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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

    publication is prohibited without prior written permission of the publisher, unless within the

    terms of licences issued by the Copyright Licensing Agency. Excerpts may be reproduced for

    the purpose of research, private study, criticism or review, or by educational institutions solely

    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

    83 Piccadilly

    London

    W1J 8QA

    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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    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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    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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    15/16

    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:

    QCA Orderline, PO Box 29, Norwich NR3 1GN

    tel: 08700 606015; fax: 08700 606017

    email: [email protected]

    Order ref: QCA/06/1923 270044