Level 2 Certificate in Further Mathematics Specification ...

1 For exams June 2012 onwardsFor certification June 2012 onwardsAQA Level 2 Certificate in Further Mathematics SpecificationLevel 2 SpecificationLevel 2 Certificate inFurther Mathematics8360 Our Specification is published on our website ( ). We will let centres know in writing aboutany changes to the Specification . We will also publish changes on our website. The definitive version of ourspecification will always be the one on our website, this may differ from printed can get Further copies of this Specification from:AQA Logistics Centre (Manchester)Unit 2 Wheel Forge WayAshburton ParkTrafford ParkManchesterM17 1 EHOr, you can download a copy from our website ( ).Copyright 2011 AQA and its licensors. All rights retains the copyright on all its publications, including the specifications. However, registered centres forAQA are permitted to copy material from this Specification booklet for their own internal Assessment and Qualifications Alliance (AQA), is a company limited by guarantee registered in Englandand Wales (company number 3644723), and a registered charity address: AQA Devas Street, Manchester M15 6EX1 ContentsLevel 2 Certificate in Further Mathematicsfor teaching from September 2011 onwards (version )1 Introduction21aWhy choose AQA?

2 21bWhy choose the AQA Level 2 Certificate in Further Mathematics ?21cHow do I start using this Specification ?31dHow can I find out more?32 Specification at a Glance4 Summary of Assessment43 Subject Content53aIntroduction53bSubject Content64 Scheme of Assessment114aAims and learning outcomes114bAssessment Objectives (AOs)114cNational Criteria124dPrevious learning requirements124eAccess to assessment: diversity and inclusion125 Administration135aAvailability of examination and certification135bEntries135cPrivate candidates135dAccess arrangements, reasonable adjustments and special consideration135eExamination language145fQualification title145gAwarding grades and reporting results145hRe-sits14 Appendices15 AFormulae sheet15 BGrade descriptions16 CSpiritual, moral, ethical, social, legislative, sustainable development,economic and cultural issues, and health and safety considerations18 Vertical black lines indicate a significant change or addition to the previous version of this specification211 IntroductionLevel 2 Certificate in Further Mathematicsfor teaching from September 2011 onwards (version )1aWhy choose AQA?

3 We are the United Kingdom s favourite exam boardand more students get their academic qualificationsfrom us than from any other board. But why are weso popular?We understand the different requirements ofeach subject by working with qualifications:help students achieve their full potentialare relevant for today s challengesare manageable for schools and collegesare easy to understand by students of all levelsof abilitylead to accurate results, delivered on timeare affordable and value for moneyWe provide a wide range of support services forteachers, including:access to subject departmentstraining for teachers, including practicalteaching strategies and approaches that work,presented by senior examinersindividual support for Controlled Assessment24-hour support through our website andonline with Ask AQApast question papers and mark schemesa wide range of printed and electronicresources for teachers and studentsfree online results analysis, with EnhancedResults are an educational charity focused on the needsof the learner.

4 All our income is spent on improvingthe quality of our specifications, examinations andsupport services. We don t aim to profit fromeducation, we want you you are already a customer we thank you for yoursupport. If you are thinking of joining us we lookforward to welcoming choose the AQA Level 2 Certificate in FurtherMathematics?This qualification fills the gap for high achievingstudents by assessing their higher order mathematicalskills, particularly in algebraic reasoning, in greaterdepth without infringing upon AS Level Mathematics ,thus preparing them fully to maximise their potential infurther studies at Level 3. It offers the opportunity forstretch and challenge that builds on the Key Stage 4curriculum and is intended as an additionalqualification to the GCSE Mathematics , rather than asa replacement. The content assumes prior knowledgeof the Key Stage 4 Programme of Study and coversthe areas of algebra and geometry, which are crucialto Further study in the subject, in greater depth andbreadth.

5 This new qualification places an emphasis onhigher order technical proficiency, rigorous argumentand problem solving also gives an introduction to calculus and matricesand develops Further skills in trigonometry, functionsand AQA Level 2 Certificate in Further Mathematicsis an untiered Level 2 linear qualificationforlearners whoeither already have, or are expected to achieve,grades A and A* in GCSE Mathematics are likely to progress to A- Level study inmathematics and possibly ContentLevel 2 Certificate in Further Mathematicsfor teaching from September 2011 onwards (version )1cHow do I start using this Specification ?You need to register ensure thatyou receive regular updates and have accessto the various resources you have decided to enter candidates you needto tell us so we can make sure that you get all thematerial you need for the examinations.

6 This is veryimportant where examination material is sent to youbefore the final entry deadline. You can let us knowby filling in the appropriate Intention to Enter and Estimated Entry your centre is registered on e-AQA you willreceive an email prompting you to submit entryinformation you are not e-AQA registered we will sendcopies to your exams officer. Both forms canbe downloaded from our website( ).If your centre has not used AQA for any examinationsin the past, please contact our centre approval teamat can I find out more?You can choose to find out more about thisspecification or the services that AQA offer ina number of AQAYou have 24-hour access to useful information andanswers to the most commonly asked questions the answer to your question is not available, youcan submit a query through Ask AQAfor our will respond within 2 working to your subject teamYou can talk directly to the Mathematics subject teamabout this Specification either bye-mailing by calling0161 957 Support MeetingsDetails of the full range of our Teacher Supportmeetings are available on our website There is also a link to our fast and convenient onlinebooking system for our Teacher Support meetings information onlineYou can find out more including the latest news.

7 Howto register for support and downloadable resourceson our website at 2 Written paper (Calculator)60% of the AQA Level 2 Certificate in Further Mathematics assessment2 hours 105 marksA question paper/answer booklet is provided for each questions are detailed content for the Specification is provided in Section content can be assessed on either paper addresses both Assessment Objectives. Details of theAssessment Objectives can be found in Section 4 of at a Glance4 Level 2 Certificate in Further Mathematicsfor teaching from September 2011 onwards (version )2 The Scheme of Assessment is linear with two question papers to be taken in the same examination series asdetailed Level 2 Certificate in Further MathematicsPaper 1 Written paper (Non-calculator)40% of the AQA Level 2 Certificate in Further Mathematics assessment1 hour 30 mins 70 marksSummary of Assessment53 Level 2 Certificate in Further Mathematicsfor teaching from September 2011 onwards (version )3 Subject Content3aIntroductionThe Specification content is set out in six distinct topicareas although questions will be asked that rangeacross these Geometry (2 dimensions only)

8 CalculusMatrix TransformationsGeometryWithin each topic area, the prescribed content isgiven in the left hand column. The right hand columnsummarises the assumed knowledge, where relevant,for the topic and then provides guidance notes andexamples to clarify the scope of the prescribedcontent. This content section should be read inconjunction with the accompanying specimen papersfor the qualification is designed to be taught:either in parallel with GCSE Mathematicsafter GCSE Mathematicsor instead of GCSE Mathematics if theassumed knowledge areas of this specificationhave been covered (possibly in Key Stage 3).The qualification is designed to be assessed as a fullLevel 2 Mathematics qualification in its own right andis therefore not dependent on GCSE there are no prior learning requirements butthere is the expectation that candidates have someassumed 2 + 45 2 763 Level 2 Certificate in Further Mathematicsfor teaching from September 2011 onwards (version )

9 3bSubject contentRef and use of numbers and the numbersystem including fractions, decimals, percentages,ratio, proportion and order of operations Manipulation of surds, including rationalisingThe use of surds in exact calculationsthe denominatorWrite 200 72 + 3 162 in the form a2 Rationalise and simplify Write the expression in the forma+ b3, where aand bare The basic processes of algebraKnowledge and use of basic skills in manipulativealgebra including use of the associative, commutativeand distributive laws, are Definition of a functionNotation f(x) will be used, eg f(x) = x2 Domain and range of a functionDomain may be expressed as, for example,x> 2, or for all x, except x= 0 and range may be expressed as f(x) > Expanding brackets and collecting like termsSimplify(y2 2y+ 3)(2y 1) 2(y3 3y2+ 4y 2)Expand and simplify (x+ 2) FactorisingFactorise fully(2x+ 3)2 (2x 5)2 Factorise15x2 34xy 16y2 Factorisex4 Manipulation of rational expressions.

10 Use of + for algebraic fractions withdenominators being numeric, linear or quadratic Use and manipulation of formulae andRearrange1 =1 +1 to make vthe Use of the factor theorem for integer values ofFactorise x3 2x2 5x+ 6the variable, including cubicsShow that x 1 is a factor of x3 3x2 4x+ 6 Solve x3+ x2 10x+ 8 = Completing the squareWork out the values of a, band csuch that2x2+ 6x+ 7 a(x+ b)2+ c x2+ 3x 10x2 9x+ 5x2+ 3xx 34x2+ 10xx3+ 2x2+ xx2+ x5x2 14x 34x2 253 3 + 73 3 5 Simplify SimplifySimplify 73 Level 2 Certificate in Further Mathematicsfor teaching from September 2011 onwards (version )Ref Sketching of functionsGraphs could be linear, quadratic or restricted to no Sketch graphs of linear and quadratic functionsmore than 3 domainsegy= x2 5x+ 6 Label clearly any points of the intersectionwith the axeseg A function f(x) is defined asf(x)= x20 x< 1= 11 x< 2= 3 x2 x< 3 Draw the graph of f(x)