KEY STAGE Mark scheme 3 for Mental mathematics KS3 SA… · for Mental mathematics LOWER TIER &...

16
National curriculum assessments 2008 Ma KEY STAGE 3 Mathematics tests Mark scheme for Mental mathematics tests A, B and C LOWER TIER & HIGHER TIERS

Transcript of KEY STAGE Mark scheme 3 for Mental mathematics KS3 SA… · for Mental mathematics LOWER TIER &...

National curriculum assessments

2008

Ma

KEY STAGE

3

Mathematics tests

Mark scheme for Mental mathematicstests A, B and CLOWER TIER &

HIGHER TIERS

282686_mmMs04.indd 1282686_mmMs04.indd 1 3/12/07 11:35:19 am3/12/07 11:35:19 am

QCA wishes to make its publications widely accessible. Please contact us if you have any specific accessibility requirements.

First published 2008

© Qualifications and Curriculum Authority 2008

ISBN 1-84721-491-6

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, providingfull acknowledgement is given.

Printed in Great Britain by the Qualifications and Curriculum Authority under the authority and superintendence of the Controller of Her Majesty’s Stationery Office and Queen’s 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 Authority83 PiccadillyLondon W1J 8QAwww.qca.org.uk

282686_mmMs04.indd 2282686_mmMs04.indd 2 3/12/07 11:35:21 am3/12/07 11:35:21 am

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 information given 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 specifi c instructions to the contrary are given in the mark scheme:

accept responses in words and/or fi gures,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

282686_mmMs04.indd 3282686_mmMs04.indd 3 3/12/07 11:35:21 am3/12/07 11:35:21 am

4

Pup

il an

swer

sh

eet

Key

sta

ge

3 m

athe

mat

ics

20

08

Men

tal m

athe

mat

ics

Test

C

Firs

t na

me

Last

nam

e

Sch

oo

l

Tota

lm

arks

Pra

ctic

e q

uest

ion

49

Tim

e: 5

sec

ond

s

167

1

41

71 4

7

22

319

3

442

664

56

7

5

67k

– 4

k6

80.

8

58

Tim

e: 1

0 se

cond

s

920

1020

0121

00

2110

2101

9

1014

15

16

10

11

£11

12tr

ain

bus

adul

t£2

.00

£1.2

0

child

£1.0

040

p

£12

1325

th J

uly

13

14m

en

wom

en

= 2

5 p

eop

le

14

153

3

215

16

°E

W

SN

16

Low

er t

ier

test

C q

ues

tio

ns

‘No

w w

e ar

e re

ady

to s

tart

th

e te

st.

For

the

fi rs

t g

rou

p o

f q

ues

tio

ns

you

will

hav

e 5

seco

nd

s to

wo

rk o

ut

each

an

swer

an

d w

rite

it d

ow

n.’

1A

dd

six

ty-s

even

an

d f

ou

rtee

n.

2H

ow

man

y si

des

do

es a

n o

ctag

on

hav

e?

3D

ou

ble

nin

etee

n.

4R

ou

nd

fo

ur

tho

usa

nd

tw

o h

un

dre

d a

nd

six

ty-s

ix t

o t

he

nea

rest

ten

.

5M

ult

iply

six

by

seve

n.

6Lo

ok

at t

he

exp

ress

ion

. Wri

te it

as

sim

ply

as

po

ssib

le.

7W

rite

on

e q

uar

ter

as a

dec

imal

.

8W

hat

is n

ou

gh

t p

oin

t ei

gh

t m

ult

iplie

d b

y fi

ve?

‘Fo

r th

e n

ext

gro

up

of

qu

esti

on

s yo

u w

ill h

ave

10 s

eco

nd

s to

wo

rk o

ut

each

an

swer

an

d w

rite

it d

ow

n.’

9Lo

ok

at t

he

nu

mb

ers

on

yo

ur

answ

er s

hee

t.Pu

t a

rin

g r

ou

nd

th

e la

rges

t n

um

ber

.

10A

dd

to

get

her

fo

urt

een

, fi f

teen

an

d s

ixte

en.

11Lo

ok

at t

he

coin

s.H

ow

mu

ch m

on

ey is

sh

ow

n a

lto

get

her

?

12Th

e ta

ble

sh

ow

s th

e p

rice

of

a jo

urn

ey b

y tr

ain

or

bu

s.H

ow

mu

ch w

ill it

co

st t

wo

ad

ult

s an

d o

ne

child

to

mak

e th

e jo

urn

ey b

y b

us?

13Jo

hn

wen

t to

Fra

nce

on

th

e tw

enty

-fi f

th o

f Ju

ly a

nd

ret

urn

ed

exac

tly

on

e w

eek

late

r.O

n w

hat

dat

e d

id J

oh

n r

etu

rn?

14Th

e ch

art

sho

ws

the

nu

mb

er o

f m

en a

nd

wo

men

wh

o w

ork

at

a fa

cto

ry.

On

e sy

mb

ol r

epre

sen

ts t

wen

ty-fi

ve

peo

ple

.H

ow

man

y m

ore

men

th

an w

om

en w

ork

at

the

fact

ory

?

15Su

btr

act

thre

e fr

om

th

ree

squ

ared

.

16Sa

m is

fac

ing

No

rth

. He

turn

s cl

ock

wis

e to

fac

e N

ort

h-E

ast.

Thro

ug

h h

ow

man

y d

egre

es d

oes

he

turn

?

‘No

w t

urn

ove

r yo

ur

answ

er s

hee

t.’

282686_mmMs04.indd 4282686_mmMs04.indd 4 3/12/07 11:35:22 am3/12/07 11:35:22 am

5

Tim

e: 1

0 se

cond

s co

ntin

ued

17

–6

° C

–4

–2

02

4

° C17

188

km5

mile

s

mile

s18

19y 2

B

A

Cx

0–

20

2

–2

(

,

)19

20√8

120

215b

+ 3

21

Tim

e: 1

5 se

cond

s

22

3 tin

s fo

r 99

p

£22

Tim

e: 1

5 se

cond

s co

ntin

ued

24

02

46

810

slee

pin

g

eatin

g

wor

king

Tim

e (h

ours

)

24

2323

25

8cm

6cm

6cm

cm25

261,

3,

6,

10

, 1

5,

26

271

red

1 gr

een

3

blu

e

27

28A

450

g

B

950

g

C g28

2929

×34

=98

6

0.29

×34

=29

30

°17

0°a

30

17Lo

ok

at t

he

tem

per

atu

re s

ho

wn

on

th

e th

erm

om

eter

.Th

e te

mp

erat

ure

dro

ps

by

fi ve

deg

rees

Cel

siu

s. W

hat

is t

he

new

tem

per

atu

re?

18Ei

gh

t ki

lom

etre

s is

ab

ou

t fi

ve m

iles.

Ab

ou

t h

ow

man

y m

iles

is t

wen

ty-f

ou

r ki

lom

etre

s?

19Lo

ok

at t

he

tria

ng

le d

raw

n o

n t

he

gri

d.

Wri

te t

he

coo

rdin

ates

of

the

po

int

mar

ked

A.

20W

hat

is t

he

squ

are

roo

t o

f ei

gh

ty-o

ne?

21Lo

ok

at t

he

exp

ress

ion

. I s

ub

trac

t th

ree

fro

m t

he

exp

ress

ion

.W

rite

th

e n

ew e

xpre

ssio

n a

s si

mp

ly a

s p

oss

ible

.

‘Fo

r th

e n

ext

gro

up

of

qu

esti

on

s yo

u w

ill h

ave

15 s

eco

nd

s to

wo

rk o

ut

each

an

swer

an

d w

rite

it d

ow

n.’

22Yo

ur

answ

er s

hee

t sh

ow

s th

e co

st o

f th

ree

tin

s o

f ca

t fo

od

.H

ow

mu

ch w

ou

ld s

ix o

f th

ese

tin

s co

st?

23I a

m t

hin

kin

g o

f a

nu

mb

er.

The

nu

mb

er c

an b

e d

ivid

ed b

y th

ree

wit

h n

o r

emai

nd

er.

It c

an a

lso

be

div

ided

by

fou

r w

ith

no

rem

ain

der

.W

hat

co

uld

my

nu

mb

er b

e?

24Th

e b

ar c

har

t sh

ow

s h

ow

Pet

e sp

ent

som

e o

f h

is d

ay.

Ho

w m

any

mo

re h

ou

rs d

id h

e sp

end

sle

epin

g t

han

wo

rkin

g?

25Lo

ok

at t

he

tria

ng

le a

nd

th

e sq

uar

e.Th

e p

erim

eter

of

the

tria

ng

le is

th

e sa

me

as t

he

per

imet

er o

f th

e sq

uar

e.W

hat

is t

he

sid

e le

ng

th o

f th

e sq

uar

e?

26Lo

ok

at t

he

seq

uen

ce o

f tr

ian

gu

lar

nu

mb

ers:

on

e, t

hre

e, s

ix, t

en, fi

fte

en.

Wh

at is

th

e n

ext

nu

mb

er in

th

e se

qu

ence

?

27B

en h

as o

ne

red

mar

ble

, on

e g

reen

mar

ble

an

d t

hre

e b

lue

mar

ble

s in

his

po

cket

.H

e is

go

ing

to

tak

e o

ne

of

the

mar

ble

s o

ut

of

his

po

cket

wit

ho

ut

loo

kin

g.

Wh

at is

th

e p

rob

abili

ty it

will

be

gre

en?

28Lo

ok

at t

he

info

rmat

ion

on

yo

ur

answ

er s

hee

t.Th

e to

tal m

ass

of

the

thre

e b

oxe

s is

tw

o k

ilog

ram

s.W

hat

is t

he

mas

s o

f b

ox

C?

29Tw

enty

-nin

e m

ult

iplie

d b

y th

irty

-fo

ur

is n

ine

hu

nd

red

an

d e

igh

ty-s

ix.

Wh

at is

no

ug

ht

po

int

two

nin

e m

ult

iplie

d b

y th

irty

-fo

ur?

30Lo

ok

at t

he

dia

gra

m. W

ork

ou

t th

e si

ze o

f an

gle

a.

‘Pu

t yo

ur

pen

s d

ow

n. T

he

test

is fi

nis

hed

.’

282686_mmMs04.indd 5282686_mmMs04.indd 5 3/12/07 11:35:22 am3/12/07 11:35:22 am

Key stage 3 mathematics 2006

Mental mathematics higher tiers Test A

Test AMark scheme

6

6 3k

Key stage 3 mathematics 2008

Mental mathematics lower tier Test C

Test CMark scheme

Time: 5 seconds

1 81

3 38

4 4270

5 42

Time: 10 seconds

92010 2001 2100

2110 2101

11 £ 1.13

13 1st August Accept anyunambiguous or commonly used

indication of the date, eg 1 Aug, 1/8 or

8/1 [US notation]Ignore years given

2 8

7 0.25 Accept equivalent decimals

Do not accept equivalent fractions

8 4 (.0)

10 45

12 £ 2.80

14 75

15 6

16 45 ° Accept 45 + any multiple of 360

282686_mmMs04.indd 6282686_mmMs04.indd 6 3/12/07 11:35:23 am3/12/07 11:35:23 am

7

Time: 10 seconds continued

17 –3 °C

19 (1, –2)

20 9 Accept –9 with 9or alone

Accept embedded valueseg 9 × 9

Time: 15 seconds continued

24 3

25 5 cm

28 600 g

18 14.9 answer 15.1 miles

21 5b

Time: 15 seconds

22 £ 1.98

23 Any multiple of 12

Accept zero or negative multiples of 12

26 21

27 15

Accept equivalentprobabilities

29 9.86 Accept equivalentfractions or decimals

30 100 °

282686_mmMs04.indd 7282686_mmMs04.indd 7 3/12/07 11:35:23 am3/12/07 11:35:23 am

8

Pup

il an

swer

sh

eet

Key

sta

ge

3 m

athe

mat

ics

20

08

Men

tal m

athe

mat

ics

Test

A

Firs

t na

me

Last

nam

e

Sch

oo

l

Tota

lm

arks

Pra

ctic

e q

uest

ion

9910

40

50

10

Tim

e: 5

sec

ond

s

142

1

28

47

49

2

64.

875

6

40.

1

44

5–

25

34

b +

5b

3

1320

%

613

Tim

e: 1

0 se

cond

s

830

08

9

cm2

9

12a

= 5

b –

412

Tim

e: 5

sec

ond

s co

ntin

ued

7y

= 3

x +

27

1155

°

25°

p

°11

14m

iles

40m

ph

14

1520

15

163

(a –

5)

16

175.

717

Hig

her

tie

rs t

est

A q

ues

tio

ns

‘No

w w

e ar

e re

ady

to s

tart

th

e te

st.

For

the

fi rs

t g

rou

p o

f q

ues

tio

ns

you

will

hav

e 5

seco

nd

s to

wo

rk o

ut

each

an

swer

an

d w

rite

it d

ow

n.’

1H

ow

man

y si

xes

are

ther

e in

fo

rty-

two

?

2Lo

ok

at t

he

nu

mb

ers

on

yo

ur

answ

er s

hee

t.W

rite

do

wn

th

e n

um

ber

th

at is

th

e m

od

e.

3Lo

ok

at t

he

exp

ress

ion

. Wri

te it

as

sim

ply

as

po

ssib

le.

4Su

btr

act

no

ug

ht

po

int

on

e fr

om

fo

ur.

5W

hat

nu

mb

er is

eig

ht

mo

re t

han

min

us

two

?

6Lo

ok

at t

he

nu

mb

er o

n y

ou

r an

swer

sh

eet.

Ro

un

d it

to

on

e d

ecim

al p

lace

.

7W

hat

is t

he

gra

die

nt

of

the

line

wit

h e

qu

atio

n y

eq

ual

s th

ree

x p

lus

two

?

‘Fo

r th

e n

ext

gro

up

of

qu

esti

on

s yo

u w

ill h

ave

10 s

eco

nd

s to

wo

rk o

ut

each

an

swer

an

d w

rite

it d

ow

n.’

8Th

ere

are

thre

e h

un

dre

d p

eop

le a

t a

con

cert

.O

ne

hu

nd

red

an

d fi

fty

-fi v

e o

f th

em a

re m

ale.

Ho

w m

any

are

fem

ale?

9Lo

ok

at t

he

shad

ed t

rian

gle

dra

wn

on

a c

enti

met

re s

qu

are

gri

d.

Wh

at is

th

e ar

ea o

f th

e tr

ian

gle

?

10W

rite

do

wn

th

e m

ult

iple

of

twel

ve b

etw

een

fo

rty

and

fi f

ty.

11Lo

ok

at t

he

tria

ng

le. W

ork

ou

t th

e si

ze o

f an

gle

p.

12Lo

ok

at t

he

equ

atio

n o

n y

ou

r an

swer

sh

eet.

Wh

en b

is t

hre

e, w

hat

is t

he

valu

e o

f a?

13Tw

enty

per

cen

t o

f a

nu

mb

er is

six

. Wh

at is

th

e n

um

ber

?

14I t

rave

l at

a co

nst

ant

spee

d o

f fo

rty

mile

s p

er h

ou

r.H

ow

far

do

I tr

avel

in t

wo

an

d a

hal

f h

ou

rs?

15O

n a

vera

ge

I tak

e tw

enty

bre

ath

s in

on

e m

inu

te.

Ho

w m

any

bre

ath

s is

th

at in

on

e h

ou

r?

16Lo

ok

at t

he

exp

ress

ion

. Mu

ltip

ly o

ut

the

bra

cket

s.

17Lo

ok

at t

he

nu

mb

er o

n y

ou

r an

swer

sh

eet.

Hal

ve it

.

‘No

w t

urn

ove

r yo

ur

answ

er s

hee

t.’

282686_mmMs04.indd 8282686_mmMs04.indd 8 3/12/07 11:35:24 am3/12/07 11:35:24 am

9

Tim

e: 1

5 se

cond

s

21

21

24

Yes

No

peo

ple

24

19£

£1.

2019

275

face

s27

2823 4

0.

328

23

23

Tim

e: 1

5 se

cond

s co

ntin

ued

25

2cm

a

m m

cm10

cm cm25

2220

×38

=76

0

21×

38=

22

26Te

levi

sion

sFr

eque

ncy

02

110

210

38

26

29

3

4

29

3082

30

Tim

e: 1

0 se

cond

s co

ntin

ued

18C

olou

rP

rob

abili

ty

red

0.4

gree

n0.

3

blu

e18

203

20

18In

a b

ag, t

her

e ar

e o

nly

red

, gre

en a

nd

blu

e b

alls

.C

om

ple

te t

he

tab

le t

o s

ho

w t

he

pro

bab

ility

of

taki

ng

a b

lue

bal

l.

19In

a s

ale,

th

e p

rice

of

a n

ote

bo

ok

is d

ecre

ased

by

ten

per

cen

t.W

hat

is t

he

new

pri

ce if

th

e o

ld p

rice

was

on

e p

ou

nd

tw

enty

?

20Lo

ok

at t

he

exp

ress

ion

. Wri

te d

ow

n t

he

valu

e o

f th

e ex

pre

ssio

n w

hen

m is

six

.

‘Fo

r th

e n

ext

gro

up

of

qu

esti

on

s yo

u w

ill h

ave

15 s

eco

nd

s to

wo

rk o

ut

each

an

swer

an

d w

rite

it d

ow

n.’

21O

ne

of

the

shap

es o

n y

ou

r an

swer

sh

eet

is t

he

net

of

a cu

bo

id.

Put

a ri

ng

ro

un

d t

he

corr

ect

shap

e.

22Tw

enty

mu

ltip

lied

by

thir

ty-e

igh

t is

sev

en h

un

dre

d a

nd

six

ty.

Wh

at is

tw

enty

-on

e m

ult

iplie

d b

y th

irty

-eig

ht?

23Lo

ok

at t

he

squ

are

gri

d.

Shad

e o

ne

mo

re s

qu

are

to g

ive

a sh

ape

wit

h r

ota

tio

n s

ymm

etry

of

ord

er t

wo

.

24Th

irty

-tw

o p

eop

le w

ere

aske

d if

th

ey t

rave

lled

to

wo

rk b

y b

us

on

e m

orn

ing

.Th

e p

ie c

har

t sh

ow

s th

e re

sult

s. H

ow

man

y p

eop

le s

aid

yes

?

25Lo

ok

at t

he

cub

oid

. It

has

a v

olu

me

of

on

e h

un

dre

d c

ub

ic c

enti

met

res.

Wo

rk o

ut

len

gth

a.

26Th

e fr

equ

ency

tab

le s

ho

ws

the

nu

mb

er o

f te

levi

sio

ns

ow

ned

by

thir

ty f

amili

es.

Alt

og

eth

er h

ow

man

y te

levi

sio

ns

did

th

ey o

wn

?

27A

pyr

amid

has

fi v

e fa

ces.

Ho

w m

any

sid

es d

oes

th

e b

ase

of

the

pyr

amid

hav

e?

28Lo

ok

at t

he

nu

mb

ers

on

yo

ur

answ

er s

hee

t. A

dd

th

em.

29Lo

ok

at t

he

rho

mb

us.

Wo

rk o

ut

its

area

.

30Ei

gh

t sq

uar

ed is

th

e sa

me

as t

wo

to

th

e p

ow

er w

hat

?

‘Pu

t yo

ur

pen

s d

ow

n. T

he

test

is fi

nis

hed

.’

282686_mmMs04.indd 9282686_mmMs04.indd 9 3/12/07 11:35:24 am3/12/07 11:35:24 am

10

Time: 5 seconds

1 7 Accept embedded values,eg 7 × 6

2 4 Accept value(s)indicated in list

3 9b

94

12 cm2 Accept equivalent

fractions or decimals

5 6

Time: 5 seconds continued

7 3

14 100 miles

Key stage 3 mathematics 2008

Mental mathematics higher tiers Test A

Test AMark scheme

13 30 Do not acceptincorrect % signs

17 2.85 Accept equivalent fractions or decimals6 4.9 Do not accept equivalent

fractions or decimals

Time: 10 seconds

8 145

10 48

11 100 °

12 11

15 1200

16 3a – 15 Acceptunconventional notation,

eg 3 × a – 15

Do not accept incomplete processing,

eg 3 × a – 3 × 5

4 3.9 Accept equivalent fractions or decimals

282686_mmMs04.indd 10282686_mmMs04.indd 10 3/12/07 11:35:25 am3/12/07 11:35:25 am

11

27 4

19 £ 1.08

20 36 Do not acceptincomplete processing,

eg 2166

Time: 10 seconds continued

18 0.3 Accept equivalent probabilities

Time: 15 seconds

21

22 798

23

24 12 people

Time: 15 seconds continued

25 5 cm

26 54

29 24 Ignore anyunits given

28 3.05 Accept equivalent fractions or decimals

30 6 Accept embedded values,eg 26

282686_mmMs04.indd 11282686_mmMs04.indd 11 3/12/07 11:35:25 am3/12/07 11:35:25 am

12

Pup

il an

swer

sh

eet

Key

sta

ge

3 m

athe

mat

ics

20

08

Men

tal m

athe

mat

ics

Test

B

Firs

t na

me

Last

nam

e

Sch

oo

l

Tota

lm

arks

Pra

ctic

e q

uest

ion

99

5

Non

eG

rad

ient

Hig

h

Pos

itive

Neg

ativ

e5

£3.

609

Tim

e: 5

sec

ond

s

11

47 100

4

81

02

8

112.

911

24.

7,

4.8,

4.

9,

,

2

34

pq3

Tim

e: 5

sec

ond

s co

ntin

ued

6%

10 o

ut o

f 25

6

Tim

e: 1

0 se

cond

s

7

001234

12

34

B

C

A (

,

)7

10m

m10

cm10

131 5

213

12

°a

12

1414

814

Hig

her

tie

rs t

est

B q

ues

tio

ns

‘No

w w

e ar

e re

ady

to s

tart

th

e te

st.

For

the

fi rs

t g

rou

p o

f q

ues

tio

ns

you

will

hav

e 5

seco

nd

s to

wo

rk o

ut

each

an

swer

an

d w

rite

it d

ow

n.’

1M

ult

iply

six

by

six.

2I s

tart

at

fou

r p

oin

t se

ven

an

d c

ou

nt

on

in e

qu

al s

tep

s: f

ou

r p

oin

t se

ven

, fo

ur

po

int

eig

ht,

fo

ur

po

int

nin

e.W

rite

do

wn

th

e n

ext

two

nu

mb

ers

in t

he

seq

uen

ce.

3D

ou

ble

th

e ex

pre

ssio

n o

n y

ou

r an

swer

sh

eet.

4W

rite

sev

en-h

un

dre

dth

s as

a d

ecim

al.

5Lo

ok

at t

he

scat

ter

gra

ph

. It

sho

ws

a ty

pe

of

corr

elat

ion

.Pu

t a

rin

g r

ou

nd

th

e w

ord

th

at d

escr

ibes

th

e ty

pe

of

corr

elat

ion

it s

ho

ws.

6W

rite

ten

ou

t o

f tw

enty

-fi v

e as

a p

erce

nta

ge.

‘Fo

r th

e n

ext

gro

up

of

qu

esti

on

s yo

u w

ill h

ave

10 s

eco

nd

s to

wo

rk o

ut

each

an

swer

an

d w

rite

it d

ow

n.’

7Lo

ok

at t

he

tria

ng

le d

raw

n o

n t

he

gri

d.

Wh

at a

re t

he

coo

rdin

ates

of

the

po

int

mar

ked

A?

8Lo

ok

at t

he

scal

e.A

bo

ut

wh

at v

alu

e is

th

e ar

row

po

inti

ng

to

?

9W

hat

is h

alf

of

thre

e p

ou

nd

s si

xty?

10H

ow

man

y m

illim

etre

s ar

e th

ere

in t

en c

enti

met

res?

11D

ou

ble

tw

o p

oin

t n

ine.

12Lo

ok

at t

he

dia

gra

m. E

stim

ate

the

size

of

ang

le a

.

13H

ow

man

y fi

fth

s ar

e th

ere

in t

wo

?

14W

hat

is o

ne

qu

arte

r o

f o

ne

hu

nd

red

an

d f

ort

y-ei

gh

t?

‘No

w t

urn

ove

r yo

ur

answ

er s

hee

t.’

282686_mmMs04.indd 12282686_mmMs04.indd 12 3/12/07 11:35:26 am3/12/07 11:35:26 am

13

2110

cm2

90cm

3

cm21

26

5

510

15

2510

026

29–

20

80

40

29

20( x

+ 2

)(x

– 1

)20

2440

p fo

r 5

min

utes

£24

27£

: 4 :

527

192

cm

S

cale

fact

or 2

cm2

19

Tim

e: 1

5 se

cond

s

22

050100

150

200

MT

WT

FS

Sd

ay

day

s22

253 5

4 5

5 6

6 9

7 10

25

30y 2

A

0–

20

2

–2

30

1821

– 3

x =

918

Tim

e: 1

5 se

cond

s co

ntin

ued

2323

2839

.92

× 4

1.06

1.98

28

1736

17

Tim

e: 1

0 se

cond

s co

ntin

ued

15

15

1617

red

13

gre

en16

x

1

15Lo

ok

at t

he

po

lyg

on

. Wri

te d

ow

n it

s m

ath

emat

ical

nam

e.

16Th

ere

are

seve

nte

en r

ed a

nd

th

irte

en g

reen

ap

ple

s in

a b

ag.

I am

go

ing

to

tak

e o

ut

an a

pp

le w

ith

ou

t lo

oki

ng

.W

hat

is t

he

pro

bab

ility

th

at t

he

app

le w

ill b

e g

reen

?

17W

hat

is t

he

nex

t sq

uar

e n

um

ber

aft

er t

hir

ty-s

ix?

18Lo

ok

at t

he

equ

atio

n. W

hat

is t

he

valu

e o

f x?

19A

sq

uar

e o

f si

de

two

cen

tim

etre

s is

en

larg

ed b

y sc

ale

fact

or

two

.W

hat

is t

he

area

of

the

enla

rged

sq

uar

e?

20Lo

ok

at t

he

exp

ress

ion

. Wh

en x

is t

hre

e, w

hat

is t

he

valu

e o

f th

e ex

pre

ssio

n?

21A

cyl

ind

er h

as a

bas

e ar

ea o

f te

n s

qu

are

cen

tim

etre

s an

d

a vo

lum

e o

f n

inet

y cu

bic

cen

tim

etre

s. W

hat

is t

he

hei

gh

t o

f th

e cy

lind

er?

‘Fo

r th

e n

ext

gro

up

of

qu

esti

on

s yo

u w

ill h

ave

15 s

eco

nd

s to

wo

rk o

ut

each

an

swer

an

d w

rite

it d

ow

n.’

22Th

e lin

e g

rap

h s

ho

ws

the

nu

mb

er o

f ic

e cr

eam

s so

ld a

t a

cin

ema

in o

ne

wee

k.O

n h

ow

man

y d

ays

wer

e th

e sa

les

mo

re t

han

on

e h

un

dre

d?

23Th

ink

abo

ut

a p

yram

id t

hat

has

a t

rian

gu

lar

bas

e.H

ow

man

y tr

ian

gu

lar

face

s d

oes

it h

ave

alto

get

her

?

24C

ar p

arki

ng

co

sts

fort

y p

ence

fo

r ev

ery

fi ve

min

ute

s.H

ow

mu

ch w

ill it

co

st t

o p

ark

for

on

e h

ou

r?

25Lo

ok

at t

he

frac

tio

ns.

Put

rin

gs

rou

nd

all

tho

se t

hat

are

gre

ater

th

an t

hre

e-q

uar

ters

.

26A

cir

cle

has

a r

adiu

s o

f fi

ve. O

ne

of

the

valu

es o

n y

ou

r an

swer

sh

eet

sho

ws

its

circ

um

fere

nce

. Pu

t a

rin

g r

ou

nd

th

e co

rrec

t va

lue.

27A

mill

ion

po

un

d lo

tter

y p

rize

is d

ivid

ed in

th

e ra

tio

on

e to

fo

ur

to fi

ve.

Ho

w m

uch

is t

he

smal

lest

sh

are

of

the

pri

ze?

28Lo

ok

at t

he

calc

ula

tio

n o

n y

ou

r an

swer

sh

eet.

Wri

te a

n a

pp

roxi

mat

e an

swer

.

29Fo

ur

nu

mb

ers

hav

e a

mea

n o

f tw

enty

-fi v

e. T

hre

e o

f th

e n

um

ber

s ar

e sh

ow

n o

n

you

r an

swer

sh

eet.

Wri

te d

ow

n t

he

mis

sin

g n

um

ber

.

30Lo

ok

at t

he

gra

ph

. Wri

te d

ow

n t

he

equ

atio

n o

f th

e lin

e la

bel

led

A.

‘Pu

t yo

ur

pen

s d

ow

n. T

he

test

is fi

nis

hed

.’

282686_mmMs04.indd 13282686_mmMs04.indd 13 3/12/07 11:35:26 am3/12/07 11:35:26 am

Key stage 3 mathematics 2006

Mental mathematics higher tiers Test A

Test AMark scheme

14

Key stage 3 mathematics 2008

Mental mathematics higher tiers Test B

Test BMark scheme

Time: 5 seconds

1 36

11 5.8 Accept equivalent fractions or decimals

9 £ 1.802 5(.0) and 5.1 Accept pair in

either order

3 8pq Do not accept unconventional notation,

eg 8 × pq

4 0.07 Accept equivalent decimals

Do not accept equivalent fractions

5None Gradient High

Positive Negative

Time: 5 seconds continued

6 40 % Do not accept equivalent fractions or decimals

Time: 10 seconds

7 ( 0, 1 )

8 1.6 answer 1.8

Accept equivalent fractions or decimals

12 110 ° answer 130 °

14 37

13 10 Accept embedded values,

eg 105

10 100 mm Do not acceptamended units

282686_mmMs04.indd 14282686_mmMs04.indd 14 3/12/07 11:35:27 am3/12/07 11:35:27 am

15

Time: 15 seconds continued

23 4

17 49

Time: 10 seconds continued

15 Octagon Ignore additional description,eg regular

16 1330

Accept equivalentfractions

Accept decimals as 0.43 or better or

percentage equivalents

18 4

19 16 cm2

21 9 cm

20 10 Do not accept incomplete processing,

eg 5 × 2

Time: 15 seconds

22 3 days

24 £ 4.80

2535

45

56

69

710

26

5 10 15

25 100

30 y = x + 1 Accept equivalentequations

Accept unconventional notation,

eg y = 1x + 1

29 0

28 800 answer 840

27 £ 100 000

282686_mmMs04.indd 15282686_mmMs04.indd 15 3/12/07 11:35:27 am3/12/07 11:35:27 am

29 Bolton StreetLondon W1J 8BT

Telephone: 08700 60 60 40Minicom: 020 7509 6546Fax: 020 7509 5908

Email: [email protected]: www.naa.org.uk/tests

For more copies:QCA Orderline, PO Box 29, Norwich NR3 1GNwww.qca.org.uk/orderline email: [email protected]: 08700 60 60 15 Fax: 08700 60 60 17QCA/08/3286 282686

282686_mmMs04.indd 16282686_mmMs04.indd 16 3/12/07 11:35:28 am3/12/07 11:35:28 am