answers for unit a - mrvahora | a maths blog · 2014. 10. 7. · 9 0.025 × £748 = £18.70 10 a...

1© Hodder Education 2011 Unit A

1 Integers

Answers to NTTEQ1 a 480 b 40002 a Anyof10,12,14,16,18or20. b 14 c 12 d Anyof11,13,17,19 e 163 a 1084,1987,2146,2164,3025,3332,4047 b −8,−4,−3,−2,0,1,4,64 a 5°C b −7°C

Answers to NTTEQ1

Thenumberis10.5.2 Amountonwords=48−20 =£28

Numberofwords=£28÷50p =2800÷50 =563 Numberofseats=56×14 =784 Spareseats =784−490 =294spareseats

2 Algebra 1

Answers to NTTEQ1 a 4p b 10x2 a 4m b 5k c 4d3 a 4+x+y b 2x+74 a 15a² b 5x+8y5 Perimeter=3x+2y+3x+2y=6x+4y Area=3x×2y=6xy

Trial Working out Result

Too small Too large

6 6 ÷ 1.5 = 4 42 = 16

12 12 ÷ 1.5 = 8 82 = 64

10 10 ÷ 1.5 = 6.666… 6.6662 = 44.444…

11 11 ÷ 1.5 = 7.333… 7.3332 = 53.777…

10.5 10.5 ÷ 1.5 = 7 72 = 49

Answers for Unit A

2 Answers © Hodder Education 2011

Ans

wer

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nit A 3 Data collection

Answers to NTTEQ1 Forexample a aleadingquestion b questionisaskingtwothingsatonce2

3 a

b 121 c 214 a

b

0Less

than 1010–19

Number of passengers

Freq

uenc

y

20–29 30–39

51015202530

40–49 50–59

Dog Cat Other Total

Boys 24 17 18 59

Girls 14 21 27 62

Total 38 38 45 121

Number of messages received Frequency

1–20 12

21–40 31

41–60 22

61–80 11

81–100 4

01–20 21–40

Number of messages

Num

ber o

f peo

ple

41–60 61–80

5101520253035

81–100


5 a Groupsoverlap,so10wouldbein2groupsetc. b Frequencies3,10,12,9,4,2 c

4 Decimals

Answers to NTTEQ1 −43.75+100−15.32=40.93 Sothebalanceis£40.932 6×5.59+9×3.49=64.95 70−64.95=£5.053 a 12 b 0.014 a i 360 ii 45 iii 0.0456 iv0.8563 b £3205 420joinsto0.2;14 joinsto0.25;1

2 joinsto0.5;1325joinsto0.52

5 Formulae

Answers to NTTEQ1 C=9n2 a F=19 b F=403 a P=52 b P=39.54 a P=28 b P=42

Answers to MEP1 a G=3 b G=−12 a K=4 b K=393 a H=6 b H=24 a Q=70 b Q=63

00–9 10–19

Freq

uenc

y

20–29 30–39

123456789

10111213

40–49 50–59


Ans

wer

s: U

nit A 6 Equations 1

Answers to NTTEQ1 a i 10 ii 3 iii −2 b i 10 ii 282 a x=4 b x=15 c x=353 464 4

5 n C= – 1204

7 Coordinates

Answers to NTTEQ1 a (3,4) b

c Trapezium2 a (2.5,4) b (8,−1

2)3 a i B(1,−2) ii C(−5,−1) b PointDisat(−4,5).4 a Ais(−2,2) Bis(3,2) Cis(3,−1) Dis(−2,−3) b i y=2 ii x=35 a x=2 b y=−4 c verticallineatx=−3 d thexaxis

8 Statistical calculations 1

Answers to NTTEQ1

2 a 88kg b 19kg3 a 22 b 9.2(276÷30) c 6to104 Modalclassis10–15minutes.5 a Pat’smean=25andrange=18. b Kim’smean=25andrange=7. Kimshouldbechosenbecausethemeanscoresare

thesamebutshehasasmallerrangeandisthereforemoreconsistent.

6 Book1:mean=5.4,medianisattopof0n5class,rangeispossibly15.

Book2:mean=6.2,medianisatbottomof5n10class,rangeispossibly20.

9 Sequences 1

Answers to NTTEQ1 a i

ii Add2 b i

ii Add3 c i

ii Add7

�5�4�3�2�1

12345y

x�5�4�3�2 �1 10 2 3 4 5

B A

C D

Number of letters in a word

Number of words

Class Interval Tally Frequency

1–3

20

4-6

19

7–9 5

11 13

16 19

36 43


2 a 42,77 b Yes.Youalternatelyaddtwooddandoneevennumber(givinganevennumber)andaddtwo

evennumbersandoneoddnumber(givinganoddnumber).3

4 a i 4 9 14 19 24 ii 13 9 5 1 −3 b i Firstterm2 Add3 ii Firstterm30 Subtract7 c Firstterm3 Add25 a i 26,31 ii Add5 b i 6,3 ii Subtract3 c i 81,243 ii Multiplyby3

10 Measures

Answers to NTTEQ1 a 48to53kg b 1.5m2 a 38°C b 45°C c 180°C3 0.375l 579ml 1234ml 2.59l 4.68l4 a 20×1.6=32km b 5×2.2=11lbs5 a 1.8–2.2metres b 4.6–5metres

11 Constructions 1

Answers to NTTEQ1 a

[Marks1eachforAB,AC±1mm,angleCBA±1°,arcatC.] b CB=4.2cm±2mm;angleBAC=14°±1°2 a Solutionswithcorrectangles±2° i 63° ii 109° iii 256° b i 36° ii 98° iii 305°all±2°3 a 43° b 158°

3, 4, 5, 6, 7 3n

3, 6, 9, 12, 15 2n + 1

15, 12, 9, 6, 3 n + 2

3, 5, 7, 9, 11 6 − n

5, 4, 3, 2, 1 18 − 3n

5.3 cm

9.1 cm

148°

C

BA


Ans

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nit A

4 a

b PQmeasures3.4cmonthediagram,sois 3.4×2=6.8km c 341°5 b AX=4.8cm

12 Using a calculator

Answers to NTTEQ 1 a 0.5 b 14.64 c 0.09 2 a 2

5×65=26g b 0.35×720=£252 3 a 1.18 b 10.78 4 a 2

3×4.56=£3.04 b 0.12×490=£58.80 c Onetincosts1.38÷3=0.46 8tinscost8×0.46=£3.68 5 a 0.28 b 1.43 c 3.7 6 Flour=360×64 =540g.

Butter=60×64=90g.

7 a 27×19.60=£5.60

b 0.125×980=£122.50 8 a 5.2 b 51.49 9 0.025×£748=£18.7010 a 15.73 b 21 c 5.1

Answers to MEP1 a 454.35 b 36.96 c 1.682 a 0.02or 1

50 b 1.33 c 19 or0.11

3 a 120g b 1920 c £15.20

4 a 847.51 b 2.41 c 1.03

13 Statistical diagrams 1

Answer to NTTEQ1

2 a Others(36°)isabouthalfofthesizeofLiberal Democrats(73°),soabout2260councillors. b 158°,acceptanyanswerfrom156–160°inclusive. c Approximately9880(9750to10000)

Conservativecouncillorsso9880−4534=5346Labourcouncillors(acceptanyanswerfrom5216–5466inclusive).

14 Integers, powers and roots

Answers to NTTEQ1 a 64 b 125 c 2562 a 30=2×15 =2×3×5 b 33 10=2×5 12=2×2×3 20=2×2×5 HCF=2 LCM=2×2×3×5 =604 25−12=135 a 7cm b 64 c 0.4or2

5

N NP

37°

O Q

Saloon

Hatchback

4×4

Sales

MPV


15 Algebra 2

Answers to NTTEQ1 a 10x b i P=15 ii P=52 a 5a b 3x+6y c 3a(1+2b)3 3(5a+2b)=15a+6b4 a 6x+2 b 3p(4p−5)5 3a(a+2b)6 a S=65 b S=40

16 Statistical diagrams 2

Answers to NTTEQ1 a

b MrsTaylorhasmadelongerjourneysonaverage,orhastravelledfurther.

MrAhmedhasmademoreshortjourneysorsmallerrangeofdistances.

2 a Ordered

1 Key: 2 1 means 21

2 1 4

3 4

4 3 4 8

5 5 6 8

6 1 4 5 9

7 2 2 3 4 6 6 8 8 9

8 1 1 1 2 2 9

9 1 2 5 8 9

b Middlevalueis17th, Median=74

3

4 a Range=3.6cmandmedian=3.0cm b

Range=4.4cmandmedian=2.9cm c ThepebblesinBob’ssethaveagreaterrangeand

arethereforemorevariedinsize.5 a

b 21(30–9) c 23

17 Equations 2

Answers to NTTEQ1 a x=0.5 b p=6 c m=122 p=163 x=3.54 a 4x+4=36 b x=8 c 80cm2

5 a x2=9 x=± 3 (bothsolutionsrequired) b 4x=6−2xor6x+1=7 6x=6 x=1

18 Ratio and proportion

Answers to NTTEQ1 a Gold=15×7

3=35g b Totalparts=10 Multiplier=20÷10=2 Gold=7×2=14g

0

10

Num

ber o

f jou

rney

s(fr

eque

ncy)

20

30

40

50

10 20

AhmedTaylor

30 40 50Mileage (m miles)

00 10 20 30 40 50

Time (t minutes)

Num

ber o

fsh

oppe

rs

10203040

1 1 2 4 8 9

2 1 1 1 2 8

3 0 2 3 4 8

4 2 5 8 9

5 5

Key 1 9 means 1.9 cm

0 9

1 3 4 5 6 7 8 8 9 9

2 0 0 0 1 1 1 1 2 3 3 3 3 3 3 4 4 5 5 6 7 7 8 9

3 0

Key: 2 4 means 24


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nit A 2 Mixedfruit=100×25

10 =250g Flour=250×25

10 =625g3 Multiplier=420÷7=60 a Vans=60 b Cars=6×60=3604 Multiplier=7000÷15=notexact Adrianreceives2×7000÷15=£933.33 Penelopereceives5×7000÷15=£2333.33 Gladysreceives8×7000÷15=£3733.33 Checktotal:933.33+2333.33+3733.33=6999.99 (Notice1poutduetoroundingerrors.)5

Specialisthebestvalueformoney.

19 Statistical calculations 2

Answers to NTTEQ1

Mean=10870150 =72.5g

2

Meanis2365÷90=26.28minutes

3 a

b 2weeks c

Meanis171÷90=1.9weeks4 Midpoints2.5,7.5,12.5,17.5,22.5 so6×2.5+11×7.5+23×12.5+8×17.5+2×22.5

=570 Meanweightofpackage=570

50 =11.4g5

(1markformidpoints,1markforproducts) Mean=3388

80

=42.35messages

20 Pythagoras’ theorem

Answers to NTTEQ1 DrawaverticallinethroughBtomeetAC.

AF=90cm UsingPythagoras

Pack Size Price Price per gram

Standard 500 g £1.15 0.23p

Family 750 g £1.59 0.212p

Special 1.2 kg £2.49 0.2075p

Weight(w grams)

Number of apples

(f)

Mid-interval value

fx

50 w 60 23 55 1265

60 w 70 42 65 2730

70 w 80 50 75 3750

80 w 90 20 85 1700

90 w 100 15 95 1425

Total 150 10870

Minutes (m) Frequency(f)

Mid-value (x)

fx

0 m 9 23 4.5 103.5

10 m 19 16 14.5 232.0

20 m 29 9 24.5 220.5

30 m 39 17 34.5 586.5

40 m 49 14 44.5 623.0

50 m 59 11 54.5 599.5

20

30

40

1015

25

35

50

0 1 2 3 4 5

Weeks (x) Frequency (f) fx

0 2 0

1 31 31

2 37 74

3 16 48

4 3 13

5 1 5

Number of messages received

Frequency Midpoint fx

1 to 20 12 10.5 126

21 to 40 31 31.5 976.5

41 to 60 22 51.5 1133

61 to 80 11 71.5 786.5

81 to 100 4 91.5 366

80 3388

F CA

B


BF2=AB2−AF2

=1102−902

=12100−8100 =4000 BF=63cm,tonearestcm Heightofshed=BF+AE =63cm+2m =2.63m2 a 9.43cm b 5.66cm3 a2=b2+c2

9.12=b2+7.82

b2=9.12−7.82

b2=21.97 b= 21 97. x=4.7cm(to1d.p.)4 a2=b2+c2

a2=4.22+1.82

a2=20.88 b= 20 88. a=4.6m(to1d.p.)5 a 122=144or62+102=136,since144≠136itisnot

aright-angledtriangle. b Since144136,angleXisbiggerthanaright

angle.

21 Planning and collecting

Answers to NTTEQ1 a Thisexcludesallthosenotlistedinthedirectory. b Thisincludesonlythosewhogoswimming.

Thosewhoonlyuseotherfacilitiesornoneatallareexcluded.

c Noteveryoneinthedistricthasachanceofbeingincluded.

2 a Aisaleadingquestion,soreplacewith‘Doyouthinkitisagoodideatoexerciseregularly?’or‘Ithasbeensaidthatitisagoodideatoexerciseregularly.Doyouagreewiththisstatement?

Bhasresponsesmissedoutsotheboxesneedtobereplacedwiththefollowing.

none upto4 morethan4andlessthan8 8ormore (Itcouldalsobearguedthatapilotsurveymight

revealthatthesehoursareexcessiveandshouldbereplacedwith0–2,2–4,4–6,6orover,forexample.)

b Wheredoyoudoyourexercise? gym running localsportsclub

videoexercise Other(pleasestate)...........................................

3 a Theanswersavailabledonotcoveracompleterangeofvalues.

b Example: Howmuchdoyouexpecttopayforamealout? A:Lessthan£5 B:between£5and£10 C:Between£10and£20 D:Morethan£20.4 Possiblequestionsinclude: Doyouownacat? Doyoubuytinnedcatfood? Doyoubuydrycatfood? Whatbrand(s)doyoubuy?Tickthefollowingboxes.

22 Sequences 2

Answers to NTTEQ1 a i +6 ii −7 b i 8,9,10,11,12 ii 2,7,12,17,222 a 98 b 5n−23 a 36 b 55isthetenthtermofthesequence.Thiscanbe

foundbyadding6to15,then7totheanswerand8tothenextanswerandsoonuntilyouadd10to45toget55.

4 a 3,7,11,15,19 b i 99 ii 1995 a subtract6 b 84 c 6n−1

23 Constructions 2

Answers to NTTEQ1

Diagramshownhalf-size.2

Diagramnotshowntogivenscale

A

B

Hedge House

Fence

FenceB

A

D

C


Ans

wer

s: U

nit A

3 24 Rearranging formulae

Answers to NTTEQ

1 a d=e – 35

b d=e + 2812

ord=e4

7

3

+

2 PV=kNT

PVNT

=kork=PVNT

3 a n= T – 2520

( )

b a= A5( )+b

c i r= Vhπ( )

iih= Vrπ 2( )

Store

£10 delivery

Store

£25 delivery

Store

Free delivery

Diagram shownhalf-size

11© Hodder Education 2011 Unit B

1 Working with numbers

Answers to NTTEQ1 a £5=500p÷10 =50 50weeks b 86−20÷2=86−10 =76 c 15.7−(0.6+2.4)=15.7−3 =12.72 a 4.5 b 4.553 48×31=1488seats4 a 4.58,5.02,5.6,5.74 b i Anston ii 6.05−5.47=0.58m=58cm5 Bellahasdonethesubtractionbeforethe

multiplication.Sheshoulddothemultiplicationfirst.

Answers to MEP

1 a 72341723

2892029643

× b )27 918

8181081080

34

–

–

2 a 129kg b 128.8kg3 a 600 b 2000 c 15.7−3.9×2=15.7−7.8 =7.94 a 178+274=452miles b 274−178=96miles5 a Amountspent=2×2.27+4.56 =4.54+4.56 =9.10 Change=20−9.10 =£10.90 b 18×82=£14.766 133÷28=£4.757 Onepizzacosts17.50÷5=3.50 Threecost3×3.50=£10.508 Amountperhour=138÷3=46 Amountin8hours=8×46=368

2 Angles, triangles and quadrilaterals

Answers to NTTEQ1 a rhombus b isoscelestriangle c rectangle2 aandb

3 a B b ABandDC c ABandADorADandDC4 a Sketchofrhombus b Rhombus5 a Anglesare37°,53°and90°. b Right-angledtriangle.

3 Fractions

Answers to NTTEQ1 a 5

2014or b 7moresquaresshaded

2 a 316 b 13

16 c 7moresquaresshaded

Answers to MEP1 3

5×340=204g

2 58×48=30

3 14×300=75cm

4 56

2024

14

624

512

1024

38

924= = = =, , ,

Soorderis 1438

512

56, , ,

5 46

1015,

Lines ofsymmetry

Answers for Unit B


Ans

wer

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nit B 4 Solving problems

Answers to NTTEQ1 9.55p.m.2 a 1hour48minutes b 14:453 45p(tonearestpenny)

Answers to MEP1 £22.702 10days3 a 18:45 b 50minutes4 £11.205 12:156 £8333.33(tonearestpenny)7 50008 30

5 Angles

Answers to NTTEQ1 a=133° Alliedanglesaddto180°. b=47° Correspondinganglesoranglesona

straightlineaddto180°. c=67° Anglesofatriangleaddto180°.2 a=116° Anglesonastraightlineaddupto180°. b=64° Correspondinganglesareequal. c=64° Anglesonastraightlineaddupto180°or

alternatetoa. d=118° Oppositeanglesareequal. e=118° Correspondingto118°oralternatetod.3 a 44° Anglesonastraightlineaddto180°. b 44° Alternateanglesareequal. c 68° Anglesinatriangleaddto180°and/or

isoscelestriangle.4 p=58°5 x=50° Verticallyoppositeanglesareequal. y=123° Anglesroundapointaddupto360°. z=45° Anglesonastraightlineaddupto180°.

6 Fractions and mixed numbers

Answers to NTTEQ1 a 2

345+ =10

151215+

=2215

=1 715

b 35

56

11

12

12× = × =

2 34

3040

710

2840

35

2440

58

2540= = = =, , ,

Orderis24402540

2840

3040, , , thatis35

58

710

34, , ,

3 a 2 138

12– =138

48–

=8838

48+ –

=78

b 23

45÷ =23

54×

=13

52

56× =

4 2 14

716– =2 4

16716+ –

=1 1616

416

716+ + –

=11316 inch left

Answers to MEP1 a 1 21

435+ =3 1

435+ +

=3 520

1220+ +

=3 1720

b 35

49× =1245

= 415

2 a 4 2316

12– =2 3

1612+ –

=2 316

816+ –

=1 1616

316

816+ + –

=11116

b 310

415÷ = 310

154× =9

8=11

8

3 1 1 1 1 1 1 112

816

716

14

416

38

616= = =, , ,

Soorderis1 1 1 114

38

716

12, , ,

4 a 45

59× =4

9

b 38 6÷ =3

816× = 1

16

7 Circles and polygons

Answers to NTTEQ1 a Thereare360°inacompleteturnsofor1kgit

moves3605

=72. b c

2 a 4 b Pentagon3

Diagramshownhalf-size

0

5 kg

2 kg3 kg

4 kg 1 kg

a)

b)

c)

4 cm


Answers to MEP1 a 60° b Equilateral c 80°2 x=73° Isoscelestriangleandanglesinatriangle

addupto180°. y=107° Exteriorangleoftriangleisequaltosumof

interioroppositesorIsoscelestriangleandanglesonastraightlineaddupto180°.

3 a x=3605

=72° b Isosceles c

Notactualsize4 Exteriorangleofpolygon=180°−168° =12° Sumofexteriorangleofpolygonis360°, sonumberofsides=360

12

=30

8 Powers and indices

Answers to NTTEQ1 iiiistrue,theotheroptionsarefalse2 a x7y5 b 6x3y5

3 a 252836,so 25 28 36

but25nearerto28than36so 28isjustover5 b 8195100and 81 95 100 so 95 liesbetween9and10butcloserto10,

about9.74 a i 4913 ii 35 b i 83 ii 365 a r5 b 9

9 Decimals and fractions

Answers to NTTEQ

1 a 25

410= =0.4 b )9 2 0 0 0

0 2 2 22 2..

……

so29 0 2= .

2 a 25

13+ =6 5

15+

=1115

b 0.4and0.333333...or0.3 =0.73 c 11

15=0.73

3 a 59 b 56

99

c 612999

isthen 68111

initssimplestform

4 a 55100isthen11

20 inlowestterms

b 361000 isthen 9

250 inlowestterms

c 224610000 isthen1123

5000inlowestterms5 a 0.303 0.33 3.03 3.3 b e.g.0.25

10 Real-life graphs

Answers to NTTEQ1 a

b i 105km ii 245km c i 1h24minto1h27min ii 3h33minto3h36min2 a i AU$50 ii AU$212.50 b i £40 ii £703 a 1p.m. b 10.30a.m. c 10°C4 a 4.5km b astopof45minutes c

d 4.5kph

72°

100Dist

ance

(km

)

150

200

250

300

c) ii)

c) i)

b) i) b) ii)

50

0 1 2Time (h)

3 4

4

6789

10

Dist

ance

from

sta

rt (k

m)

23

5

1

0 2 3Time (hours)

4 5 61

BC

D

A


Ans

wer

s: U

nit B Answers to MEP

1 a b 42.5litres c 150km d 500km 2 a i HK$210 ii HK$560 b i £27to£30(£28.57) ii £5to£6(£5.36)

3 a b i 10to12litres(11litres) ii 38to39litres(38.5litres) c i 8to10pints(9pints) ii 63to64pints(63.6pints)

4 a

Fuel

left

(litre

s)

Distance(km)

10

20

30

40

50

0 50 100 150 200

Litre

s

Pints

10

20

30

40

50

5

15

25

35

45

55

0 10 20 30 40 50 60 70 80 90 100

�20

�10

0

10

20

30

40

Time

Tem

pera

ture

(°C

)

0200 0400 0600 0800 10000000 1200 1400 1600 1800 2000 2200 2400


b i 39°C ii –14°C c i 53°C ii 5°C iii7hours5 a 86°F b 46°C6 a 32kilometres b 62to63miles(62.5)7 a £42.50 b 3miles8 a 22to23litres(22.5) b 16to17gallons(16.7)9 a 11pounds b 34kilograms

11 Reflection

Answers to NTTEQ1

2 a TriangleBisat(−1,4),(−2,4)and(−1,6). b TriangleCisat(1,−2),(2,−2),and(1,−4).3 44

5 a

b

12 Percentages

Answers to NTTEQ1 a 15squaresshaded b i 0.6 ii 3

52 66%,3

5,0.62,0.59,55%=0.66,0.6,0.62,0.59,0.55 Order0.55,0.59,0.6,0.62,0.66=55%, 0.59,3

5,0.62,66%3 NumberwhostudyFrench=0.15×140 =214 Pensionfund=0.08×15000 =£12005 Numberover65= 67

100 ×630 =4226 68+32=100

Answers to MEP1 a 6% b 40%2 Deposit=0.05×840 =£423 Saleprice=0.8×45 =£364 Fractionoccupied=271

320 =0.846875 Percentageoccupied=84.69%5 Lengthleft=250−90 =60 Percentageleft=160

250 ×100 =64%6 Deductions=34720−26734.4 =£7985.60 Percentagededuction=7985 634720

. ×100 =23%7 Creditcardcost=570×1.015 =£578.55

13 Rotation

Rotation symmetry

Answers to TTEQa Linesofsymmetry:8,2,0b Orderofsymmetry:8,2,5

Recognising and describing rotations

Answers to NTTEQ1 DandF2 Rotationthrough90°clockwiseabout(0,0)

Mirror line

AImage


Ans

wer

s: U

nit B

3 a Reflectionintheliney=x b

14 Estimation

Answers to NTTEQ1 a 0.42×20=3.2or0.421 soanswerislessthan

18.6 b Dividingbyanumberlargerthan1leadstoan

answerlowerthan24.608,andtheanswerisnotsoisnotcorrect

c 808 5

8013+ = whichisroughly6sotheansweristoo

large.2 a Multiplyingbyanumberlessthan1willmakethe

answersmaller. b Dividingbyanumberlessthan1willmakethe

answerlarger. c Thethreenumbersareallnegativesotheanswer

willbenegativealso.

3 8 9350 017 6 914

90 02 7

90 14

.. . . .× ≈ × =

=64.2857… =60(to1s.f.)4 a 129kg b 128.8kg5 Estimate=24+6×3 =24+18 =£42 £45willbeplenty.

15 Enlargement

Answers to NTTEQ1

2 a i 2 ii (2,2)

b

3 Enlargementcentre(0,0),scalefactor0.54 Centre(−1,2)scalefactor25 a 3 b (1,0) c 3 d 9

16 Scatter diagrams and time series

Answers to NTTEQ1 aandb

c i 8.6milliontons ii Methodsofproductioncouldhavechanged.2

4

2

5

3

1

�1�2�3�4�5

4C

5 x

y

2 31�1�2�3�4�5 0

A

D

B

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a 5pointsplottedcorrectly b Positivecorrelation c Suitablelineofbestfit d Valuereadofftheirlineatn=173 a

b AlwaysmoreonFridayandSaturday,leastonMonday.SlightupwardtrendinWeeks1and2followedbydownwardtrendinWeek3.

4 aandc

b Positivecorrelation. d 4mistoofaroutsidetherangeofthedatatomake

areliableprediction.5 a

17 Straight lines and inequalities

Straight-line graphs

Answers to NTTEQ1 a (2.5,4) b (8,–1

2)2 Gradient=2

Answers to MEP1 a

b i gradient=3 ii y=3x−k,wherekcanbeanyvalueexcept−1.2 Gradient=−2.53 a Gradient=7 b y=7x+k,wherekcanbeanyvalue,k≠3.

Graphical solution of simultaneous equations

Answer to NTTEQ1

x=−0.5,y=2.5

Inequalities

Answers to NTTEQ1 a ix7 ii 3x−6 x−2 b i

ii

2 a x2.5 b x4.5or4.5x3 −1x2

4 3,4,5,6,718

Congruence and transformations

400

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500

600

300

2000

TuM W

Week 1 Week 2 Week 3

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18 Answers ©HodderEducation2011

Ans

wer

s: U

nit A 18 Congruence and transformations

Answers to NTTEQ1 A and F B and H C and E2

a and b See diagram. c Reflection in the x-axis.

3 B and C As they have the same angles, and have a 2.5 cm

length between 43° and 70° angles.4

0 1–1–2–3–4–5–6–7 2 3 4 5 6 7 x

1

–1–2–3–4–5–6–7

2345

AB

C

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19© Hodder Education 2011 Unit C

Answers to NTTEQ1 Hereisapossiblenet.Checkthemeasurementson

yournet.

2 a 8 b 12 c

3

Answers to MEP1

2 Hereisapossiblenet.Checkthemeasurementsonyournet.

3

2 Probability 1

Calculating probabilities

Answers to NTTEQ1 a 4 b

c

2 a Fivemoreflagswithcorrectcolours:ACB,BAC,BCA,CAB,CBA

b 13

Answers to MEP1 a Certain b Evens c UnlikelyorVeryunlikely d Impossible2 a 1

4520or b 7

20

c 34

1520or d 0

1 Two-dimensional representation of solids

7.4 cm

5.2 cm

5.2 cm

5.2 cm

7.4 cm

7.4 cm

7.4 cm7.4 cm

P S

3 cm

8 cm

2 cm

2 cm

2 cm

3 cm

4 cm

3 cm3 cm

3 cm

0 1

There are no numbers less than 4 on the spinner.

0 1

Six of the eight numbers are even.

Answers for Unit C


3 a

b Notallsandwichesareequallypopular. c Petermight,ormightnot,becorrect.Thereare

ninedifferentpossibilitiesandoneofthemisbrownbreadandcheesebutthechoicesarenotequallylikely.IfPeteriscorrect,theprobabilityofnotbuyingabrownbreadandcheesesandwichwouldbe45 .

Experimental probabilities

Answers to NTTEQ

1 a 190300

1930=

b 110300

1130=

2 a 15500

3100=

b 65500

13100=

3 a 55 b 72

2009

25=

4 725

2801000or

3 Perimeter, area and volume 1

Perimeter and area of a rectangle

Answers to NTTEQ1 a 13.8cm b 11.18cm²2 Twoof:12by1or1by12cm,Perimeter26cm 2by6or6by2cm,perimeter16cm 3by4or4by3cm,perimeter14cm

Answers to MEP1 a Perimeter=16cm,Area=15cm2

b Perimeter=20cm,Area=18cm2

2 Between9km2and11km2

3 4cm4 3279.52(3280)m2

5 Perimeter=22m,area22m2

The volume of a cuboid

Answers to NTTEQ1 35.88m3

2 10cm

4 Measures

Answers to NTTEQ1 a i 22656cm2

ii 2.2656m2(2.27m2to2d.p.) b 353.5cmto354.5cmand63.5cmto64.5cm2 a 639.6cm3 b 959.4g3 a 16556cm(tothenearestcm)or165.6m(to1d.p.) b 9.9km/h(to1d.p.)4 128or130peopleperkm2

5 Upperbound=64cm;lowerbound=60cm6 a 0.5hours b 36mph

Answers to NTTEQ1 a Areaoftriangle=1

2 base×height

=12×4.6×5.0

=11.5cm2

b a2=b2+c2

=4.62+5.02

=46.16 a= 46 16. a=6.8cm(to1d.p.)2 Areaofshape=areaofrectangle+areaoftriangle =6×0.7+1

2×5×4.6 =15.7cm2

3 12 ×BC×4.5=18.9

BC×4.5=37.8 BC=37.8÷4.5=8.4cm4 a 9×5.2=46.8cm²

b AD= 3 5 22 2+( ). =6.00 Perimeter=5.2+6+5.2+6=22.4cm5 a 5×3=15cm² b Areaofrectangles =4×8+5×8+4×8+5×8 =32+40+32+40 =144cm² Totalarea=15+15+144=174cm²6 Areaoftriangle=1

2×8.5×5.6=23.8 4.8×h=23.8 h=23.8÷4.8=4.96cm

Bread Filling

B C

B E

B H

W C

W E

W H

G C

G E

G H

5 The area of triangles and parallelograms

Ans

wer

s: U

nit C


6 Probability 2

Answers to NTTEQ1 2

52 a 0.15 b 0.75 c

Answers to MEP1 a i 9

20 ii 340 iii 29

32

b No.Trafficpatternsvaryaccordingtothetimeofday.

c 725 or 280

1000

2 a 1−(0.65+0.23)=0.12 b 0.65×42=27(tonearestgame)3 0.7+0.35=1.05,whichisgreaterthan1soboth

cannotberight.4 No.Mosnahasnotthrownthediceenoughtimesfor

theresultstosettledown.Sheneedstorollthediceatleast100times.

7 Perimeter, area and volume 2

Answers to NTTEQ1 Areaoflawn=areaofrectangle−areaofsemicircle

withradius12m =28×24−1

2 ×π×122

=445.8m2(to1d.p.)2 C=2πr 26=2×π×r

r= 262 × π

4.1cm(to1d.p.)3 a C=2×π×2.5=15.7m b A=π×32−π×2.52=8.64m2

4 a 38cm b 10×2+4×2+3×2=34cm²5 a 80−1

2×7×4=80−14=66cm²

b Hypotenuse= 7 42 2+( )=8.06cm Perimeter=8+3+4+8.06+8+10=41.06cm 6 2×1.5×0.5+2×1.5×0.8+2×1.5×0.2=1.5+2.4

+0.6 =4.5m3

7 Areaoftheend=12×5.2×5.2=13.52cm2

Volume=13.52×7.4=100.048=100cm³(to3s.f.)

8 15cm3

9 a 42cm3 b 96cm2

10 1154.5cm3(to1d.p.)

8 Using a calculator

Answers to NTTEQ 1 a 5700 b 23000 c 0.006 d 0.006074 e 0.90 2 a 1.6 b 13 3 a 0.43×640=£275.20 b 2

5×47.5=19m c 60.7 4 a 0.24 b 6.82 c 1.21 5 a 14.97 b 0.02 c 4.59 6 a 16.81 b 3.10 c 3.4 d3

7×164=£70.29 7 1627÷5=£325.40 8 a 3.68−0.83=£2.85 b 0.75×3.68=£2.76 Sothegardencentreischeaperby2.85−2.76=9p. 9 Onecosts2.76×12=0.23. Fivecost5×0.23=£1.15.10 Hedidnotusebracketssoworkedout4÷2+3

Answers to MEP1 a 7 5

12 b 1921 c 9

352 a 15625 b 5.57 c 6.43 £135264 a 130.42 b 2.47 c 0.215 a 6.61 b 1.406 a 2.65 b 12.2 c 2.337 a 7

12 b 124 c 25

9 Trial and improvement

Answers to NTTEQ1 a 4x×x× (x+1)=200cm3

4x 3+4x 2=500 x 3+x 2=50 b x=3.382 x=2.87

Answers to MEP1 x=3.82 x=2.413 a Whenx=2,x 3−8x+5=−3 Whenx=3,x 3−8x+5=8 Astheoutcomeshavedifferentsigns,theremusta

rootbetweenx=2andx=3 b x=2.4

Colour Orange White Yellow

Number of sweets

1 3 4

Colour Green Red

Number of sweets

5 7


4 a

x 1 2 3 4 5 6

V 7 32 81 160 275 432

b x=4.4

Dimensionsare4.4cm×4.4cm×10.4cm

10 Enlargement

Answers to NTTEQ1 a 10.5cm b 6cm2 a 11.2cm b 6.5cm3 a 3cm b 9

164 a 12.5cm b 3.6cm5 a 6.875cm b i 5

8 ii 2564

11 Graphs

Distance–time and other real-life graphs

Answers to NTTEQ1 a 68to70metres b 28.5seconds c 27.5seconds d 1.3to1.5secondsand26.5to27seconds2 a 11m2

b i £187to£203.50 ii £17to£18.50 c Straightlinethrough(0,0)and(10,60)

Answers to MEP1 a OK b 62kg c 155cm d 43kgto44kgand60kg2 a 7.6km b 8.47a.m. c 2.5minutes d 18km/h3

4 Forexample:Acaracceleratesandthentravelsatasteadyspeedandthenstopssuddenly(e.g.crashes).

Quadratic graphs

Answers to NTTEQ1 a

b x=−0.7andx=2.72 a

b i x=2 ii Betweenx=0.6andx=3.4

0800

2

Dist

ance

in k

m

4

6

8

10

1

3

5

7

9

0810 0820 0830Time

x −1 0 1 2 3

y 4 1 0 1 4

0.5

1

1.5

2

2.5

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3

3.5

4

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x −1 0 1 2 3 4 5

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nit C


Answers to MEP1 a

b x=−2andx=22 a

b x=−1.2andx=4.2

3 a

b x=−4.8andx=0.8approximately c x=−3.7andx=−0.3approximately4 a (7,3,1) b (4,0,1) c (4,1.5,2)

12 Percentages

Percentage increase and decrease

Answers to NTTEQ1 SellingpriceincludingVAT=6.95×1.175 =8.16625 =£8.172 Saleprice=0.85×80 =£683 Valueafter6months=185000×(1.01)6

=196381.2279 =£196381

Answers to MEP1 Newprice=0.9×750 =£6752 Saleprice=0.8×45 =£363 Lowsugarcontent=0.58×260 =150.8g4 Reducedrent=0.95×140 =£1335 Totalcost=650×1.125 =£731.256 Creditcardcost=570×1.015 =£578.557 Amountafter4years=5000×1.045

=£6083.268 a Valueafter1year=899×0.7 =£629.30 b Valueafter5years=899×0.75

=£151.09Solving problems

Answers to NTTEQ1 14.9%2 a 52.3% b £97.45(approx£95)

x −3 −2 −1 0 1 2 3

y 5 0 −3 −4 −3 0 5

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0

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x −2 −1 0 1 2 3 4 5

y 5 −1 −5 −7 −7 −5 −1 5

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0

�3

�2

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�5

�6

�7

�8

�9

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4

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3

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answers for unit a - mrvahora | a maths blog · 2014. 10. 7. · 9 0.025 × £748 = £18.70 10 a...

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