GCSEMaths

GRADEBOOSTERHIGHERRevisionWorkbook

ANSWERS

2

1.1Multiples,Factors,LCM,HCFandPrimeFactorsA)KeyWordsCrosswordAcross:2)Highest;3)Lowest;4)Overlap;7)UnionDown:1)Factors;5)Venn;6)PrimeB)Questions1)2,7,19,37,61,892.a)Factorsof15=1,3,5,15 Multiplesof15=15,30,45,60,75 Factorsof18=1,2,3,6,9,18 Multiplesof18=18,36,54,72,902.b)LCM=90HCF=33.) 180 2 2 45 3 3 5

2"×3&×5C)UsingSetDiagramstofindtheLCMandHCF1)𝑎 = 2,𝑏 = 2,𝑐 = 12)LCM=630,HCF=21D)EXAMQUESTIONS1.)a)84b)62.)1.00PM

3

1.2CalculationswithFractionsA)MethodsInstructions

Findthelowestcommondenominator

Multiplythenumerators Keepthefirstfractionthesame

Findtheequivalentfractions Multiplythedenominators Flipthesecondfraction

Calculate(donotaddorsubtractthedenominators)

Simplify Changetheproblemtoamultiplication,thencalculate

Simplify Simplify

B)MixedNumbers&ImproperFractionsCorrectanswers(circled): 8

3=2 2

3 12

5=2 2

5

Corrections: 2 35= 13

5 3 2

5= 17

5 2 3

4= 11

4 29

6=4 5

6

C)Multiplying&DividingFractions23&2 33

3&1 2

49 &2

"&

D)Adding&SubtractingFractionsa)1 5

4 b) 3

&6 c)3 37

&6

EXAMQUESTION334

4

1.3RecurringDecimalsA)TerminatingandRecurringDecimals

R 0. 12 T 0.2T 0.375 R 0. 45R 0. 87 R 0. 285714

B)ChangingRecurringDecimalsintoFractionsa)&

" b)&5

"" c)&7

65 d):3"

7;;

C)EXAMQUESTION"63:5

5

1.4Power,RootsandIndicesA)Calculationsa)3",27 b)7<&, 3

67 c)15&,225 d)0.5<&,4 e)3<&,3

7

B)NegativeIndicesa)3

2 b) 3

3: c) 3

&5 d) 3

&2 e) 3

:6

C)FractionalIndicesa)8 b)5 c)3

" d)16 e)8

D)NegativeandFractionalIndicesa)3

6 b)3

4 c)2

& d)32 e):6

&2

EXAMQUESTIONa)4b)3

7

c)6

7

6

1.5StandardFormA)OrdinaryNumbersintoStandardFormandViceVersa1.a)1.4×10<&b)7.6×10"c)1.23×10<6d)1.5×1052.a)0.0065b)2415c)0.0000654d)0.000212B)CalculatingwithStandardForma)2.823×10"b)5.706×106c)3.84×10<"d)3.2×10<"e)3×10&f)2×10:C)EXAMQUESTIONS1.)1.2915×10332.)6.6×10&

7

1.6SurdsA)SimplifyingSurdsa)4 3b)5 5c)5 2d)6 2B)ManipulatingSurds𝑎x𝑏

𝑎𝑏

donothing!𝑎& + 2𝑎 𝑏 + 𝑏𝑎& − 𝑏@A×

AA

@

A± B×A∓ BA∓ B

Questionsa)4b) 5c)2 2 − 2d)4 3 + 7EXAMQUESTIONS1.)8 + 2 6

2.)a)5 &&

b):D& &

2

8

2.1SubstitutionintoFormulaeA)SubstitutionintoCircleFormulaeAreaofcircle=𝜋𝑟&Circumferenceofcircle=𝜋𝑑Lengthofarc= H

":;𝜋𝑑

Areaofsector= H

":;𝜋𝑟&

Areaofacircle,𝑟 = 7 47.0𝑐𝑚PerimeterofaSemi-Circle,𝑑 = 10 25.7𝑐𝑚AreaofaSector,𝑟 = 14, 𝜃 = 60° 153.9𝑐𝑚&PerimeterofaSector,𝑟 = 11, 𝜃 = 130° 102.6𝑐𝑚&

B)EquationsofMotiona)𝑣 = −17b)𝑠 = 260c)𝑢 = ±12.5(1𝑑𝑝)C)EXAMQUESTION£28,500

9

2.2AlgebraicIndicesA)LawsofIndices

𝑏"×𝑏<6 ≠ 𝑏3 𝑎" ÷ 𝑎<5 ≠ 𝑎<&

4& ≠ 4 𝑎; ≠ 0B)SimpleEquations

𝑥6 = 16 43W=27 32WD3 = 32 12&W = 1024 2𝑥6 = 𝑥5 5

EXAMQUESTION16𝑏7

3𝑎&

C)HarderEquationsa)𝑥 = −5b)𝑥 = 2EXAMQUESTION𝑥 =3

10

2.3StraightLineGraphsA)PlottingStraightLineGraphs𝑦 = 3𝑥 − 4

-10 -7 -4 2

𝑦 =12𝑥 + 2

3 2.5 2 1.5 Correctlydrawngraphs.B)FindingtheEquationofaStraightLineGradientline1:𝑚 = 1.5Gradientline2:𝑚 = −2EquationLine1:𝑦 = 1.5𝑥– 2EquationLine2:𝑦 = −2𝑥 + 3C)ParallelandPerpendicularLinesNeitherPerpendicularParallelPerpendicular

EXAMQUESTIONa)𝑦 = 2𝑥 − 11b)𝑦 = − 3

&𝑥 − 3.5

11

2.4SimultaneousEquations–1A)BasicSimultaneousEquations

𝑥 + 𝑦 = 52𝑥 + 𝑦 = 9

3𝑦 = 15

𝑥 = 4, 𝑦 = 1

2𝑥 + 2𝑦 = 14𝑥 − 2𝑦 = −8 𝑥 = 4 𝑥 = 4, 𝑦 = −1

3𝑥 + 2𝑦 = 103𝑥 − 5𝑦 = 17 7𝑦 = −7 𝑥 = 2, 𝑦 = 5

B)SolvingSimultaneousEquationsGraphicallyCorrectlydrawngraph.𝑥 = −1,𝑦 = 3C)SolvingHarderSimultaneousEquationsa)𝑥 = 3, 𝑦 = 4b)𝑥 = −1, 𝑦 = 3EXAMQUESTION£2.30

12

2.5FactorisingandSolvingQuadraticEquationsA)FactorisingQuadraticExpressions

𝑥& + 8𝑥 + 16 −9, +20 𝑥 + 4 (𝑥 − 4)𝑥& − 16 −1, −12 (𝑥 − 4)(𝑥 + 3)

𝑥& − 9𝑥 + 20 0, −16 𝑥 + 4 &𝑥& − 𝑥 − 12 +8, +16 (𝑥 − 4)(𝑥 − 5)

B)SolvingQuadraticEquationsa)𝑥 = 7and-7b)𝑥 = 8and4c)𝑥 = −3and8C)SolvingHarderQuadraticEquations2𝑥& − 3𝑥 − 20 = 0 SD3𝑥& + 14𝑥 + 8 = 4𝑥 IA4𝑥& − 4𝑥 = 15 URRADIUSEXAMQUESTIONa)Correctlyshown.b)64cm3

13

2.6TheQuadraticFormulaA)SubstitutionintotheQuadraticFormulaa)𝑥 = −1.27and6.27b)𝑥 = 3.12and−1.12B)TheDiscriminantandRootsa)Onerepeatedrootb)Norealrootsc)TwodistinctrootsC)CommonErrors

𝑥 = <5± (<5)Z<6×3×6&×3

𝑥 = <"± <"Z<6×"×5&×"

First−5shouldbe5,−(−5) = 5 Equationneedsputtingequaltozerobeforeusingquadraticformulatosolve:

𝑥& − 3𝑥 − 5 = 0First−3shouldbe3,−(−3) = 3−3&shouldbe(−3)&5shouldbe−5

EXAMQUESTION𝑥 = 0.17and−2.37

14

2.7CompletingTheSquareA)WritingExpressionsinCompletedSquareForm

𝑥& + 6𝑥 − 4 (𝑥 − 9)& − 74𝑥& − 6𝑥 + 12 (𝑥 − 3)& + 3𝑥& + 9𝑥 + 4 (𝑥 + 3)& − 13𝑥& − 18𝑥 + 7 𝑥 + 4.5 & − 16.25

B)FindingtheMinimumPointandSketchinga)(𝑥– 1)& − 3 = 0b)𝑥 = 1 ± 3c)(1,-3)d)-2e)Correctsketch.EXAMQUESTION𝑎 = 8𝑏 = −28

15

2.8RearrangingFormulaeA)Multi-StepFormulae

𝑦 = 2𝑥 − 4 𝑥 =𝑦 − 42

𝑦 = 2𝑥 + 4 𝑥 =𝑦& − 42

𝑦 = 2𝑥 + 4

𝑥 =𝑦 + 42

𝑦 = 2𝑥& + 4 𝑥 =𝑦 − 42

𝑦 = (2𝑥 + 4)& 𝑥 =(𝑦 − 4)&

2

B)WordedProblemsInvolvingEquationsofMotiona)2m/sb)112.5mC)RearrangingFormulaewheretheSubjectAppearsTwice

Trash,shouldbe𝑎 = − 3𝑏5 Trash,shouldbe𝑎 = 3𝑏−9

6−𝑏

Trash,shouldbe𝑎 = 4−3𝑏𝑏−1 Tick

EXAMQUESTION

𝑏 =2𝑎 − 4𝑎 + 3

16

2.9Non-LinearGraphsA)PlottingQuadraticGraphs

3 −5 3Correctlyplottedcurve.𝑥 = −1.6and1.6B)SolvingQuadraticEquationsusingQuadraticGraphsSuitablelinesdrawn.a)𝑥 = −2.3and1.3b)𝑥 = −2.2and2.2c)𝑥 = −3.6and1.6C)RecognisingGraphs

𝑦 = 𝑥& + 6𝑥 + 10 B

𝑦 = −𝑥& − 4𝑥 − 3 A

𝑦 =2𝑥 D

𝑦 = 𝑥" + 6𝑥& + 8𝑥 C

EXAMQUESTION𝑝 = −8𝑞 = 22

17

2.10SimultaneousEquations–2A)AlgebraicMethodsa)𝑥 = −1,𝑦 = 3𝑥 = 2,𝑦 = 6b)𝑥 = 0,𝑦 = 5𝑥 = −4,𝑦 = −3B)GraphicalMethods𝑥 = 2,𝑦 = 5𝑥 = −2,𝑦 = 1C)SolvingSimultaneousEquations𝑥 = −2.2,𝑦 = 3.3𝑥 = 3.2,𝑦 = −2.4EXAMQUESTION𝑥 = 2,𝑦 = 12𝑥 = − &

",𝑦 = 4

18

2.11TheEquationofaCircleA)EquationofaCircleCorrectlydrawncirclewithcentre(0,0)andradius4B)TangentstoaCircle

43 −

34 𝑦 = −

34𝑥 + 6.25

−34

43 𝑦 =

43𝑥 +

73

−43

34 𝑦 =

34𝑥 − 6.25

EXAMQUESTION5𝑥 + 2𝑦 = 29

19

2.12AlgebraicFractionsA)SimplifyingAlgebraicFractions

3𝑥 − 4

+2

𝑥 + 2

12(𝑥 − 4)(𝑥 + 2)

2𝑥 − 4

−3

𝑥 + 2

12(4 − 𝑥)(𝑥 + 2)

−3𝑥 − 4

×4

𝑥 + 2

−𝑥 + 16(𝑥 − 4)(𝑥 + 2)

6𝑥 − 4

÷𝑥 + 22

5𝑥 − 2

(𝑥 − 4)(𝑥 + 2)

B)SolvingEquationswithNumericalDenominators

15(2𝑥 + 4)3

−15 3𝑥 − 1

5= 2

5(2𝑥 + 4) − 3(3𝑥 − 1) = 2 10𝑥 + 20 − 9𝑥 − 3 = 2𝑥 + 17 = 2𝑥 = −15

Correctsolution𝑥 = 7C)SolvingEquationswithAlgebraicDenominators1.)(i)Correctlyshown.(ii)𝑥 = −3and22.)(i)Correctlyshown.(ii)𝑥 = 1.93and−2.76(2dp)EXAMQUESTIONCorrectlyshown.

Followthrough

Followthrough

20

2.13TransformingGraphsA)BasicTransformations1.) 6 1 -3 -2 Correctlydrawncurve2.)Correctlydrawncurve (0,−5)3.)Correctlydrawncurve(−1,−3)B)TransformingGraphsintheForm𝒚 = 𝒇(𝒙)1.)a)(4,3) b)(2,6)2.)Correctlydrawncurve. a)Correctlydrawncurve(reflectionof𝑦 = 𝑓(𝑥)inthex-axis). b)Correctlydrawncurve(reflectionof𝑦 = 𝑓(𝑥)inthey-axis).C)RecognisingTransformations

1.)a) 04

b)𝑦 = 𝑥& + 2𝑥 + 12.)a)𝑦 = 0 b)𝑦 = −𝑥& − 2𝑥 + 3EXAMQUESTIONa)𝑦 = (𝑥 − 4)& + 2b)𝑦 = −𝑥& + 8𝑥 − 16or𝑦 = −(𝑥 − 4)&

21

3.1Percentages–1B)ApplyingPercentageChangeBen&Jerry’s£4.40PotNoodle£1.04BeefMince£2.97ChickenThighs£2.24Marmite£2.64ShowerGel£1.14C)CalculatingPercentageChange

33. 3%increase

25%decrease

45. 45%decrease

83. 3%increase

20%decrease

25%increase

9. 09%decrease

10%increase

D)FindingProfitandLoss

20.0%profit 48.5%profit 28.7%lossEXAMQUESTION1.)£2002.)£12.51

22

3.2Percentages–2A)CompoundInterestMultiplierMatch-Up

Increaseby6% 1.94Decreaseby6% 1.06Increaseby94% 0.94Decreaseby94% 0.06

Question(a)i.£77416.04ii.£155776.28iii.£66921.60(b)7yearsB)Growth&Decay(a)i.𝐶3 = 202.5ii.𝐶6 = 107.6(b)𝑘 = 7minutesEXAMQUESTIONAccountA£1966.91AccountB£1941.86AccountAgivesbestreturn

23

3.3Speed,DensityandPressureB)Speed,DistanceandTime:ThePlanets

27,462 687 34,720

4,497 EXAMQUESTION1.) Lowerboundcalculation Upperboundcalculation 147.5

67.5= 2.185 = 2hours11mins

7:50am+2hours11mins=10:01am

152.562.5

= 2.44 = 2hours26mins7:50am+2hours26mins=10:16am

Lukewilldefinitelybelate,hisearliestpossiblearrivaltimeis10:01am.Hislatestpossiblearrivaltimeis10:16am.C)Density,MassandVolume

3.6kg/cm" 1.4kg 0.70cm" 300cm"

360m" 32g 710kg 0.83g/cm" 850kg/m" 1100kg

EXAMQUESTION2.)CuboidDensity1.2g/cm"Volume480cm3

Mass576gCylinderMass920gVolume502.7cm3(1dp)Density1.8g/cm"(1dp)Johniscorrect.Massofcylinder(920g)isgreaterthanmassofcuboid(576g).Beckiisincorrect.Densityofcuboid(1.2g/cm")islessthandensityofcylinder(1.8g/cm").D)Pressure,MassandAreaa)3.3𝑁b)141𝑁/𝑚&EXAMQUESTION3.)1200N/m&

24

3.4DirectandInverseProportionA)DirectorInversea)Inverse d)Inverseb)Direct e)Directc)Inverse f)Direct

B)ProportionalityStatements

𝑟 ∝ 𝑦& 𝑟 = 𝑘𝑦&

𝑟 ∝ 𝑦 𝑟 = 𝑘 𝑦

𝑟 ∝1𝑦"

𝑟 =𝑘𝑦"

𝑟 ∝1𝑦&

𝑟 =𝑘𝑦&

C)GraphsADirectBDirectCInverseD)OrderingActivity

PandQaredirectlyproportional.IfP=30whenQ=6,findPwhenQ=8

P ∝ Q

P = 𝑘Q

30 = 𝑘x6

𝑘 = 5

P = 5Q

P = 5x8

P = 40

25

yisinverselyproportionaltox.y=6whenx=1.5,findxwheny=2

𝑦 ∝ 1𝑥

𝑦 = 𝑘𝑥

6 = 𝑘1.5

𝑘 = 9

𝑦 = 9𝑥

2 = 9𝑥

𝑥 = 4.5

PracticeQuestions1.)a)𝑟 = 63b)𝑠 = 102.)a)𝑦 = 0.16b)𝑥 = 0.89(2dp)EXAMQUESTION6minutes

26

3.5RealLifeGraphsA)Distance-TimeGraphsa)Correctlysketched.b)9kmB)Velocity-TimeGraphsa)Correctlydrawn.b)138mc)0.25m/s&EXAMQUESTION1.)No,shetravelled300mC)RatesofChange1. 6cm/sAreasunderCurvesa)19.5b)Underestimate.Mostofareacalculatedliesunderthecurve.EXAMQUESTION2.)a)Steepestgradientbetween55and60seconds. b)0.104m3/spersecond±0.004

27

4.1CongruenceandSimilarityA)CongruentTriangles ASA SSS RHS SAS AASaandiASAbandjSSScandhASAdandfSASeandgRHSB)SimilarTriangles a)i)LSF=2.5or0.4 ii)𝑥 = 20cm 𝑦 = 7.2cmb)i)LSF=0.75or6

" ii)𝑥 = 12m 𝑦 = 6.75m

c)i)LSF=1.4or52 ii)𝑥 = 17.64cm𝑦 = 10cm

C)ReasoningandProofSTEP1:Anglesinatrianglesumto180°STEP2:70o+30o=100oSTEP3:AngleCDF=180o–100o=80oSTEP4:AngleEDF=80o–50o=30oSTEP5:ΔDEFisisoscelesSTEP6:DE=EF=8cm

STEP7:LSF = 108 = 1.25

STEP8:𝑥 = 7.37×1.25 = 9.21cm(2dp)STEP9:𝑦 = 8.15 ÷ 1.25 = 6.52cmEXAMQUESTIONa)AngleBDA=XDC=90oasDAisaperpendicularbisector. AngleDCX=30oasCXisananglebisectorandanglesinanequilateraltriangleareeach60o,anglesinatriangle sumto180ohenceangleCXD=180o–90o–30o=60o AngleABD=60o(equilateraltriangle)henceangleDAB=180o–90o–60o=30o(anglesinatriangle) So,angleDCX=angleDAB=30o,angleCXD=angleABD=60o,andangleBDA=angleXDC=90o,hencebytheAAArule,thetwotrianglesaresimilar.b)ADandCDarecorrespondingsidesDC=1cm(Dismid-pointofBCandBC=AB=2cm,isoscelestriangle)AD= 3,hencetheLSF= 3 ÷ 1 = 3BDandXDarecorrespondingsides.BD=DC=1cm.henceXD= 3

"

28

4.2Length,AreaandVolumeScaleFactorsA)AreaandVolumeUnitConversions1.) 1m2 1m2 1,000,000m2 100mm2 1cm2 10,000cm2 1,000,000mm2 1km2

2.) 1m3 1m3 109mm3 109m3 1km3 1cm3 1,000mm3 1,000,000cm3

B)LSF,ASFandVSFa)i)0.33m2 ii)3300cm2b)128cm3EXAMQUESTIONS1.)a)12cm b)150πcm32.)2500g

29

4.3CircleTheoremsA)RecallingandNamingTheorems

1.)Theangleatthecentreofacircleistwicetheangleatthecircumference2.)Anglesinthesamesegmentareequal3.)Theangleinasemi-circleis90degrees4.)Oppositeanglesinacyclicquadrilateraladdupto180degrees5.)Theperpendicularbisectorofachordpassesthroughthecentreofthecircle6.)Atangentandradiusmeetat90degrees7.)Tangentsfromthesamepointarethesamelength8.)ThealternatesegmenttheoremB)SeeingtheWoodfortheTrees1.) • Anglesinthesamesegmentareequal

2.) • Theangleinasemi-circleis90degrees

• Oppositeanglesinacyclicquadrilateraladdupto180degrees

• Theangleatthecentreofacircleistwicetheangleatthecircumference

3.) • Theangleatthecentreofacircleistwice

theangleatthecircumference• Atangentandradiusmeetat90degrees• Tangentsfromthesamepointarethe

samelength

4.) • Anglesinthesamesegmentareequal• Theangleatthecentreofacircleistwice

theangleatthecircumference

5.) • Tangentsfromthesamepointarethesamelength

• Thealternatesegmenttheorem

6.) • Theperpendicularbisectorofachordpassesthroughthecentreofthecircle

EXAMQUESTIONS1.)a)i)40oii)Theangleatthecentreofacircleistwicetheangleatthecircumference b)i)10oii)Oppositeanglesinacyclicquadrilateraladdupto180o,baseanglesinanisoscelestriangleareequal2.)a)35o b)WXY=110oduetothealternatesegmenttheorem.TriangleWXYisisosceles,baseanglesareequalandthetotalanglesumis180o.

30

4.4Pythagoras’TheoremandTrigonometryA)Pythagoras’Theorem1) 10cm

2) No( 85 ≠ 81)

3) a)5.7cm b)4 2

4) 24.1m(1dp)B)Trigonometry1) 36.3o2) 6.8m3) 11.4m4) a)33.6o b)17mC)CommonTrigonometricValues

0o 30o 45o 60o 90o

sinx 012

12 3

2 1

cosx 1 32

12

12 0

tanx 013 1 3 ∞

EXAMQUESTIONS1) 8.5m2) a)6.1km b)059o

31

4.5TheSine&CosineRulesandUsingArea=𝟏𝟐absinC

A)TheSineRulea) 4.2cmb) 39.3oB)TheCosineRulea)13.6mb)78.5oC)Area=𝟏

𝟐absinC

a) 143.3m2b) 30oEXAMQUESTIONa)8.51cmb)12.4cm

32

4.6VectorsA)ParallelVectorsa)|| b)|| c)||d)|| e)|| f)||B)FindingVectorsa) a+2b b)a+2b c)2b–a d)b–3ae) b–2a f)2a+4b g)a+2b h)0C)QuestionXY = a + bBC = 3(a + b)Thevectorsareparallel,BC = 3XYEXAMQUESTIONa) i)OP = 3

&𝐚 ii)QX = 3

"𝐚 − 3

:𝐛

b) QA = 𝐚 − 3&𝐛

QX = 3"QA

QXandQAareparallel.Qiscommonpoint.Therefore,Q,XandAlieonthesameline.

33

5.1SetsandVennDiagramsA)Notation1.)23572.)135793.)24.)357B)ShadingRegionsonVennDiagramsCorrectlyshadedregions.EXAMQUESTIONa)211102b)(i)33

&5

(ii)333"> 33

&3(1)apupilwholikesmarmitealsolikingmarmalade 33

3"ismorelikelythan(2)apupilwholikes

marmaladealsolikingmarmite 33&3

34

5.2TreeDiagramsandFrequencyTreesA)TreeDiagramsa)Correctlycompletedtreediagramswithbranchesasfollows:

0.7

0.3 0.7 0.3

b)0.49c)0.91EXAMQUESTION1.a)Correctlycompletedtreediagramswithbranchesasfollows:

3"

&2 &

"

52 3

"

&"

b)(i) &&3

(ii)37&3

B)FrequencyTreesa) 2 12 10 1 73 72

b)3:

c) &3&÷ 3

2"≈ 12

EXAMQUESTION2.a)

12 60 48

100 3 40 37

b)7.5%

35

5.3ConditionalProbabilityA)WithTreeDiagramsa) "

4

67

54

6

4

57

64

b)(i)6

7

(ii)3&

(iii)3"34

B)WithoutTreeDiagrams1. 6

"5

2. 6

35

EXAMQUESTIONa)Correctlydrawntreediagramwithbranchesasfollows:Gettinguplate Arriveatwork

late 7

3;

3"

33;

3

5

&"

65

b)(i) 3

3;

(ii)32";

36

6.1StratifiedSamplingA)SamplingQuestiona)Notafair/representativesample.b)Short8Medium17Long5EXAMQUESTION15

37

6.2FrequencyTables–AveragesandRangeA)FrequencyTables

64 45 60 11

20 1801.)202.)83.)94.)95.)3B)GroupedFrequencyTables

37.5 300 55 330 75 300

30 10801.)a)36b)Mid-pointsusedasestimate2.)a)0 ≤ 𝑡 < 25b)25 ≤ 𝑡 < 50EXAMQUESTIONa)£207.0(1dp)b)Josephisincorrect.20outof28coatscostmorethan£100,whichis71%

38

6.3CumulativeFrequencyGraphsandBoxPlotsA)CumulativeFrequencyGraphsa)112148178194200

Correctlydrawncumulativefrequencycurve.b)(i)37years±1(ii)25years±2B)BoxPlotsBoxplotdrawncorrectlyatthefollowingpoints:

Min LQ Median UQ Max10 14 16 20 29

EXAMQUESTIONS1.a)36%b)Yes,90%wereatleast20grams2.a) GirlsCumulative

FrequencyBoysCumulative

Frequency 4 8 12 20 32 52 52 56 60 60

Bothcumulativefrequencycurvesdrawncorrectly.b)Onaverage,boysdidbetterasindicatedbytheirlowermediantimeof44seconds(comparedtogirls50seconds).Boyswerealsomoreconsistentatestimatingtherighttime,asindicatedbytheirlowerinterquartilerangeof10comparedtogirls14.

LQ Median UQ IQR Girls 42 50 56 14 Boys 38 44 48 10

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6.4UsingBoxPlotsDifferentaveragesandmeasuresofspread:Mean,mode,median,range,interquartilerangeA)ComparingBoxPlotsa)Onaverage,boysscoredbetterthangirlsasindicatedbytheirhighermedianof10outof20comparedtogirls8outof20.b)GirlsIQR=10BoysIQR=7Girlswerelessconsistentasindicatedbytheirinterquartilerangeof10comparedwithboys7.EXAMQUESTIONTheticketsweremoreexpensiveinMayasindicatedbythemedianof£26comparedwith£21inMay.TherewasagreaterspreadofpricesinAprilasindicatedbytheinterquartilerangeof£14comparedwith£12inMay.

Min LQ Median UQ MaxApril 3 15 21 29 50May 7 18 26 30 42

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6.5HistogramsA)FrequencyDensity

3 20 5 4 5 2.45 10 1 10

B)DrawingHistogramsa)Correctlydrawnhistogramusingthefollowingdata:

Time(𝑡minutes) FrequencyDensity

0 ≤ 𝑡 < 8 98 ≤ 𝑡 < 12 2112 ≤ 𝑡 < 16 1416 ≤ 𝑡 < 20 9

b)Findthetotalareaofthebars.C)CompletingHistogramsa)

4820

b)Correctlydrawnhistogramusingthefollowingdata:

Wage,𝑤(£) FrequencyDensity

5 ≤ 𝑤 < 8 168 ≤ 𝑤 < 10 1710 ≤ 𝑤 < 14 614 ≤ 𝑤 < 24 2

EXAMQUESTIONa)Correctlydrawnhistogramusingthefollowingdata:

Age(𝑎𝑦𝑒𝑎𝑟𝑠) FrequencyDensity15 ≤ 𝑎 < 25 1.4

25 ≤ 𝑎 < 30 330 ≤ 𝑎 < 40 1.340 ≤ 𝑎 < 60 0.4

b)28.8years

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7ProblemSolvingEXAMQUESTIONS1.)£4.80profit2.)Madeleineiscorrect. Fuelpoured60m3(1000L=1m3) Volumecylinder68.4m3(1dp) Maximumcapacitycylinder61.6m3(1dp) Massfuelpoured51,000kg=51tonnes(1000kg=1tonne) Itissafebecauselessfuelispouredthanthemaximumpermittedcapacityandweight.