Mathematics• OneofthemostoutstandingMathsdepartmentsinthecountry–

wewereawardedgrade1inthelastOfstedinspection

• Thereareapproximately600studentsacrosstheMathsfaculty

• Outstandingfacilitiesincluding8spaciousclassrooms,acomputersuiteandafullyresourcedstudentworkbase

• Approachableandexperiencedstaff

• Extensivesupportsystemsincludingdailytimetabledtutorials

• Opportunitiesfortrips,extensionawardsandcompetitions

• AhighproportionofstudentsprogressontoHigherEducation

25 Yearsof inspiringindividuals

1987-2012

25 Yearsof inspiringindividuals

1987-2012

AS/A2 MathematicsAS/A2 Further MathsAS/A2 StatisticsAS/A2 Use of Maths2013 Entry

Rebecca’s PerspectiveIenjoylifeatCarmelbecausethecollegehasanoverallgreatatmosphereandtheteachershavealotofdedicationtostudentshelpingtoachievethebestthattheycan.IlikestudyingMathsbecausethestaffareallveryapproachableandhelpandadviceisalwaysreadilyavailable.Theschemeofworkisverywellstructuredanditbringsnewchallengeseveryday.SofaratCarmelIhavebeenveryimpressedwiththeamountIhavelearnedandthesupportIhavehad.IamhopingtoleavecollegeandcarryontostudyPharmacyatdegreelevelandIhavenodoubtsthattheteachersatCarmelwillhelpmeachievethat.IwoulddefinitelyrecommendCarmeltoanybodywhoiswillingtoworkandwantstoachievethebestthattheycan.

Rebecca RocheStEdmundArrowsmith,Ashton

Studying: Mathematics,Chemistry,Biology,Economics

Meet the Tutors

Paul VaughanAssistantPrincipal

Ian MoranHeadofMaths

Paul MorrisonAssistantHeadofMaths

Exam Board AQA

AS/A2 Mathematics

Why choose Mathematics at Carmel?

HavingsuccessfullycompletedyourGCSEcourseyouarenowinapositiontotackleMathsatamoreadvancedlevel.ThisisahighlyregardedandenjoyableALevel.EvenstudentswhomaynothaveenjoyedGCSEMathsatschool,findALevelMathsamuchmorestimulatingandrewardingcourse.

HereatCarmelweareveryproudofourmathsstudents’outstandingrecordofachievementovermanyyears.Wecanguaranteethateverystudentwillreceivefirstclasstuitionusingavarietyofteachingstrategiesinamodernspaciousenvironment.ThiscoupledwithourexcellentsupportprogrammemakesCarmel,inouropinion,theonlyplacetostudyMaths.

What will I study?

TheMathscoursehasamodularstructurewiththreemodulesleadingtoanASLevelinthefirstyearandsixmodulestoanALevel.ThecoreofthesubjectisthePureMathsmodules(Core1,2,3and4).ThefirstmoduleextendscertaintopicsyouhavestudiedatGCSE(number,algebra,graphsandtrigonometry)andintroducesnewones(e.g.calculus)sothatyouhavethebasictoolsneededtostudymathsatamoreadvancedlevelinCore2,3and4.InadditionstudentswillstudysomeAppliedMathsmodules.

ThesemodulesareconcernedwithhowMathscansolvereal-lifeproblems.TheappliedchoicesareStatistics,MechanicsandDecision.

How is the course examined?

AtASLevel,youwilltakeCore1inJanuaryfollowedbyDecision1orMechanics1andCore2inJune.AtA2Level,youwilltakeCore3inJanuaryfollowedbyCore4andStatistics1inJune.Eachmoduleisofequalweightandisexaminedbyaoneandahalfhourpaper.Thereisnocoursework.

Where does this course lead?

Mathscanleadtoamyriadofcoursesinbothfurtherandhighereducation.Obviouscareersincludeaccountancy,banking,engineering,medicine,computingandscientificstatisticalresearch.

However,therearemanyotherdiverseareaswheremathematicalskillsarerecognisedasinvaluableandessential.

A Level Mathematics results

Total Total Pass Year A* A B C D E U Entries Passes Rate

2008 62 34 30 19 8 2 155 153 98%

2009 74 47 39 17 4 2 183 181 99%

2010 25 51 38 22 22 5 0 163 163 100%

2011 51 61 51 35 15 7 1 221 220 99.5%

2012 15 70 74 48 19 5 0 231 231 100%

Rachel’s PerspectiveMyenjoymentofMathshasdefinitelygrownsinceIhavecometoCarmel.OnereasonforthisisthatIhaveparticularlylovedtheMechanicsunitinASFurtherMaths,asitshowshowMathscanbeappliedtoreallifeproblems.Also,IhavefoundtheMathsdepartmenttobeverysupportive,especiallyintheleaduptoexams.ThishasbeenveryreassuringasIamhopingtogainentranceintoatopuniversitytostudyMedicine.Aswellasworkinghard,IamalsolookingforwardtotheMathstriptoChinainthesummer!

Rachel PenningtonStGregory’sCatholicHighSchool

Studying: Maths,FurtherMaths,Biology,Chemistry,CriticalThinking

Meet the Tutors

Peter Olsen

Nichola Mercer

Michael Griffiths

Matthew Pennington

Joshua Robinson

Laura Ashurst

Philip Kearsley

Katherine Jones

Exam Board AQA

AS/A2 Further Maths

What is Further Maths?

IfyougetagradeAatGCSEyoushouldseriouslyconsiderstudyingFurtherMaths.AsMathsissuchavastsubjectitisimpossibletocoveritallinoneALevel.HenceFurtherMathsdevelopssomeoftheconceptsmetinALevelMathsandbringsittoahigherplane.Itattractsstudentswhothoroughlyenjoythesubjectandarekeentoextendtheirunderstandingandknowledge.

Why study Further Maths?

ThiscourseischieflyforastudentwhowishestostudyMathematics,EngineeringoranyrelatedsubjectinHigherEducation.Manystudentswhostudythiscoursegoofftouniversityandfindtheworkcoveredisofgreatbenefit.Itisalsogoodforthosestudentswhoareconsideringapplyingforacompetitivedegreecourse,forexampleMedicine,VeterinaryScienceand/orisconsideringOxbridgeentry.FurtherMathsisaveryimpressiveALeveltohaveonyourCVandisnotasdifficultincontentasyoumightexpect.

What will I study?

TheFurtherMathscoursehasamodularstructurewiththreemodulesleadingtoanASLevelandsixmodulestoanALevel.TheFurtherPuremodulesextendtheworkcoveredinthecoreMathsmodules.Inadditiontothesemodules,studentswilltakeavarietyofappliedmodulesincludingDecisionMaths,MechanicsorStatistics.

ManystudentswhofollowthefullALevelcourseopttostudy7ratherthan6modulestoenhancetheirunderstandingofthesubjectandtogivethemselvesabetterchanceofatopgrade.Forthosewhostudyjustthe6modulesthereisanelementofchoiceinwhichmodulestotake.

How is the course examined?

AtASLevel,youwilltakeMechanics1andDecision2inJanuaryfollowedbyFurtherPure1inJune.

AtA2Level,youwilltakethree(orfour)modulesfromFurtherPure2,FurtherPure3,Statistics2andMechanics2.

A Level Further Maths results

Total Total Pass Year A* A B C D E U Entries Passes Rate

2008 15 13 4 2 0 0 34 34 100%

2009 13 10 3 3 0 0 29 29 100%

2010 9 12 2 4 1 1 0 29 29 100%

2011 11 16 7 1 3 0 0 38 38 100%

2012 3 12 7 15 2 0 0 39 39 100%

Daniel’s PerspectiveIlikethewayStatisticsbringsmathematicstolifeasyouareabletoseethereallifeimplicationsofthecalculationswedoinclass.Thehighlightofmytimeherehasbeentheoverallatmospherearoundcollegeandtheextraresponsibilityofbeingtreatedlikeanadult.IhavetakenpartintheCollegeSkitripandtheMathstriptoChina.Ihaveenjoyedmeetingnewpeopleandformyenrichmentoption,Ihaveplayedinthecollegefirstteamforfootballandmademanynewfriends.IfeelCarmelhaspreparedmefullyforthefutureandwhatitbringsandwhenIleave,IhopetodoaFinanceandAccountancydegree.

Daniel Borg-OliverStEdwardsCollege

Studying: Statistics,Maths,Economics,Computing

Exam Board AQA

AS/A2 Statistics

What is Statistics?

StatisticsisanapplicationofMathematicsbutisagrowingfieldofstudyinitsownright;moreandmoreareasofourlivesareinfluencedbyStatisticsandknowingjusthowtheyfitintootherstudiesmustbeanadvantage.

StatisticsisusedineverythingfromdecidinghowmuchorangejuiceTescowillbuynextyeartowhetherornotanewdrugwillindeedcureaseriousillness.Itissaidthatno-onecannowexpecttogetthroughtheirworkinglifewithoutsomecontactwithcomputers;thesameisrapidlybecomingtrueofStatistics.

What will I study?

AswithallotherASandALevelsthecourseisdividedintosixmodules.

Atfirstmuchoftheworkislearningthe‘toolsofthetrade’,butwesoonstarttoapplytheminanalysingdataandunderstandingwhatitistellingus.Wewillconsidertypesofdataandhowtohandleit,wewillbedoingprobabilityagain,butmoreimportantlywemovefromthe

GCSEMathsworktolookatthepatternsinStatisticsandhowtheseareusedintheanalysesofsituationsinordertomakereasonablejudgements.

How will I be assessed?

Eachmoduleisexaminedwithoutanycourseworkelement.Module1inJanuaryofLowerSixth,followedbymodules2and3inJune.ThepatternisthesamefortheUpperSixth–module4inJanuaryandfinallymodules5and6inJune.Duringtheyearyouwillcompletepracticesheetsandtherewillbetopictestsandamocktestattheendofeachmodule.

What will Statistics prepare me for?

StatisticsALevelisareputablesubjectandagoodgradeinthiswillhelpwithanyHigherEducationapplication.ItwillalsobeamajorbenefittoanyqualificationinvolvingPsychology,GeographyandBiology.StatisticsisnowusedsowidelythatmanyemployerswouldseesomequalificationinStatisticsasadistinctadvantage.ManystudentshaveenjoyedStatisticssomuchthattheygoontostudyitfurtheratuniversity.

UK Senior Maths Challenge

A Level Statistics results

Total Total Pass Year A* A B C D E U Entries Passes Rate

2008 1 3 4 2 2 0 12 12 100%

2009 2 2 6 2 0 0 12 12 100%

2010 0 1 2 3 1 0 0 7 7 100%

2011 1 6 7 12 4 1 0 31 31 100%

2012 1 0 6 6 4 1 1 19 18 95%

Danny’s PerspectiveCarmelhasafriendlyandenjoyableatmospherethatprovidesafreshchallengeaftermovingupfromhighschool.IreallyenjoytheUseofMathscourseasitallowsmetorelatethemathstoeverydayuses,whichissignificantlybeneficialtomeasitcanlinkintomyBusinessandProductDesignlessons.TheMathsdepartmentalsooffersanendofyeartriptoBarcelonawhichishighlyrecommendedasagreatwaytoendtheyear.AfterCarmelIplantogotouniversitytostudyBusinessandManagement.

Danny McNallyWadeDeacon

Studying: UseofMaths,ProductDesign,BusinessStudies

Exam Board AQA

AS/A2 Use of Mathematics

Why study this subject?

ThiscourseprovidesanopportunitytostudyMathematicsbeyondGCSEforthosewhoenjoyorneedMathematicsatASLevelbutwhodonotrequirethetraditionalALevelMathematicsqualificationtopursuetheirfuturecareer.ThecoursedevelopsunderstandingandresourcefulnessintheuseofmathematicsandcoversthemathematicsrequiredtosupportallSciencesubjects,Psychology,Geography,andothersubjectsatALevelandbeyond.

What will I study?

Thecourseconsistsofthreeunitswhichareeachworth1/3oftheASqualification:

Algebra:Youwillmodelrealdatawithappropriatefunctionsandinvestigatefunctionscommonlyusedtomodelpracticalsituationsusinggraphingandanalyticaltechniques.

Data Analysis: Youwilllearnaboutstatisticalmeasuresanddiagramsanddevelopanunderstandingofkeyideasaboutthedistributionofdata,theuseofimportantstatisticalmodels,andaboutcorrelationandregression.

Decision Mathematics:Thishasbecomepopularinrecentdecadesbecauseofitsapplicationstocomputerscience.Manyofthe

problemsinvolveOptimisation(findinganefficientsolution)andhencemethodsareapplicabletomanyrealworldsituations.

Teaching and learning styles

Youwillexperiencetraditionallessons,selfstudyunits,useofIT,tutorialsupport,andregularstructuredhomeworkassignments.Youwillinvestigatesituationsandusedatathatismeaningfultotherestofyourstudyprogram,workorinterests.YouwillusethegraphiccalculatorCASIOFX-9750GPLUSthroughoutthecourse.

Where can this subject lead?

StudentsintendingtofollowadegreepathinComputing,Economics,Engineering,MedicineorPhysicswillprobablyfindthetraditionalALevelMathematicsaconditionofentrytouniversitycourses,howeverallothercourseswillwelcomeALevelUseofMathematics.StudentsintendingtofollowapathinFinance,Business,theSciencesorSocialScienceswillfindthisqualificationofbenefitontheiruniversitycourse.Mathematicalskillsarehighlyprizedandaqualificationinsomeformofmathematicswillbevaluablewhenapplyingforuniversityentryandwillgiveyouaverysignificantadvantageinthejobmarket.

TheparticularlygiftedmathematicianatCarmelwillhavetheopportunitytostudyfortheAdvancedExtensionAward.ThisisanationallyrecognisedqualificationthatwillbenefitthosestudentswhowanttostudyMathsatthemostprestigiousuniversities.Studentswillalsoreceivetuitionfortheentryexams(STEPpapers)requiredforOxfordandCambridge.

Mathsstudentscanalsotakepartincompetitionsincluding:theUKSeniorMathsChallengeandtheNationalSeniorMathsTeamChallenge,bothofwhichareorganisedbytheUKMathsTrust.2011alsosawtwoteamsofA2MathsstudentstakingpartintheSixthFormPopMathsQuizorganisedbyTheLiverpoolMathsSocietyatJohnMooresUniversity.ThecompetitioninvolvedsolvingavarietyofmathematicalproblemsagainstteamsfromothercollegesacrossMerseyside.Bothteamsperformedverywellandachievedrunners-upprizesfortheireffortswhichwereworth£20ofWHSmithvouchers.

StudentshavetheopportunitytoparticipateinmanymathsenrichmentopportunitieshereatCarmel.Forexample,thisyearASFurtherMathsstudentswenttoLiverpooltoattendalectureintheMathsInspirationseries.GuestspeakersincludedthedesigneroftheLondonEyeand“TheBigOne”inBlackpool.Thegroupdiscoveredthemathematicalsecretsofrollercoasters,globalwarming…andTheSimpsons!

Inpreviousyears,studentshaveattendedlectureswheretheyheardandsawMathsappliedtoMusic,PsychologyandComputing.TheyhavealsovisitedtheUniversityofLiverpooltohearProfessorMarcusduSautoy,presenterofBBCseries‘TheStoryofMaths’,presentonthetopicFinding Moonshine: a Mathematician’s Journey through Symmetry.

Overthelastfewyears,theMathsdepartmenthasorganisedtwo4-daytripstoParisandBarcelonaplusa9daytriptoChinain2012.InBarcelona,thegroupvisitsincludedGaudi’sSagradaFamiliaandParcGuell,theGothicQuarter,CampNouandPortAventura.InChinatheitineraryincludedvisitstotheOlympicPark,TiananmenSquare,theGreatWall,TerracottaWarriors,HuaqingHotSpringParktonamebutafew!Allthevisitswereahugesuccessandenjoyedbystudentsandstaffalike!

Trips Abroad

Extension Awards and Competitions

Enrichment Opportunities

Magic square in door of Sagrada Familia

The Olympic Stadium (Birds Nest), Beijing

UK Senior Maths Challange Gold winner 2012

Gaudi’s Sagrada Familia

UK Senior Maths ChallangeSilver winners 2012

UK Senior Maths Challenge winners 2011

Students at The Great Wall of China

AveryhighpercentageofmathsstudentsprogressfromCarmelontohighereducation.Everyyear,progressionratesarewellover80%.Wearealsoproudofthefactthateachyearapproximatelyaquarterofthesestudentsgoontostudymathsoramathsrelatedsubjectatuniversity.YetmoreevidencethatstudentshavefoundtheirmathsstudiesenjoyableandstimulatingatCarmel!

Robert ReynoldsRainfordTechnologyCollegeUniversityofLiverpoolAccounting(2:1)

AfterleavingCarmelIwenttoLiverpoolUniversityandstudiedAccounting,andgraduatedwitha2:1in2007.InMayofthatyearIwaselectedtomylocalparishcouncilandoverthesummerIspentthreedaysworkingasanassistanttoaMemberoftheEuropeanParliamentinBrussels.InAugustIstartedworkingincorporatetaxforKPMGoneofthe“bigfour”accountingfirmsinLiverpool.Ireallyenjoymyworkandlikethechallengeofstudyingfortwocharteredaccountingqualifications.MyworkhasalreadytakenmetoLondonandEdinburghandIhopetopursuefurtheropportunitiestotravelinfuture.

IreallyenjoyedmytimeatCarmelandtherelaxedatmosphereandfocusonindependentstudyreallyhelpedpreparemeforlifeatuniversity.

Lisa HollandCowleyLanguageCollegeUniversityofDurhamMathematics(finalyear)

AfterleavingCarmelIwenttotheUniversityofDurhamtostudyMathematicswhereIamthoroughlyenjoyingthecourseandallaspectsofuniversitylife!IhavechosentostudyamoduleinBusinessStudiesalongsidemyMathsmodulesasthecourseisveryflexible,andhavejoinednumeroussocietiessincearrivinginDurham,suchasMusic,DanceandSingstar!Thetraditionalsideoftheuniversityisalsofantasticandthecollegiatesystemgivesanamazingsenseofcommunityandopportunitytomeetlotsofpeopleofallages.AfteruniversityIamconsideringarangeofcareersincludingAccountancyandManagement.

Carmelhasagreatatmospherewithfabulousteachingandtheopportunitytomeetlotsofnewpeople.I’drecommendittoanyoneforagreattwoyearsandperfectpreparationforuniversity!

Progression to Higher Education

Paul SwiftDe La Salle SchoolCambridge, Trinity CollegeNatural Sciences

Phyo KhaingSt Gregory’s Catholic High SchoolUniversity of BirminghamMedicine

Michael BriersPrescot SchoolUniversity of LiverpoolMathematics

Lauren ChisnallRainhill High SchoolImperial College LondonGeophysics

What is the Maths department like?

TheMathsdepartmentislocatedinitsownteachingblockwhichhousesasuiteof8modern,brightandspaciousclassrooms.Eachclassroomhasamulti-mediaprojectorandinteractivewhiteboardwhichislinkedtothecollegenetworkandinternet.Inaddition,theMathsblockalsohasacomputersuiteandafullyresourcedstudentworkbase.Dailytimetabledsupporttutorialstakeplaceinthisworkbase.

What support will I receive?

ThesupportsystemswithintheMathsdepartmentarealmostlegendary.Eachstudent’sneedsarecontinuallyassessedandmonitoredthroughouttheyear.Formaldailytutorialsaretheninplacetoaddressthespecificproblemsstudentsarehaving.

Studentsalsogetagreatdealofindividualsupportfromtheirtutorswhoregularlygiveuptheirfreetime.

Atexamstimethedepartmentalsorunsamuchvaluedcomprehensiveseriesofrevisiontutorialsto

supplementastudent’sownrevisionprogramme.

NoMathsstudentatCarmeliseverstrugglingforsupportatthiscriticaltimeintheacademicyear.

How successful are Carmel’s Maths students?

AtCarmelweareextremelyproudoftheoutstandingresultsMathematicsstudentshaveobtainedoveraperiodofmanyyearsandforasubstantialnumberthishasbeenagradeAorB.Forothershoweverapassgradeisarealachievementandwearejustasproudofthis.Weaimtobringouttheverybestinallourstudents,whatevertheirpotentialortheiracademicability.

What are the entry requirements for these courses?

AS Maths –GCSEgradeBinMaths

AS Further Maths–GCSEgradeAinMaths

AS Statistics–GCSEgradeBinMathsorgradeBinStatistics

AS Use of Maths–GCSEgradeCinMaths

More InformationCourseSpecificationsareavailablefromtheAQAExamBoardwebsite:

www.aqa.org.uk

Why are our Maths results so outstanding?• anexcellentcoursestructure• individualtargetssetforeachstudent,whicharemonitoredand

checkedonregularoccasionsthroughoutthecourse• rigoroushomeworkpolicy• highexpectationsofallofourstudents• regulartestingandmonitoringofprogress• intensivetutorialprogrammeinperiodsleadinguptoexternal

examinations• excellentrelationshipsbetweenstudentsandstaff• veryapproachableandexperiencedstaff• extensivesupportsystems

Frequently Asked Questions