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better future – brighter hope

Iffiveconsecu,venumbersareaddedtogetherandthemiddleonesubtracted,theresultis124.Whatishighestofthefivenumbers?

Alicegetsali?homefromschool.Theyleaveat1540andthecarjourneytakes28minutes.What,medidAlicegethome?

Youcanonlyusethenumbers1,2,3or4.EachrowandeachcolumnhavetoadduptothetotalsshownNonumberscanberepeatedinanyroworcolumn.

Whileyouwait:


Strive for Five Maths Student Conference

Name:

School:

Mathematics Teacher:


Outline of Conference Content

o


Session1

AlgebraicArguments

3b + 5

2a

Length - Perimeter

Perimeter = 48cm.

Find the value of x


Show algebraically that the perimeters of these shapes are identical

Find the values of a and b


Findxineachofthese

triangles2x−9 x+54x+8

3x+12

6x


Whatisthearea?

x4

4

x

Theareaofthesquareis10cm2.Showthatx2+6x=1


Angles6x

4x

2x(10y+7)°

(5y+3)°

127°

88°

Findxandy


Whatisspecialhereabouttheangles?

52° y°

(14x +6)°

2z

2z

2z +24

3z −15


Hereisaparallelogram.Workoutthevalueofxandthevalueofy.

(5x −20)° (4y −5x)°

(2x +43)°


Whatisspecialhereabouttheangles?

5x +10°

y°2x +85°

AB,CDandEFarestraightlines.BenassumesthatABandCDareparallel.Whatanswershouldshegetforthesizeofangley? Infact,ABandCDarenotparallel.Anglewis60°.

Whateffectdoesthishaveonthesizeofangley?Tickaboxandshowworkingtosupportyouranswer.



Session2

PercentagesEssen7als

PercentageofanAmount150%

10%

50%

280

Find17%of280


Percentage Increase+100%

Mul7plier÷100

Decrease–100%

Mul7plier÷100

6% 106% 1.06 94% 0.94

12% 112% 1.12 88% 0.88

8.5% 108.5% 1.085 91.5% 0.915

120% 220% 2.2 Notpossible

Mul,pliersforIncrease&Decrease

Percentage Increase+ 100%

Multiplier ÷ 100

Decrease- 100%

Multiplier ÷ 100

6% 106% 1.06 94% 0.9412% 112% 1.12 88% 0.888.5% 108.5% 1.085 91.5% 0.915120% 220% 2.2 Not possible

Multipliers for Increase & Decrease


PercentageChangeOriginalAmount × Mul7plier = New

Amount

Ben’sweeklysalaryis£250.Hereceivesa7%increase.Whatishisnewweeklysalary?

Acoatcosts£30.Theshophasasalewith20%offallprices.Onthefinaldaytheyreduceallsalepricesby25%.Whatisthepriceofthecoatonthefinalday?


Rachel’smonthlypayincreasedby2.5%to£3895.WhatwasRachel’spaybeforetheincrease?

Inasale,normalpricesarereducedby20%.

Janebuysaroadbikefor£440.Whatisthenormalpriceofthebike?

ReversePercentageChange


CompoundIncrease&Decrease

OriginalAmount × Mul7plier = New

Amount

Noofyears

MissSmithinvests£7300for4yearsinasavingsaccount.Shegets2.7%perannumcompoundinterest.HowmuchmoneywillMissSmithhaveinhersavingsaccountattheendof4years?


Raj purchased a new laptop for £550.Each year the value of his laptop depreciated by 2%.Calculate the number of years after which the value of his laptop was less than £500.

Compound Increase & Decrease



Session3

ShapeComboQues7ons

Machewisgoingtocoverthepa7owithpavingslabs…

Sallyhastofillthecontainerwithoil…

30cm

50cm

40cm

3.6m

3m

…thenheisgoingtoputafenceroundit.

…thensheisgoingtopainttheoutsideofthecontainer.

Choosebetween perimeter area volume


•  ForPerimeter–usestandardlengthconversions•  ForArea–usestandardlengthconversionsSQUARED•  ForVolume–usestandardlengthconversionsCUBED

Unit(Length)Conversions

Convert:(a)  8kmintom

(b)  250mmintom

(c)  2cm2intomm2

(d)  920mm3intocm3


Perimeter:foundbyaddingtogetheralllengthsBUTwemayhavesomemissinglengthstofindfirst…

16m

10m

7m

14m

11m

4m

4m


cross-sec7on

Volumes:prac,ceVolumeofaprism=areaofcross-sec,on×length

length

4cm5cm

8cm 8cm

8cm3cm

10cm4cm


Applica,ons

3m

3.6m

Thediagramshowsapa,ointheshapeofarectangle.

Manhewisgoingtocoverthepa,owithpavingslabs.

Eachpavingslabisasquareofside60cm.

Pavingslabsaresoldinpacksof10.Priceperpackis£12.

However,ifyouarebuying3ormorepacksthereisa10%discount.

Howmuchdoesitcosttobuyenoughpavingslabstocoverthepa,o?


ApplicationsThe diagram shows a container for oil. The container is in the shape of a cuboid. The container is empty.

Sally has to fill the container with oil. A bottle of oil normally costs £3.50 but prices have just been increased by 15 . There is 3000cm3 of oil in each bottle.

Sally must not spend more than £82 buying the oil. Can Sally buy enough oil to fill the container?


Applica,ons14m

11m

4m

Thediagramshowspartofafield.Afarmerwantstoputafenceallthewayaroundtheedgeofthispartofthefield.

Theshopsellsfencingin3metrepanels.Thepriceperpanelis£57.

Thefarmerwillhavetotakealoantopurchasethefencingfromthebank.Thebankwillcharge2%compoundinterestperyear.Calculatetheamountowedtothebanka?er3years.



Session4

Polygons

Polygons


Find the number of sides of this regular polygonFind interior angle sum (regular pentagon)

A regular 6 sided polygon has interior angle sum of 720°. Find the size of one exterior angle.

Find the size of angle x


Session5

UsingNumberLists


2 56

Whatistheconnec,on?

7 691

3 604

14 3018

2 158

If6applescost£2,howmuchwill9applescost?


PaulandKa,esharesomesweetsinthera,o3:8.Ka,egets32sweets.HowmanysweetsdoesPaulget?

Sandrahasapieceofstring150cmlong.Shecutsthestringintothreelengths,inthera,o5:2:3.Workoutthelength,incm,ofeachpieceofstring.


PatandJuliesharesomemoneyinthera,o2:7.Juliegets£45morethanPat.HowmuchmoneydidPatget?

Talilisgoingtomakesomeconcretemix.Heneedstomixcement,sandandgravelinthera,o1:3:5byweight.Talilwantstomake180kgofconcretemix.Talilhas45kgofcement,45kgofsandand150kgofgravel.Doeshehaveenoughcement,sandandgravel?


Recipefor16gingerbreadmen180gflour40gginger110gbuner

Recipefor10gingerbreadmen flourginger

buner

Edmakessomegingerbreadmen.Hehasonlygot12gofginger,buthasplentyoftheotheringredients.Howmanycompletegingerbreadmencanhemake?


Manhewmakes32pancakes.Workouthowmuchflourheuses.

Recipefor10pancakes300mlmilk120gflour2eggs

Taramakessomepancakes.Sheuses750mlofmilk.Workouthowmanypancakesshemakes.


Inthisques+on,assumethatthecarusesthesameamountofpetrolforeachmileittravels.

Acaruses16litresofpetroltotravel95miles.Howfarwouldthecartravelon80litresofpetrol?Howmuchpetrolwouldthecaruseonatripof380miles?

P1XL


Milkissoldintwobonlesizes.

A4pintbonleofmilkcosts£1.18.A6pintbonleofmilkcosts£1.74.Whichbonleofmilkisthebestvalueformoney?


MargaretisonholidayinFrance.ShebuysanEnglishnewspaper.

Thecostofthenewspaperis5euros.

InEngland,thecostofthesamenewspaperis£2.50

Theexchangerateis£1=1.16euros

WorkoutthedifferencebetweenthecostofthenewspaperinFranceandthecostofthenewspaperinEngland.


Simoncaughttwotench.Howmanyroachdidhecatch?

Thereare12redcarsHowmanysilvercarsarethere?Howmanybluecarsarethere?


A

B

CD

E

3.6cm

1.2cm

3cm

TriangleACDissimilartoABE.EBisparalleltoDCFindthelengthofDE



Session 1: Algebraic Argumentsq Simplify, expand, substitute, solve equationsq Algebra applied to perimeter / area problemsq Algebra applied to angle problems

Session 5: Using Number Listsq Sharing Ratioq Recipe Ratioq Best Buyq Currency Conversionsq Pie Chartsq Similarity

Session 2: Percentages Essentialsq % of amountsq % increase / decreaseq Reverse % changeq Compound %

Session 3: Shape Combo Questions

q Recognise and find perimeters, areas and volumes

q Combine with money calculations

Review of Conference Content

Session 4: Polygon Anglesq Use exterior angle sum to find

one exterior or number of sides

q Use exterior + interior = 180°

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