Year 9 Revision Booklet - Riverside Campus

Year 9 Revision Booklet Watch the video before attempting the worksheets.

The videos can be found at: https://corbettmaths.com/contents

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!Rounding:to1/2/3etcdecimalplaces

Video278onwww.corbettmaths.com

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Question1: Roundeachofthenumbersbelowto1decimalplace.(a)3.47 (b) 0.11 (c)9.84 (d)12.75

Question2: Roundeachofthefollowingnumbersto1decimalplace.

(a) 4.82 (b)6.19 (c)9.77 (d)10.63 (e)21.41 (f)3.14 (g)48.18

(h)29.26 (i)80.85 (j)0.43 (k)248.38 (l)637.51(k)62.89 (l)9.99

Question3: Roundeachofthenumbersbelowtoonedecimalplace. (a)4.282 (b) 7.725 (c)2.548 (d)1.6631

Question4: Roundeachofthenumbersbelowtothenearesttenth(1decimalplace)

(a) 5.191 (b)8.246 (c)10.087 (d)39.555 (e)0.831

(f)93.2941 (g)38.3152 (h)7.26229 (i)0.54868696

Question5: Roundeachofthenumbersbelowto2decimalplaces.(a)5.123 (b) 7.869 (c)0.435 (d)16.0149

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https://corbettmaths.com/2013/09/07/rounding-to-1-or-2-decimal-places/

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https://corbettmaths.com/2013/09/07/rounding-to-1-or-2-decimal-places/


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!Rounding:to1/2/3etcdecimalplaces


Question6: Roundeachofthenumbersbelowto2decimalplaces

(a) 3.487 (b)2.613 (c)1.984 (d)10.046 (e)8.155

(f)19.367 (g)3.141 (h)6.0698 (i)4.26317 (j)93.46197

Question7: Roundeachofthenumbersbelowto3decimalplaces

(a) 0.0346 (b)6.7568 (c)4.2251 (d)1.7583

(e)40.48546 (f)128.01891 (g)0.5059802 (h)384.456094

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Question1: 51.26%ofthepeoplelivinginatownarefemale. RoundthisNiguretoonedecimalplace.

Question2: Walterhasworkedoutacalculationonacalculator Shownonthecalculatoristheanswer.

(a)Roundtheanswertoonedecimalplace (b)Roundtheanswertotwodecimalplaces

Question3: Danielhasbeenaskedtoround1.725toonedecimalplace. Hisansweris172.5 ExplainDaniel’smistake.

Question4: Nicolehasroundedanumbertoonedecimalplace. Heransweris9.2 Writedown10differentpossiblenumbersthatshecouldhaverounded.

Question5: Achocolatebarcontains0.4715gofsalt. Roundthistotwodecimalplaces.

Question6: Dominicwritesdowntwonumbers,AandB. AandBhave2decimalplaces. DominicroundsAto1decimalplaceandcallshisanswerC. HeroundsBto1decimalplaceandcallshisanswerD. DominicsaysthedifferencebetweenAandBcannotbethesameasthe differencebetweenCandD. Showheisincorrect

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Answers© CORBETTMATHS 2017 Clickhere

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https://corbettmaths.com/2017/06/05/rounding-decimal-places-answers/


https://corbettmaths.com/2017/06/05/rounding-decimal-places-answers/

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!Rounding:Signi+icantFiguresVideo279aonwww.corbettmaths.com

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Question1: Roundeachofthefollowingnumbersto1signi+icant+igure

(a)36 (b)22 (c)83 (d)68 (e)97 (f)120 (g)519

(h)260 (i)741 (j)888 (k)408 (l)650 (m)148 (n)972

(o)3900 (p)5400 (q)4125 (r)2732 (s)6349 (t)8099 (u)6499


(a)12000 (b)46000 (c)74500 (d)83771 (e)95120 (f)330000

(g)863000 (h)248220 (i)489331 (j)13800000


(a)2.9 (b)3.2 (c)5.7 (d)46.81 (e)57.25 (f)80.96 (g)94.9

(h)115.1 (i)8.482 (j)13.65 (k)66.321 (l)5501.4 (m)48.02 (n)99.99


(a) 0.54 (b)0.86 (c)0.161 (d)0.048 (e)0.0943 (f)0.0071 (g)0.0038

(h)0.06482 (i)0.8835 (j)0.00064 (k)0.00098 (l)0.00002789

Question5: Roundeachofthefollowingnumbersto2signi+icant+igures

(a)844 (b)665 (c)129 (d)2840 (e)9250 (f)1359 (g)298

(h)504 (i)999 (j)3841 (k)48500 (l)13.7 (m)58.3 (n)49.6

(o)1.41 (p)42.64 (q)0.3189 (r)22490 (s)186110 (t)0.04912 (u)4.98

(v)997826 (w)2.99517 (x)0.06014

Examples

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https://corbettmaths.com/2013/09/07/rounding-significant-figures/

https://corbettmaths.com/2013/09/07/rounding-significant-figures/


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!Rounding:Signi+icantFiguresVideo279aonwww.corbettmaths.com

Question6: Roundeachofthefollowingnumbersto3signi+icant+igures

(a)9433 (b)1891 (c)2496 (d)3.226 (e)37756 (f)57147 (g)7.0078

(h)51.564 (i)0.90341 (j)2.7892 (k)0.08906 (l)0.007812 (m)9909.1 (n)0.6006

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Question1: Inanelection43.8%ofpeoplevotedforacandidate. Roundthis+iguretoonesigni+icant+igure

Question2: 32641peoplewatcharugbymatchbetweenItalyandArgentina. Roundthisnumberto2signi+icant+igures.

Question3: Roundthefollowingnumbersto1signi+icant+igure

(a)eightmillion,sixhundredthousand (b)theproductof19and351

Question4: Tomhasbeenaskedtoroundthenumberonthecalculatorto2signi+icant +igures. Tomsaystheansweris516.16

CanyouexplainTom’smistake?

Question5: ThepopulationofFrometo2signi+icant+iguresis26,000. (a)WritedownthelowestnumberofpeoplethatcouldliveinFrome?

(b)WritedownthegreatestnumberofpeoplethatcouldliveinFrome?

Question6: Round to2signi+icant+igures. Giveyouranswerasanordinarynumber.

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Answers

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https://corbettmaths.com/2017/07/01/rounding-significant-figures-answers/


https://corbettmaths.com/2017/07/01/rounding-significant-figures-answers/

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!Rounding:Highest/LowestValues

Video280onCorbettmaths

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Question1: Rhysthinksofanumberandroundsittothenearest10. Hisansweris80.

(a)WhatisthesmallestpossiblenumberRhyscouldhavethoughtof? (b)WhatisthegreatestpossiblenumberRhyscouldhavethoughtof?

Question2: Charlottethinksofanumberandroundsittothenearest10. Heransweris140.

(a)WhatisthesmallestpossiblenumberCharlottecouldhavethoughtof? (b)WhatisthegreatestpossiblenumberCharlottecouldhavethoughtof?

Question3: Melodythinksofanumberandroundsittothenearest10. Heransweris800.

(a)WhatisthesmallestpossiblenumberMelodycouldhavethoughtof? (b)WhatisthegreatestpossiblenumberMelodycouldhavethoughtof?

Question4: Steffanthinksofanumberandroundsittothenearest100. Hisansweris500.

(a)WhatisthesmallestpossiblenumberSteffancouldhavethoughtof? (b)WhatisthegreatestpossiblenumberSteffancouldhavethoughtof?

Question5: Fleurthinksofanumberandroundsittothenearest100. Heransweris1900.

(a)WhatisthesmallestpossiblenumberFleurcouldhavethoughtof? (b)WhatisthegreatestpossiblenumberFleurcouldhavethoughtof?

Question6: Rhianthinksofanumberandroundsittothenearest1000. Heransweris24000.

(a)WhatisthesmallestpossiblenumberRhiancouldhavethoughtof? (b)WhatisthegreatestpossiblenumberRhiancouldhavethoughtof?

Examples

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https://corbettmaths.com/2013/10/24/rounding-smallest/

https://corbettmaths.com/2013/10/24/rounding-smallest/

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Question7: Thesigniscorrecttothenearestten.

(a)WhatisthelowestpossiblenumberofpeoplethatliveinKingstone?

(b)WhatisthegreatestpossiblenumberofpeoplethatliveinKingstone?

Question8: Thesigniscorrecttothenearesthundred.

(a)WhatisthelowestpossiblenumberofpeoplethatliveinKeswick?

(b)WhatisthegreatestpossiblenumberofpeoplethatliveinKeswick?

Question9: Thesigniscorrecttothenearesthundred.

(a)WhatisthelowestpossiblenumberofpeoplethatliveinKeswick?

(b)WhatisthegreatestpossiblenumberofpeoplethatliveinKeswick?

Question10: Anewspapersaysthenumberofpeopleatarugbymatchis37,000tothe nearest1,000.

Whatisthegreatestpossiblenumberofpeopleatthematch?

Question11: ThepopulationofWalesis3.1millions,tothenearesthundredthousand.

(a) WhatisthelowestpossiblenumberofpeoplethatliveinWales?(b) WhatisthegreatestpossiblenumberofpeoplethatliveinWales?

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Question1: Owenhas200marblestothenearesthundred.

Hesaysthatmeansthegreatestnumberofmarbleshecould haveis250.

ExplainwhyOwenisincorrect.

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Question2: Apacketofsweetscontains30sweetstothenearest10. MissSimpsongiveseachofthe20studentsinherclassapacketofsweets.

WhatisthelowestpossibletotalnumberofsweetsthatMissSimpsoncould havegivenout?

Question3: Tomasorganisesaconcerttoraisemoneyforcharity. Entrytotheconcertis£5.00 Thenumberofpeopleattendingtheconcertis700tothenearesthundred.

Whatisthegreatestpossibleamountofmoneyheraisedforcharity?

Question4: Evelynhas8bagsof20pcoins. Eachbagcontains50coinstothenearest10. Workoutthedifferencebetweenthegreatestandsmallestpossibleamountof moneythatEvelynhas.

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https://corbettmaths.com/wp-content/uploads/2018/11/Rounding-High-Low-answers-pdf.pdf

https://corbettmaths.com/wp-content/uploads/2018/11/Rounding-High-Low-answers-pdf.pdf

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!ProductofPrimes:LCMandHCFVideo224onwww.corbettmaths.com

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Question1: Findthelowestcommonmultiple(LCM)ofeachpairofnumbers.

(a)15and35 (b)14and22 (c)15and21 (d)9and33

(e)12and15 (f)18and30 (g)16and20 (h)24and30

(i)16and36 (j)26and39 (k)25and30 (l)16and18

(m)24and56 (n)36and45 (o)60and72 (p)42and90

Question2: Findthehighestcommonfactor(HCF)ofeachpairofnumbers

(a)21and49 (b)35and45 (c)18and24 (d)18and45

(e)30and75 (f)28and42 (g)60and90 (h)48and64

(i)56and72 (j)18and23 (k)84and96 (l)38and95

(m)66and121 (n)56and140 (o)180and225 (p)64and224

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Question1: Given60=2²×3×5and84=2²×3×7

Find(a)thelowestcommonmultiple(LCM)

and(b)thehighestcommonfactor(HCF)

Question2: Findthelowestcommonmultiple(LCM)of15,20and25.

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https://corbettmaths.com/2012/08/20/lcm-and-hcf-using-product-of-primes/

https://corbettmaths.com/2012/08/20/lcm-and-hcf-using-product-of-primes/


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!ProductofPrimes:LCMandHCFVideo224onwww.corbettmaths.com

Question3: AredlightYlashesevery28seconds. AgreenlightYlashesevery24seconds. TheybothYlashatthesametime. AfterhowmanysecondswilltheynextbothYlashatthesametime?

Question4: AbusheadingtoBelfastleavesAntrimevery36minutes. AbusheadingtoBallymenaleavesAntrimevery45minutes At10ambustoBelfastandabustoBallymenabothleaveAntrimBusStation. Workoutthenexttimethatbothbusesleaveatthesametime.

Question5: Findthelowestcommonmultipleof124and200.

Question6: TheLCMoftwonumbersis130. TheHCFofthesametwonumbersis13. Bothnumbersarelessthan100. Writedowntwopossiblenumbers.

Question7: Fredsaysthat20and21havegotahighestcommonfactorof0. ExplainwhyFrediswrong.

Question8: AbbyandAnniehavethesamenumberofcoins. Abbyhassortedhercoinsintogroupsof80. Anniehassortedhercoinsintogroupsof75. Theyeachhavelessthan2000coins. Howmanycoinsdotheyaltogether?

Question9: Adamisworkingoutthehighestcommonfactorof100and112. Hehasworkeditouttobe22. Canyouexplainwhathehasdonewrong?

� Answers


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https://corbettmaths.com/2016/07/16/textbook-answers-lcmhcf-using-product-of-primes/

https://corbettmaths.com/2016/07/16/textbook-answers-lcmhcf-using-product-of-primes/

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!LawsofIndices


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Question1: Writeasasinglepowerof2.

(a)2²x2² (b)2²x2³ (c)2⁶x2² (d)2⁴x2³ (e)2⁶x2⁸ (f)2²x2 (g)2x2⁴

(h)2⁸x2⁸ (i)2⁹x2² (j)2x2⁸ (k)2⁶x2⁵ (l)2²x2²x2²x2²


(a)5⁵÷5² (b)5⁸÷5³ (c)5⁹÷5² (d)5⁷÷5⁵ (e)5³÷5 (f)5⁸÷5 (g)5⁷÷5⁴

(h)5⁹÷5³ (i)5⁴÷5⁸ (j)5÷5³ (k)5⁴⁵÷5⁵ (l)5³÷5³


(a) (b) (c) (d)

(e) (f) (g) (h)


(a)(8⁵)² (b)(8³)² (c)(8⁴)³ (d)(8⁵)⁴ (e)(8³)⁶ (f)(8⁷)³ (g)(8⁶)⁶

(h)(8⁹)² (i)(8⁴)⁸ (j)(8³)−⁵ (k)(8−⁵)²

Question5: Writeasasinglepowerofy.

(a) y⁷xy³ (b)y⁹÷y⁷ (c)y⁶÷y² (d)(y³)⁵ (e)y⁷÷y (f)y³÷y⁷ (g)(y⁹)⁵

(h) y⁶xy⁷ (i)y⁶xy⁵xy²(j)y⁸xyxy³(k)

Examples

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https://corbettmaths.com/2013/03/13/laws-of-indices-algebra/

https://corbettmaths.com/2013/03/13/laws-of-indices-algebra/

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!LawsofIndices


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Question1: Canyouspotanymistakes?

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Question2: Findthreedifferentpairsofvaluesformandn.

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https://corbettmaths.com/wp-content/uploads/2019/02/Laws-of-Indices-Answers.pdf

https://corbettmaths.com/wp-content/uploads/2019/02/Laws-of-Indices-Answers.pdf

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!StandardForm

Videos300,301,302and303onCorbettmaths

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Question1: Writeeachofthefollowingnumbersinstandardform.

(a)40000 (b)2000000 (c)8000000 (d)7000

(e)100000000 (f)900 (g)250000 (h)1900

(i) 54000000 (j)11000000 (k)89000 (l)3600000000

(m)43500 (n)91900000 (o)1230000000 (p)71120

(q)9804000 (r)471500 (s)55403 (t)2936000

(u)93508000 (v)333810000 (w)9800200000 (x)49300

(y)804000 (z)69702000000

Question2: Writeeachofthefollowingasordinarynumbers

(a) 3×10⁴ (b)9×10³ (c)6×10⁶ (d)2×10¹⁰

(e)5×10⁷ (f)1.2×10² (g)2.9×10⁵ (h)8.4×10⁸

(i)7.7×10⁴ (j)3.51×10⁵ (k)9.89×10⁷ (l)1.27×10⁹

(m)4.05×10⁶ (n)1.616×10⁵ (o)2.0651×10³ (p)8.829×10⁷

(q)1.0051×10⁶ (r)2.143578×10⁴

Question3: Writeeachofthefollowingnumbersinstandardform.

(a)0.002 (b)0.0005 (c)0.9 (d)0.00000004

(e)0.00065 (f)0.0022 (g)0.0361 (h)0.000558

(i) 0.00000423 (j)0.0000000981 (k)0.00407 (l)0.02052

(m)0.0000515 (n)0.006015 (o)0.0000000082 (p)0.00007005

(q)0.000000024 (r)0.00000000000005

Examples

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https://corbettmaths.com/2018/09/20/standard-form-videos/

https://corbettmaths.com/2018/09/20/standard-form-videos/

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Question4: Writeeachofthefollowingasordinarynumbers

(a) 2×10⁻³ (b)7×10⁻² (c)3×10⁻⁶ (d)9×10⁻⁸

(e)4.8×10⁻⁴ (f)6.7×10⁻³ (g)9.2×10⁻⁶ (h)4.1×10⁻²

(i)3.16×10⁻⁵ (j)8.62×10⁻⁴ (k)7.09×10⁻⁶ (l)5.71×10⁻³

(m)2.05×10⁻⁸ (n)4.112×10⁻² (o)1.651×10⁻³ (p)2.0019×10⁻⁷

Question5: Writethesenumbersinstandardform

(a) onemillion (b)ninethousand (c)fortythousand (d)ninebillion

(e)500² (f)200³ (g)30,000² (h)twothousandths

Question6: Writeeachofthesenumbersinstandardform

(a)72×10³ (b)84×10⁶ (c)500×10² (d)210×10⁴

(e)0.8×10⁷ (f)0.46×10⁵ (g)0.06×10⁸ (h)0.007×10¹²

(i) 3000×10¹⁴ (j)24×10⁻⁵ (k)0.8×10⁻¹⁰ (l)0.0055×10⁻²

(m)0.0372×10⁻⁹ (n)65213×10⁻⁷ (n)2933×10²¹ (o)759300×10⁻¹

Question7: Workouttheanswerstothefollowingmultiplications. Youmaynotuseacalculator.

(a)2×10³×3×10⁴ (b)(4×10⁸)×(2×10⁵) (c)1.2×10⁴×6×10⁴

(d)(3×10⁻⁹)×(3×10³) (e)4×10⁻⁷×3×10⁻² (f)6×10¹⁰×4×10⁸

(g)7×10¹²×8×10⁻⁹ (h)3.7×10⁵×5×10⁶ (i)(8×10³)×(5×10⁵)

(j)5×10⁻¹⁴×4×10⁻⁷ (k)1.8×10²×2×10⁻⁸ (l)5.8×10⁶×4×10⁷

(m)4.5×10²⁰×9×10⁻¹⁴ (n)(1.1×10⁻⁵)×(1.2×10⁻²) (o)6.2×10⁴×7×10⁹

(p)2.8×10⁸×1.3×10⁷ (q)1.25×10⁻¹⁶×3.2×10¹⁰ (r)8.7×10²×9.2×10⁶

(s)2×10²×3×10⁷×6×10⁴ (t)3×10⁶×2.1×10⁻⁸×5×10¹²


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Question8: Workouttheanswerstothefollowingdivisions. Youmaynotuseacalculator.

(a)(8×10⁵)÷(2×10³) (b)(9×10⁹)÷(3×10⁴) (c)(5×10⁶)÷(2×10²)

(d)(9×10⁹)÷(4×10⁹) (e)(1.2×10⁴)÷(3×10⁸)(f)(3.5×10²)÷(5×10⁹)

(g)(4.8×10¹⁵)÷(3×10⁴) (h)(6.4×10³)÷(8×10¹⁶)(i)(2.7×10⁻³)÷(9×10⁷)

(j)(1.44×10⁸)÷(12×10⁻⁵) (k)(2×10¹⁰)÷(5×10⁻²)(l)(1×10⁻⁵)÷(4×10⁻²)

(m)(5×10⁻⁶)÷(8×10⁻¹⁴) (n)(8.1×10⁻⁹)÷(2.7×10³)(o)(1.6×10⁷)÷(8×10²)

(p)(3×10²²)÷(8×10⁹) (q)(3.92×10⁸)÷(1.4×10⁻⁶)(r)(3×10⁻⁴)÷(1.2×10⁷)

Question9: Workouttheanswerstothefollowing. Youmaynotuseacalculator.

(a)(3×10³)² (b)(2×10⁶)² (c)(5×10⁴)² (d)(8×10⁵)²

(e)(9×10¹⁰)² (f)(6×10⁻³)² (g)(2.5×10⁻⁶)² (h)(1.2×10⁸)²

(i)(2×10⁵)³ (j)(4×10⁹)³ (k)(3×10¹⁵)³ (l)(5×10⁻⁷)³

(m)(2×10⁶)⁴ (n)(1×10⁻⁴)⁶ (o)(8.3×10⁻²)² (p)(9.7×10³)²

Question10: Workouteachofthefollowing

(a)5×10⁴+3×10⁴ (b)4×10³−2×10³ (c)2.5×10⁵+3.3×10⁵

(d)7×10⁻²+2×10⁻² (e)6×10³+8×10² (f)2×10⁶−8×10⁵

(g)2.6×10⁸+4.5×10⁹ (h)5.12×10⁵−1.89×10⁴ (i)(8×10⁷)+(3×10⁵)

(j)5.07×10¹⁰+2.77×10⁹ (k)6.12×10⁻³−1.07×10⁻² (l)4×10⁻⁷+9×10⁻⁵

(m)3.44×10⁸+7.03×10⁶+9.89×10⁷


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!StandardForm


Question11:Usingacalculator,workoutthefollowing

(a)3.57×10³×6.7×10⁷ (b)9.5×10⁴+3.8×10⁵ (c)1.8×10⁹×5.2×10⁹

(d)7×10⁻⁸×2×10⁻⁶ (e)(7.71×10¹⁵)÷(6×10⁴) (f)(8×10⁹)³

(g)(5×10⁻⁷)⁻³ (h)2.55×10⁷×8.02×10⁴×1.1×10⁵

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Question1: ThedistancebetweenLondonandNewYorkis5,567,000metres. Writethisnumberinstandardform.

Question2: ThedistancefromtheSuntoPlutois3.67billionmiles. Writethisnumberinstandardform.

Question3: Thelengthofacellis0.016mm Writethisnumberinstandardform.

Question4: Thepopulationofacountryis6.51×10⁵ Writethepopulationofthecountryasanordinarynumber.Question5: 32,010peopleattendafootballmatchbetweenWestHamandSouthampton. Writethisnumberinstandardform.

Question6: Thereareapproximately5×10⁴grainsofriceinaonekilogrambagofrice. Approximatelyhowmanygrainsofricewillbein20onekilogrambagsofrice?

Question7: Apennyweighs0.0036kg. Findthetotalmassof£400worthofpennies.

Question8: A=6×10⁵ B=30000 C=5×10⁻² (a)WorkoutAB (b)WorkoutC²

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Question9: ThepopulationoftheUnitedKingdomin1950was5.06×10⁷ ThepopulationoftheUnitedKingdomin2015was6.47×10⁷ WorkouthowmanymorepeopleliveintheUnitedKingdomin2015than1950. Giveyouranswerasanordinarynumber.

Question10: Peterhasmultipliedtwonumbersusinghiscalculator. Thecalculatorshowstheanswer. Hecanrememberthatonenumberwas5000. Whatwastheothernumberusedinthemultiplication?

Question11: Anasteroidtravelsat25kilometrespersecond. Howfardoesittravelinonehour? Giveyouranswerinstandardform.

Question12: Withoutusingacalculator,workout.

Question13: ThemassofEarthis5.97×10²⁴ ThemassofJupiteris1.898×10²⁷ Usingacalculator,workouthowmanytimesheavierJupiteristhanEarth. Giveyouranswertoonedecimalplace.

Question14: ThedensityofNitrogenis1.25×10⁻⁶kg/cm³ CalculatethemassofonecubicmetreofNitrogen.

� Answers



https://corbettmaths.com/2019/10/10/standard-form-textbook-answers/

https://corbettmaths.com/2019/10/10/standard-form-textbook-answers/

Workout

Question 1: Work out each of the following

(a) √3 ╳ √5 (b) √7 ╳ √2 (c) √11 ╳ √6 (d) √2 ╳ √3

(e) √8 ╳ √2 (f) √3 ╳ √3 (g) √5 ╳ √6 (h) √5 ╳ √2

(i) √6 ╳ √6 (j) √10 ╳ √3 (k) √5 ╳ √20 (l) √11 ╳ √10

(m) √2 ╳ √5 ╳ √3 (n) √2 ╳ √6 ╳ √3 (o) √10 ╳ √7 ╳ √3

(p) √2 ╳ √2 ╳ √2 (q) √2 ╳ √3 ╳ √2 ╳ √3


(a) (√3)² (b) (√7)² (c) (√10)² (d) (√5)²


(a) (√2)³ (b) (√6)³ (c) (√10)³ (d) (√3)³

(e) (√3)⁴ (f) (√5)⁴ (g) (√10)⁴ (h) (√2)⁵


(a) 2√3 ╳ 3√5 (b) 7√2 ╳ 4√11 (c) 2√13 ╳ 2√2 (d) 10√2 ╳ 5√3

(e) √3 ╳ 6√5 (f) 2√2 ╳ √7 (g) 4√3 ╳ 2√3 (h) 2√2 ╳ 3√8

(i) 2√2 ╳ √5 ╳ 4√3 (j) 3√2 ╳ 2√6 ╳ 2√3


(a) √10 ÷ √5 (b) √21 ÷ √7 (c) √30 ÷ √6 (d) √8 ÷ √2

(e) √80 ÷ √5 (f) √56 ÷ √7 (g) √15 ÷ √3 (h) √72 ÷ √8

(i) √7 ÷ √7 (j) √26 ÷ √13 (k) √48 ÷ √12 (l) √48 ÷ √8

!

SurdsVideos 305, 306, 307, 308 on Corbettmaths



(a) 4√6 ÷ 2√2 (b) 12√10 ÷ 3√5 (c) 9√15 ÷ 3√3 (d) 7√30 ÷ √2

(e) 20√8 ÷ 5√2 (f) 40√80 ÷ 20√5 (g) 51√7 ÷ 3√7 (h) 36√54 ÷ 18√6


(a) (b) (c) (d)

Question 8: Simplify the following

(a) √8 (b) √75 (c) √20 (d) √32 (e) √48 (f) √200

(g) √300 (h) √80 (i) √50 (j) √98 (k) √63 (l) √800

(m) √180 (n) √220 (o) √96 (p) √175 (q) √1000 (r) √60

Question 9: Simplify the following

(a) 5√8 (b) 2√20 (c) 4√50 (d) 3√98 (e) 15√32 (f) 10√75

Question 10: Work out each of the following. Simplify each answer.

(a) √6 ╳ √10 (b) √15 ╳ √10 (c) √30 ╳ √6

(d) √22 ╳ √10 (e) 3√2 ╳ √6 (f) √14 ╳ 4√2

(g) 4√6 ╳ 3√15 (h) 2√70 ╳ 3√10 (i) 5√10 ╳ 2√30

Question 11: Work out the following additions/subtractions

(a) √8 + √18 (b) √50 + √8 (c) √75 + √27 (d) √200 − √32

(e) √8 + √2 + √72 (f) √300 − √48 (g) √1000 + √90 (h) √28 + √63

Question 12: Work out the following additions/subtractions

(a) 3√8 + √2 (b) 4√27 − √75 (c) 2√50 + 5√32 (d) √200 − 3√18

(e) 4√80 + 3√45 (f) 6√75 − 2√12 (g) 10√7 + 2√175

!



Question 13: Expand each of the following. Simplify if possible.

(a) √2(√3 + 5) (b) √3(√5 + √2) (c) √6 (2 − √3) (d) √10 (5 + √10)

(e) √2(√18 − √2) (f) √5 ( 3√2 − √5) (g) 2√3 (3√2 + √3) (h) 4√11( 5√2 + 2√11)

(i) √27 (√2 + √3) (j) √12 (7 − √3)


(a) (2 + √3)(1 + √3) (b) (√2 + 5)(1 + √2) (c) (√3 + 1)(√3 + 4)

(d) (3 + √5)(4 − √5) (e) (√7 − 1)(√7 − 1) (f) (5 − √3)(5 + √3)

(g) (3 + √2)(1 + √3) (h) (√12 + √3)(√3 + 2) (i) (4 − √2)(3 + √8)

(j) (√7 + √2)(√8 + √7) (k) (1 + 2√2)(2 − √2) (l) (3√5 + 7)(2√5 + 1)

(m) (3 + √2)² (n) (1 + √5)² (o) (10 − √2)²

(p) (√5 + √2)² (q) (2√3 − 1)² (r) (5√2 + 3√3)²


(a) (4 + √3)(4 − √3) (b) (1 − √6)(1 + √6) (c) (√10 + 1)(√10 − 1)

(d) (√7 + √5)(√7 − √5) (e) (2√3 − 1)(2√3 + 1) (f) (5 − 4√3)(5 + 4√3)

Question 16: Rationalise the denominators for each of the following

(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

!



Question 17: Rationalise the denominators for each of the following

(a) (b) (c) (d)

(e) (f) (g) (h)

Question 1: Find the area of each of these rectangles

(a) (b) (c)

Question 2: Find the perimeter of each of these rectangles

(a) (b) (c)

Question 3: Calculate x for each of the following right angled triangles. Give your answer as a simpli\ied surd (or integer).

(a) (b)

(c) (d)

!



Apply

Question 4: A shed has dimensions, in metres, of height √5, width √6 and length √10 Find the volume of the shed. Give your answer as a simpli\ied surd.

Question 5: Mrs Jenkins is making decorations for a wedding. She needs 18√5 metres of ribbon in total. Mrs Jenkins has 40 metres of ribbon. Does she have enough ribbon?

Question 6: The midpoints of the sides of a square of side 16cm are joined to form another square. This process is then repeated to create the shaded square.

Find the area of the shaded square.

Question 7: The area of a rectangle is √125 cm² The length of the rectangle is (2 + √5) cm. Calculate the width of the rectangle. Express your answer in the form a + b√5, where a and b are integers.

Question 8: The triangle below has an area of 2√6 cm². Find the height of the triangle, x. Give your answer as a simpli\ied surd.

!



� �

!Increasing/DecreasingbyaPercentage


�

�

Question1

(a) Increase20by50% (b)Increase60pby10% (c)Increase12gby25%

(d)Increase400litresby20% (e)Increase32mlby75% (f)Increase70mby40%

(g)Increase9000by5% (h)Increase£7by20% (i)Increase9kgby100%

Question2

(a)Decrease40by10% (b)Decrease30hoursby50%(c)Decrease8kgby25%

(d)Decrease55cmby40% (e)Decrease64by75% (f)Decrease£3by10%

(g)Decrease1400by30% (h)Decrease500gby3% (i)Decrease6kgby5%

Question3

(a)Increase80mlby9% (b)Increase420gby70%(c)Decrease8by12%

(d)Decrease£1250by38% (e)Increase6000kmby23%(f)Decrease48GBby6%

(g)Increase204by98% (h)Decrease149mmby91%(i)Increase88by185%

Question4

(a)Decrease90mlby7.5% (b)Increase£670by1.2% (c)Increase3by67.4%

(d)Increase750cmby0.8%

Examples

Workout


Clickhere




https://corbettmaths.com/2012/08/21/increasing-or-decreasing-by-a-percentage/

https://corbettmaths.com/2012/08/21/increasing-or-decreasing-by-a-percentage/

� �



�

Question1: Lastyear,therewas20studentsinaclass. Thisyear,thereare30%morestudents. Howmanystudentsareintheclassthisyear?

Question2: ATVnormallycosts£520. Inasale,allpricesarereducedby10% CalculatethesalepriceoftheTV

Question3: Overthepast10years,thepopulationofatownhasincreasedby25% Thepopulationofthetown10yearsagowas18000 Whatisthepopulationofthetownnow?

Question4: Astandardbagof[lourcontains600gof[lour. Aspecialeditionbagcontains35%more[lour. Howmuch[lourisinthespecialeditionbag?Question5: Richardownsacoffeeshop. InFebruary,4500hotchocolatesweresold. ThenumberofhotchocolatessoldinMarchwas3%less. HowmanyhotchocolatesaresoldinMarch?

Question6: Gabriel’ssalaryis£24500. Nextyearheisduetogeta9%increase. Whatwillhisnewsalarybe?

Question7: Irisspends£40amonthonwater. Bychangingcompany,Iriscansave16%. HowmuchwouldIrispayeachmonth?

Question8: Anempty[lowerpothasamassof800g. Themassofthe[lowerpotincreasesto4kgwhen[illedwithsoil.

Adifferent[lowerpotis25%lighterbutholds40%moresoil. Calculatethemassofthis[lowerpotwhenitisfullofsoil.

Apply




� �



Question9: Louisseesthisspecialofferinashop.

Louisbuysbothitems. Howmuchdoeshepay?

Question10: Anadultticketforthecinemacosts£13.40 Achildticketishalfthepriceofanadultticket. MrandMrsHendersonandtheirsixchildrengotoseeamovie. MrsHendersonhasavoucherfor18%off. WorkouthowmuchMrsHendersonpaysforthetickets.

Question11: Zarawantstobuy72candles. Eachcandlecosts£4.80

Thereisaspecialoffer

Workoutthecostofbuying72candlesusingthespecialoffer.

Question12: Whenatennisballisdropped,itbouncesandthenrises. Theballrisesto80%oftheheightfromwhichitisdropped. Theballisdroppedfromaheightof4metres.

(a)Calculatetheheightoftheriseafterthe[irstbounce. (b)Calculatetheheightoftheriseafterthesecondbounce. Theballcarriesonbouncing,eachtimerisingto80%ofthelastrise.

(c)Forhowmanybouncesdoestheballrisetoaheightgreaterthan10cm?

�Answers


Clickhere


https://corbettmaths.com/wp-content/uploads/2018/11/Increasing_Decreasing-By-a-Percentage-1.pdf

https://corbettmaths.com/wp-content/uploads/2018/11/Increasing_Decreasing-By-a-Percentage-1.pdf



!CompoundInterest


Question1: Paulleaves£4000inthebankfortwoyears.Itearnscompoundinterestof5%peryear.CalculatethetotalamountPaulhasinthebankattheendofthetwoyears.

Question2: Thepopulationofbirdsonanislandisestimatedtoincreaseby10%everyyear.Thepopulationofbirdsontheislandis20000.Calculateanestimateforthepopulationofbirdsinthreeyearstime.

Question3: Thevalueofacardecreasesby5%eachyear.Sophieboughtacartwoyearsagofor£10000Workoutthevaluenow.

Question4: Saminvests£1800inthebankforfouryears.Itearnscompoundinterestof4%eachyear.CalculatethetotalamountSamhasinthebankattheendoffouryears.

Question5: Afullwatertankholds500litres.Thetankbeginstoleakwaterandislosing14%ofitscontentseveryhour.Findhowmuchwaterisleftinthetankafter8hours.

Question6: Theheightofatreeincreasesby60%eachyear.Whenplantedthetreewas40cmtall.Howtallwillthetreebein5yearstime.

Question7: Carrieinvests£800for4yearsat3%interestperyear.Howmuchinterestdoessheearn?

Question8: Ahousewasboughtfor£100,000Itsvalueappreciatesby7.5%eachyearfortheNirstthreeyears.Whatwasitsvalueattheendofthethreeyears?

Examples

Workout


Clickhere



https://corbettmaths.com/2012/08/21/compound-interest/


https://corbettmaths.com/2012/08/21/compound-interest/

� �

!CompoundInterest


Question9: Thenumberofpeoplelivingonaremoteislanddecreasesby9%every10years. In1950therewere18000livingontheisland. Calculatehowmanylesspeoplewillbelivingontheislandin2020.

Question10: Acarwasboughtfor£20,000. Itsvaluedepreciatesby31%eachyearfortheNirstfouryears. Whatisitsvaluesattheendofthefouryears?

Question11: Atreeis80cmwhenplanted. Eachyeartheheightofthetreeincreasesby22%. Afterhowmanycompleteyearswilltheheightoftreebeatleast3m?

Question12: Thenumberofpolarbearsinaregionisdecreasingby5%peryear. Thereare3000polarbearsintheregionin2017. WhatyearwillbetheNirstyearwithlessthan1000polarbearsinthe region?

Question13: Michaelhasstartedworkingforacompanyonasalaryof£15000. Eachyearhewillbegivena6%payrise. HowmanyyearswillittakeforMichael’ssalarytoexceed£30000?

Question14: Thevalueofacardecreasesby7.2%eachyear. Whenboughtthecarcost£6200. Howmanyyearswillittakethecartohaveavaluelessthan£1000?

Question15: Afullwatertankhassprungaleak. 4%ofthewaterislosteveryminute. Whatpercentageofwaterisleftinthetankaftertwentyminutes?

Question16: ANishtank,thatisfullofwater,hassprungaleak. 12%ofthewaterislosteveryhour. Whatpercentageofthewaterislostafterthreehours?

�Question1: Florenceinvests£200fortwoyearsat5%compoundinterest,paidyearly. LiamsaysthattheinterestthatFlorencewillreceivewillbe£20. IsLiamright?

Apply




� �

!CompoundInterest


Question2: Thevalueofamotorcyclewas£14000on1stApril2014. Everythreemonthsthevalueofthemotorcycledecreasesby2%ofitsvalueat thestartofthatthreemonths. Whatwasthevalueofthemotorcycleon1stApril2016?Question3: Whenaballisdropped,itbouncesandthenrises. Theballrisesto90%oftheheightfromwhichitisdropped. Theballisdroppedfromaheightof4m.

(a)CalculatetheheightoftheriseaftertheNirstbounce. (b)Calculatetheheightoftheriseafterthesecondbounce.

Theballcarriesonbouncing,eachtimerisingto90%ofthelastrise. (c)Forhowmanybouncesdoesitrisetoheightgreaterthan1m?

Question4: Thepopulationofacountryisincreasingby5%ayear. Howmanyyearswillittakethepopulationofthecountrytodouble?

Question5: RaheemandBeninvestmoneyin2010.

Raheeminvests£1000atBanks’R’us,whopay3%interestperyear. Beninvests£1400atBankWorld,whopay1%interestperyear

InwhichyearwillRaheem’sinvestmentbeworthmorethanBen’s?

Question6: Thepopulationofacountryincreasesbyx%eachyear. In2014thepopulationofthecountrywas24,000,000. Threeyearslater,thepopulationwas26,996,736. Findx.

Question7: Charlotteinvests£5000. Thebankpays10%interestfortheNirstyearandtheny%everyyearafterthat. Afterthreeyears,Charlottehas£5610.55 Calculatey.

�Answers




https://corbettmaths.com/2017/01/02/compound-interest-answers/


https://corbettmaths.com/2017/01/02/compound-interest-answers/

� �

!Pythagoras

Videos257,260,261onwww.corbettmaths.com

�

�

Question1: Foreachrightangletrianglebelow,workoutx

(a) (b) (c)

Question2: Calculatex Giveeachanswerto2decimalplaces.

(a) (b) (c)

(d) (e) (f)

Question3: Calculatex Includesuitableunitsandgiveeachanswerto1decimalplace.

(a) (b) (c)

Question4: Foreachrightangletrianglebelow,workoutx(a) (b) (c)

Examples

Workout


Clickhere



https://corbettmaths.com/2012/08/19/pythagoras-video/


https://corbettmaths.com/2012/08/19/pythagoras-video/

� �

!Pythagoras


Question5: Calculatex Giveeachanswerto2decimalplaces.(a) (b) (c)

(d) (e) (f)

Question6: Calculatexforeachrightangletriangle. Giveeachanswerto2decimalplaces.(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

(j) (k) (l)




� �

!Pythagoras


Question7: Workoutifeachtrianglebelowisrightangledornot. Thetrianglesarenotdrawnaccurately.

(a) (b) (c)

�

Question1: A9mladderisplacedagainstawall. Thefootoftheladderis1.5mfromthefootofthewall. Howfarupthewalldoestheladderreach?

Question2: Shownisasquarewithsidelength5cm. Findthelengthofthediagonal,x.

Question3: Shownisarightangletriangle. Calculate:

(a)theperimeterofthetriangle. (b)theareaofthetriangle.

Question4: Arectangleis20cmlongand8cmwide. Findthelengthofthediagonaloftherectangle.

Question5: AnairplaneisYlyingfromRedvilletoLeek. TheairplaneYlies50milesEastandthen180milesSouth. HowfarisLeekfromRedvilledirectly?

Question6: Aframeismadefromwire. Theframeisatrapezium Calculatethetotalamountofwireneededtomake theframe.

Giveyouranswerto1decimalplace.

Apply




� �

!Pythagoras


Question7: ABCisanisoscelestriangle. (a)Findh.

(b)Findtheareaofthetriangle.

Question8: Shownisanequilateraltriangle.

Findtheareaoftheequilateraltriangle.

Question9: Stanleyhasdrawnarightangletriangle. Onesideis14cmandanotheris18cm. Therearetwopossiblelengthsforthethirdside. Whatarethey?

Question10: ABCandBCDarerightangletriangles. FindthelengthofAB

Question11: AwoodenYlagpoleis25foottall. Inastorm,theYlagpoleisbrokenanditstop touchestheground5footfromthebase.

FindthelengthsofthesegmentsoftheYlagpole.

Question12: Benjaminhascompletedthisquestion. Canyouspotanymistakes?




� �

!Pythagoras


Question13: Chantellehascompletedthisquestion. Canyouspotanymistakes?

Question14:Victorhascompletedthisquestion. Canyouspotanymistakes?

�Answers


Clickhere


https://corbettmaths.com/wp-content/uploads/2019/02/Pythagoras-Answers.pdf


https://corbettmaths.com/wp-content/uploads/2019/02/Pythagoras-Answers.pdf


� �

!Trigonometry

Video329,330,331onwww.corbettmaths.com

�

�

Question1: Findthesizeofthemissinganglesinthetrianglesbelow.(a) (b) (c)

� (d) (e) (f)

�

(g) (h) (i)

�

(j) (k) (l)

�

Examples

Workout


Clickhere


https://corbettmaths.com/2018/04/25/trigonometry-videos/

https://corbettmaths.com/2018/04/25/trigonometry-videos/

� �

!Trigonometry


Question2: Findthelengthsofthesideslabelledxbelow.(a) (b) (c)

�

(d) (e) (f)

�

(g) (h) (i)

(j) (k) (l)


� �

!Trigonometry


Question3: Findthesizeofthemissingangles/sideslabelledxbelow.

(a) (b) (c)

�

(d) (e) (f)

�

�

Ineachquestion,drawadiagramunlessithasbeengiven.

Question1: A4metrelongladderisplacedagainstawall.Theanglebetweentheladderand thegroundis75°.Howfarupthewalldoestheladderreach?

Question2: A5metrelongladderisplacedagainstawall.Itreaches4.3metresupthewall. Whatistheanglebetweentheladderandtheground?

Question3: Aladderisplacedagainstawall.Thebaseoftheladderis4footfromthe bottomoftheladder.Theanglebetweentheladderandthegroundis80°.Whatisthelengthoftheladder?Question4: Arectangleis12cmlongand5cmwide.Findthesizeoftheanglemarkedx.

Question5: (a)FindthelengthofAC. (b)FindthelengthofAB. (c)FindtheperimeteroftriangleABC. (d)FindtheareaoftriangleABC.

Apply


� �

!Trigonometry


Question6: AhelicopterleavesAandZlies40milesdueeast.ThenthehelicopterZlies 10milesduesouthandarrivesatB.WorkoutthebearingofBfromA.

Question7: Aboatleavesaportandsails55kmduewestandthen30kmduenorthand arrivesatanoilrig.Whatisthebearingoftheoilrigfromtheport?

Question8: Shownisanisoscelestriangle.Calculateitsarea.

� Question9: Shownisarhombusofsidelength10cm. Calculateitsarea.

Question10: Canyouspotanymistakesinthequestionbelow?

�

�Answers


Clickhere


https://corbettmaths.com/wp-content/uploads/2018/12/Trigonometry-1.pdf

https://corbettmaths.com/wp-content/uploads/2018/12/Trigonometry-1.pdf

Year 9 Revision Booklet - Riverside Campus

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