AS Mathematics - Weebly
ASMathematicsSubjectio nFTatq u alactoOfDR Ac r e ditThis draft qualification has not yet been accredited by Ofqual. It is published to enable teachers to have early sight ofour proposed approach to Pearson Edexcel Level 3 Advanced Subsidiary GCE in Mathematics (8MA0). Further changesmay be required and no assurance can be given at this time that the proposed qualification will be made available in itscurrent form, or that it will be accredited in time for first teaching in September 2017 and first award in 2018.SpecificationPearson Edexcel Level 3 Advanced Subsidiary GCE in Mathematics (8MA0)First teaching from September 2017First certification from 2018
Subjectio nFTatq u alactoOfDR Ac r e dit
Contents1Introduction2Why choose Edexcel AS Level Mathematics?2Supporting you in planning and implementing this qualification3Qualification at a glance527Subject content and assessment informationPaper 1: Pure Mathematics11Paper 2: Statistics and Mechanics20Assessment Objectives26328Administration and general informationEntries28Access arrangements, reasonable adjustments, special consideration andmalpractice28Student recruitment and progression31DR AAppendix 3: Use of calculatorsq u alAppendix 4: Assessment Objectives34toOfAppendix 2: NotationSubjectFTio nAppendix 1: Formulae37434446Appendix 6: Transferable skills48acatAppendix 5: The context for the development of this qualificationc r e ditAppendix 7: Level 3 Extended Project qualification49Appendix 8: Codes51
1 IntroductionWhy choose Edexcel AS Level 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. Our new exam papers will deliver everything you’dexpect from us as the leading awarding body for maths. They’ll take the moststraightforward and logical approach to meet the government’s requirements. They’ll usethe same clear design that you’ve told us makes them so accessible, while also ensuring arange of challenge for all abilities.SubjecttoOf A wide range of exam practice to fully prepare students and help you track progress.q u alDR AFTio nWith 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 theacatspecification. 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 such as schemes ofwork, topic tests and progression maps.c r e dit The published resources you know and trust, fully updated for 2017. Our newA Level Maths and Further Maths textbooks retain all the features you know and loveabout the current series, while being fully updated to match the new specifications.Each textbook comes packed with additional online content that supports independentlearning, and they all tie in with the free qualification support, giving you the mostcoherent approach to teaching and learning.2Pearson Edexcel Level 3 Advanced Subsidiary GCE in MathematicsSpecification – Draft 1.4 – 27 January 2017 – Pearson Education Limited 2017
Supporting you in planning and implementingthis qualificationPlanning 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 suityour department. Our mapping documents highlight the content changes between the legacy modularspecification and the new linear specification.Teaching and learningThere will be lots of free teaching and learning support to help you deliver the newqualifications, including: topic guides covering new content areasSubject teaching support for problem solving, modelling and the large data set student guide containing information about the course to inform your students andq u alDR AtoOfPreparing for examsFTio ntheir parents.We will also provide a range of resources to help you prepare your students for theassessments, including:acat specimen papers written by our senior examiner team practice papers made up from past exam questions that meet the new criteria secure mock papersc r e dit 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.Pearson Edexcel Level 3 Advanced Subsidiary GCE in MathematicsSpecification – Draft 1.4 – 27 January 2017 Pearson Education Limited 20163
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,access to 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 up.Emporium websiteOver 12 000 documents relating to past and present Edexcel mathematics qualificationsavailable free. Visit www.edexcelmaths.com/ to register for an account.Subject4io nFTatq u alactoOfDR Ac r e ditPearson Edexcel Level 3 Advanced Subsidiary GCE in MathematicsSpecification – Draft 1.4 – 27 January 2017 – Pearson Education Limited 2017
Qualification at a glanceContent and assessment overviewThe Pearson Edexcel Level 3 Advanced Subsidiary GCE in Mathematics consists of twoexternally-examined papers.Students must complete all assessment in May/June in any single year.Paper 1: Pure Mathematics (*Paper code: 8MA0/01)Written examination: 2 hours62.5% of the qualification100 marksContent overview Topic 1 – Proof Topic 2 – Algebra and functions Topic 3 – Coordinate geometry in the (x, y) planeSubject Topic 7 – Differentiation Topic 9 – VectorsAssessment overviewDR Aq u al Topic 8 – Integrationac Students must answer all questions.toOf Topic 6 – Exponentials and logarithmsFTio n Topic 5 – Trigonometryat Topic 4 – Sequences and seriesc r e dit Calculators can be used in the assessment.Pearson Edexcel Level 3 Advanced Subsidiary GCE in MathematicsSpecification – Draft 1.4 – 27 January 2017 Pearson Education Limited 20165
Paper 2: Statistics and Mechanics (*Paper code: 8MA0/02)Written examination: 1 hour 15 minutes37.5% of the qualification60 marksContent overviewSection A: Statistics Topic 1 – Statistical sampling Topic 2 – Data presentation and interpretation Topic 3 – Probability Topic 4 – Statistical distributions Topic 5 – Statistical hypothesis testingSection B: Mechanics Topic 6 – Quantities and units in mechanics Topic 7 – Kinematics Topic 8 – Forces and Newton’s lawsSubjectAssessment overview The assessment comprises two sections: Section A – Statistics andDR Aq u al Calculators can be used in the assessment.FTio n Students must answer all questions.toOfSection B – Mechanics.ac6at*See Appendix 8: Codes for a description of this code and all other codes relevant tothis qualification.c r e ditPearson Edexcel Level 3 Advanced Subsidiary GCE in MathematicsSpecification – Draft 1.4 – 27 January 2017 – Pearson Education Limited 2017
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 a way that promotes confidence,fosters enjoyment and provides 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 reasoningSubject generalise mathematically construct mathematical proofstoOf use their mathematical skills and techniques to solve challenging problems that requireDR Athem to decide on the solution strategyq u alFTio n 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 theminterpret solutionsacat draw diagrams and sketch graphs to help explore mathematical situations andc r e dit make deductions and inferences and draw conclusions by using mathematical reasoning interpret solutions and communicate their interpretation effectively in the context ofthe problem 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 it maybe inappropriate to use them take increasing responsibility for their own learning and the evaluation of their ownmathematical development.Pearson Edexcel Level 3 Advanced Subsidiary GCE in MathematicsSpecification – Draft 1.4 – 27 January 2017 Pearson Education Limited 20167
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 todevelop skills in working scientifically over the course of this qualification. The skills showteachers which skills need to be included as part of the learning and assessment of thestudents.Overarching theme 1: Mathematical argument, language and proofAS Mathematics students must use the mathematical notation set out in the bookletMathematical Formulae and Statistical Tables and be able to recall the mathematicalformulae and identities set out in 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, variable.OT1.2Understand and use mathematical language and syntax as set out inthe content.OT1.3Understand and use language and symbols associated with set theory, as setout in the content. Apply to solutions of inequalities.OT1.4Not applicable to AS Mathematics.OT1.5Comprehend and critique mathematical arguments, proofs and justificationsof methods and formulae, including those relating to applications ofmathematics.Subjectio nFTatq u alactoOfDR Ac r e ditOverarching theme 2: Mathematical problem solvingKnowledge/skillOT2.1Recognise the underlying mathematical structure in a situation and simplifyand abstract appropriately to enable problems to be solved.OT2.2Construct extended arguments to solve problems presented in anunstructured form, including problems in context.OT2.3Interpret and communicate solutions in the context of the original problem.OT2.4Not applicable to AS Mathematics.OT2.5Evaluate, including by making reasoned estimates, the accuracy or limitationsof solutions.OT2.6Understand 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 repeatthe cycle.OT2.7Understand, interpret and extract information from diagrams and constructmathematical diagrams to solve problems, including in mechanics.8Pearson Edexcel Level 3 Advanced Subsidiary GCE in MathematicsSpecification – Draft 1.4 – 27 January 2017 – Pearson Education Limited 2017
Overarching theme 3: Mathematical modellingKnowledge/skillOT3.1Translate a situation in context into a mathematical model, makingsimplifying assumptions.OT3.2Use a mathematical model with suitable inputs to engage with and exploresituations (for a given model or a model constructed or selected bythe 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 bythe student).OT3.4Understand that a mathematical model can be refined by considering itsoutputs and simplifying assumptions; evaluate whether the modelis appropriate.OT3.5Understand and use modelling assumptions.Subjectio nFTatq u alactoOfDR Ac r e ditPearson Edexcel Level 3 Advanced Subsidiary GCE in MathematicsSpecification – Draft 1.4 – 27 January 2017 Pearson Education Limited 20169
Use of data in statisticsPearson has provided a large data set, which will support the assessment of statistics inPaper 2: Statistics and Mechanics. Students are required to become familiar with the dataset in advance of the final assessment.Assessments will be designed in such a way that questions assume knowledge andunderstanding of the data set. The expectation is that these questions should be likely togive a material advantage to students who have studied and are familiar with the data set.They might include questions/tasks that: assume familiarity with the terminology and contexts of the data, and do not explainthem in a way that gives students who have not studied the data set the sameopportunities to access marks as students who have studied them use summary statistics or selected data from, or statistical diagrams based on, the dataset – these might be given in the question/task, or as stimulus materials are based on samples related to the contexts in the data set, where students’ work withthe data set will help them understand the background context, and/or require students to interpret data in ways that would be too demanding in anunfamiliar context.SubjectStudents will not be required to have copies of the data set in the examination, nor will theybe required to have detailed knowledge of the actual data within the data set.10io nacFTatq u alDR AtoOfThe data set can be downloaded from our website, qualifications.pearson.com. This data setshould be appropriate for the lifetime of the qualification. However we will review the dataset on an annual basis to ensure it is appropriate. If we need to make changes to the dataset, we will notify centres before the beginning of the one-year course before studentscomplete their examination.c r e ditPearson Edexcel Level 3 Advanced Subsidiary GCE in MathematicsSpecification – Draft 1.4 – 27 January 2017 – Pearson Education Limited 2017
Paper 1: Pure MathematicsTopics1What students need to learn:Content1.1ProofGuidanceUnderstand and use thestructure of mathematicalproof, proceeding fromgiven assumptions througha series of logical steps to aconclusion; use methods ofproof, including:Examples of proofs:Proof by deductionProof by deduction,e.g. using completion of the square, provethat n2 6n 10 is positive for all values ofn or, for example, differentiation from firstprinciples for small positive integer powersof x. This is the most commonly used methodSubjectProof by exhaustion2.1Algebra andfunctionsDisproof by counter example – show thatthe statementFTio nacThis involves trying all the options. Supposex and y are odd integers less than 7. Provethat their sum is divisible by 2.“n2 – n 1 is a prime number for all valuesof n” is untrueatq u al2Proof by exhaustiontoOfDR ADisproof by counterexample.of proof throughout this specification.c r e ditUnderstand and use the lawsof indices for all rationalexponents.a m a n a m n , a m a n a m n ,(am)n amnmThe equivalence of a n andna m should beknown.2.2Use and manipulate surds,including rationalising thedenominator.Students should be able to simplifyalgebraic surds using the results( x)2 x, xy x y and( x y) ( x – y) x – yPearson Edexcel Level 3 Advanced Subsidiary GCE in MathematicsSpecification – Draft 1.4 – 27 January 2017 Pearson Education Limited 201611
Topics2What students need to learn:ContentGuidance2.3Work with quadraticfunctions and their graphs.The notation f(x) may be usedThe discriminant of aquadratic function, includingthe conditions for real andrepeated roots.Need to know and to useAlgebra andfunctionscontinuedb2 – 4ac 0, b2 – 4ac 0 andb2 – 4ac 0Completing the square.2b b ax bc c a x c x 2 2a 4a 2Solution of quadratic equations byfactorisation, use of the formula, use of acalculator and completing the square.including solving quadraticequations in a function ofthe unknown.These functions could include powers of x,trigonometric functions of x, exponentialand logarithmic functions of x.Solve simultaneousequations in two variablesby elimination and bysubstitution, including onelinear and one quadraticequation.The quadratic may involve powers of 2 inone unknown or in both unknowns,Subjecty 2x 3, y x2 – 4x 8or2x – 3y 6, x2 – y2 3x 50io nq u alFTSolve linear and quadraticinequalities in a singlevariable and interpret suchinequalities graphically,actoOf2.5DR Ae.g. solveFor example, solvingax b cx d,at2.4Solution of quadraticequations,px2 qx r 0,c r e d i tpx qx r ax b2and interpreting the third inequality as therange of x for which the curvey px2 qx r is below the line withequation y ax bincluding inequalities withbrackets and fractions.These would be reducible to linear orquadratic inequalitiese.g.12a b becomes ax bx2xExpress solutions throughcorrect use of ‘and’ and ‘or’,or through set notation.So, for example, x a or x b is equivalentto { x : x a } { x : x b }and { x : c x } { x : x d } is equivalentto x c and x dRepresent linear andquadratic inequalities suchas y x 1 andy ax2 bx c graphically.Shading and use of dotted and solid lineconvention is required.Pearson Edexcel Level 3 Advanced Subsidiary GCE in MathematicsSpecification – Draft 1.4 – 27 January 2017 – Pearson Education Limited 2017
2What students need to learn:Content2.6Algebra andfunctionscontinued2.7GuidanceManipulate polynomialsalgebraically, includingexpanding brackets andcollecting like terms,factorisation and simplealgebraic division; use of thefactor theorem.Only division by (ax b) or (ax – b) will berequi
Pearson Edexcel Level 3 Advanced Subsidiary GCE in Mathematics (8MA0) First teaching from September 2017 First certification from 2018 This draft qualification has not yet been accredited by Ofqual. It is published to enable teachers to have early sight of our proposed approach to Pearson Edexcel Level 3 Advanced Subsidiary GCE in Mathematics .
IBDP MATHEMATICS: ANALYSIS AND APPROACHES SYLLABUS SL 1.1 11 General SL 1.2 11 Mathematics SL 1.3 11 Mathematics SL 1.4 11 General 11 Mathematics 12 General SL 1.5 11 Mathematics SL 1.6 11 Mathematic12 Specialist SL 1.7 11 Mathematic* Not change of base SL 1.8 11 Mathematics SL 1.9 11 Mathematics AHL 1.10 11 Mathematic* only partially AHL 1.11 Not covered AHL 1.12 11 Mathematics AHL 1.13 12 .
as HSC Year courses: (in increasing order of difficulty) Mathematics General 1 (CEC), Mathematics General 2, Mathematics (‘2 Unit’), Mathematics Extension 1, and Mathematics Extension 2. Students of the two Mathematics General pathways study the preliminary course, Preliminary Mathematics General, followed by either the HSC Mathematics .
2. 3-4 Philosophy of Mathematics 1. Ontology of mathematics 2. Epistemology of mathematics 3. Axiology of mathematics 3. 5-6 The Foundation of Mathematics 1. Ontological foundation of mathematics 2. Epistemological foundation of mathematics 4. 7-8 Ideology of Mathematics Education 1. Industrial Trainer 2. Technological Pragmatics 3.
4 Rig Veda I Praise Agni, the Chosen Mediator, the Shining One, the Minister, the summoner, who most grants ecstasy. Yajur Veda i̱ṣe tvo̱rje tv ā̍ vā̱yava̍s sthop ā̱yava̍s stha d e̱vo v a̍s savi̱tā prārpa̍yat u̱śreṣṭha̍tam āya̱
2. Further mathematics is designed for students with an enthusiasm for mathematics, many of whom will go on to degrees in mathematics, engineering, the sciences and economics. 3. The qualification is both deeper and broader than A level mathematics. AS and A level further mathematics build from GCSE level and AS and A level mathematics.
Enrolment By School By Course 5/29/2015 2014-15 100 010 Menihek High School Labrador City Enrolment Male Female HISTOIRE MONDIALE 3231 16 6 10 Guidance CAREER DEVELOPMENT 2201 114 73 41 CARRIERE ET VIE 2231 32 10 22 Mathematics MATHEMATICS 1201 105 55 50 MATHEMATICS 1202 51 34 17 MATHEMATICS 2200 24 11 13 MATHEMATICS 2201 54 26 28 MATHEMATICS 2202 19 19 0 MATHEMATICS 3200 15 6 9
The Nature of Mathematics Mathematics in Our World 2/35 Mathematics in Our World Mathematics is a useful way to think about nature and our world Learning outcomes I Identify patterns in nature and regularities in the world. I Articulate the importance of mathematics in one’s life. I Argue about the natu
1.1 The Single National Curriculum Mathematics (I -V) 2020: 1.2. Aims of Mathematics Curriculum 1.3. Mathematics Curriculum Content Strands and Standards 1.4 The Mathematics Curriculum Standards and Benchmarks Chapter 02: Progression Grid Chapter 03: Curriculum for Mathematics Grade I Chapter 04: Curriculum for Mathematics Grade II
