level 1 mathematics and statistics (91028) 2013 · 2013-11-13 · no part of this publication may...

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© New Zealand Qualifications Authority, 2013. All rights reserved.No part of this publication may be reproduced by any means without the prior permission of the New Zealand Qualifications Authority.

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Level 1 Mathematics and Statistics, 201391028 Investigate relationships between tables,

equations and graphs

9.30 am Wednesday 13 November 2013 Credits: Four

Achievement Achievement with Merit Achievement with ExcellenceInvestigate relationships between tables, equations and graphs.

Investigate relationships between tables, equations and graphs, using relational thinking.

Investigate relationships between tables, equations and graphs, using extended abstract thinking.

Check that the National Student Number (NSN) on your admission slip is the same as the number at the top of this page.

You should attempt ALL the questions in this booklet.

Show ALL working.

If you need more space for any answer, use the page(s) provided at the back of this booklet and clearly number the question.

Check that this booklet has pages 2 – 10 in the correct order and that none of these pages is blank.

YOU MUST HAND THIS BOOKLET TO THE SUPERVISOR AT THE END OF THE EXAMINATION.

You are advised to spend 60 minutes answering the questions in this booklet.

QUESTION ONE

(a) EachyearatChristmas,Jamie’sgrandmothergavehimfivedollarsplustwodollarsforeachyearofhislife.HisageandtheamounthereceivedforthreeChristmasesisshowninthetablebelow.

Age, n AmountJamiereceived, A

1 $72 $93 $11

(i) Writetheequationfortheamount,A,Jamiewasgivenbyhisgrandmotherintermsofhis age, n, atChristmas.

(ii) FindtheamountJamiewasgivenbyhisgrandmotheratChristmaswhenhewas12.

Youmustshowuseofyourequationfrompart(i).

(iii) OnthegridbelowplotthegraphthatshowstheamountofmoneythatJamie’sgrandmotherhadgivenhimforeachChristmas.

5 10

10

20

30

age n (years)

A ($)

If you need to redraw

this graph, use the grid on page 8.

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Mathematics and Statistics 91028, 2013


(iv) Jamie’ssisterArnaisthreeyearsyoungerthanhim.

EachChristmashergrandmotheralsogaveherfivedollarsplustwodollarsforeachyearofArna’slife.

Onthegridforpart(iii),sketchthegraphshowingthetotal amount that their grandmotherhadgiventhemeachChristmas.

(v) ThisChristmasJamieandArnareceivedatotalof$44fromtheirgrandmother.

WriteatleastoneequationandusethistofindhowoldJamiewasthisChristmas.

(vi) GivetheequationtocalculatethetotalamountJamie’sgrandmotherhadgivenhiminn Christmases.

(b) Givetheequationofthegraphbelow.

1–1–2–3–4–5–6 2

5

–5

10

15

20

25

3 4 5 6 7 8 9 x

y

Equation:

3



QUESTION TWO

(a) Marnieisabouttostartsavingforaschoolnetballtrip. Shehasapart-timejob. HernetballteampractiseseachFriday. Thereare14morepracticesbeforethetrip. Shedecidestogivehercoach$20forthetripateachofthe14Fridaypractices.

(i) Plotthegraphofthetotalamount,T,Marniehasgivenhercoachattheendofeachpractice,P.

2 31 4 5 6 7 98 10 11 12 13 14

40

60

100

140

180

220

260

20

80

120

160

200

240

280

300

320

T ($)

P

(ii) Ifalineisdrawnthroughthetotalamountsshehasgivenhercoachateachpractice,givetheequationofthisline.

(iii) Thetotalcostofthetripis$300. Afterseveralpractices,whenMarniehaspaidhercoach,sheistoldthatsheisnotgoing

tohaveenoughmoneyforthetrip. Marnieneedstostartpayingthecoach$30aweeksothatshemeetsher$300target.

Ontheabovegrid,plotthegraphofthechangedamountsheneedstopay.

(iv) ForhowmanyweeksdoesMarnieneedtopaytheincreasedamountsothatshemeetsher$300targetatthe14thpractice?



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(v) Givetheequationforthegraphrepresentingtheincreasedpayments.

(b) Samfoundapuzzleinabook.

Hewastoldtothinkofanumberandthentofollowsomeinstructionsandseewhatnumberhehadastheanswer.

Samwascurioussohemadeatableandfilledinsomenumbers:

1st try 2nd try 3rd column

Think of a number 5 10 N

Add 2 7 N + 2

Multiply by 3 36

Add on your number 26

Add 6 32 52

Divide by 4 8 13

Take away your number 3

(i) Completethe3rdcolumnofthetable.

(ii) Explainindetailwhytheanswerisalways3,nomatterwhatnumberhestartswith.

5



QUESTION THREE

(a) Susieridesherbiketoherfriend’shouseataconstantspeed.

Theythenwalktoschooltogetherataconstantspeed.

ThedistancethatSusieisfromschoolisgiveninthetablebelow.

Susie Time t since leaving home in minutes

Distance d from school in metres

Leaves home 2500Arrivesatfriend’shouse 2 2000Leavesfriend’shouse 15 2000Arrivesatschool 35

(i) Ontheaxisbelowsketchthegraphofthedistance,d,thatSusieisfromschoolatanytime, tminutesafterleavinghome.

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

500

1000

1500

2000

2500

3000

d(metres)

t(minutes)

(ii) ForyourgraphgivetheequationtofindhowfarSusieandherfriendarefromschoolatanytimefor:

• 2≤t≤15

• 15<t<35



6



(b) Charneismakingtablesofnumbers.

x y

–3 –2 –1 1 2 3 4 5

–5

–4

–3

–2

–1

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

x

y

–2 5–1 00 –31 –42 –33 04 55 12

(i) Ontheabovegridplotthegraphoftherelationshipshowninthetable.

(ii) Givetheequationthatshewouldhaveusedtogetthissetofnumbers.

(iii) Ifthegraphwasmovedsothatitslowestpointwasat(3,–1),describehowthegraphwouldchange,andgivethenewequationofthegraph.



7



IfyouneedtoredrawthegraphfromQuestionOne(a)(iii),drawitonthegridbelow.Makesureitisclearwhichgraphyouwantmarked.

5 10

10

20

30

age n (years)

A ($)

IfyouneedtoredrawthegraphfromQuestionTwo(a)(i),drawitonthegridbelow.Makesureitisclearwhichgraphyouwantmarked.

2 31 4 5 6 7 98 10 11 12 13 14

40

60

100

140

180

220

260

20

80

120

160

200

240

280

300

320

T ($)

P

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IfyouneedtoredrawthegraphfromQuestionThree(a)(i),drawitonthegridbelow.Makesureitisclearwhichgraphyouwantmarked.

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40

500

1000

1500

2000

2500

3000

d(metres)

t(minutes)

IfyouneedtoredrawthegraphfromQuestionThree(b),drawitonthegridbelow.Makesureitisclearwhichgraphyouwantmarked.

–3 –2 –1 1 2 3 4 5

–5

–4

–3

–2

–1

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

x

y

9



10



QUESTION NUMBER

Extra paper if required.Write the question number(s) if applicable.

91

02

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level 1 mathematics and statistics (91028) 2013 · 2013-11-13 · no part of this publication may...

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