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GCSEMATHEMATICSKEYTOPIC
PRACTICESHEETS
EXPRESSIONS,FORMULAEANDSUBSTITUTION
(AQAHIGHER)
ThesequestionsaresuitableforHigherTierstudents.
Questions1to14shouldbedonewithoutacalculator.
Question15canbedonewithacalculator.
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SAM
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KeyTopicPracticeSheets Expressions,FormulaeandSubstitution(AQAHigher)
Copyrighttutor2u2017 2
1 𝑢 = 𝑣 − 𝑎𝑡
Whatisthevalueof𝑢inwhen𝑣 = 8,𝑎 = −2and𝑡 = 12
Circlethecorrectanswer.[1mark]
-32 -16 18 322 Ashopsellssmallandlargebagsofpotatoes.
Thereare10potatoesinasmallbag.Thereare40potatoesinalargebag.Hakimbuysssmallbagsandllargebags.CirclethecorrectexpressionforthetotalnumberofpotatoesboughtbyHakim.
[1mark]
𝑠 + 𝑙 10𝑠 + 40𝑙 50 40𝑠 + 10𝑙
3 Pressure = ForceArea 1kilonewton = 1000newtons Findthepressureexertedbyaforceof0.35kilonewtonsonanareaof7mE.
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KeyTopicPracticeSheets Expressions,FormulaeandSubstitution(AQAHigher)
Copyrighttutor2u2017 8
10 ExpressOP− O
Qasasinglefraction.
[2marks]
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[2marks]
………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………. Answer……………………………………………………………………………………………………………………………………………………………………………………………….11(b) Thebathcurrentlycontainsxlitresofwater.Writedownanexpressionforhowlongittookin minutestosupplythebathwithxlitresofwater.
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SAM
PLE
RESOURCE
KeyTopicPracticeSheets Expressions,FormulaeandSubstitution(AQAHigher)
Copyrighttutor2u2017 9
12 Atentismadeintheshapeofasemi-circularprismoflength3metres.Thetentincludesabuilt-ingroundsheet.
Theradiusofthesemi-circleattheendofthetentis𝑥metres. Findanexpressionforthetotalsurfaceareaofthetentmaterialused. Giveyouranswerintermsof𝜋.
[4marks]
………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………. Answer……………………………………………………………………………………………………………………………………………………………………………………………….
𝑥
3𝑚
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KeyTopicPracticeSheets Expressions,FormulaeandSubstitution(AQAHigher)
Copyrighttutor2u2017 10
13 PauladrivesfromSunderlandtoNewcastleatanaveragespeedof50mph.Shedrivesbackatanaveragespeedof30mph.
ThedistancefromSunderlandtoNewcastleis𝑑miles.13(a) Findanexpressionforthetotaljourneytime(inhours)intermsof𝑑.
[2marks]
………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………. Answer……………………………………………………………………………………………………………………………………………………………………………………………….13(b) WorkoutPaula’smeanspeedforthewholejourney.
Expressyouranswerassimplyaspossible.[4marks]
………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
SAM
PLE
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KeyTopicPracticeSheets Expressions,FormulaeandSubstitution(AQAHigher)
Copyrighttutor2u2017 11
14 Theformulaforthegraphofacubicfunctionis
𝑦 = 𝑎𝑥S + 𝑏𝑥E + 𝑐𝑥 + 𝑑 where𝑎,𝑏,𝑐and𝑑areconstants. Acubicfunctionhasthefollowingvalues: 𝑎 = 1 𝑏 = −6 𝑐 = 11 𝑑 = −6 Doesthegraphtouchthex-axiswhen𝑥 = 3? Explainyouranswerclearly.
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SAM
PLE
RESOURCE
KeyTopicPracticeSheets Expressions,FormulaeandSubstitution(AQAHigher)
Copyrighttutor2u2017 12
15 Theformulabelowisusedtoworkoutthefinalspeedofacar
𝑣 = 𝑢E + 2𝑎𝑠 Where
• u=initialspeed(m/s)• v=finalspeed(m/s)• a=acceleration(m/s2)• s=distancetravelled(m)
Aspeedcameraphotographsacarwhenitpassesat10%ormoreabovethespeedlimit.Thespeedlimitis70milesperhour.
Acarpassesunderabridgewithaninitialspeedof70milesperhour,beforeitreachesaspeedcamerapositioned100mafterthebridge.Thecarsaccelerationis1m/s2.
Doesthecartriggerthespeedcamera?
Showyourstagesofworkingclearlyandexplainyouranswer.
Use5miles=8kilometres.[6marks]
………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
SAM
PLE
RESOURCE
GCSEMATHEMATICSKEYTOPIC
PRACTICESHEETS
EXPRESSIONS,FORMULAEANDSUBSTITUTION
(AQAHIGHER)
ThesequestionsaresuitableforHigherTierstudents.
Questions1to14shouldbedonewithoutacalculator.
Question15canbedonewithacalculator.
www.tutor2u.net/maths
MODELANSWERS
SAM
PLE
RESOURCE
KeyTopicPracticeSheets Expressions,FormulaeandSubstitution(AQAHigher)
Copyrighttutor2u2017 9
12 Atentismadeintheshapeofasemi-circularprismoflength3metres.Thetentincludesabuilt-ingroundsheet.
Theradiusofthesemi-circleattheendofthetentisGmetres. Findanexpressionforthetotalsurfaceareaofthetentmaterialused. GiveyouranswerintermsofR.
[4marks]
………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………. Answer……………………………………………………………………………………………………………………………………………………………………………………………….
G
3J
SAM
PLE
RESOURCE
KeyTopicPracticeSheets Expressions,FormulaeandSubstitution(AQAHigher)
Copyrighttutor2u2017 10
13 PauladrivesfromSunderlandtoNewcastleatanaveragespeedof50mph.Shedrivesbackatanaveragespeedof30mph.
ThedistancefromSunderlandtoNewcastleisMmiles.13(a) Findanexpressionforthetotaljourneytime(inhours)intermsofM.
[2marks]
………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………. Answer……………………………………………………………………………………………………………………………………………………………………………………………….13(b) WorkoutPaula’smeanspeedforthewholejourney.
Expressyouranswerassimplyaspossible.[4marks]
………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
SAM
PLE
RESOURCE
KeyTopicPracticeSheets Expressions,FormulaeandSubstitution(AQAHigher)
Copyrighttutor2u2017 11
14 Theformulaforthegraphofacubicfunctionis
H = %GS + NGE + IG + M where%,N,IandMareconstants. Acubicfunctionhasthefollowingvalues: % = 1 N = −6 I = 11 M = −6 Doesthegraphtouchthex-axiswhenG = 3? Explainyouranswerclearly.
[4marks]
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SAM
PLE
RESOURCE
KeyTopicPracticeSheets Expressions,FormulaeandSubstitution(AQAHigher)
Copyrighttutor2u2017 12
15 Theformulabelowisusedtoworkoutthefinalspeedofacar
# = !E + 2%*
Where• u=initialspeed(m/s)• v=finalspeed(m/s)• a=acceleration(m/s2)• s=distancetravelled(m)
Aspeedcameraphotographsacarwhenitpassesat10%ormoreabovethespeedlimit.Thespeedlimitis70milesperhour.
Acarpassesunderabridgewithaninitialspeedof70milesperhour,beforeitreachesaspeedcamerapositioned100mafterthebridge.
Thecarsaccelerationis1m/s2.
Doesthecartriggerthespeedcamera?
Showyourstagesofworkingclearlyandexplainyouranswer.
Use5miles=8kilometres.[6marks]
………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….
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