7/30/2019 Mark Scheme Mental

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7/30/2019 Mark Scheme Mental

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First published in 2006

Qualifications and Curriculum Authority 2006

Reproduction, storage, adaptation or translation, in any form or by any means, of this

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for educational purposes, without permission, provided full acknowledgement is given.

Produced in Great Britain by the Qualifications and Curriculum Authority under the authority

and superintendence of the Controller of Her Majestys Stationery Office and Queens Printer

of Acts of Parliament.

The Qualifications and Curriculum Authority is an exempt charity under Schedule 2 of the

Charities Act 1993.

Qualifications and Curriculum Authority

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www.qca.org.uk

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3

Introduction

This booklet contains the mark schemes for the lower tier test (Test C) and the

higher tiers tests (Tests A and B). The pupil answer sheets will be marked by

external markers who will follow the mark schemes in this booklet, which are

provided here for teachers reference.

General guidance for markers

Please note that pupils should not be penalised if they record any informationgiven in the question or show their working. Ignore any annotation, even if in the

answer space, and mark only the answer. Accept an unambiguous answer written

in the stimulus box, or elsewhere on the page, but clearly attributable to the

relevant question.

General guidance for marking the written tests also applies to marking the mental

mathematics tests. In addition, please apply the following principles unless specific

instructions to the contrary are given in the mark scheme:

accept responses in words and/or figures,

eg 7 point 3, 4 hundred

accept any unambiguous indication of the correct response from a given list,

eg circling, ticking, underlining

accept unambiguous misspellings

accept units that have been correctly converted to a different unit provided the

new unit is indicated. Where units have been given on the answer sheet, do not

penalise pupils for writing the units again

accept responses with commas as spacers,

eg 50,000

but do not accept a point used as a spacer,

eg 50.000

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4

Pupilanswersheet

Keystage3mathematics

2006

Mentalmathematics

Tes

tC

Firstname

Lastname

School

Total

marks

Practicequestion

25

Time:5secondscontinued

8

7

8

9

3dd

9

16

5

8

5

5

8

7

5

6

6

16

Time:5seconds

1

1

2

2

3

3

4

feet

151feet

4

5

33

5

6

secon

ds

6

7

920

7

Time:10seconds

10

pupils

24

6

10

11

N

11

12

24

50

12

13

11

13

14

16+x=23

14

15

3.7

0.5

15

17

%

17

Low

ertierTestCquestions

Now

wearereadytostartthetest.

Forthefirstgroupofquestionsyouwillh

ave5secondstoworkouteachanswer

andwriteitdown.

1

Writeinfiguresthenumbersevenhundredandthree.

2

Howmanyrightanglesdoesarectan

glehave?

3

Multiplyeightbythree.

4

TheheightoftheStatueofLibertyisonehundredandfifty-onefeet.

Whatisthisheighttothenearesthu

ndredfeet?

5

WhatnumberdoIneedtoaddtoth

irty-threetomakeonehundred?

6

Howmanysecondsarethereinthreeminutes?

7

Divideninehundredandtwentybyten.

8

Whatnumberisfourlessthanminus

seven?

9

Lookattheexpressiononyouransw

ersheet.

Writeitassimplyaspossible.

Forthenextgroupofquestionsyouwill

have10secondstoworkouteachanswer

andwriteitdown.

10

Agroupofpupilssharetwenty-four

pounds.Theyeachgetexactlysixpounds.

Howmanypupilsareinthegroup?

11

Lookatthediagramonyouranswer

sheet.

Putaringroundthearrowthatispo

intingsouth-west.

12

Subtracttwenty-fourfromfifty.

13

Fortwoadultstoseeafilm,thecost

iselevenpoundsaltogether.

Howmuchdoesitcostforoneadult

toseethefilm?

14

Lookattheequation.Whatistheva

lueofx?

15

Lookatthenumbersonyouranswersheet.Addthem.

16

Lookatthedataonyouranswershe

et.Whichnumberisthemode?

17

Lookatthediagramdrawnonasquaregrid.

Whatpercentageofthediagramisshaded?

Now

turnoveryouranswersheet.

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5

Time:10secondscon

tinued

18

Cereal

Toast

Eggs

1014

2

5

6

3 people

18

29

1.4

5

29

27

132

6

=

22

132

3

=

27

21

BC

A

x

y 2 0 2

2

0

2

(

,

)

21

23

7

23

20

20

22

78

22

19

9

12

19

Time:15seconds

24

Witha

calculator

Withouta

calculator

pupils

24

25

p

60p

25

26

Mirror

line

26

28

28

30

cm

6c

m

30cm

2

30

18

Thediagramshowswhatsomepeoplehadforbreakfast.

Howmanypeoplehadbothcerealandtoast,butnoteggs?

19

Writeanumberthatisafactorofbo

thnineandtwelve.

20

Ihaveafairsix-sideddicenumbered

onetosix.

Iamgoingtorollthedice.

WhatistheprobabilitythatIwillrollanoddnumber?

21

Lookatthetriangledrawnonthegr

id.

Writedownthecoordinatesofthep

ointmarkedA.

22

Twoanglesfittogethertomakeastraightline.

Oneangleisseventy-eightdegrees.

Howmanydegreesarethereintheo

therangle?

23

Whatisthenextprimenumberafter

seven?

For

thenextgroupofquestionsyouwillhave15secondstoworkouteacha

nswer

and

writeitdown.

24

Thetallychartshowsthenumberof

pupilswithandwithoutacalculator.

Altogether,howmanypupilsarethe

re?

25

Threepencilscostsixtypence.

Howmuchwouldfourpencilscost?

26

Lookatthediagramonthesquareg

rid.

Drawthereflectionoftheshapeinthemirrorline.

27

Youranswersheetshowstheanswer

toonehundredandthirty-two

dividedbysix.

Usethisinformationtohelpyouworkouttheanswertoonehundredand

thirty-twodividedbythree.

28

Lookattheshapemadefromequilateraltriangles.

Shadetwomoretrianglessothatthe

shapehasrotationsymmetryoford

erthree.

29

Abirthdaycardcostsonepoundand

forty-fivepence.

Howmuchdothreeofthesecardsco

st?

30

Arectanglehasalengthofsixcentim

etresandanareaof

thirtysquarecentimetres.

Whatisthewidthoftherectangle?

Putyourpensdown.

Thetestisfinished.

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Key stage 3 mathematics 2006

Mental mathematics higher tiers Test A

Test AMark scheme

6

Key stage 3 mathematics 2006

Mental mathematics lower tier Test C

Test CMark scheme

Time: 5 seconds continued

8 11

Time: 5 seconds

1 703Do not accept responses

given in words

2 4

3 24

4 200 feet

5 67Accept embedded values,

eg 33 + 67

6 180 secondsDo not acceptamended units

7 92

9 2d

Time: 10 seconds

10 4 pupilsAccept embedded values,

eg 4 6

11 N Accept anyunambiguous indication

12 26

13 5.50

14 7Accept embedded values,

eg 16 + 7

15 4.2Accept equivalent

fractions or decimals

16 5 Accept valueindicated in list

17 25 % Do not accept equivalentfractions or decimals

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7

Time: 10 seconds continued

18 4 people

25 80 p

27 44

26

Mirror

line

Accept lines not drawn accurately, providedthe pupils intention is clear

21

( 2 , 1 )

Time: 15 seconds

24 20 pupils

22 102

19 1 or 3

2012

Accept equivalentprobabilities

23 11

28

29 4.35

30 5 cm

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8

Pupilanswersheet

Keystage3mathematics2006

Mentalmathematics

Tes

tA

Firstname

Lastname

School

Total

marks

Practicequestion

37

11

13

1 8

1 4

1 3

1 2

3 4

11

4

mm

4

2

300

2

Time:5secondscontinued

7

3.6

8

7

16

5%

300

16

3

9

3

Time:5seconds

1

0

10

20

1

5

2

5

6

6

8

10y

2

3y

2

8

Time:10seconds

9

Right

Wrong

pupils

9

10

cm

10

12

50

A

B

w

12

13

2x8

13

14

10cm:2km

15cm

km

14

15

15

HighertiersTestAquestions

Now

wearereadytostartthetest.

Forthefirstgroupofquestionsyouwillh

ave5secondstoworkouteachanswer

andwriteitdown.

1

Whatnumberisthearrowpointingtoonthenumberline?

2

Dividethreehundredbyten.

3

Multiplysixbynine.

4

Howmanymillimetresarethereineightcentimetres?

5

Whatnumberissixlessthanminustwo?

6

Writeinfiguresthenumberthatiso

nelessthanonemillion.

7

Roundthreepointsixeighttoonedecimalplace.

8

Lookattheexpressiononyouransw

ersheet.Writeitassimplyaspossible.

Forthenextgroupofquestionsyouwill

have10secondstoworkouteachanswer

andwriteitdown.

9

Inaquiz,pupilswereaskedaquestion.

Thepictogramshowshowmanypup

ilswererightandhowmanywerew

rong.

Eightpupilswereright.Howmanyp

upilswerewrong?

10

Theperimeterofasquareistwentycentimetres.

Whatisthelengthofonesideofthe

square?

11

Inaclassoftwenty-eightpupils,thirteenareboys.

Aboutwhatfractionoftheclassare

boys?

Putaringroundthefractionthatisclosest.

12

ABisastraightline.Workoutthesiz

eofanglew.

13

Lookattheexpressiononyouransw

ersheet.

Whenxisnine,whatisthevalueoftheexpression?

14

Thescaleonamapistencentimetrestotwokilometres.

Onthemapthedistancebetweentw

opointsisfifteencentimetres.

Howmanykilometresaretherebetw

eenthetwopoints?

15

Ihaveafairsix-sideddice,numbered

onetosix.Irollthedice.

WhatistheprobabilitythatIrollan

umbergreaterthantwo?

16

Whatisfivepercentofthreehundredpounds?

Now

turnoveryouranswersheet.

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9

17

Findthevolumeofacuboidmeasuringtwocentimetresbyeightcentime

tres

byfourcentimetres.

18

Materialcostsfourpoundsfiftypermetre.

Howmanymetresofthismaterialca

nIbuywithtwenty-sevenpounds?

19

Usingthreeasanapproximationfor

pi,findthecircumferenceofacircle

with

diametereightcentimetres.

20

JakeandSarjunsharesomemoneyintheratioonetothree.

Sarjunsshareisonehundredandfiftypounds.

Altogether,howmuchmoneydidtheyshare?

21

Lookattheexpression.

Whenyissix,workoutthevalueoftheexpression.

For

thenextgroupofquestionsyouwillhave15secondstoworkouteacha

nswer

and

writeitdown.

22

Youranswersheetshowstheanswer

totwenty-sevenmultipliedbythirty

-two.

Usethisinformationtohelpyouworkouttheanswertotwenty-sevenmultiplied

bysixteen.

23

Inasurvey,somepeoplewereasked

iftheyusealibrary.

Thepiechartshowstheresults.

Twelvepeoplesaidno.Howmanype

oplewereaskedaltogether?

24

Amachinecopiesexactlyfiftypages

aminute.

Howmanypagescanitcopyinhalfanhour?

25

Thediagramshowsanarrowofheig

htthreecentimetres.

Ienlargeitbyascalefactoroftwoa

ndahalf.

Whatistheheightoftheenlargeda

rrow?

26

Thetableonyouranswersheetshow

sthenumberofmilkbottlesorderedfor

twentydifferenthouses.

Altogether,howmanymilkbottlesw

ereordered?

27

Whatisthesquarerootoffortythou

sand?

28

Lookattheright-angledtriangle.Workouttheheightofthetriangle.

29

Lookatthegrid.Whatistheequatio

nofthelinemarkedB?

30

Ninemultipliedbyninehasthesame

valueasthreetothepowerwhat?

Putyourpensdown.

Thetestisfinished.

Time:15secondscontinued

26

Numberof

milkbottles

Frequency

0

6

1

3

2

8

3

1

4

2

26

30

99

30

28

height

8 10

28

Time:15seconds

22

27

32

=

864

27

16

=

22

29

6 4 2 00

2

4

6

B

x

y

29

Time:10secondscon

tinued

17

2cm

by8cm

by4cm

cm

3

17

18

m

4

.50

27

18

19

cm

8cm

19

20

1:

3

150

20

21

y(y3)

21

23

No

Yes

23

24

50

24

25

cm

3cm

25

27

40000

27

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10

15 23

Accept equivalentprobabilities, including

0.66, 0.67 or better,or their percentage

equivalents

Time: 10 seconds

9 3 pupils

2 30

Time: 5 seconds

1 8

3 54

4 80 mm

5 8

6 999 999 Do not accept responsesgiven in words

Time: 5 seconds continued

7 3.7Do not accept equivalent

fractions or decimals

8 7y2

10 5 cm

1118

14

13

12

34

12 130

13 10

14

3 km

16 15 Do not acceptincorrect % signs

Key stage 3 mathematics 2006

Mental mathematics higher tiers Test A

Test AMark scheme

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11

27 200Accept 200 with

200 or alone

28 6 Ignore units given

25 712

cmAccept equivalent

fractions or decimals

Time: 10 seconds continued

17 64 cm3

18 6 m

19 24 cm

20 200

21 18

Time: 15 seconds

22 432

23 60

24 1500

Time: 15 seconds continued

26 30

29 x= 2 Accept unconventionalnotation,

eg 1x = 2, x1 2 = 0

30 4 Accept embedded values,eg 34

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13

16

Theratioofboystogirlsinaclassisthreetofive.Therearetwelveboys.

Howmanygirlsarethere?

17

Therectangleonyouranswersheethasbeenenlargedbyascalefactoro

ftwo.

Writedownthedimensionsofthere

ctanglebeforetheenlargement.

18

Lookattheexpressiononyouransw

ersheet.

Whatisthevalueofthisexpressionwhenyisfour?

19

A3-Dshapehasexactlysixfaces.All

sixfacesarerectangles.

Whatisthenameofthe3-Dshape?

20

Fromthree-quarters,subtractnough

tpointtwo.

21

Acartravelledtwokilometresinfive

minutes.

Whatwasthecarsaveragespeedin

kilometresperhour?

For

thenextgroupofquestionsyouwillhave15secondstoworkouteacha

nswer

and

writeitdown.

22

Writeamultipleofninethatisbiggerthanseventyandsmallerthaneigh

ty.

23

Lookatthepatternonthesquaregr

id.

Shadetwomoresquaressothatthe

gridhastwolinesofsymmetry.

24

Youranswersheetshowstheanswer

tosevenmultipliedbyfifty-eight.

Usethisinformationtohelpyouworkouttheanswertothreeandahalf

multipliedbyfifty-eight.

25

Forty-fourpeoplepaidtwenty-fivep

enceeachtogointoabooksale.

Howmuchmoneyisthataltogether?

26

Inaboxofpens,onehalfareblack,onesixthareredandtherestareblu

e.

Whatfractionofthepensisblue?

27

Onthegrid,sketchthestraightlinewithequationyequalsxplustwo.

28

Whatisthesquarerootofninetwen

ty-fifths?

29

Somepeoplewereaskedwhichcolourcartheypreferred.

Thepiechartshowstheresults.

Whatpercentageofthepeoplesaid

blue?

30

msquaredequalsonehundred.

Writedownthetwopossiblevaluesofmp

lusfifteen.

Putyourpensdown.

Thetestisfinished.

Time:15secondscontinued

24

7

58=

406

31 2

58=

24

29

Blue

R

ed

72

%

29

25

44

25p

25

27

4 2 00

2

4

x

y

27

23

23

Time:10secondscon

tinued

16

3:5

16

17

3cm

2cm

cm

and

cm

17

18

1 2y

2

18

19

19

20

3 4

0.2

20

Time:15seconds

22

70

80

22

26

1 2

1 6

26

28

925

28

30

m2

=1

00

m+1

5

and

30

21

km/h

2km

5minutes

21

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Key stage 3 mathematics 2006

Mental mathematics higher tiers Test A

Test AMark scheme

14

Key stage 3 mathematics 2006

Mental mathematics higher tiers Test B

Test BMark scheme

Time: 10 seconds

8 25 answer 35

Do not accept incorrect % signs

Time: 5 seconds

1 5

2 88 000Do not accept responses

given in words

334

Accept equivalentfractions or decimals

4 42 cm2

5 3 %

6 4

7 11.5 m Accept equivalentfractions or decimals

9 35 minutes

10 ( 4 , 1 )

11 25

12 9k+ 5m

13 20

14 165 cm

15 12Accept embedded values,

eg 1230

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15

26 13

Accept equivalentfractions but do notaccept equivalent

decimals

25 11

23

or

Time: 10 seconds continued

16 20Do not accept

12 : 20

171 cm and 1

12

cm

Accept pair in either order

Accept equivalent fractions or decimals

18 8

19 CuboidAccept rectangular prism

Condone cube orsquare prism

20 0.55Accept equivalent

fractions or decimals

21 24 km/h

Time: 15 seconds

22 72Do not accept

8 9

Time: 15 seconds continued

24 203

27

4

2

00 2 4 x

y

Accept line at least two diagonals in length,and line not drawn accurately,

provided the pupils intention is clear

28 35

Accept equivalentfractions or decimals

Accept 3

5with 3

5or alone

29 20 %Do not accept equivalent

fractions or decimals

30 5 and 25 Accept pair ineither order

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EARLY YEARS

NATIONALCURRICULUM516

GCSE

GNVQ

GCE A LEVEL

NVQ

OTHERVOCATIONALQUALIFICATIONS

Further teacher packs may be purchased (for any purpose other than statutory

assessment) by contacting:

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tel: 08700 606015; fax: 08700 606017

email: orderline@qca.org.uk

Order ref: QCA/06/1923 270044