them so accessible, while also ensuring a range of challenge for all abilities. A wide range of exam practice to fully prepare students and help you track progress.With the new linear exams your students will want to feel fully prepared and know howthey’re progressing. We’ll provide lots of exam practice to help you and your studentsunderstand and prepare for the assessments, including secure mock papers, practicepapers and free topic tests with marking guidance. Complete support and free materials to help you understand and deliver thespecification. Change is easier with the right support, so we’ll be on-hand to listen andgive advice on how to understand and implement the changes. Whether it’s through ourLaunch, Getting Ready to Teach, and Collaborative Networks events or via the renownedMaths Emporium; we’ll be available face to face, online or over the phone throughout thelifetime of the qualification. We’ll also provide you with free materials like schemes ofwork, topic tests and progression maps. The published resources you know and trust, fully updated for 2017. Our new A LevelMaths and Further Maths textbooks retain all the features you know and love about thecurrent series, whilst being fully updated to match the new specifications. Each textbookcomes packed with additional online content that supports independent learning, and theyall tie in with the free qualification support, giving you the most coherent approach toteaching and learning.2Pearson Edexcel Level 3 Advanced Subsidiary GCE in Further MathematicsSpecification – Issue 3 – July 2020 – Pearson Education Limited 2020
Supporting you in planning and implementing thisqualificationPlanning Our Getting Started guide gives you an overview of the new AS Level qualification tohelp you to get to grips with the changes to content and assessment as well as helpingyou understand what these changes mean for you and your students. We will give you a course planner and scheme of work that you can adapt to suit yourdepartment. Our mapping documents highlight the content changes between the legacy modularspecification and the new linear specifications.Teaching and learningThere will be lots of free teaching and learning support to help you deliver the newqualifications, including: topic guides covering new content areas teaching support for problem solving, modelling and the large data set student guide containing information about the course to inform your students and theirparents.Preparing for examsWe will also provide a range of resources to help you prepare your students for theassessments, including: specimen papers written by our senior examiner team practice papers made up from past exam questions that meet the new criteria secure mock papers marked exemplars of student work with examiner commentaries.ResultsPlus and Exam WizardResultsPlus provides the most detailed analysis available of your students’ examperformance. It can help you identify the topics and skills where further learning wouldbenefit your students.Exam Wizard is a data bank of past exam questions (and sample paper and specimen paperquestions) allowing you to create bespoke test papers.Get help and supportMathematics Emporium - Support whenever you need itThe renowned Mathematics Emporium helps you keep up to date with all areas of mathsthroughout the year, as well as offering a rich source of past questions, and of course accessto our in-house Maths experts Graham Cumming and his team.Sign up to get Emporium emailsGet updates on the latest news, support resources, training and alerts for entry deadlinesand key dates direct to your inbox. Just email mathsemporium@pearson.com to sign upEmporium websiteOver 12 000 documents relating to past and present Pearson/Edexcel Mathematicsqualifications available free. Visit www.edexcelmaths.com/ to register for an account.Pearson Edexcel Level 3 Advanced Subsidiary GCE in Further MathematicsSpecification – Issue 3 – July 2020 – Pearson Education Limited 20203
Qualification at a glanceContent and assessment overviewThis Pearson Edexcel Level 3 Advanced Subsidiary GCE in Further Mathematics builds on theskills, knowledge and understanding set out in the whole GCSE subject content formathematics and the subject content for the Pearson Edexcel Level 3 Advanced Subsidiaryand Advanced GCE Mathematics qualifications. Assessments will be designed to rewardstudents for demonstrating the ability to provide responses that draw together differentareas of their knowledge, skills and understanding from across the full course of study forthe AS level Further Mathematics qualification and also from across the A level Mathematicsqualification. Problem solving, proof and mathematical modelling will be assessed in FurtherMathematics in the context of the wider knowledge which students taking AS FurtherMathematics will have studied.In this qualification, option F and option K (see Appendix 9) are routes that can be taughtalongside the Pearson Edexcel Level 3 Advanced Subsidiary in Mathematics qualification.The Pearson Edexcel Level 3 Advanced Subsidiary GCE in Further Mathematics consists oftwo externally-examined papers.Students must complete all assessments in May/June in any single year.Paper 1: Core Pure Mathematics (*Paper code: 8FM0/01)Written examination: 1 hour and 40 minutes50% of the qualification80 marksContent overviewProof, Complex numbers, Matrices, Further algebra and functions, Further calculus, FurthervectorsAssessment overview Students must answer all questions. Calculators may be used in the assessment. Information on the use of calculators duringthe examinations for this qualification can be found in Appendix 3: Use of calculators.4Pearson Edexcel Level 3 Advanced Subsidiary GCE in Further MathematicsSpecification – Issue 3 – July 2020 – Pearson Education Limited 2020
Paper 2: Further Mathematics Options (*Paper codes: 8FM0/2A-2K)Written examination: 1 hour and 40 minutes50% of the qualification80 marksContent overviewStudents take one of the following ten options:2A: Further Pure Mathematics 1 and Further Pure Mathematics 22B: Further Pure Mathematics 1 and Further Statistics 12C: Further Pure Mathematics 1 and Further Mechanics 12D: Further Pure Mathematics 1 and Decision Mathematics 12E: Further Statistics 1 and Further Mechanics 12F: Further Statistics 1 and Decision Mathematics 12G: Further Statistics 1 and Further Statistics 22H: Further Mechanics 1 and Decision Mathematics 12J: Further Mechanics 1 and Further Mechanics 22K: Decision Mathematics 1 and Decision Mathematics 2Assessment overview Students must answer all questions. Calculators may be used in the assessment. Information on the use of calculators duringthe examinations for this qualification can be found in Appendix 3: Use of calculators.*See Appendix 8: Codes for a description of this code and all other codes relevant to thisqualification.Pearson Edexcel Level 3 Advanced Subsidiary GCE in Further MathematicsSpecification – Issue 3 – July 2020 – Pearson Education Limited 20205
2 Subject content and assessmentinformationQualification aims and objectivesThe aims and objectives of this qualification are to enable students to: understand mathematics and mathematical processes in ways that promote confidence,foster enjoyment and provide a strong foundation for progress to further study extend their range of mathematical skills and techniques understand coherence and progression in mathematics and how different areas ofmathematics are connected apply mathematics in other fields of study and be aware of the relevance of mathematicsto the world of work and to situations in society in general use their mathematical knowledge to make logical and reasoned decisions in solvingproblems both within pure mathematics and in a variety of contexts, and communicate themathematical rationale for these decisions clearly reason logically and recognise incorrect reasoning generalise mathematically construct mathematical proofs use their mathematical skills and techniques to solve challenging problems which requirethem to decide on the solution strategy recognise when mathematics can be used to analyse and solve a problem in context represent situations mathematically and understand the relationship between problems incontext and mathematical models that may be applied to solve them draw diagrams and sketch graphs to help explore mathematical situations and interpretsolutions make deductions and inferences and draw conclusions by using mathematical reasoning interpret solutions and communicate their interpretation effectively in the context of theproblem read and comprehend mathematical arguments, including justifications of methods andformulae, and communicate their understanding read and comprehend articles concerning applications of mathematics and communicatetheir understanding use technology such as calculators and computers effectively, and recognise when suchuse may be inappropriate take increasing responsibility for their own learning and the evaluation of their ownmathematical development.6Pearson Edexcel Level 3 Advanced Subsidiary GCE in Further MathematicsSpecification – Issue 3 – July 2020 – Pearson Education Limited 2020
Overarching themesThe overarching themes should be applied along with associated mathematical thinking andunderstanding, across the whole of the detailed content in this specification.These overarching themes are inherent throughout the content and students are required to developskills in working scientifically over the course of this qualification. The skills show teachers which skillsneed to be included as part of the learning and assessment of the students.Overarching theme 1: Mathematical argument, language and proofA Level Mathematics students must use the mathematical notation set out in the booklet MathematicalFormulae and Statistical Tables and be able to recall the mathematical formulae and identities set outin Appendix 1.Knowledge/SkillOT1.1Construct and present mathematical arguments through appropriate use ofdiagrams; sketching graphs; logical deduction; precise statements involvingcorrect use of symbols and connecting language, including: constant,coefficient, expression, equation, function, identity, index, term, variableOT1.2Understand and use mathematical language and syntax as set out in theglossaryOT1.3Understand and use language and symbols associated with set theory, as setout in the glossaryOT1.5Comprehend and critique mathematical arguments, proofs and justifications ofmethods and formulae, including those relating to applications of mathematicsOverarching theme 2: Mathematical problem solvingKnowledge/SkillOT2.1Recognise the underlying mathematical structure in a situation and simplify andabstract appropriately to enable problems to be solvedOT2.2Construct extended arguments to solve problems presented in an unstructuredform, including problems in contextOT2.3Interpret and communicate solutions in the context of the original problemOT2.6Understand the concept of a mathematical problem solving cycle, includingspecifying the problem, collecting information, processing and representinginformation and interpreting results, which may identify the need to repeat thecycleOT2.7Understand, interpret and extract information from diagrams and constructmathematical diagrams to solve problemsPearson Edexcel Level 3 Advanced Subsidiary GCE in Further MathematicsSpecification – Issue 3 – July 2020 – Pearson Education Limited 20207
Overarching theme 3: Mathematical modellingKnowledge/SkillOT3.1Translate a situation in context into a mathematical model, making simplifyingassumptionsOT3.2Use a mathematical model with suitable inputs to engage with and exploresituations (for a given model or a model constructed or selected by the student)OT3.3Interpret the outputs of a mathematical model in the context of the originalsituation (for a given model or a model constructed or selected by the student)OT3.4Understand that a mathematical model can be refined by considering itsoutputs and simplifying assumptions; evaluate whether the model isappropriate]OT3.5Understand and use modelling assumptions8Pearson Edexcel Level 3 Advanced Subsidiary GCE in Further MathematicsSpecification – Issue 3 – July 2020 – Pearson Education Limited 2020
Paper 1: Core Pure MathematicsTopics1What students need to learn:ContentGuidance1.1To include induction proofs for:ProofConstruct proofs usingmathematical induction.Contexts include sums ofseries, divisibility and powersof matrices.(i)summation of series,ne.g. showr 3r 1142n ( n 1)2orshownn( n 1)( n 2)r 13 r (r 1) (ii) divisibility, e.g. showdivisible by 432n 11 is(iii) matrix products, e.g. shown 3 4 2n 1 4n 1 1 n 1 2n 22.1ComplexnumbersSolve any quadratic equationwith real coefficients.Solve cubic or quarticequations with realcoefficients.Given sufficient information to deduce atleast one root for cubics or at least onecomplex root or quadratic factor forquartics, for example:(i)f(z) 2z3 5z2 7z 10Given that z 2 is a factor of f(z), usealgebra to solve f(z) 0 completely.(ii)g(x) x4 – x3 6x2 14x – 20Given g(1) 0 and g(–2) 0, use algebrato solve g(x) 0 completely.2.2Add, subtract, multiply anddivide complex numbers inthe form x iy with x and yreal.Students should know the meaning of theterms, ‘modulus’ and ‘argument’.Understand and use the terms‘real part’ and ‘imaginarypart’.2.3Understand and use thecomplex conjugate.Knowledge that if z1 is a root ofthen z1 * is also a root.f(z) 0Know that non-real roots ofpolynomial equations withreal coefficients occur inconjugate pairs.Pearson Edexcel Level 3 Advanced Subsidiary GCE in Further MathematicsSpecification – Issue 3 – July 2020 – Pearson Education Limited 20209
Topics2What students need to learn:ContentGuidance2.4Use and interpret Arganddiagrams.Students should be able to represent thesum or difference of two complex numberson an Argand diagram.2.5Convert between theCartesian form and themodulus-argument form of acomplex number.ComplexnumberscontinuedKnowledge of radians isassumed.2.6Multiply and divide complexnumbers in modulusargument form.Knowledge of radians andcompound angle formulae isassumed.Knowledge of the results,z1 z2 z1z2 ,z1z2 z1z2arg ( z1 z 2 ) arg z1 arg z 2 z1 arg z1 arg z 2 z2 arg 2.7Construct and interpretsimple loci in the arganddiagram such as z a randarg (z – a) θKnowledge of radians isassumed.33.1MatricesTo include loci such as z a b, z a z b ,arg (z a) β, and regions such as z a z b , z a b,α arg (z – a) βAdd, subtract and multiplyconformable matrices.Multiply a matrix by a scalar.3.2Understand and use zero andidentity matrices.3.3Use matrices to representlinear transformations in 2-D.Successive transformations.Single transformations in3-D.For 2-D, identification and use of thematrix representation of single andcombined transformations from: reflectionin coordinate axes and lines y x,rotation through any angle about (0, 0),stretches parallel to the x-axis and y-axis,and enlargement about centre (0, 0), withscale factor k, (k 0), where k ℝ.Knowledge that the transformationrepresented by AB is the transformationrepresented by B followed by thetransformation represented by A.3-D transformations confined to reflectionin one of x 0, y 0, z 0 or rotationabout one of the coordinate axes.Knowledge of 3-D vectors is assumed.10Pearson Edexcel Level 3 Advanced Subsidiary GCE in Further MathematicsSpecification – Issue 3 – July 2020 – Pearson Education Limited 2020
Topics3What students need to learn:ContentGuidance3.4Find invariant points and linesfor a linear transformation.For a given transformation, studentsshould be able to find the coordinates ofinvariant points and the equations ofinvariant lines.3.5Calculate determinants of:Idea of the determinant as an area scalefactor in transformations.Matricescontinued2
Paper 2: Further Mathematics Options, Further Mechanics 1, Section 2.1 – Further guidance added 23 Paper 2: Further Mathematics Options, Further Mechanics 2, Section 3.1 – Text in the . Maths and Further Maths textbooks retain all the features you know and love about the current series, whilst being fully updated to match the new .File Size: 920KB
Edexcel International A Level Mathematics Pure 3 Student Book 978 1 292244 92 1 21.00 Edexcel International A Level Mathematics Pure 3 Teacher Resource Pack 978 1 292244 93 8 100.00 Edexcel International A Level Mathematics Pure 4 Student Book 978 1 292245 12 6 21.00 Edexcel International A Level Mathematics Pure 4 Teacher Resource Pack
Pearson Edexcel International Advanced Subsidiary/Advanced Level in Mathematics, Further Mathematics and Pure Mathematics Mathematical Formulae and Statistical Tables For use in Pearson Edexcel International Advanced Subsidiary and Advanced Level examinations Pure Mathematics P1 - P4 Further Pure Mathematics FP1 - FP3 Mechanics M1 - M3
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Pearson Edexcel GCE in Core Mathematics C2 (6664/01) Edexcel and BTEC Qualifications Edexcel and BTEC qualifications are awarded by Pearson, the UK’s largest awarding body. We provide a wide range of qualifications including academic, vocational, occupational and specific programmes for employers. For further information visit our qualifications websites at www.edexcel.com or www.btec.co.uk .
Level in Mathematics, Further Mathematics and Pure Mathematics Mathematical Formulae and Statistical Tables For use in Pearson Edexcel International Advanced Subsidiary and Advanced Level examinations Pure Mathematics P1 – P4 Further Pure Mathematics FP1 – FP3 Mechanics M1 – M3
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Edexcel GCSE June 2014 . Understanding our Edexcel GCSE grade boundaries This document shows the grade boundaries for our Edexcel GCSE qualifications. For each set of grade boundaries, the maximum number of available marks is also shown. For our Edexcel GCSE Mathematics A specification, the maximum mark and raw mark grade boundaries are shown for the overall qualification. This means that the .
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