Specification MATHEMATICS B (MEI) · 2 OCR 2017 . AS Level in Mathematics B (MEI) 1. 1a. Why choose...

AS LEVELSpecification

MATHEMATICS B (MEI)

AS LEVEL Mathematics B (MEI)

ocr.org.uk/aslevelmathsmei

H630For first assessment in 2018

Version 1.1 (June 2018)

http://ocr.org.uk/aslevelmathsmei

Registered office: 1 Hills Road Cambridge CB1 2EU

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1© OCR 2017 AS Level in Mathematics B (MEI)

ContentsContents

1 WhychooseanOCRASLevelinMathematicsB(MEI)? 21a. WhychooseanOCRqualification? 21b. WhychooseanOCRASLevelinMathematicsB(MEI)? 31c. Whatarethekeyfeaturesofthisspecification? 41d. HowdoIfindoutmoreinformation? 5

2 Thespecificationoverview 62a. OCRASLevelinMathematicsB(MEI)(H630) 62b. ContentofASLevelinMathematicsB(MEI) 72c. ContentofASLevelinMathematicsB(MEI) 182d. Prior knowledge, learning and progression 43

3 AssessmentofASLevelinMathematicsB(MEI) 443a. Formsofassessment 443b. AssessmentObjectives(AO) 453c. Assessmentavailability 463d. Retakingthequalification 463e. Assessmentofextendedresponse 463f. Synopticassessment 473g. Calculatingqualificationresults 47

4 Admin:whatyouneedtoknow 484a. Pre-assessment 484b. Specialconsideration 494c. Externalassessmentarrangements 494d. Resultsandcertificates 494e. Post-results services 504f. Malpractice 50

5 Appendices 515a. Overlapwithotherqualifications 515b. Accessibility 515c. Mathematicalnotation 515d. Mathematicalformulaeandidentities 55

Summary of updates 59

2© OCR 2017

AS Level in Mathematics B (MEI)

11a. WhychooseanOCRqualification?

Choose OCR and you’ve got the reassurance that you’reworkingwithoneoftheUK’sleadingexamboards.OurnewASLevelinMathematicsB(MEI)coursehasbeendevelopedinconsultationwithteachers,employersandHigherEducationtoprovidelearnerswithaqualificationthat’srelevanttothemand meets their needs.

We’re part of the Cambridge Assessment Group, Europe’slargestassessmentagencyandadepartment of the University of Cambridge. Cambridge Assessment plays a leading role in developing and delivering assessments throughout theworld,operatinginover150countries.

Weworkwitharangeofeducationproviders,including schools, colleges, workplaces and other institutionsinboththepublicandprivatesectors.Over13,000centreschooseourALevels,GCSEs andvocationalqualificationsincludingCambridgeNationalsandCambridgeTechnicals.

OurSpecifications

Webelieveindevelopingspecificationsthathelp youbringthesubjecttolifeandinspireyourlearnersto achieve more.

We’vecreatedteacher-friendlyspecificationsbasedonextensiveresearchandengagementwiththeteachingcommunity.They’redesignedtobestraightforwardandaccessiblesothatyoucantailorthe delivery of the course to suit your needs. We aim to encourage students to become responsible for theirownlearning,confidentindiscussingideas,innovativeandengaged.

We provide a range of support services designed to helpyouateverystage,frompreparationthroughtothedeliveryofourspecifications.Thisincludes:

• Awiderangeofhigh-qualitycreativeresourcesincluding:o Delivery Guideso TransitionGuideso TopicExplorationPackso LessonElementso …and much more.

• AccesstoSubjectAdvisorstosupportyouthroughthetransitionandthroughoutthelifetimeofthespecification.

• CPD/Trainingforteacherstointroducethequalificationsandprepareyouforfirstteaching.

• ActiveResults–ourfreeresultsanalysisserviceto help you review the performance of individual learners or whole schools.

• ExamBuilder–ournewfreeonlinepastpapersservice that enables you to build your own testpapersfrompastOCRexamquestions canbefoundonthewebsiteat: www.ocr.org.uk/exambuilder

AllASlevelqualificationsofferedbyOCRareaccreditedbyOfqual,theRegulatorforqualificationsofferedinEngland.TheaccreditationnumberforOCRASLevelinMathematicsB(MEI)isQN603/0991/X.

1 WhychooseanOCRASLevelinMathematicsB(MEI)?

http://www.ocr.org.uk/exambuilder


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1b. WhychooseanOCRASLevelinMathematicsB(MEI)?

OCRASLevelMathematicsB(MEI)hasbeendevelopedinpartnershipwithMathematicsinEducationandIndustry(MEI).

OCRASLevelinMathematicsB(MEI)providesaframework within which a large number of young peoplecontinuethesubjectbeyondGCSE(9–1).Itsupportstheirmathematicalneedsacrossabroadrangeofsubjectsatthislevelandprovidesabasisforsubsequentquantitativeworkinaverywiderangeofhighereducationcoursesandinemployment.ItalsosupportsthestudyofALevelMathematicsandASFurtherMathematics.

OCRASLevelinMathematicsB(MEI)buildsfromGCSE(9–1)mathematicsandintroducescalculusanditsapplications.Itemphasiseshowmathematicalideasareinterconnectedandhowmathematicscanbeappliedtomodelsituationsusingalgebraandotherrepresentations,tohelpmakesenseofdata,tounderstand the physical world and to solve problems inavarietyofcontexts,includingsocialsciencesandbusiness.Itpreparesstudentsforfurtherstudyandemployment in a wide range of disciplines involving theuseofmathematics.

ASLevelMathematicsB(MEI),whichcanbeco-taughtwiththeALevelasaseparatequalification,consolidatesanddevelopsGCSELevelmathematicsandsupportstransitiontohighereducationoremployment in any of the many disciplines that make useofquantitativeanalysis,includingthoseinvolvingcalculus.

ThisqualificationispartofawiderangeofOCRmathematicsqualifications,allowingprogression

fromEntryLevelCertificate,throughGCSEtoCoreMaths, AS and A Level.

We recognise that teachers want to be able to choose qualificationsthatsuittheirlearnerssoweoffertwosuitesofqualificationsinmathematicsandfurthermathematics.

MathematicsB(MEI)buildsonourexistingpopularcourse. We’ve based the redevelopment of our current suite around an understanding of what works well in centres and have updated areas of content andassessmentwherestakeholdershaveidentifiedthat improvements could be made. We’ve undertaken asignificantamountofconsultationthroughourmathematicsforums(whichincluderepresentativesfromlearnedsocieties,HE,teachingandindustry)and through focus groups with teachers.

MathematicsB(MEI)isbasedontheexistingsuiteofqualificationsassessedbyOCR.MEIisalongestablished, independent curriculum development body;indevelopingthisspecification,MEIhasconsultedwithteachersandrepresentativesfromHigherEducationtodecidehowbesttomeetthelong-termneedsoflearners.MEIprovidesadviceandCPDrelatingtoallthecurriculumandteachingaspectsofthecourse.Italsoprovidesteachingresources,whichforthisspecificationcanbefoundonthewebsite(www.mei.org.uk).

Allofourspecificationshavebeendevelopedwithsubjectandteachingexperts.WehaveworkedincloseconsultationwithteachersandrepresentativesfromHigherEducation(HE).

www.mei.org.uk

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Aimsandlearningoutcomes

OCRASLevelinMathematicsB(MEI)encourageslearnersto:

• understandmathematicsandmathematicalprocessesinawaythatpromotesconfidence,fostersenjoymentandprovidesastrongfoundationforprogresstofurtherstudy

• extendtheirrangeofmathematicalskillsandtechniques

• understandcoherenceandprogressioninmathematicsandhowdifferentareasofmathematicsareconnected

• applymathematicsinotherfieldsofstudyandbeawareoftherelevanceofmathematicstotheworldofworkandtosituationsinsociety in general

• usetheirmathematicalknowledgetomakelogical and reasoned decisions in solving problemsbothwithinpuremathematicsandinavarietyofcontexts,andcommunicatethemathematicalrationaleforthesedecisionsclearly

• reasonlogicallyandrecogniseincorrectreasoning

• generalisemathematically

• constructmathematicalproofs

• usetheirmathematicalskillsandtechniquestosolve challenging problems which require them todecideonthesolutionstrategy

• recognisewhenmathematicscanbeusedtoanalyseandsolveaproblemincontext

• representsituationsmathematicallyandunderstandtherelationshipbetweenproblemsincontextandmathematicalmodelsthatmaybe applied to solve them

• drawdiagramsandsketchgraphstohelpexploremathematicalsituationsandinterpretsolutions

• makedeductionsandinferencesanddrawconclusionsbyusingmathematicalreasoning

• interpretsolutionsandcommunicatetheirinterpretationeffectivelyinthecontextoftheproblem

• readandcomprehendmathematicalarguments,includingjustificationsofmethodsand formulae, and communicate their understanding

• readandcomprehendarticlesconcerningapplicationsofmathematicsandcommunicatetheir understanding

• usetechnologysuchascalculatorsandcomputerseffectivelyandrecognisewhen such use may be inappropriate

• takeincreasingresponsibilityfortheirownlearningandtheevaluationoftheirownmathematicaldevelopment.

1c. Whatarethekeyfeaturesofthisspecification?

OCRASLevelinMathematicsB(MEI)hasbeendesignedtohelplearnerstofulfiltheirpotentialinmathematicsandtosupportteachersinenablingthemtodothis.Thespecification:

• encourageslearnerstodevelopadeepunderstandingofmathematicsandanabilitytouseitinavarietyofcontexts

• encourageslearnerstouseappropriatetechnologytodeepentheirmathematicalunderstandingandextendtherangeofproblems which they are able to solve

• usespre-releasedatainstatisticstoenablelearners to develop an understanding of working with real data to solve real problems


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• isassessedinawaywhichisdesignedtoenable all learners to show what they are able to do

• isclearlylaidoutwithdetailedguidanceregarding what learners need to know, understand and be able to do

• isresourcedandsupportedbyMEIinlinewiththe aims and learning outcomes of the qualification.

Thisspecificationisdesignedtobeco-teachablewithAlevelMathematicsB(MEI).

1d. HowdoIfindoutmoreinformation?

IfyouarealreadyusingOCRspecificationsyoucancontactusat:www.ocr.org.uk.

IfyouarenotalreadyaregisteredOCRcentrethenyoucanfindoutmoreinformationonthebenefitsofbecomingoneat:www.ocr.org.uk.

Ifyouarenotyetanapprovedcentreandwouldliketobecomeonegoto:www.ocr.org.uk.

Wanttofindoutmore?

GetintouchwithoneofOCR’sSubjectAdvisors:

Email:[email protected]

CustomerContactCentre:01223553998

Teachersupport:www.ocr.org.uk

AdviceandsupportisalsoavailablefromMEI;contactdetails can be found on www.mei.org.uk.

www.ocr.org.uk

www.ocr.org.uk

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mailto:[email protected]

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2a. OCRASLevelinMathematicsB(MEI)(H630)

LearnersmusttakebothComponents01and02tobeawardedtheOCRASLevelinMathematicsB(MEI).

Contentisinthreeareas:

1 Puremathematics2 Mechanics3 Statistics

ContentOverview AssessmentOverview

Component01assessescontentfrom areas 1 and 2

PureMathematics and Mechanics

(01)

70marks

1hour30minutes

Writtenpaper

50%of totalAS Level

Component02assessescontentfromareas1and3

PureMathematics andStatistics

(02)

70marks

1hour30minutes

Writtenpaper

50%of totalAS Level

2 Thespecificationoverview


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2b. ContentofASLevelinMathematicsB(MEI)

ThisASlevelqualificationbuildsontheskills,knowledgeandunderstandingsetoutintheGCSE(9–1)subjectcontentformathematicsforfirstteachingfrom2015.

ASLevelMathematicsB(MEI)isalinearqualification,withnooptions.Thecontentislistedbelow,underthree areas.

1. Puremathematicsincludesproof,algebra,graphs,anintroductiontobinomialexpansions,trigonometry, logarithms, calculus and vectors.

2. Mechanicsincludeskinematicsin1dimension,working with forces and Newton’s laws.

3. Statisticsincludesworkingwithdatafromasampletomakeinferencesaboutapopulation,simpleprobabilitycalculations,usingthebinomialdistributionasamodelandstatisticalhypothesistesting.

Therewillbetwoexaminationpapers,attheendofthe course, to assess all the content.

• PureMathematicsandMechanics(01),a1½hourpaperassessingmathematicalprocesses,puremathematicsandmechanics.

• PureMathematicsandStatistics(02),a1½hourpaperassessingmathematicalprocesses,puremathematicsandstatistics.

Although the content is listed under three separate areas, links should also be made between pure mathematicsandeachofmechanicsandstatistics;some of the links which can be made are indicated in the notes in the detailed content.

Theoverarchingthemesshouldbeapplied,alongwithassociatedmathematicalthinkingandunderstanding, across the whole of the detailed contentinpuremathematics,statisticsandmechanics.

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Pre-releasematerial

Pre-release material will be made available in advanceoftheexaminations.Itwillberelevanttosome(butnotall)ofthequestionsincomponent02.Thepre-releasematerialwillbealargedataset(LDS)that can be used as teaching material throughout the course.Itiscomparabletoasettextforaliteraturecourse.Itwillbepublishedinadvanceofthecourse.Intheexaminationitwillbeassumedthatlearnersarefamiliarwiththecontextscoveredbythisdatasetand that they have used a spreadsheet or other statisticalsoftwarewhenworkingwiththedata.QuestionsbasedontheseassumptionswillbesetinPureMathematicsandStatistics(02).

Theintentionisthatthesequestionsshouldgiveamaterial advantage to learners who have studied, and are familiar with, the prescribed large data set. Theymightincludequestionsrequiringlearnerstointerpret data in ways which would be too demandinginanunfamiliarcontext.

LearnerswillNOThaveaprintoutofthepre-releasedatasetavailabletothemintheexaminationbutselecteddataorsummarystatisticsfromthedatasetmaybeprovided,withintheexaminationpaper.

Differentdatasetswillbeissuedfordifferent years; three large data sets will be available at any time.Onlyoneofthesedatasetswillbeusedinagivenseriesofexaminations.Eachdatasetwillbeclearlylabelledwiththeyearoftheexaminationseriesinwhichitwillbeused.Theexpectationisthatteachers will use all three data sets but they do have thechoiceofconcentratingmoreontheexaminationdataset(orofusingjustthatoneiftheywish).Tosupport progression and co-teachability, students takingASLevelMathematicsB(MEI)willusethesamedatasetiftheytakeALevelMathematicsB(MEI)inthefollowingyear.

Theintentionofthelargedatasetisthatitandassociatedcontextsareexploredintheclassroom

using technology, and that learners become familiar withthecontextandmainfeaturesofthedata.

Tosupporttheteachingandlearningofstatistics with the large data set, we suggest that the followingactivitiesarecarriedoutthroughout thecourse:

1. Exploratorydataanalysis:LearnersshouldexploretheLDSwithbothquantitativeandvisual techniques to develop insight into underlyingpatternsandstructures,suggesthypotheses to test and to provide a reason for furtherdatacollection.Thiswillincludetheuse of the following techniques.• Creatingdiagrams:Learnersshoulduse

spreadsheetsorstatisticalgraphingtoolsto create diagrams from data.

• Calculations:Learnersshoulduseappropriate technology to perform statisticalcalculations.

• Investigatingcorrelation:LearnersshoulduseappropriatetechnologytoexplorecorrelationbetweenvariablesintheLDS.

2. Modelling:LearnersshouldusetheLDStoprovideestimatesofprobabilitiesformodellingandtoexplorepossiblerelationshipsbetweenvariables.

3. Repeatedsampling:LearnersshouldusetheLDSasamodelforthepopulationtoperformrepeatedsamplingexperimentstoinvestigatevariabilityandtheeffectofsamplesize.Theyshouldcomparetheresultsfromdifferentsamples with each other and with the results from the whole LDS.

4. Hypothesistesting:LearnersshouldusetheLDSasthepopulationagainstwhichtotesthypotheses based on their own sampling.


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Useoftechnology

Itisassumedthatlearnerswillhaveaccesstoappropriate technology when studying this course suchasmathematicalandstatisticalgraphingtoolsandspreadsheets.Whenembeddedinthemathematicsclassroom, the use of technology can facilitate the visualisationofabstractconceptsanddeepenlearners’overallunderstanding.Learnersarenotexpected tobefamiliarwithanyparticularsoftware,buttheyareexpectedtobeabletousetheircalculatorfor anyfunctionitcanperform,whenappropriate.Examinationquestionsmayincludeprintoutsfromsoftwarewhichlearnerswillneedtocompleteorinterpret.Theyshouldbefamiliarwithlanguageusedto describe spreadsheets such as row, column and cell.

Tosupporttheteachingandlearningofmathematicsusing technology, we suggest that the following activitiesarecarriedoutthroughthecourse:

1. Graphingtools:Learnersshouldusegraphingsoftwaretoinvestigatetherelationshipsbetween graphical and algebraic representations,e.g.understandingtheeffectof changing the parameter k in the graphs of

y x k1= + or y x kx2= - ;e.g.investigating

tangents to curves.

2. Spreadsheets:Learnersshouldusespreadsheets to generate tables of values forfunctions,toinvestigatefunctionsnumericallyandasanexampleofapplyingalgebraicnotation.Learnersshouldalsousespreadsheetsoftwaretoinvestigatenumericalmethodsforsolvingequationsandformodellinginstatisticsandmechanics.

3. Statistics:Learnersshouldusespreadsheetsorstatisticalsoftwaretoexploredatasetsandstatisticalmodelsincludinggeneratingtablesand diagrams, and performing standard statisticalcalculations.

4. Mechanics:Learnersshouldusegraphing and/orspreadsheetsoftwareformodelling,includingkinematicsandprojectiles.

5. ComputerAlgebraSystem(CAS):LearnerscoulduseCASsoftwaretoinvestigatealgebraicrelationships,includingderivativesandintegrals,andasaninvestigativeproblemsolvingtool.Thisisbestdoneinconjuctionwithothersoftwaresuchasgraphingtoolsandspreadsheets.

Useofcalculators

Calculators must comply with the published Instructions for conducting examinations, which can be found at http://www.jcq.org.uk/

Itisexpectedthatcalculatorsavailableintheexaminationswillincludethefollowingfeatures:

• Aniterativefunctionsuch as an ANS key.• Theabilitytocomputesummarystatisticsand

accessprobabilitiesfromthebinomialdistribution.

When using calculators, candidates should bear in mindthefollowing:

1. Learnersareadvisedtowritedownexplicitlyanyexpressions,includingintegrals,thattheyuse the calculator to evaluate.

2. Learners are advised to write down the values of any parameters and variables that they input intothecalculator.Candidatesarenotexpectedtowritedowndatatransferredfromquestionpaper to calculator.

3. Correctmathematicalnotation(ratherthan“calculatornotation”)shouldbeused;incorrectnotationmayresultinlossofmarks.

Formulae

Learners will be given formulae in each assessment onpage2ofthequestionpaper.SeeSection5dforalist of these formulae.

http://www.jcq.org.uk

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Simplifyingexpressions

Itisexpectedthatlearnerswillsimplifyalgebraic andnumericalexpressionswhengivingtheirfinalanswers,eveniftheexaminationquestiondoes notexplicitlyaskthemtodoso.

• 80 23

shouldbewrittenas40 3,

• 21 1 2 2x 2

1#+ -^ h shouldbewrittenas

either 1 2x 21

+ -^ h or x1 2

1+

,

• ln ln ln2 3 1+ - shouldbewrittenasln 6,

• Theequationofastraightlineshouldbegiven in the form y mx c= + or ax by c+ = unless otherwise stated.

Themeaningsofsomeinstructionsusedinexaminationquestions

Ingeneral,learnersshouldshowsufficientdetailoftheir working and reasoning to indicate that a correct methodisbeingused.Thefollowingcommandwordsareusedtoindicatewhenmore,orless,specificdetail is required.

ExactAnexactanswerisonewherenumbersarenot giveninroundedform.Theanswerwilloftencontainanirrationalnumbersuchas 3, e or π and these numbersshouldbegiveninthatformwhenanexactanswer is required. Theuseoftheword‘exact’alsotellslearnersthatrigorous(exact)workingisexpectedintheanswer tothequestion. e.g.Findtheexactsolutionofln x 2= . Thecorrectanswerise2 and not 7.389 056.e.g.Findtheexactsolutionof3 2.x =

Thecorrectansweris 32x = or 0.6x = o , not 0.67x =

or similar.

ShowthatLearners are given a result and have to get to thegivenresultfromthestartinginformation.Becausetheyaregiventheresult,theexplanation hastobesufficientlydetailedtocovereverystepoftheir working,

e.g.Showthattheequation ( )x x 3 22- = can be expressedasx x x6 9 2 03 2- + - = .

DetermineThiscommandwordindicatesthatjustificationshouldbe given for any results found, including working where appropriate.

Give,State,WritedownThesecommandwordsindicatethatneitherworkingnorjustificationisrequired.

Inthisquestionyoumustshowdetailedreasoning. Whenaquestionincludesthisinstructionlearnersmustgiveasolutionwhichleadstoaconclusionshowingadetailedandcompleteanalyticalmethod.Theirsolutionshouldcontainsufficientdetailtoallowthelineoftheirargumenttobefollowed.Thisisnotarestrictiononalearner’suseofacalculatorwhentacklingthequestion,e.g.forcheckingananswerorevaluatingafunctionatagivenpoint,butitisarestrictiononwhatwillbeacceptedasevidenceofacomplete method.

Intheseexamplesvariationsinthestructureoftheanswersarepossible,forexample,usingadifferentbaseforthelogarithmsinexample1,anddifferentintermediate steps may be given.

Example1:Uselogarithmstosolvetheequation3 4x2 1 100=+ , givingyouranswercorrectto3significantfigures.Theanswerisx = 62.6, but the learner must include the steps log 3 4x2 1 100=+ , ( ) log logx2 1 3 4100+ = and anintermediateevaluationstep,forexample

. ...x2 1 126 18+ = .Usingthesolvefunctiononacalculator to skip one of these steps would not result inacompleteanalyticalmethod.

Example2:

Evaluate .x x x4 1d0

13 2+ -y

Theansweris712 , but the learner must include at

least x x x41

344 3

0

1

+ -; E andthesubstitution41

34 1+ - .

Justwritingdowntheanswerusingthedefiniteintegralfunctiononacalculatorwouldthereforenotbe awarded any marks.


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Example3:Solvetheequation sin cosx x for x3 2 0 180c c# #= . Theanswerisx = 9.59°, 90° or 170° (to 3sf), but the learner must include … sin cos cosx x x6 0- = ,

or( ) ,cos sin cos sinx x x x6 1 0 0 61

- = = = .

Agraphicalmethodwhichinvestigatedthe intersectionsofthecurves siny x3 2= and cosy x=

wouldbeacceptabletofindthesolutionat90° if carefullyverified,buttheothertwosolutionsmustbefoundanalytically,notnumerically.

Hence Whenaquestionusestheword‘hence’,itisanindicationthatthenextstepshouldbebasedon whathasgonebefore.Theintentionisthatlearnersshould start from the indicated statement.e.g. You are given that f ( ) 2 7 6x x x x3 2= - - + . Show that ( 1)x- is a factor of f ( )x .Hencefindthethreefactors of f ( )x .

Henceorotherwiseisusedwhentherearemultiplewaysofansweringagivenquestion.Learnersstartingfrom the indicated statement may well gain some informationaboutthesolutionfromdoingso,andmayalreadybesomewaytowardstheanswer.Thecommand phrase is used to direct learners towards usingaparticularpieceofinformationtostartfromortoaparticularmethod.Italsoindicatestolearnersthatvalidalternativemethodsexistwhichwillbegivenfullcredit,butthattheymaybemoretime-consumingorcomplex.

E.g.Showthat( )cos sin sinx x x1 22+ = + for all x. Hence,orotherwise,findthederivativeof( )cos sinx x 2+ .

YoumayusetheresultWhen this phrase is used it indicates a given result thatlearnerswouldnotalwaysbeexpectedtoknow,butwhichmaybeusefulinansweringthequestion. Thephraseshouldbetakenaspermissive;useofthegiven result is not required.

PlotLearners should mark points accurately on graph paperprovidedinthePrintedAnswerBooklet.Theywill either have been given the points or have had to calculatethem.Theymayalsoneedtojointhemwitha curve or a straight line. e.g.Plotthisadditionalpointonthescatterdiagram.

Sketch(agraph)Learners should draw a diagram, not necessarily to scale,showingthemainfeaturesofacurve.Thesearelikelytoincludeatleastsomeofthefollowing:

• Turningpoints• Asymptotes• Intersectionwiththey-axis• Intersectionwiththex-axis• Behaviourforlargex (+or–)

Any other important features should also be shown.

Sketchthecurvewithequation ( )y x 11

=-

Draw Learners should draw to an accuracy appropriate to theproblem.Theyarebeingaskedtomakeasensiblejudgementaboutthelevelofaccuracywhichisappropriate. e.g.Drawadiagramshowingtheforcesactingontheparticle. e.g.Drawalineofbestfitforthedata.

OthercommandwordsOthercommandwords,forexample“explain”or“calculate”,willhavetheirordinaryEnglishmeaning.

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OverarchingThemes

TheseOverarchingThemesshouldbeapplied,alongwithassociatedmathematicalthinkingandunderstanding,acrossthewholeofthedetailedcontentinthisspecification.ThesestatementsareintendedtodirecttheteachingandlearningofASLevelMathematics,andtheywillbereflectedinassessmenttasks.

OT1 Mathematicalargument,languageandproof

Knowledge/Skill

OT1.1 Constructandpresentmathematicalargumentsthroughappropriateuseofdiagrams;sketchinggraphs;logicaldeduction;precisestatementsinvolvingcorrectuseofsymbolsandconnectinglanguage,including:constant,coefficient,expression,equation,function,identity,index,term,variable

OT1.2 Understandandusemathematicallanguageandsyntaxassetoutinthecontent

OT1.3 Understand and use language and symbols associated with set theory, as set out in the content

Applytosolutionsofinequalities

OT1.4 NotApplicabletoASMathematics

OT1.5 Comprehendandcritiquemathematicalarguments,proofsandjustificationsofmethodsandformulae,includingthoserelatingtoapplicationsofmathematics

OT2 Mathematicalproblemsolving

Knowledge/Skill

OT2.1 Recognisetheunderlyingmathematicalstructureinasituationandsimplifyandabstractappropriately to enable problems to be solved

OT2.2 Constructextendedargumentstosolveproblemspresentedinanunstructuredform,includingproblemsincontext

OT2.3 Interpretandcommunicatesolutionsinthecontextoftheoriginalproblem

OT2.4 NotApplicabletoASMathematics.

OT2.5 Evaluate,includingbymakingreasonedestimates,theaccuracyorlimitationsofsolutions

OT2.6 Understandtheconceptofamathematicalproblemsolvingcycle,includingspecifyingtheproblem,collectinginformation,processingandrepresentinginformationandinterpretingresults,whichmayidentifytheneedtorepeatthecycle

OT2.7 Understand,interpretandextractinformationfromdiagramsandconstructmathematicaldiagrams to solve problems, including in mechanics


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OT3 Mathematicalmodelling

Knowledge/Skill

OT3.1 Translateasituationincontextintoamathematicalmodel,makingsimplifyingassumptions

OT3.2 Useamathematicalmodelwithsuitableinputstoengagewithandexploresituations(foragivenmodeloramodelconstructedorselectedbythestudent)

OT3.3 Interprettheoutputsofamathematicalmodelinthecontextoftheoriginalsituation(foragivenmodeloramodelconstructedorselectedbythestudent)

OT3.4 Understandthatamathematicalmodelcanberefinedbyconsideringitsoutputsandsimplifyingassumptions;evaluatewhetherthemodelisappropriate

OT3.5 Understandandusemodellingassumptions

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MathematicalProblemSolvingCycle

Mathematicalproblemsolvingisacorepartofmathematics.TheconceptofamathematicalproblemsolvingcycleisoutlinedincompetencestatementMp10anddevelopedmorefullybelow.Theproblemsolvingcyclegivesageneralstrategyfordealingwithproblemswhichcanbesolvedusingmathematicalmethods;itcanbeusedforproblemswithinmathematicalcontextsandforproblemsinreal-worldcontexts.

Process Description

Problemspecificationand analysis

Theproblemtobeaddressedneedstobeformulatedinawaywhichallowsmathematicalmethodstobeused.Itthenneedstobeanalysedsothataplancanbemadeastohowtogoaboutit.Theplanwillalmostalwaysinvolvethecollectionofinformationinsomeform.Theinformationmayalreadybeavailable(e.g.online)oritmaybenecessarytocarryoutsomeformofexperimentalorinvestigationalworktogatherit.

Insomecasestheplanwillinvolveconsideringsimplecaseswithaviewtogeneralisingfromthem.Inothers,physicalexperimentsmaybeneeded.Instatistics,decisionsneedtobemade at this early stage about what data will be relevant and how they will be collected.

Theanalysismayinvolveconsideringwhetherthereisanappropriatestandardmodeltouse(e.g.theNormaldistributionortheparticlemodel)orwhethertheproblemissimilarto one which has been solved before.

Atthecompletionoftheproblemsolvingcycle,thereneedstobeconsiderationofwhethertheoriginalproblemhasbeensolvedinasatisfactorywayorwhetheritisnecessarytorepeattheproblemsolvingcycleinordertogainabettersolution.Forexample,thesolutionmightnotbeaccurateenoughormightonlyapplyinsomecases.

Informationcollection

Thisstageinvolvesgettingthenecessaryinputsforthemathematicalprocessingthatwilltakeplaceatthenextstage.Thismayinvolvedecidingwhicharetheimportantvariables,findingkeymeasurementsorcollectingdata.

Processingandrepresentation

Thisstageinvolvesusingsuitablemathematicaltechniques,suchascalculations,graphsordiagrams,inordertomakesenseoftheinformationcollectedinthepreviousstage.Thisstageendswithaprovisionalsolutiontotheproblem.

Interpretation Thisstageoftheprocessinvolvesreportingthesolutiontotheprobleminawaywhichrelatestotheoriginalsituation.CommunicationshouldbeinclearplainEnglishwhich can be understood by someone who has an interest in the original problem but is not an expertinmathematics.Thisshouldleadintoreflectiononthesolutiontoconsiderwhetheritissatisfactoryoriffurtherworkisneeded.


2

TheModellingCycle

Theexaminationswillassumethatlearnershaveusedthe full modelling cycle during the course.

Mathematicscanbeappliedtoawidevarietyofproblemsarisingfromrealsituationsbutreallifeiscomplicated, and can be unpredictable, so some assumptionsneed to be made to simplify the situationandallowmathematicstobeused.Onceanswers have been obtained, we need to comparewithexperienceto make sure that the answers are useful.Forexample,thegovernmentmightwantto

know how many primary school children there will be in the future so that they can make sure that thereareenoughteachersandschoolplaces.Tofindareasonableestimate,theymightassumethat the birthrateoverthenextfiveyearswillbesimilartothatforthelastfiveyearsandthosechildrenwillgotoschoolintheareatheywerebornin.Theywould evaluatetheseassumptionsbycheckingwhethertheyfitinwithnewdataand reviewtheestimatetoseewhetheritisstillreasonable.

References to competence statements are included on the modelling cycle below.

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2

Learningoutcomes

Learning outcomes are designed to help users by clarifying the requirements, but the following points need to be noted.

• Contentthatiscoveredbyalearningoutcomewith a reference code may be tested in an examinationquestionwithoutfurtherguidancebeing given.

• Learningoutcomesmarkedwithanasterisk* are assumed knowledge and will not form the focusofanyexaminationquestions.Thesestatements are included for clarity and completeness.

• Manyexaminationquestionswillrequirelearners to use two or more learning outcomes atthesametimewithoutfurtherguidancebeinggiven.Learnersareexpectedtobeabletomakelinksbetweendifferentareasofmathematics.

• Learnersareexpectedtobeabletousetheirknowledge and understanding to reason

mathematicallyandsolveproblemsbothwithinmathematicsandincontext.Contentthatiscovered by any learning outcomes may be required in problem solving, modelling and reasoningtasksevenifthatisnotexplicitlystated in the learning outcome.

• Eachlearningoutcomehasanimpliedprefix: ‘Alearnershould…’.

• Eachreferencecodeforalearningoutcome isunique.Forexample,inthecodeMc1,MreferstoMathematics,crefersto‘calculus’ (seebelow)and1meansthatitisthefirst suchlearningoutcomeinthelist.Toassist withco-teaching,ASMathematicsB(MEI) uses the same learning outcomes as in A LevelMathematicsB(MEI)forthesamecontent.

• Thelettersusedinassigningreferencecodes to learning outcomes are common to all qualificationsinspecB(H630,H640,H635andH645).OnlythoseusedinASLevel MathematicsB(MEI)areshownbelow.

a algebra Ab Bc calculus C Curves, Curve sketchingd D Datapresentation&interpretatione equations E Exponentialsandlogarithmsf functions F Forcesg geometry, graphs Gh H Hypothesistestingi Ij Jk kinematics Kl Lm Mn Newton’s laws No Op mathematicalprocesses(modelling,proof,etc) Pq Qr R Random variabless sequences and series St trigonometry Tu probability(uncertainty) Uv vectors Vw Wx Xy projectiles Yz Z


2

Notes,notationandexclusions

Thenotes,notationandexclusionscolumnsinthespecificationareintendedtoassistteachersandlearners.

• Thenotescolumnprovidesexamplesandfurther detail for some learning outcomes. Allexemplarscontainedinthespecificationareforillustrationonlyanddonotconstituteanexhaustivelist.

• Thenotationcolumnshowsnotationandterminologythatlearnersareexpectedtoknow, understand and be able to use.

• Theexclusionscolumnlistscontentwhichwillnot be tested, for the avoidance of doubt when interpretinglearningoutcomes.

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2c. ContentofASLevelinMathematicsB(MEI)

Specification Ref. Learningoutcomes Notes Notation Exclusions

PUREMATHEMATICS:PROOF

Proof Mp1 Understand and be able to use the structure of mathematicalproof.

Use methods of proof, including proof by deductionandproofbyexhaustion.

Proceedingfromgivenassumptionsthroughaseries of logical steps to a conclusion.

p2 Beabletodisproveaconjecturebytheuseofacounterexample.

PUREMATHEMATICS:ALGEBRA

Algebraic language

Ma1 Know and be able to use vocabulary and notationappropriatetothesubjectatthislevel.

Vocabularyincludesconstant,coefficient,expression,equation,function,identity,index,term, variable, unknown.

( )xf

Solutionofequations

* Beabletosolvelinearequationsinoneunknown.

Includingthosecontainingbrackets,fractionsand the unknown on both sides of the equation.

* Beabletochangethesubjectofaformula. Includingcaseswherethenewsubjectappearson both sides of the original formula, and cases involving squares, square roots and reciprocals.

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Solutionofequations

Ma2 Beabletosolvequadraticequations. Byfactorising,completingthesquare,usingtheformula and graphically.Includesquadraticequationsinafunctionofthe unknown.

a3 Beabletofindthediscriminantofaquadraticfunctionandunderstanditssignificance.

Theconditionfordistinctrealrootsofax bx c 02 + + = is:Discriminant > 0. Theconditionforrepeatedrootsis:Discriminant = 0. Theconditionfornorealrootsis: Discriminant < 0.

Forax bx c 02 + + = the discriminant is b ac42 - .

Complexroots.

a4 Beabletosolvelinearsimultaneousequationsin two unknowns.

Byeliminationandbysubstitution.

a5 Beabletosolvesimultaneousequationsintwounknownswithoneequationlinearandonequadratic.

Byeliminationandbysubstitution.

a6 Knowthesignificanceofpointsofintersectionoftwographswithrelationtothesolutionofequations.

Includingsimultaneousequations.

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PUREMATHEMATICS:ALGEBRA

Inequalities Ma7 Beabletosolvelinearinequalitiesinonevariable.Beabletorepresentandinterpretlinearinequalitiesgraphicallye.g. .y x 1> +

Includingthosecontainingbracketsandfractions.

a8 Beabletosolvequadraticinequalitiesinonevariable.Beabletorepresentandinterpretquadraticinequalitiesgraphicallye.g.y ax bx c> 2 + + .

Algebraicandgraphicaltreatmentofsolutionofquadraticinequalities.

Forregionsdefinedbyinequalitieslearnersmuststate clearly which regions are included and whether the boundaries are included. No particularshadingconventionisexpected.

Complexroots.

a9 Beabletoexpresssolutionsofinequalitiesthroughcorrectuseof‘and’and‘or’,orbyusingsetnotation.

Learnerswillbeexpectedtoexpresssolutionstoquadraticinequalitiesinanappropriateversionofone of the following ways.

• x 1# or x 4$ • : :x x x x1 4,# $" ", ,• x2 5< < • x x5 2and< >

• : :x x x x5 2< >+" ", ,

:x x 4>" ,

SurdsIndices

a10 Beabletouseandmanipulatesurds.

a11 Beabletorationalisethedenominatorof a surd. e.g.

5 31

225 3

+=-

a12 Understand and be able to use the laws of indicesforallrationalexponents.

,x x xa b a b# = + , ( )x x x x xa b a b a n an' = =-

a13 Understandandbeabletousenegative,fractionalandzeroindices.

,x x1aa=- x 10 = ( )x 0! , x xa a

1=

Proportion a14 Understandanduseproportionalrelationshipsand their graphs.

Foronevariabledirectlyorinverselyproportionalto a power or root of another.

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PUREMATHEMATICS:FUNCTIONS

Polynomials Mf1 Beabletoadd,subtract,multiplyanddividepolynomials.

Expandingbracketsandcollectingliketerms. Division by non-linear expressions.

f2 Understand the factor theorem and be able to use it tofactoriseapolynomialortodetermineitszeros.

( ) ( )a x a0f += - is a factor of ( )xf .Includingwhensolvingapolynomialequation.

Equationsofdegree > 4.

PUREMATHEMATICS:GRAPHS

Graphs MC1 Understandandusegraphsoffunctions.

Sketching curves C2 Understandhowtofindintersectionpointsofacurvewithcoordinateaxes.

Includingrelatingthistothesolutionofanequation.

C3 Understand and be able to use the method of completingthesquaretofindthelineofsymmetry and turning point of the graph of a quadraticfunctionandtosketchaquadraticcurve(parabola).

Thecurve ( )y a x p q2= + + has• aminimum at ( , )p q- for a 0> or amaximumat( , )p q- for a 0<• aline of symmetry x p= - .

C4 Beabletosketchandinterpretthegraphsofsimplefunctionsincludingpolynomials.

Includingcasesofrepeatedrootsforpolynomials.

C5 Beabletousestationarypoints when curve sketching.

Includingdistinguishingbetweenmaximumand minimum turning points.

C6 Beabletosketchandinterpretthegraphsofy x

a= and y x

a2= .

Includingtheirverticalandhorizontalasymptotes and recognising them as graphs of proportionalrelationships.

Transformations MC7 Beabletosketchcurvesoftheforms( ), ( ) , ( )y a x y x a y x af f f= = + = + and

( )y axf= , given the curve of ( )y xf= and describetheassociatedtransformations.Beabletoformtheequationofagraphfollowingasingletransformation.

Includingworkingwithsketchesofgraphswherefunctionsarenotdefinedalgebraically.

Map(s)onto.Translation,stretch, reflection.

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PUREMATHEMATICS:COORDINATEGEOMETRY

Thecoordinategeometry of straight lines

* Understandandusetheequationy mx c= + .

Mg1 Knowandbeabletousetherelationshipbetween the gradients of parallel lines and perpendicular lines.

Forparallellinesm m1 2= .

Forperpendicularlinesm m 11 2=- .

g2 Beabletocalculatethedistancebetweentwopoints.

g3 Beabletofindthecoordinatesofthemidpointofalinesegmentjoiningtwopoints.

g4 Beabletoformtheequationofastraightline. Including( )y y m x x1 1- = - and

.ax by c 0+ + =

g5 Beabletodrawalinegivenitsequation. Byusinggradientandinterceptorinterceptswithaxesaswellasbyplottingpoints.

g6 Beabletofindthepointofintersectionoftwolines.

Bysolutionofsimultaneousequations.

g7 Beabletousestraightlinemodels. Inavarietyofcontexts;includesconsideringtheassumptionsthatleadtoastraightlinemodel.

Equationsofstraightlines

ManylearnerstakingASMathematicswillbefamiliarwiththeequationofastraightlineintheformy mx c= + .TheirunderstandingatASlevelshouldextendto

differentformsoftheequationofastraightlineincluding ( )y y m x x1 1- = - , ax by c 0+ + = and y yy y

x xx x

2 1

1

2 1

1

-

-= -

-.

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PUREMATHEMATICS:COORDINATEGEOMETRY

Thecoordinategeometry of curves

Mg8 Beabletofindthepoint(s)ofintersectionofaline and a curve or of two curves.

g9 Beabletofindthepoint(s)ofintersectionofaline and a circle.

g10 Understandandusetheequationofacircleinthe form ( ) ( )x a y b r2 2 2- + - = .

Includescompletingthesquaretofindthecentre and radius.

g11 Know and be able to use the following properties:

• theangleinasemicircleisarightangle;

• theperpendicularfromthecentreofa circle to a chord bisects the chord;

• theradiusofacircleatagivenpointon its circumference is perpendicular to the tangent to the circle at that point.

Theseresultsmaybeusedinthecontextofcoordinate geometry.

PUREMATHEMATICS:SEQUENCESANDSERIES

Binomialexpansions

Ms1 Understandandusethebinomialexpansionof( )a bx n+ where nisapositiveinteger.

s2 Knowthenotationsn! and Cn r and that Cn r is thenumberofwaysofselectingr distinctobjectsfromn.

Themeaningofthetermfactorial.napositiveinteger.Linktobinomialprobabilities.

! ( ) !!

! . . ...

!

,

r n rn

n nC C

Cnr

1 2 31

0 1

Cn r

n n n

nr

0

=-

=

= =

=J

L

KKKKKK

N

P

OOOOOO

Cn r will only be used in thecontextof binomial expansionsand binomial probabilities.

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PUREMATHEMATICS:TRIGONOMETRY

Basictrigonometry

* Know how to solve right-angled triangles using trigonometry.

Trig.functions Mt1 Beabletousethedefinitionsofsin i, cos i and tan i for any angle.

Byreferencetotheunitcircle,

, ,sin cos tany x xy

i i i= = = .

t2 Know and use the graphs of sin i, cos i and tan i for all values of i, their symmetries and periodicities.

Stretches,translationsandreflectionsofthesegraphs.

Period. More than one transformationof a trig graph.

* Knowandbeabletousetheexactvaluesof sin i and cos i for i = 0°, 30°, 45° , 60° and 90° andtheexactvaluesoftan i for i = 0°, 30°, 45° and 60°.

Area of triangle; sine and cosine rules

t3 Know and be able to use the fact that the area of a triangle is given by ½ sinab C.

t4 Know and be able to use the sine and cosine rules.

Use of bearings may be required.

Identities t5Understand and be able to use tan

cossin

iii

= .e.g. solve sin cos3i i= for 0 360c c# #i .

t6 Understandandbeabletousetheidentitysin cos 12 2i i+ = .

e.g. solve sin cos2i i= for 0 360c c# #i .

Equations t7 Beabletosolvesimpletrigonometricequationsin given intervals and know the principal values fromtheinversetrigonometricfunctions.

e.g. .sin 0 5i = , in [ , ] ,0 360 30 150+c c c ci =

Includesequationsinvolvingmultiplesoftheunknown angle e.g. sin cos2 3 2i i= .

Includesquadraticequations.

arcsin x sin–1x arccos x cos–1x arctan x tan–1x

General solutions.

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PUREMATHEMATICS:EXPONENTIALSANDLOGARITHMS

Exponentialsand Logarithms

ME1 Knowandusethefunctiony ax= and its graph. Fora 0> .

E2 Beabletoconvertfromanindextoalogarithmic form and vice versa.

logx a y xya+= = for a 0> and .x 0>

E3 Understand a logarithm as the inverse of the appropriateexponentialfunctionandbeabletosketchthegraphsofexponentialandlogarithmicfunctions.

logy x a xay+= = for a 0> and .x 0>

Includesfindingandinterpretingasymptotes.

E4 Understand the laws of logarithms and be able to apply them, including to taking logarithms of bothsidesofanequation.

( )

( )

log log log

log log log

log log

xy x y

yx x y

x k x

a a a

a a a

ak

a

= +

= -

=

J

L

KKKKN

P

OOOO

Including,forexamplek 1=- and k 21

=-

Change of base of logarithms.

E5 Know and use the values of log aa and log 1a . log a 1a = , log 1 0a =

E6 Beabletosolveanequationoftheforma bx = . Includessolvingrelatedinequalities.

E7 Knowhowtoreducetheequationsy axn= and y abx= tolinearformand,usingexperimentaldata,touseagraphtoestimatevaluesoftheparameters.

Bytakinglogarithmsofbothsidesandcomparingwiththeequationy mx c= + .

Learners may be given graphs and asked to select an appropriate model.

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PUREMATHEMATICS:EXPONENTIALSANDLOGARITHMS

Exponentialsand natural logarithms

ME8 Knowandbeabletousethefunctiony ex= and its graph.

E9 Know that the gradient of ekx is kekx and hence understandwhytheexponentialmodelissuitableinmanyapplications.

E10 Knowandbeabletousethefunction lny x= anditsgraph.Knowtherelationshipbetweenln x and ex.

ln xistheinversefunctionofex. log lnx xe =

Exponentialgrowth and decay

E11 Beabletosolveproblemsinvolvingexponentialgrowth and decay; be able to consider limitationsandrefinementsofexponentialgrowth and decay models.

Understandanduseexponentialgrowthanddecay:useinmodelling(examplesmayincludetheuseofeincontinuouscompoundinterest,radioactivedecay,drugconcentrationdecay,exponentialgrowthasamodelforpopulationgrowth);considerationoflimitationsandrefinementsofexponentialmodels.Findinglong term values.

Graphswithgradientproportionaltooneofthecoordinates

xy

xdd? resultsinaquadraticgraph. x

yyd

d? resultsinanexponentialgraph.

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PUREMATHEMATICS:CALCULUS

Basicdifferentiation

Mc1 Know and use that the gradient of a curve at a point is given by the gradient of the tangent at the point.

c2 Know and use that the gradient of the tangent at a point A on a curve is given by the limit of the gradient of chord AP as P approaches A along the curve.

Themodulusfunction.

c3 Understandandusethederivativeoff(x) as the gradient of the tangent to the graph of y = f(x) at a general point (x, y). Know that the gradient

function xy

dd

gives the gradient of the curve and

measures the rate of change of y with respect to x.

Beabletodeducetheunitsofrateof change for graphs modelling real situations.Thetermderivativeofafunction.

xy

xy

dd

Limx 0 d

d=

"d

( )( ) ( )

x hx h x

f Limf f

h 0=

+ -

"l

J

L

KKKKKKK

N

P

OOOOOOO

c4 Beabletosketchthegradientfunctionforagivencurve.

Differentiationoffunctions

c5 Beabletodifferentiatey kxn= where k is a constant and nisrational,includingrelatedsumsanddifferences

Differentiationfromfirstprinciplesforsmallpositiveintegerpowers.

Applicationsofdifferentiationtofunctionsand graphs

c6 Understandandusethesecondderivativeastherate of change of gradient. ( )x x

yf d

d2

2

=ll

c7 Beabletousedifferentiationtofindstationarypointsonacurve:maximaandminima.

Distinguishbetweenmaximumandminimum turning points.

c8 Understandthetermsincreasingfunctionanddecreasingfunctionandbeabletofindwherethefunctionisincreasingordecreasing.

Inrelationtothesignof xy

dd

.

c9 Beabletofindtheequationofthetangentandnormal at a point on a curve.

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PUREMATHEMATICS:CALCULUS

Integrationasreverse of differentiation

Mc19 Knowthatintegrationisthereverseofdifferentiation. FundamentalTheoremofCalculus.

c20 Beabletointegratefunctionsoftheformkxn where k is a constant and n 1!- .

Includingrelatedsumanddifferences.

c21 Beabletofindaconstantofintegrationgivenrelevantinformation.

e.g.Findyasafunctionofx given

that xy

x 2dd

2= + and y 7= when

x 1= .

Integrationtofindareaundera curve

c22 Knowwhatismeantbyindefiniteanddefiniteintegrals.

Beabletoevaluatedefiniteintegrals.e.g. ( )x x x3 5 1 d

1

32 + -y .

c23 Beabletouseintegrationtofindtheareabetweenagraph and the x-axis.

Includesareasofregionspartlyabove and partly below the x-axis.

General understanding that the area under a graph can be found as the limit of a sum of areas of rectangles.

FormalunderstandingofthecontinuityconditionsrequiredfortheFundamentalTheoremofCalculus.

TheFundamentalTheoremofCalculus

Onewaytodefinetheintegralofafunctionisasfollows.

Theareaunderthegraphofthefunctionisapproximatelythesumoftheareasofnarrowrectangles(asshown).Thelimitofthissumastherectanglesbecomenarrower(andtherearemoreofthem)istheintegral.Thefundamentaltheoremofcalculussaysthatthisisthesameasdoingthereverseofdifferentiation.

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PUREMATHEMATICS:VECTORS

General vectors

Mv1 Understand the language of vectors in two-dimensions.

Scalar, vector, modulus, magnitude, direction,positionvector,unitvector,cartesian components, equal vectors, parallel vectors, collinear.

Vectors printed in bold.

Unit vectors i, j, rt Themagnitudeofthe vector a is written|a|ora.

a

aa

1

2

=

J

L

KKKKKK

N

P

OOOOOO

v2 Beabletoaddandsubtractvectorsusingadiagramoralgebraically,multiplyavectorbyascalar,andexpressavectorasacombinationofothers.

Geometricalinterpretation.Includesgeneralvectorsnotexpressedincomponent form.

v3 Beabletocalculatethemagnitudeanddirectionofavector and convert between component form and magnitude-directionform.

Magnitude-direction

Positionvectors

v4 Understandandusepositionvectors. Includinginterpretingcomponentsofapositionvectorasthecartesiancoordinates of the point.

AB –b a=

OB or b.

x

yr =J

L

KKKKKK

N

P

OOOOOO

v5 Beabletocalculatethedistancebetweentwopointsrepresentedbypositionvectors.

Using vectors v6 Beabletousevectorstosolveproblemsinpuremathematicsandincontext,includingproblemsinvolving forces.

Includesinterpretingthesumofvectorsrepresentingforcesastheresultantforce.

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STATISTICS:SAMPLING

Populationandsample

Mp21 Understandandusethetermspopulationandsample.

p22 Beabletousesamplestomakeinformalinferencesaboutapopulation,recognisingthatdifferentsamplesmightleadtodifferentconclusions.

e.g. using sample mean or variance as anestimateofpopulationmeanorvariance.

Sampling techniques

p23 Understand and be able to use the concept of random sampling.

Simplerandomsampling.Everysampleoftherequiredsizehasthesame probability of being selected.

p24 Understand and be able to use a variety of sampling techniques.

Opportunitysampling,systematicsampling,stratifiedsampling,quotasampling, cluster sampling, self-selected samples.

Anyothertechniqueswillbeexplainedinthequestion.

p25 Beabletoselectorevaluatesamplingtechniquesinthecontextofsolvingastatisticalproblem.

Includesrecognisingpossiblesourcesof bias and being aware of the practicalitiesofimplementation.

Populationandsample

Populationinstatisticsmeansalltheindividualsweareinterestedinforaparticularinvestigatione.g.allcodinanareaofthesea.Apopulationcanbeinfinitee.g.allpossibletossesofaparticularcoin.Aprobabilitydistributioncanbeusedtomodelsomecharacteristicofthepopulationwhichisofinterest.

A sampleisasetofitemschosenfromapopulation.Whensamplingfromaninfinitepopulationitdoesnotmatterwhetherthesamplingiswithorwithoutreplacement.Whentakingasampleofindividuals,e.g.forasamplesurvey,itisusualtosamplewithoutreplacementtoavoidgettingdatafromthesameindividualmore than once.

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STATISTICS:DATAPRESENTATIONANDINTERPRETATION

Data presentationfor single variable

MD1 Beabletorecogniseandworkwithcategorical,discrete,continuousandrankeddata.Beabletointerpret standard diagrams for grouped and ungrouped single-variable data.

Includesknowingthisvocabulary anddecidingwhatdatapresentationmethodsareappropriate:barchart,dotplot,histogram,verticallinechart,pie chart, stem-and-leaf diagram, box-and-whiskerdiagram(boxplot),frequency chart.

Learners may be asked to add to diagramsinexaminationsinordertointerpret data.

A frequency chart resembles a histogram with equal width bars butitsverticalaxisis frequency. A dot plot is similar to a bar chart but with stacks of dots in lines to represent frequency.

Comparativepiecharts with area proportionaltofrequency.

D2 Understand that the area of each bar in a histogramisproportionaltofrequency.Beabletocalculateproportionsfromahistogramandunderstandthemintermsofestimatedprobabilities.

Includesuseofareascaleandcalculationoffrequencyfromfrequency density.

D3 Beabletointerpretacumulativefrequencydiagram.

D4 Beabletodescribefrequencydistributions. Symmetrical, unimodal, bimodal, skewed(positivelyandnegatively).

Measures of skewness.

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Data presentation

MD5 Understandthatdiagramsrepresentingunbiasedsamplesbecomemorerepresentativeoftheoreticalprobabilitydistributionswithincreasingsamplesize.

e.g.Abarchartrepresentingtheproportionofheadsandtailswhenafair coin is tossed tends to have the proportionofheadsincreasinglycloseto50%asthesamplesizeincreases.

D6 Beabletointerpretascatterdiagramforbivariatedata,interpretaregressionlineorotherbestfitmodel,includinginterpolationandextrapolation,understandingthatextrapolationmightnotbejustified.

Includingthetermsassociation,correlation,regressionline.

Learners should be able to interpret otherbestfitmodelsproducedbysoftware(e.g.acurve).

Learners may be asked to add to diagramsinexaminationsinorder to interpret data.

Calculationofequationofregression line from data or summary statistics.

D7 Beabletorecognisewhenascatterdiagramappearstoshowdistinctsectionsinthepopulation.Beabletorecogniseandcommentonoutliersinascatterdiagram.

An outlier is an item which is inconsistent with the rest of the data.

Outliersinscatterdiagramsshouldbejudgedbyeye.

D8 Beabletorecogniseanddescribecorrelationinascatterdiagramandunderstandthatcorrelationdoesnotimplycausation.

Positivecorrelation,negativecorrelation,nocorrelation,weak/strongcorrelation.

D9 Beabletoselectorcritiquedatapresentationtechniquesinthecontextofastatisticalproblem.

Includinggraphsfortimeseries.

Bivariatedata,associationandcorrelation

Bivariatedataconsistsoftwovariablesforeachmemberofthepopulationorsample.Anassociationbetweenthetwovariablesissomekindofrelationshipbetween them.Correlationmeasureslinearrelationships.AtASlevel,learnersareexpectedtojudgerelationshipsfromscatterdiagramsbyeye.

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Summary measures

MD10 Know the standard measures of central tendency and be able to calculate and interpret them and to decide when it is most appropriate to use one of them.

Median,mode,(arithmetic)mean,midrange.Themainfocusofquestionswillbeoninterpretationratherthancalculation.

Includesunderstandingwhenitisappropriate to use a weighted mean e.g.whenusingpopulationsasweights.

Mean x=

D11 Know simple measures of spread and be able to use and interpret them appropriately.

Range,percentiles,quartiles,interquartilerange.

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Summary measures

MD12 Know how to calculate and interpret variance and standarddeviationforrawdata,frequencydistributions,groupedfrequencydistributions.

Beabletousethestatisticalfunctionsofacalculatortofindmeanandstandarddeviation.

samplevariance:s nS

1xx2=-

(†)

where ( )S x xxx ii

n2

1= -

=

|

samplestandarddeviation:

s variance= (‡)

s2

s

Correctionsforclass interval in these calculations.

D13 Understandthetermoutlierandbeabletoidentifyoutliers. Know that the term outlier can be applied to anitemofdatawhichis:• atleast2standarddeviationsfromthemean;OR• atleast1.5 × IQRbeyondthenearerquartile.

An outlier is an item which is inconsistent with the rest of the data.

D14 Beabletocleandataincludingdealingwithmissingdata, errors and outliers.

Notationforsamplevarianceandsamplestandarddeviation

Thenotationss2 and sforsamplevarianceandsamplestandarddeviation,respectively,arewrittenintobothBritishStandards(BS3534-1,2006)andInternationalStandards(ISO3534).Thedefinitionsarethosegivenaboveinequations(†)and(‡).Thecalculationsarecarriedoutusingdivisor( )n 1- .

Inthisspecification,theusagewillbeconsistentwiththesedefinitions.Thusthemeaningsof‘samplevariance’,denotedbys2, and‘samplestandarddeviation’,denoted by s,aredefinedtobecalculatedwithdivisor( )n 1- .

Inearlyworkinstatisticsitiscommonpracticetointroducetheseconceptswithdivisorn rather than ( )n 1- .Howeverthereisnorecognisednotationtodenotethequantitiessoderived.

Studentsshouldbeawareofthevariationsinnotationusedbymanufacturersoncalculatorsandknowwhatthesymbolsontheirparticularmodelsrepresent.

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STATISTICS:PROBABILITY

Probability of events in a finitesamplespace

* Beabletocalculatetheprobabilityofanevent. Usingmodellingassumptionssuchasequally likely outcomes.

P(A)

* Understand the concept of a complementary event and know that the probability of an event may be foundbymeansoffindingthatofitscomplementaryevent.

A´ is the event “not-A”.

Probability of two or more events

* Beabletocalculatetheexpectedfrequencyofanevent given its probability.

Expectedfrequency= nP(A)

* Beabletouseappropriatediagramstoassistinthecalculationofprobabilities.

e.g. tree diagrams, sample space diagrams, Venn diagrams.

Mu1 Understandandusemutuallyexclusiveeventsandindependent events.

Formalnotationanddefinitions.

u2 Knowtoaddprobabilitiesformutuallyexclusiveevents.

e.g.tofind ( )A BP or .

u3 Knowtomultiplyprobabilitiesforindependentevents. e.g.tofind ( )A BP and .

Includingtheuseofcomplementaryevents,e.g.findingtheprobabilityofatleastone6infivethrowsofadice.

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STATISTICS:PROBABILITYDISTRIBUTIONS

Situationsleading to a binomial distribution

MR1 Recognisesituationswhichgiverisetoabinomialdistribution.

R2 Beabletoidentifytheprobabilityofsuccess,p, for the binomialdistribution.

Thebinomialdistributionasamodel for observed data.

B(n, p), q p1= - + means‘hasthedistribution’.

Calculationsrelatingtobinomial distribution

R3 Beabletocalculateprobabilitiesusingthebinomialdistribution.

Includinguseofcalculatorfunctions.

Mean and expectedfrequencies for binomial distribution

R4 Understand and use mean = np. Derivationofmean = np

R5 Beabletocalculateexpectedfrequenciesassociatedwiththebinomialdistribution.

Discrete probability distributions

R6 Beabletouseprobabilityfunctions,givenalgebraically or in tables. Know the term discrete random variable.

Restrictedtosimplefinitedistributions.

X for the random variable.

x or r for a value of the random variable.

R7 Beabletocalculatethenumericalprobabilitiesforasimpledistribution.Understandthetermdiscreteuniformdistribution.

Restrictedtosimplefinitedistributions.

( )X xP =( )X xP #

CalculationofE(X) or Var(X).

Situationswhichgiverisetoabinomialdistribution

• Anexperimentortrialisconductedafixednumberoftimes.• Thereareexactly2outcomes,whichcanbethoughtofas“success”or“failure”.• Theprobabilityof“success”isthesameeachtime.• Theprobabilityof“success”onanytrialisindependentofwhathashappenedinprevioustrials.• Therandomvariableofinterestis“thenumberofsuccesses”.

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STATISTICS:STATISTICALHYPOTHESISTESTING

Hypothesis testing

MH1 Understandtheprocessofhypothesistestingandtheassociated language.

Nullhypothesis,alternativehypothesis. Significancelevel,teststatistic,1-tailtest, 2-tail test. Criticalvalue,criticalregion(rejectionregion),acceptanceregion,p-value.

H2 Understand when to apply 1- tail and 2- tail tests.

H3 Understand that a sample is being used to make an inferenceaboutthepopulationandappreciatethatthesignificancelevelistheprobabilityofincorrectlyrejectingthenullhypothesis.

Forabinomialhypothesistest,theprobabilityoftheteststatisticbeing intherejectionregionwillalwaysbeless than or equal to the intended significancelevelofthetest,andwillusuallybelessthanthesignificancelevel of the test. Learners will not be testedonthisdistinction.Ifaskedtogive the probability of incorrectly rejectingthenullhypothesisforaparticularbinomialtest,eithertheintendedsignificancelevelortheprobabilityoftheteststatisticbeing intherejectionregionwillbeacceptable.

Nullandalternativehypotheses

Thenullhypothesisforahypothesistestisthedefaultpositionwhichwillonlyberejectedinfavourofthealternativehypothesisiftheevidenceisstrongenough.Assumingthenullhypothesisistrue,asadefaultposition,allowsthecalculationofvaluesoftheteststatisticwhichwouldbeunlikely(havelowprobability)ifthenullhypothesisweretrue;thisisthecriticalregion(rejectionregion).

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STATISTICS:STATISTICALHYPOTHESISTESTING

Hypothesis testingforabinomial probability p

H4 Beabletoidentifynullandalternativehypotheses (H0 and H1)whensettingupahypothesistestbased on a binomial probability model.

H0 of form p =aparticularvalue,withp a probability for the whole population.

H0 , H1

H5 Beabletoconductahypothesistestatagivenlevelofsignificance.Beabletodrawacorrectconclusionfromthe results of a hypothesis test based on a binomial probabilitymodelandinterprettheresultsincontext.

Normal approximation.

H6 Beabletoidentifythecriticalandacceptanceregions.

Conclusionfromahypothesistest

Learnersareexpectedtomakenon-assertiveconclusionsincontext.E.g.“Thereisnotenoughevidencetoconcludethattheproportionof...hasincreased.”E.g.“Thereisenoughevidencetoindicatethattheprobabilityof.....haschanged.”

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MECHANICS:MODELSANDQUANTITIES

Standard models in mechanics

Mp31 Know the language used to describe simplifying assumptionsinmechanics.

Includingthewords:light;smooth;uniform;particle;inextensible;thin;rigid; long term.

p32 Understandandusetheparticlemodel.

Units and quantities

p33 UnderstandandusefundamentalquantitiesandunitsintheS.I.system:length,time,mass.

Metre(m),second(s),kilogram(kg).

p34 Understandandusederivedquantitiesandunits:velocity,acceleration,force,weight.

Metrepersecond(m s–1),metrepersecondpersecond(m s–2),newton(N).

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MECHANICS:KINEMATICSIN1DIMENSION

Motionin1dimension

Mk1 Understandandusethelanguageofkinematics. Position,displacement,distancetravelled;speed,velocity;acceleration,magnitudeofacceleration;relativevelocity(in1-dimension).

Average speed = distance travelled ÷elapsedtime

Average velocity = overall displacement ÷elapsedtime

k2 Knowthedifferencebetweenposition,displacement,distance and distance travelled.

k3 Knowthedifferencebetweenvelocityandspeed,andbetweenaccelerationandmagnitudeofacceleration.

Kinematicsgraphs

k4 Beabletodrawandinterpretkinematicsgraphsformotioninastraightline,knowingthesignificance(whereappropriate)oftheirgradientsandtheareasunderneath them.

Position-time,displacement-time,distance-time,velocity-time, speed-time,acceleration-time.

Calculus in kinematics

k5 Beabletodifferentiatepositionandvelocitywithrespecttotimeandknowwhatmeasuresresult.

,v tr a t

vtr

dd

dd

dd

2

2= = =

k6 Beabletointegrateaccelerationandvelocitywithrespecttotimeandknowwhatmeasuresresult.

,r v t v a td d= =y yConstant accelerationformulae

k7 Beabletorecognisewhentheuseofconstantaccelerationformulaeisappropriate.

Learners should be able to derive the formulae.

s ut at21 2= +

s vt at21 2= -

v u at= +

( )s u v t21

= +

v u as22 2- =

Problem solving

k8 Beabletosolvekinematicsproblemsusingconstantaccelerationformulaeandcalculusformotioninastraight line.

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MECHANICS:FORCES

Identifyingand representingforces

MF1 Understandthelanguagerelatingtoforces. Weight, tension, thrust or compression, normalreaction(ornormalcontactforce),frictionalforce,resistance,drivingforce.

Understand that the value of the normal reactiondependsontheotherforcesacting.

Understandthattheremaybefrictionalforcewhenthesurfaceisnotsmooth(i.e.isrough).

F2 Knowthattheaccelerationduetogravityisnotauniversalconstantbutdependsonlocationintheuniverse.Knowthatonearth,theaccelerationduetogravityisoftenmodelledtobe a constant, g m s–2.

g . 10, g . 9.8

Unlessotherwisespecified,inexaminationsthe value of g should be taken to be 9.8.

Accelerationdue to gravity, g m s–2.

Inversesquare law for gravitation.

F3 Beabletoidentifytheforcesactingonasystemandrepresent them in a force diagram. Understand the differencebetweenexternalandinternalforcesandbeabletoidentifytheforcesactingonpartofthesystem.

Vector treatment of forces

F4 Beabletofindtheresultantofseveralconcurrentforceswhen the forces are parallel or in two perpendicular directionsorinsimplecasesofforcesgivenas2-Dvectorsincomponent form.

F5 Understand the concept of equilibrium and know that a particleisinequilibriumifandonlyifthevectorsumoftheforcesactingonitiszerointhecaseswheretheforcesareparallelorintwoperpendiculardirectionsorinsimplecasesof forces given as 2-D vectors in component form.

Accelerationduetogravity

Theaccelerationduetogravity(g m s–2)variesonearthbetween9.76 and 9.83.Itdependsonlatitudeandheightabovesealevel.Thestandardaccelerationduetogravityisinternationallyagreedtobe9.80665;thisvalueisstoredinsomecalculators.

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MECHANICS:NEWTON’SLAWSOFMOTION

Newton’s laws foraparticle

Mn1 Know and understand the meaning of Newton’s three laws. Includesapplyingthelawstoproblems.

n2 Understandthetermequationofmotion.

n3 Beabletoformulatetheequationofmotionforaparticlemovinginastraightlinewhentheforcesactingareparallelorintwoperpendiculardirectionsorinsimplecasesofforces given as 2-D vectors in component form.

Includingmotionundergravity. F ma= where F is the resultant force.

mF a= where F is the resultant force.

Variable mass.

Connected particles

n4 Beabletomodelasystemasasetofconnectedparticles. e.g. simple smooth pulley systems, trains.

Internalandexternalforcesforthesystem.

n5 Beabletoformulatetheequationsofmotionfortheindividualparticleswithinthesystem.

n6 Know that a system in which none of its components have anyrelativemotionmaybemodelledasasingleparticlewiththe mass of the system.

e.g.Train.

Newton’slawsofmotion

I Anobjectcontinuesinastateofrestoruniformmotioninastraightlineunlessitisactedonbyaresultantforce.II AresultantforceF actingonanobjectoffixedmassmgivestheobjectanaccelerationa given by F = ma.III Whenoneobjectexertsaforceonanother,thereisalwaysareactionwhichisequalinmagnitudeandoppositeindirectiontotheactingforce.


2

• ItisassumedthatlearnersarefamiliarwiththecontentofGCSE(9–1)Mathematicsforfirstteachingfrom2015.

• ASLevelMathematicsB(MEI)provides the framework within which a large number ofyoungpeoplecontinuethesubjectbeyondGCSE.Itsupportstheirmathematicalneedsacrossabroadrangeofothersubjectsatthislevel and provides a basis for subsequent quantitativeworkinaverywiderangeofhighereducationcoursesandinemployment.ItalsosupportsthestudyofALevelMathematicsandASLevelFurther MathematicsB(MEI).

• ASLevelMathematicsB(MEI)buildsfrom GCSEMathematicsandintroducescalculus anditsapplications.Itemphasiseshowmathematicalideasareinterconnectedandhowmathematicscanbeappliedtohelpmakesense of data, to understand the physical world andtosolveproblemsinavarietyofcontexts,includingsocialsciencesandbusiness.Itprepares students for further study and

employment in a wide range of disciplines involvingtheuseofmathematics.

• SomelearnersmaywishtofollowamathematicscourseonlyuptoASLevel,inorder to broaden their curriculum, and to develop their interest and understanding of differentareasofthesubject.Othersmayfollowaco-teachableroute,completingaone–yearAScourseandthencontinuingtocompletethesecondyearofthetwo–yearAlevel course, developing a deeper knowledge andunderstandingofmathematicsanditsapplications.

• LearnerswhowishtospecialiseinmathematicsorSTEMsubjectssuchasphysicsorengineeringcanfurtherextendtheirknowledgeandunderstandingofmathematicsanditsapplicationsbytakingASorALevelFurtherMathematicsB(MEI).

ThereareanumberofMathematicsspecificationsatOCR.Findoutmoreatwww.ocr.org.uk

2d. Priorknowledge,learningandprogression

www.ocr.org.uk

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3a. Formsofassessment

OCRASLevelinMathematicsB(MEI)consistsoftwocomponentsthatareexternallyassessed.

Thetwoexternallyassessedcomponents(01–02)containsomesynopticassessmentandsomeextendedresponsequestions.

PureMathematicsandMechanics(Component01)

Thiscomponentisworth50%ofthetotalASlevel. Allquestionsarecompulsoryandthereare70marksintotal;18to22ofthemarksareformechanics.The

paperhasagradientofdifficultyfromshortertolongerquestionsandfromeasiertoharderquestions.

PureMathematicsandStatistics(Component02)

Thiscomponentisworth50%ofthetotalASlevel. Allquestionsarecompulsoryandthereare70marksintotal;28to32ofthemarksareforstatisticswithsomeofthesebeingforquestionsbasedonthepre-releasedataset.Thepaperhasagradientofdifficultyfromshortertolongerquestionsandfromeasiertoharderquestions.

3 AssessmentofASLevelinMathematicsB(MEI)


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3b. AssessmentObjectives(AO)

Thereare3AssessmentObjectivesinOCRASLevelMathematicsB(MEI).Thesearedetailedinthetablebelow.

AssessmentObjectivesWeightings*

AS level

AO1 UseandapplystandardtechniquesLearnersshouldbeableto:• selectandcorrectlycarryoutroutineprocedures;and• accuratelyrecallfacts,terminologyanddefinitions.

60%(±2%)

AO2 Reason,interpretandcommunicatemathematicallyLearnersshouldbeableto:• constructrigorousmathematicalarguments(includingproofs);• makedeductionsandinferences;• assessthevalidityofmathematicalarguments;• explaintheirreasoning;and• usemathematicallanguageandnotationcorrectly.

Where questions/tasks targeting this assessment objective will also credit Learners for the ability to ‘use and apply standard techniques’ (AO1) and/or to ‘solve problems within mathematics and other contexts’ (AO3) an appropriate proportion of the marks for the question/task will be attributed to the corresponding assessment objective(s).

20%(±2%)

AO3 SolveproblemswithinmathematicsandinothercontextsLearnersshouldbeableto:• translateproblemsinmathematicalandnon-mathematicalcontextsinto

mathematicalprocesses;• interpretsolutionstoproblemsintheiroriginalcontext,and,where

appropriate,evaluatetheiraccuracyandlimitations;• translatesituationsincontextintomathematicalmodels;• usemathematicalmodels;and• evaluatetheoutcomesofmodellingincontext,recognisethelimitationsof

modelsand,whereappropriate,explainhowtorefinethem.

Where questions/tasks targeting this assessment objective will also credit Learners for the ability to ‘use and apply standard techniques’ (AO1) and/or to ‘reason, interpret and communicate mathematically’ (AO2) an appropriate proportion of the marks for the question/task will be attributed to the corresponding assessment objective(s).

20%(±2%)

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AOweightingsinASLevelinMathematicsB(MEI)

TherelationshipbetweentheAssessmentObjectivesandthecomponentsareshowninthefollowingtable:

ComponentAOmarkspercomponent

AO1 AO2 AO3

PureandMechanics(H630/01) 40–44marks 10–14marks 14–18marks

PureandStatistics(H630/02) 40–44marks 14–18marks 10–14marks

%ofOCRASLevelinMathematicsB(MEI)(H630) 58–62% 18–22% 18–22%

Across both papers combined in any given series, AO totals will fall within the stated percentages for the qualification.Morevariationisallowedpercomponent,however,toallowforflexibilityinthedesignofitems.

3c. Assessment availability

TherewillbeoneexaminationseriesavailableeachyearinMay/Junetoall learners.

Allexaminedcomponentsmustbetakeninthesameexaminationseriesattheendofthecourse.

ThisspecificationwillbecertificatedfromtheJune2018examinationseriesonwards.

3d. Retakingthequalification

Learnerscanretakethequalificationasmanytimesastheywish.Theymustretakeallcomponentsofthequalification.

3e. Assessmentofextendedresponse

Theassessmentmaterialsforthisqualificationprovide learners with the opportunity to demonstrate their ability to construct and develop a sustained and coherentlineofreasoningandmarksforextended

responses are integrated into the marking criteria. Taskswhichofferthisopportunitywillbefoundacross both components.


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3f. Synopticassessment

• Synopticassessmentisthelearner’sunderstandingoftheconnectionsbetweendifferentelementsofthesubject.Itinvolvestheexplicitdrawingtogetherofknowledge,skillsandunderstandingwithindifferentpartsof the AS Level course.

• TheemphasisofsynopticassessmentistoencouragetheunderstandingofMathematicsas a discipline.

• Synopticassessmentallowslearnerstodemonstrate the understanding they have acquired from the course as a whole and their ability to integrate and apply that understanding.Thislevelofunderstandingisneeded for successful use of the knowledge and skills from this course in future life, work and study.

• Learnersarerequiredtoknowandunderstandthecontentofallthepuremathematicsandtobe able to apply the overarching themes, along withassociatedmathematicalthinkingandunderstanding, in both the assessment componentsofASMathematicsB(MEI).

• Inalltheexaminationpapers,learnerswillberequired to integrate and apply their understanding in order to address problems which require both breadth and depth of understandinginordertoreachasatisfactorysolution.

• Learnerswillbeexpectedtoreflectonandinterpretsolutions,drawingontheirunderstandingofdifferentaspectsofthecourse.

3g. Calculatingqualificationresults

Alearner’soverallqualificationgradeforASLevelinMathematicsB(MEI)willbecalculatedbyaddingtogether their marks from the two components taken to give their total mark.

Thismarkwillthenbecomparedtothequalificationlevelgradeboundariesfortherelevantexamseriestodeterminethelearner’soverallqualificationgrade.

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Theinformationinthissectionisdesignedtogiveanoverview of the processes involved in administering thisqualificationsothatyoucanspeaktoyourexamsofficer.AllofthefollowingprocessesrequireyoutosubmitsomethingtoOCRbyaspecificdeadline.

Moreinformationabouttheprocessesanddeadlinesinvolved at each stage of the assessment cycle can be foundintheAdministrationareaoftheOCRwebsite

OCR’s Admin overview is available on the OCR website at http://www.ocr.org.uk/administration.

4 Admin:whatyouneedtoknow

4a. Pre-assessment

Estimatedentries

Estimatedentriesareyourbestprojectionofthenumber of learners who will be entered for a qualificationinaparticularseries.Estimatedentries

shouldbesubmittedtoOCRbythespecifieddeadline.Theyarefreeanddonotcommityourcentre in any way.

Finalentries

FinalentriesprovideOCRwithdetaileddataforeachlearner,showingeachassessmenttobetaken.Itisessentialthatyouusethecorrectentrycode,considering the relevant entry rules.

FinalentriesmustbesubmittedtoOCRbythepublished deadlines or late entry fees will apply.

AlllearnerstakingASLevelinMathematicsB(MEI)mustbeenteredforH630.

Entrycode

Title Component code

Componenttitle Assessment type

H630 MathematicsB(MEI)

01 PureMathematicsandMechanics

ExternalAssessment

02 PureMathematicsandStatistics

ExternalAssessment

http://www.ocr.org.uk/administration


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4b. Specialconsideration

Specialconsiderationisapost-assessmentadjustmenttomarksorgradestoreflecttemporaryinjury,illnessorotherindispositionatthetimetheassessment was taken.

DetailedinformationabouteligibilityforspecialconsiderationcanbefoundintheJCQpublication A guide to the special consideration process.

4c. Externalassessmentarrangements

RegulationsgoverningexaminationarrangementsarecontainedintheJCQInstructions for conducting examinations.

4d. Resultsandcertificates

GradeScale

ASlevelqualificationsaregradedonthescale: A,B,C,D,E,whereAisthehighest.Learnerswho failtoreachtheminimumstandardforEwillbe

Unclassified(U).OnlysubjectsinwhichgradesAtoEareattainedwillberecordedoncertificates.

Headofcentreannualdeclaration

TheHeadofCentreisrequiredtoprovideadeclarationtotheJCQaspartoftheannualNCNupdate,conductedintheautumnterm,toconfirmthatthecentreismeetingalloftherequirementsdetailedinthespecification.Anyfailurebyacentre

toprovidetheHeadofCentreAnnualDeclarationwillresult in your centre status being suspended and could lead to the withdrawal of our approval for you to operate as a centre.

Privatecandidates

Private candidates may enter for OCR assessments.

A private candidate is someone who pursues a course of study independently but takes an examinationorassessmentatanapprovedexaminationcentre.Aprivatecandidatemay beapart-timestudent,someonetakingadistancelearning course, or someone being tutored privately. TheymustbebasedintheUK.

Private candidates need to contact OCR approved centres to establish whether they are prepared to hostthemasaprivatecandidate.Thecentremaycharge for this facility and OCR recommends that the arrangement is made early in the course.

FurtherguidanceforprivatecandidatesmaybefoundontheOCRwebsite:http://www.ocr.org.uk

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4e. Post-resultsservices

Anumberofpost-resultsservicesareavailable:

• Reviewofmarking–Ifyouarenothappy with the outcome of a learner’s results, centres mayrequestareviewofmarking.Fulldetails of the post-results services are provided on the OCR website.

• Missingandincompleteresults–Thisserviceshouldbeusedifanindividualsubjectresultfor a learner is missing, or the learner has been omittedentirelyfromtheresultssupplied.

• Accesstoscripts–Centrescanrequestaccessto marked scripts.

4f. Malpractice

Anybreachoftheregulationsfortheconductofexaminationsandnon-examassessmentmayconstitutemalpractice(whichincludesmaladministration)andmustbereportedtoOCRas

soonasitisdetected.DetailedinformationonmalpracticecanbefoundintheJCQpublication Suspected Malpractice in Examinations and Assessments: Policies and Procedures.

Results

Results are released to centres and learners for informationandtoallowanyqueriestoberesolvedbeforecertificatesareissued.

Centres will have access to the following results informationforeachlearner:

• thegradeforthequalification

• therawmarkforeachcomponent

• thetotalmarkforthequalification.

Thefollowingsupportinginformationwillbeavailable:

• rawmarkgradeboundariesforeachcomponent

• rawmarkgradeboundariesforthequalification.

Untilcertificatesareissued,resultsaredeemedtobeprovisionalandmaybesubjecttoamendment.

Alearner’sfinalresultswillberecordedonanOCRcertificate.Thequalificationtitlewillbeshownonthecertificateas‘OCRLevel3AdvancedSubsidiaryGCEinMathematicsB(MEI)’.


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5a. Overlapwithotherqualifications

ThisqualificationoverlapswithALevel MathematicsAandwithotherspecifications

inALevelMathematicsandASLevel Mathematics.

5 Appendices

5b. Accessibility

Reasonableadjustmentsandaccessarrangementsallowlearnerswithspecialeducationalneeds,disabilitiesortemporaryinjuriestoaccesstheassessment and show what they know and can do, without changing the demands of the assessment. Applicationsfortheseshouldbemadebeforetheexaminationseries.Detailedinformationabouteligibility for access arrangements can be found in theJCQAccess Arrangements and Reasonable Adjustments.

TheASLevelqualificationandsubjectcriteriahavebeenreviewedinordertoidentifyanyfeaturewhichcould disadvantage learners who share a protected CharacteristicasdefinedbytheEqualityAct2010.Allreasonable steps have been taken to minimise any such disadvantage.

5c. Mathematicalnotation

ThetablesbelowsetoutthenotationthatmustbeusedbyASmathematicsspecifications.Studentswillbeexpectedtounderstandthisnotationwithoutneedforfurtherexplanation.

1 SetNotation

1.1 ! is an element of

1.2 " is not an element of

1.3 3 is a subset of

1.4 1 is a proper subset of

1.5 { , , }x x1 2 f the set with elements , ,x x1 2 f

1.6 { :...}x the set of all x such that f

1.7 ( )An the number of elements in set A

1.8 Q the empty set

1.9 f the universal set

1.10 Al the complement of the set A

1.11 N the set of natural numbers, { , , , }1 2 3 f

1.12 Z the set of integers, { , , , , }0 1 2 3! ! ! f

1.13 Z+ thesetofpositiveintegers,{ , , , }1 2 3 f

1.14 Z0+ thesetofnon-negativeintegers,{0, 1, 2, 3, ...}

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1.15 R the set of real numbers

1.16 Q thesetofrationalnumbers, : , qpp qZ Z! ! +' 1

1.17 , union

1.18 + intersection

1.19 ( , )x y the ordered pair x, y

1.20 [ , ]a b the closed interval { : }x a x bR! # #

1.21 [ , )a b the interval { : }x a x b<R! #

1.22 ( , ]a b the interval { : }x a x b<R! #

1.23 ( , )a b the open interval { : }x a x b< <R!

2 MiscellaneousSymbols

2.1 = is equal to

2.2 ! is not equal to

2.3 / isidenticaltooriscongruentto

2.4 . isapproximatelyequalto

2.5 3 infinity

2.6 " isproportionalto

2.7 Ñ therefore

2.8 Ö because

2.9 < is less than

2.10 G, # is less than or equal to, is not greater than

2.11 > is greater than

2.12 H, $ is greater than or equal to, is not less than

2.13 p q& p implies q(ifp then q)

2.14 p q% p is implied by q(ifq then p)

2.15 p q+ p implies and is implied by q(p is equivalent to q)

3 Operations

3.1 a b+ a plus b

3.2 a b- a minus b

3.3 , , .a b ab a b# amultipliedbyb

3.4 a ÷ b, ba

a divided by b


5

3.7 a thenon-negativesquarerootofa

3.9 !n nfactorial: ! ( ) ... , ; !n n n n1 2 1 0 1N# # # # != - =

3.10,

nr Cn r

J

L

KKKKKK

N

P

OOOOOO , Cn r

thebinomialcoefficient ! ( ) !!

r n rn-

for n, r ! Z0+, r G n

or !( ) ( )

rn n n r1 1f- - +

for n ! Q, r ! Z0+

4 Functions

4.1 ( )xf thevalueofthefunctionf at x

4.2 : x yf 7 thefunctionf maps the element x to the element y

4.5 ( )lim xfx a" the limit of ( )xf as x tends to a

4.6 , x xdD an increment of x

4.7xy

dd

thederivativeofy with respect to x

4.8xy

dd

n

n

the nthderivativeofy with respect to x

4.9 ( ), ( ), , ( )x x xf f f( )nfl m thefirst,second,...,nthderivativesof ( )xf with respect to x

4.10 , , x x fo p thefirst,second,...derivativesofx with respect to t

4.11 y xdy theindefiniteintegralofy with respect to x

4.12 y xda

by thedefiniteintegralofy with respect to x between the limits x a= and x b=

5 ExponentialandLogarithmicFunctions

5.1 e base of natural logarithms

5.2 , exp xex exponentialfunctionofx

5.3 log xa logarithm to the base a of x

5.4 , ln logx xe natural logarithm of x

6 TrigonometricFunctions

6.1 , ,sin cos tan thetrigonometricfunctions

6.2, ,, ,

sin cos tanarcsin arccos arctan

1 1 1- - -

2 theinversetrigonometricfunctions

6.3 ° degrees

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9 Vectors

9.1 a, a, a~ the vector a, a, a

~;thesealternativesapplythroughoutsection9

9.2 ABthevectorrepresentedinmagnitudeanddirectionbythe directed line segment AB

9.3 â aunitvectorinthedirectionofa

9.4 ,i j unitvectorsinthedirectionsofthecartesiancoordinateaxes

9.5 , a a the magnitude of a

9.6 ,AB AB the magnitude of AB

9.7 ,a

ba b i j+

J

L

KKKKKKK

N

P

OOOOOOOcolumnvectorandcorrespondingunitvectornotation

9.8 r positionvector

11 ProbabilityandStatistics

11.1 , , , .A B C etc events

11.4 ( )AP probability of the event A

11.5 Al complement of the event A

11.7 , , , .X Y R etc random variables

11.8 , , , .x y r etc values of the random variables , ,X Y R etc.

11.9 , ,x x1 2 f valuesofobservations

11.10 , ,f f1 2 f frequencieswithwhichtheobservations , ,x x1 2 f occur

11.11 p(x), P(X = x) probabilityfunctionofthediscreterandomvariableX

11.12 , ,p p1 2 fprobabilitiesofthevalues , ,x x1 2 f of the discrete random variable X

11.15 + hasthedistribution

11.16 ( , )n pBbinomialdistributionwithparametersn and p, where n is the number of trials and p is the probability of success in a trial

11.17 q q p1= - forbinomialdistribution

11.22 n populationmean

11.25 x sample mean

11.26 s2 sample variance

11.27 s samplestandarddeviation

11.28 H0 Null hypothesis

11.29 H1 Alternativehypothesis


5

12 Mechanics

12.1 kg kilograms

12.2 m metres

12.3 km kilometres

12.4 m/s, m s–1 metrespersecond(velocity)

12.5 m/s2, m s–2 metrespersecondpersecond(acceleration)

12.6 F Forceorresultantforce

12.7 N Newton

12.9 t time

12.10 s displacement

12.11 u initialvelocity

12.12 v velocityorfinalvelocity

12.13 a acceleration

12.14 g accelerationduetogravity

5d. Mathematicalformulaeandidentities

LearnersmustbeabletousethefollowingformulaeandidentitiesforASmathematics,withouttheseformulaeandidentitiesbeingprovided,eitherintheseformsorinequivalentforms.Theseformulaeandidentitiesmayonlybeprovidedwheretheyarethestartingpointforaprooforasaresulttobeproved.

PureMathematics

QuadraticEquations

ax bx c ab b ac

0 24

has roots22!

+ + =- -

LawsofIndices

a a ax y x y/ +

a a ax y x y' / -

( )a ax y xy/

LawsofLogarithms

logx a n xna+= = for a 0> and x 0>

( )

( )

log log log

log log log

log log

x y xy

x y yx

k x x

a a a

a a a

a ak

/

/

/

+

-J

L

KKKKN

P

OOOO

56© OCR 2017


5

CoordinateGeometry

A straight line graph, gradient m passing through ( , )x y1 1 hasequation( )y y m x x1 1- = -

Straight lines with gradients m1 and m2 are perpendicular when m m 11 2=-

Trigonometry

InthetriangleABC

Sinerule: sin sin sinAa

Bb

Cc

= =

Cosinerule: cosa b c bc A22 2 2= + -

Area sinab C21

=

cos sinA A 12 2 /+

Mensuration

Circumference and Area of circle, radius r and diameter d:C r d A r2 2r r r= = =

Pythagoras’Theorem:Inanyright-angledtrianglewherea, b and c are the lengths of the sides and c is the hypotenuse:

c a b2 2 2= +

Areaofatrapezium= ( )a b h21+ , where a and b are the lengths of the parallel sides and h is their

perpendicularseparation.

Volume of a prism =areaofcrosssection× length

CalculusandDifferentialEquations

Differentiation

Function Derivative

xn nxn – 1

ekx kekx ( ) ( )x xf g+ ( ) ( )x xf g+l l

Integration

Function Integral

xn , n x c n11 1n 1 !+

+ -+

( ) ( )x xf g+l l ( ) ( )x x cf g+ +

Area under a curve ( )y x y 0da

b$= y


5

Vectors

( )x y x yi j 2 2+ = +

Mechanics

ForcesandEquilibrium

Weight = gmass#

Newton’ssecondlawintheform:F ma =

Kinematics

Formotioninastraightlinewithvariableacceleration:

v tr a t

vtr

dd d

ddd 2

2= = =

r v t v a td d= = yy

Statistics

Themeanofasetofdata:x nx

f

fx= =|

||

58© OCR 2017


5

Learnerswillbegiventhefollowingformulaesheetineachquestionpaper:

FormulaeASLevelMathematicsB(H630)

Binomialseries

( ) ( )a b a a b a b a b b nC C C Nn n n n n n nr

n r r n1

12

2 2 –f f !+ = + + + + + +- - ,

where ! ( ) !!n

r r n rnCn r = =-

J

L

KKKKKKK

N

P

OOOOOOO

( ) !( )

!( ) ( )

( , )x nxn n

x rn n n r

x x n1 1 21 1 1

1 Rn r2 ff

f 1 !+ = + +-

+ +- - +

+

Differentiationfromfirstprinciples

( )( ) ( )

limx hx h x

ff f

h 0=

+ -

"l

Samplevariance

where ( )s n S S x x x nx

x nx11

xx xx i ii

i2 2 2

2

2 2=-

= - = - = -_ i| |||

Standarddeviation,s variance=

Thebinomialdistribution

If ( , )X n pB+ then ( )P X r p qCn rr n r–= = where q p1= -

Mean of X is np

Kinematics

Motioninastraightline

v u at= +

s ut at21 2= +

( )s u v t21

= +

v u as22 2= +

s vt at21 2= -


Summaryofupdates

Date Version Section Titleofsection Change

June2018 1.1 Frontcover Disclaimer AdditionofDisclaimer

60© OCR 2017


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Specification MATHEMATICS B (MEI) · 2 OCR 2017 . AS Level in Mathematics B (MEI) 1. 1a. Why choose...

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