National 5LifeskillsMaths Practice Assessment1 Geometryand Measures

FORMULAE LIST

1Anna ismoving toBrisbane,Australia.Shehasthefollowinginformation:

DistancetoBrisbane fromLondon / 16 532km
Aircraftspeed / 850km/h
Timedifference / +9hours
Stopoverin HongKong / 3 hours30minutes

(a)CalculatehowlongthejourneyfromLondonto Brisbane will take including a stopoverin Hong Kong.

Give youranswerin hoursandminutes.

4

(b)IfAnnatakestheMondayflightleavingLondon at1315,whattimewill she arrive in Brisbane?

1

(c)Anna’ssister,who lives in London, plansto phoneand chatto Annaon Tuesdayat1830 UK time.Willthisbe asuitable time tophone?Justifyyour answer.

2

(d)Anna will be atworkfrom0900to1730 Mondayto Friday.She likesto be in bed by2200.Givehersisteradvice on thebesttimeto contactheron weekdaysfromherhome in the UK.

1

2A helicopterfliesfromAberdeentotwo oil rigsfollowing theroutebelow.

From Aberdeenthehelicopterflies:

Route

300kmon abearing of050°tothe Everest Platform

Then

150kmon abearing of120°tothe ElginPlatform

(a)Usingasuitablescale,makea scale drawingofthe helicopter’sflight.

4

(b)Thehelicopterreturns directlyto Aberdeenfromthe Elgin Platform.

Calculatethe distanceofthereturnjourney.

3

(c)Ifthehelicopterflies atasteadyspeed of110km/h±10%calculatethe minimumandmaximumtimetakentocompletethe whole journey.

6

3John makes waxcandles.Eachcandle is in the shape ofa cone,with diameter6cmand slantheight8cm,asshown.

8 cm

V1r2h

3

6 cm

a)John buyswax in5 litretubs.Howmanycandlescan hemakefromone tub ofwax?

5

(b)John also wantstomakecandles intheshape ofacylinder.Ifeach hasheightof5 cmandthe

samevolumeasthecone-shaped candle.

Calculatetheradius ofthe mouldforthenew candle.

5cm

2

4Adamismovinghouse.He has hiredaremovalvan as shown below:

4.0m

2.5m

A2.5m

Adamhasa lotofboxestogo intothe van.The size ofeachbox isgiven below:

50 cm

This way up

20 cm

30 cm

WhatisthemaximumnumberofboxesAdamcan packintothe van?

Justifyyouranswer.

4

5You haveinvited friendsfordinner.Thefollowingisa listofthingsyou need todo:

ACookfood

BWithdrawenoughmoneyforfoodfromacashmachine CPreparefood

DGoto supermarket EBuy ingredients

FArrangetable

GEatthefood

HWash dishes

Someofthese activities mightbedoneatthesametime.

Completetheprecedencetable belowbyputting the activities into a logical order andidentifyoneoccasion whentwo activitiescould bedone atthe sametime.

Put thesecondactivity inthe right-handcolumn.

Orderofactivities / Activities thatcould be done atthesame time

2

6Mostavalanchesoccuron slopeswithgradients which lie in the range 0·7to 1·0.

A ski company in Europeislooking atahill to seeifitsafeto develop itas aski run.

a)Thetoppartoftherunstartsata heightof1840m,is150min length and dropstoa heightof1750m,asshown in thediagram.

1840m

150m

1750 m

Isthe slopeconsideredsafefromavalanches?(5)

1

(b)The lowerpartoftherun isconsideredsafe as ithasagradientof.

3

Itstartsfromaheightof1750manddropstoa heightof1650 m.

Whatisthe lengthoftheslope?(3)

7Tiawantsto paintherloungewalls.

Theroomhasthefollowing dimensions(diagramnotto scale):

(a)Tia wantstogive thewalls2 coatsofpaint.

Howmanylitresofpaintmustshe buyto paintherlounge?

5

(b)Paintissold in either1 litreor2∙5 litretins.

1 litretins cost £8∙40 each 2∙5 litretinscost £18∙10each

Whatistheminimumcostofpainting the lounge?

3

(c)Tia wantsto laydecking in the shapeofaquartercircle,asshown in the diagram.

Thecheapestquote is £60perm².

Tia hasa budgetof£450forthe decking.Cansheaffordthedecking?

Justifyyouranswer.

4

Question Number / Pointsof strategyandprocessandofcommunicationin assessment forcandidates
Each •illustrates onemark
1 (a)
(b)
(c)
d) / S:knowto useformula
P:calculatetime Communication:convert to hours and minutes
P:addstop-overtime
P:calculate UK and Australian time
Communication:convert time
Communication:conclusion with justification
Communication:conclusion with justification /
  • time=distance/speed
=16532÷850=19∙45hours
  • 19hours 27mins
+3hours30mins
=22hours57mins
  • 1315add22hours57mins
1212 UK
+9hours=2112Brisbane
  • 1830Tues UK=0330Wed Brisbane
  • Thisisn’tasuitabletimeasshewill
probablybeinbed
  • 1800– 2200Brisbane
She should call anytimebetween 0900– 1300 UKweekdays.Acceptanytime between these limits.
2
(a)
(b) / S:scalestated
Process:Constructangles Process:Constructsides Communication:scaledrawing completeand annotated
N
Everest
120°
300 km(6 cm)
150 km(3 cm)
N
050°Elgin /
  • 1cm:50km(oranysuitablescale)
  • Anglesof050ºand120º
  • 60mmand30mm
  • Bearingsanddistances
  • 7·4cm(acceptanerrortoleranceof± 0∙2cm)

Aberdeen
P:evidence ofmeasuringfinal leg
(c) / Communication:conversion tokm Communication:Bearing ofreturn journey
S:calcmax/minspeed
P:startto calculatemaxtime
P:complete
C:time in hoursandmins
P:complete formin time
Communication:minimumand maximumnumberofhoursstated / 7·4×50=370km
  • Bearinganswer±2º
  • Speedands
820/121
820/121=6·78hours
=6hoursand·78 of1hour
=6hours+·78×60mins
=6hours47minsminimum
820/99=8·28hours
=8hours+·28of1 hour
=8hours+·28×60mins
=8hoursand17minsmaximum
3 / S:knowformulae / h²=8²–3²=64–9=55cm
(a) / h=√55=7∙4cm
P:calculateheightofcone
  • V=1/3πr2h

P:calculatevolume / =1÷3×3∙14×3²×7∙4
=69∙71 cm³
S:convert litresto cm³andknowto divide / 5litres=5000cm³÷69∙71
Communication:calculatenumberof candles andround correctly / =71∙73 so71candles
S:equatetofindradius
(b) /
  • V=πr2h

69∙71=3∙14× r²×5
P:calculatetheradius / 69∙71÷15∙7=r²
r²=4∙44
r= 2∙11cm
4 / S:knowsboxes can bepacked differentways
P:calculatesnumberofboxes to be packedusing20cmfacing /
  • Showstwowaysofpackingboxes
  • Numberof20cmboxes
=20×8×5
=800boxes
  • Numberof30cmboxes

P:calculatesnumberofboxes to be packedusing30cmfacing
Communication:maximumnumber with justification / =13×12×5
=780boxes
  • 800boxes ifpacked20cmfacing sideAofvan,20morethanif30cm packedfacingsideAof van.

5 / S:knowstoorder
Communication:orders appropriatelyforexample
OrderofActivities
Activities thatcould be done at the same
time
B D E C
A F
G H /
  • Uses lettersorphrases
  • Acceptanylogicalorderandatleastone activitythatcouldbedoneatthesame timeasanother.GandHshouldbelast two,butacasecouldbemadeforother approaches.
N.B.Justificationnotrequired.
6
(a)
(b) / Process:Calculateheight
Strategy:Knowand startto use Pythagoras
Process:Calculateside
Strategy:Calculategradient
Communication:Correctconclusion
Strategy:Usegradienttofind missing side
Process:Knowand startto use Pythagoras
Process:Calculate length /
  • 90m
1502=902+x2
120m
90/120=0∙75
  • Notsafefromavalanchessince0∙75lies withintherangeof0∙7to1∙0.
⅓=100/300
1002+3002=r2
316∙2m
7 (a) / S:knowformulaforarea
P:calculateareaofwalls /
  • Area=l×b
(10×2∙5)+(12×2∙5)+(7×2∙5)+(3× 2∙5)+(3×2·5)+(9×2·5)=110m²
(b)
(c) / P:calculateareaofdoorand window
S:starttocalculatenumberoftinsto be bought
Communication:state numberof litretinsrequired
Process:costofone option Process:costofremaining options Communication: state correct combination
S:knowformulaforareaofcircle
P:calculateareaofdecking
P:calculatecostofdecking
Communication:answerwith justification using result / =(3×2)+(1×1.5)=7.5m²
=110– 7·5=102·5m²
  • 1litrecovers16m² NumberofTins=205/16
=12∙8
  • Shemustbuy13litres
  • Oneoptionfrom:2∙5litre= £18∙10
=40m²
3 tinscost3×£18∙10=£54∙30 OR
2×2.5litretins=2×£18·10=£36·20
+2×1litretin=2×£8·40=£16·80
=£53
  • Second optionfromabove
  • Minimumcost=£53
  • Ar2
=1÷4×3∙14×3²
=7∙065m²
Cost=60×7∙065=£423∙90
  • Tiacanaffordtolaythedeckingasit costs£26·10lessthatherbudget.