GCSE Mathematics (Specification A) Mark Scheme …

1 Version Certificate of Secondary EducationMathematics 4306 specification APaper 1 HigherMark Scheme2009 examination - November seriesMark schemes are prepared by the Principal Examiner and considered, together with therelevant questions, by a panel of subject mark Scheme includes anyamendments made at the standardisation meeting attended by all examiners and is the schemewhich was used by them in this examination. The standardisation meeting ensures that themark Scheme covers the candidates responses to questions and that every examinerunderstands and applies it in the same correct way. As preparation for the standardisationmeeting each examiner analyses a number of candidates scripts: alternative answers notalready covered by the mark Scheme are discussed at the meeting and legislated for. If, afterthis meeting, examiners encounter unusual answers which have not been discussed at themeeting they are required to refer these to the Principal must be stressed that a mark Scheme is a working document, in many cases furtherdeveloped and expanded on the basis of candidates reactions to a particular about future mark schemes on the basis of one year s document should beavoided; whilst the guiding principles of assessment remain constant, details will change,depending on the content of a particular examination copies of this Mark Scheme are available to download from the AQA Website: 2009 AQA and its licensors.

2 All rights retains the copyright on all its publications. However, registered centres for AQA are permitted to copy materialfrom this booklet for their own internal use, with the following important exception: AQA cannot give permission tocentres to photocopy any material that is acknowledged to a third party even for internal use within the and published by the Assessment and Qualifications Assessment and Qualifications Alliance (AQA) is a company limited by guarantee registered in England and Wales (company number 3644723) and a registered charity (registered charity number 1073334).Registered address: AQA, Devas Street, Manchester M15 6 EXDr Michael Cresswell Director GeneralMathematics - AQA GCSE Mark Scheme 2009 November series3 Glossary for Mark SchemesGCSE examinations are marked in such a way as to award positive achievement wherever possible. Thus,for GCSE Mathematics papers, marks are awarded under various marks are awarded for a correct method which could lead to acorrect marks are awarded when following on from a correct is not necessary to always see the method.

3 This can be awarded independent of method mark dependent on a previous method mark being mark that can only be awarded if a previous independent mark hasbeen through marks. Marks awarded following a mistake in an case. Marks awarded within the Scheme for a commonmisinterpretation which has some mathematical equivalent. Accept answers that are , accept as well as21 Mathematics - AQA GCSE Mark Scheme 2009 November series4 QAnswersMarkComments1450 and 15 and 90B3B2 for any two of 450, 15 and 90B1 for any one of 450, 15 and 90orfor sight of3/4oeorfor3/2(or2/3) (T) or1/20(or 20) (M)or3/10(or10/3) (C)2-2(3 3 + 1) or betterM1eg. -2 (9 + 1) or -2 10 or (-2 9) + (-2 1)-20or -2 2 or -18 + -255M1dep-4A1SC2 for 43200 - 110 (boys)M1or110/200 100 or 110 2 or 55 Their 90/200 100 or their 90 2M1or 100 their 5545A14(a)Sight ofx+ 125 orx+ (x+ 125) (= 8x)A1oe4(b)375 = 5xor 375 = 8x 3xM175A1 Allow marks for solution done in (a) unless there is acontradiction in (b)5(a)4876179395in correct cellsB3B2 for 3 or 4 correctB1 for 1 or 2 correctLook for any answers clearly stated in the working5(b)For how long do you use thetreadmill?

4 B1oeMust be a time related questionnoteg. how many times used Boxes to cover all possibilitiesTheremustbe a reference tominutes or hours in either thequestion or the response sectionB1At least 3 boxes including 0 Must not overlap, no gaps6(a)Correct reflectionB2B1 for reflection inx= 1 orx-axis ory-axis6(b)Correct rotationB3B2 for 90 rotation clockwise about any point other thanOB2 for 90 rotationanticlockwise aboutOB1 for 90 rotationanticlockwise about any point otherthanOSC2 for theirBcorrectly rotated7 Graphical methodAlgebraic methodx 3 = 2M1correct graph ofy = x 3B1x= 5A1correct graph ofy= 2B1(5, 2)B1 ft if M1 earned(5, 2)B1SC1 forycoordinate of 2 seenMathematics - AQA GCSE Mark Scheme 2009 November series58 Sight of use of 8 for dotted lengthB1 Sight of use of 8 for dotted lengthAltTop triangle area=1/2 their 8 6 (= 24)M1 AltArea LH trap =1/2(10 + 4) their 8 (= 56)Lower rectangle area = 11 4(= 44)

5 M1 Area RH rectangle = 4 3 (= 12)AltArea surrounding rectangle= 11 10 (= 110)M1 Sight of use of 8 for dotted lengthB1 Area missing trapezium=1/2(11 + 3) 6 (= 42)M1 Alt Area LH scalene =1/2 10 their 8 (= 40)M1 Their 110 their 42M1 Area RH trap =1/2(11 + 3) 4 (= 28)M168A1cm2B19 Anytwoof 400 or 3 or 400 6 or 800 1194or 398 6 or 796 2388ft for A1 for correct divisionby if first M1 earned10(a)(i)48/200B1oe10(a)(ii) correct theoretical values forthe colours red = 100 green = 50blue = 25 yellow =25orCorrectly comparing all of therelative frequencies with thetheoretical probabilitiesorCorrectly comparing the ratios ofall the colours, both experimentaland theoreticalE2E1 of the correct theoretical values for the coloursorOne correct relative frequency/theoretical probabilitycomparisonorCorrectly comparing the ratios of two colours, bothexperimental and theoretical10(b)Not enough trialsE1oe11(a)2x + x +90 = 180M1oe30A111(b)AngleCAD= (their)30M1 Look for angles marked on the diagram[180 (their)30] 2M175A1 Mathematics - AQA GCSE Mark Scheme 2009 November series612(a)n2+n+n+ 1 orn2 n n+ 1M13 out of 4 terms correct for either expansionn2+ 2n+ 1 +n2- 2n+ 1A1 Convincing algebra to get 2n2+ 2A1 Answer given, must show cancelling of terms clearly12(b)2n2+ 2 = 2(n2+ 1)

6 2 anything must be evenor2 n2is even, 2 is even,even + even = evenE2 Alternatively .. E2+ E2= E E + E E = E + E = or ..O2+ O2= O O + O O = O + O = EE1 for partial explanation1315/8( )12/5M1 Allow one error in numerators180/40or3/2 3/1A1ftoeft their improper fractions if M1 earned41/2or9 of long multiplicationM1 Allow one error1875 (000)A114 LengthNone of theseVolumeB3B1 for each15(a)5m - pB115(b)52pB1oeeg. 52 p5p + p166x- 4y= 183x- 2y= 9x+ 4y= 103x+ 12y= 30M1 Allow error inoneterm7x= 2814y =21M1 Correct elimination from their equationsx= 4andy =11/2A1SC1 correct answers with no working or using T&Ialternatively3(10 4y) 2y= 9M1oeRearrangeandsubstitute .. allow one error14y =21M1 Correct simplification from their equationx= 4andy =11/2A117D: 2x+ 5y= 10B: 5x+ 2y= 10A: 5y+ 10 = 2xC: 2y+ 10= 5xB3B2 if two correct or three correctB1 if 1 correctMathematics - AQA GCSE Mark Scheme 2009 November series718(a)Twoorthree correct pairs ofanglesAngleBAC =AngleDECA ngleABC =AngleEDCA ngleACB= AngleECDB2B1 for one correct pair of anglesLook for angles marked on the diagramTwoorthree correct reasons alternate forBACandDEC alternate forABCandEDC (vertically) opposite forACBandECDB118(b)DC/20=6/8orDC/6=20/8M 1 Identifying scale factor of (20/8) or (2/5) oe6 208M1dep6 or 6 or 6 their (20/8)or 6 their (2/5)oe15A119BD/18=8/BDM1 Accept cosx= ?

7 Andtany= 8for M118?BD2= 18 8 (= 144)M1dep12A120y(x 2) =w + xM1yx 2y=w + xM1depxy x = w +2yorx(y 1) =w +2yM1dep-2y w = x xyor-2y w = x(1 y).. for rearranging/factorisingx=w +2yy 1A1x =-2y wmust havex= .. (A0 if not)1 y21(a)Attempt at ( ) 11M1 Sight of63/99scores ( )A14 minimum21(b)x= x= (=13/33)A1SC1 for =39/99(=13/33)alternatively21(b)13/33=7/ 11 13/(7 3)M1(13/33=) 13/21= 13M1(13/33=) - AQA GCSE Mark Scheme 2009 November series822(a)2ndbar drawn at height of = 100B122(b)Answer in region 110 <T< 120M120/50of 20 or sight of 8or30/50of 20 or sight of 12or 100 small squares = 20 vehiclesM1oefor example, if drawn on 1cm2grid,4 cm2= 20 vehicles or 1cm2= 5 vehicles112A123 Sight of a correct product7/10 6/9or7/10 3/9or3/10 7/9or3/10 2/9M17/10 3/9+3/10 7/9+3/10 2/9M11 -7/10 6/948/90or24/45or16/30or8/15A1oe24y 1/xory=k/xor 9 =k/8M1k= 72 ory= 72/xA1z yorz=c yor 20 =c 16M1c= 5 orz= 5 yA1(whenx= 2)y= 36M1depft their value dependent on 1stM1(wheny= 36)z= 30A1ftfttheir value ofcand(their)y= 36if first two M1 marks earnedSC1 forx 1/z2oe25(s=) 20B1(area ABC=)

8 (20 2 8 10)M1 Allow their 20 if froms = a + b + c2 3200A1oe1/2 10 h= their 3200or40 2 seenM1depDependent on 1stM1ands> 18h = their 3200 or 40 255M1depDependent on 2ndM1(h =) 8 2A1alternativelycosC= (10 +12 -18 ) / (2 10 12)M1 Correct expression for cosine of obtuse angleCcosC= -1/3A1CD= 4A1 Dis (their) foot of perpendicular (h =) 12 - 4 M1(h=) 128M1dep(h=) 8 2A1