Y = 2x + 1 y = -x - 1

[Pages:7]Ratios, rates and the number plane

Teacher Book - Series I-2

y = 2x + 1 y = -x - 1

Mathletics Instant

Workbooks

Copyright ?

RRRaaattitoiioo, s,r,arrataetestseasanndadnthtdheetnhnueummnbbeuermrppblaleanner eplane

TToOTpOPiPIcCICTTeETsSEtTST

Instructions This part consists of 12 multiple-choice questions

InIsntsrutrcutciotinosns? ?

??TFEihalTFlicsihihlnlipsqioanupnretoalsynrtcitoloOyncnNoOsisnEiNsswtCEisosItrCRotshfICRo11LfCE5m1LfamE5orkrufmoletruiaplectliahepclcqhehucqoehuiscoeteiisoctqeniouqneusetisotniosns

? ?EFailElciahncoqhnulqeyusOetiNsotEnioCinsIRiwsCowLrEtohrfto1hr em1aacmhrkaqrukestion

? ?CaClcauullclaauttoloarsrtsoarrmseamNyOabyTeabuleloswuesededd

PPAPARARTRTATAA

TTiTmimimee eallalloolwlwoewedd:e1:d51: m51i5m numitneiusntuetses

TotTaolTtmoatalarmkl sma=rak1rs2ks==1515

1 1 WhWehneantaantakniks i25s f25ulflutlhl etrheeries 1is2102000L0iLn iint.iTt.heThteottaoltaclapcacpiatcyitoyf othf ethteantakniks is

MaMMrakarsrkkss

A A 4840800L0 L

B B6860800L0 L

C C 18108000L0 L

D D 30300000L0 L

11

2 2 If I$f3$03i0s disivdiidveideidn itnhethreatriaoti3o:32,: 2th, ethsemsamllaelrlearmaomuonut nist is

A A $1$010

B B$1$212

C C $1$818

D D $2$020

11

3 3 TheThreatriaotioof o9f g9ragmrasmtso t4o k4ilkoigloragmrasmis is

A A 9 :94: 4

B B3 :32: 2

C C 9 :940: 4000

D D 9 :940: 40000

11

4 4 A cAarcatratvrealvse2ls42k4mkmbetbwetewenee9n:390:3a0.ma.ma.ndan1d01:105:1a5.ma.mW.hWaht aist itssitasvearvaegreagsepesepdeeidn iknmk/mh?/h?

A A 181k8mk/mh/h

B B303k0mk/mh/h

C C 323k2mk/mh/h

D D 363k6mk/mh/h

11

5 5 OreOries risemreomveodvefdrofmroma maimneinaet atthethreatreatoef o2f7207t0ontonnens epserpehrohuor.uEr.xpErxepsrsestshitshins ikng/ksg./s.

A A 7.57.k5g/ksg/s

B B757k5g/ksg/s

C C 45405k0g/ksg/s

D D 4540500k0g/ksg/s

11

6 6 If I5f:53:=3 x=: x1:t1hethnexnexqueaqlusals

33

55

AA 5 5

BB 33

CC2 2

D D3 3

11

7 7 AnAanmaomuonut nist disivdiidveideidn itnhethreatriaoti2o:23.: 3If. Ithf ethsemsamllaelrleprarptairst $is3$03, 0th, ethoeriogriingailnalmaomuonut nwtaws as

A A $4$545

B B$5$050

C C $7$575

D D $7$878

11

8 8 If Iyfouyoduivdiidveid$e6$56i5n itnhethreatriaoti6o:67,: 7w,hwaht aist tishethsemsamllaelrleprarpta?rt?

A A $1$313

B B$2$626

C C $3$030

D D $3$535

11

9 9 InItnratvrealvleinllgin1g0100k0mkma caarcaurseusse2s02L0oLf opfetpreotlr.oAl.tAtthitshrisatrea,teh,ohwomwamnyanlyitrleitsreosf opfetpreotlroalreare

neendeedetdo ttoratvrealve1l k1mk?m?

A A 0.002.0L2 L

B B0.20.L2 L

C C 0.50.L5 L

D D 5 L5 L

11

1010 GivGeinvetnhatht a5t:54:=4 m= :m1:t1hetnhemn mequeaqlusals

44 AA 5 5

55 BB

44

C C 1 11 1

D D nonoenoef othf etsheese

11

55

6060

ii Ratios, rates EaXnCEdEXLCtEhESLSeEENSnSTuIEANmLTSIbAKLIeLSLrSK:pILYLlEaSA:nYReE8AMR A8TMHEAMTHAETMICASTIRCESVRISEIOVINSIOANDAENXDAEMXAWMOWRKOBROKOBKO2O?K E2X?TEENXSTEIONNSION

Mathletics Instant Workbooks ? Series I 2 Copyright ? 3P Learning

Ratios, rates and the number plane

Topic Test

PART A continued

RRaattioio,, rraatteess aanndd tthhee nnuummbbeerr pplalannee

1111 AArerecicpipeerereqquuirieressmmggrarammssoof fflfolouur rfofor rnnppeeoopplel.e.HHoowwmmaannyyggrarammssaarerenneeeddeeddfofor roonneeppeersrosonn??

AA mm??nn

BB nn??mm

CC

nn mm

DD

mm nn

Marks MMaarkrkss

11

1122 $$11220000isisddiviivdideeddininththeeraratitoio22: 3: 3. .ThTheelalargrgeer raammoouunnttisis

AA $$8844000

BB $$770000

CC $$7722000

DD $$4488000

11

1133 WWhheenn$$22200isisddiviivdideeddininththeeraratitoio55: 6: 6, ,ththeesmsmaallleler raammoouunnttisis

AA $$114400

BB $$112200

CC $$9900

DD $$11000

11

1144 ThTheeraratitoiooof f33.5.5kgkgtoto5566kgkgisis

AA 88: 1: 1

BB 11: 1: 166

CC 1166: 1: 1

DD 2288: 3: 3

11

1155 yy==33xx++22; ;fifninddyywwhheennxx==44

AA 1122

BB 1144

CC 1100

DD 2200

11

TToottaal lmmaarrkkssaacchhieievveeddfoforrPPAARRTTAA Total marks achieved for PART A

1155

15

Ratios, rates and the number plane

iii

Mathletics Instant Workbooks ? Series I Copyright ? 3P Learning

RRRaaatttiiiooo,,sr,raartateetsseaasnnaddntthdheetnhnueummnbbueemrr ppbllaaennreeplane

TTToOOpPPicIICCTTeTEsEStSTT

PPAPAARRRTTTBBB

Instructions This part consists of 15 questions IInnssttrruuccttiioonnss ?? TThhisisppaarrttccoonnssisisttssooff1155qquueessttioionnss

??EEaEacahcchqhuqqeusueteisostntioiiosnnwisiosrwtwhoo1rrtmthha1r1kmmaarrkk ??WWWrirterititeaenasanwnseswrwseeirnrssthinientathnhesew`A`eAnrnss-swowneelryrsscooolnunlmyly'n'ccoolulummnn

Time allowed: 20 minutes

Total marks = 15

TTiimmeeaalllloowweedd::1155mmQiinuneuusttteieossns

QQuueessttioionnss

TTootAtaanllsmwmeaarrsrkkossn=l=y 1155 Marks

AAnnsswweerrssoonnlyly

MMaarrkkss

EExxppreresssstthheefofollolowwininggaassrarattioiossininssimimpplelessttfoformrm..

11 $$1122: :$$1155

______________________________________ 11

22 2200mmininuutteess: :22hhoouursrs

______________________________________ 11

33 110000kkgg: :335500kkgg

______________________________________ 11

44 $$112255isisddivividideeddinintthheerarattioio1122: :1133..WWhhaattisistthheelalargrgeerrppaartrt??

______________________________________ 11

55 AAccaarrisisttraravveellilninggaatt4455kkmm//hh..HHoowwmmaannyymmeettreressddooeessititttraravveell

inin44sseeccoonnddss??

______________________________________ 11

66 EExxppreressss00.0.088: :00.3.322ininititssssimimpplelessttfoformrm..

______________________________________ 11

77 WWrirtitee 3333 :: 22 11 ininititssssimimpplelessttfoformrm..

55 1100

88 CChhaannggee112200kkmm//hhttoomm//ss 99 HHoowwmmuucchhttimimeewwilillititttaakkeettoottraravveell11220000kkmmaatt9900kkmm//hh?? 1100DDivivididee664400mminintthheerarattioio22: :33 1111 33bbooookkssaarerebboouugghhttfoforr$$2233.4.400..HHoowwmmuucchhwwoouuldld77bbooookkssccoosstt?? 1122 EExxppreressss33pp222: :66ppqqininititssssimimpplelessttfoformrm.. 1133 IIffxx: :33==88: :55,,wwhhaattddooeessxxeeqquuaal?l?

______________________________________ 11 ______________________________________ 11 ______________________________________ 11 ______________________________________ 11 ______________________________________ 11 ______________________________________ 11 ______________________________________ 11

1144 AA3300liltitrereccoonnttaainineerrfufull looffwwaatteerrisisleleaakkininggaattaararatteeooff110000mmLLppeerr

hhoouur.r.HHoowwmmuucchhwwilillbbeeleleftftinintthheeccoonnttaainineerraaftfteerr33ddaayyss??

______________________________________ 11

1155 TThheetthhrereeeaanngglelessooffaattriraiannggleleaarereinintthheerarattioio22: :33: :44..FFininddtthheessizizee

oofftthheessmmaallelessttaanngglele..

______________________________________ 11

6622

TToottaallmmaarrkkssaacchhiieevveeddffoorrPPAARRTTBB

1155

Total marks achieved for PART B

15

EEXEXXCCCEELELLEESESSSESENENNTTIITAAIALLLSSKSKKIILLILLSSL:S: Y:YYEEAEAARRR888MMMAAATTHHTHEEMEMMAAATTIITCCICSSSRRREEVEVVIISSIISIOOIONNNAAANNNDDDEEXEXXAAAMMMWWWOOORRRKKKBBOBOOOOOKKK222???EEXEXXTTEETNENNSSISIOOIONNN

Ratios, rates and the number plane

iv

Mathletics Instant Workbooks ? Series I 2 Copyright ? 3P Learning

Ratios, rates and the number plane

TRoapticioT,ersattes and the number plane

TOPIC TEST Instructions This part consists of 4 questions

Each question is worth 5 marks

Instructions

? ?

ShTEohawcishaplqlanureetcscetosiosnnasriysistswoofrt4hq5uemsatiroknss

Time allowed: 2?0 mShinowutaelsl necessary working

PART C PART C

Total marks = 20

Time allowed: 20 mQiuneustteiosns

Marks

Total marks = 20

Marks

1 a Simplify the ratio 80 g : 2 kg __________________________________________________

b There are 70 girls at a party. If the ratio of boys to girls is 7 : 5, how many boys are at the party? _______________________________________________

c $75 is divided in the ratio 3 : 2. Find the smaller part. _____________________________

5

d A car travels at an average speed of 75 km/h, how long will it take to cover 350 km?

__________________________________________________________________________

e If John earns $86.50 for 25 hours, how much will he earn for 40 hours? __________________________________________________________________________

2

a

If 2 = x find x 5 25

___________________________________________________________

b Simplify the ratio 12 : 156 ____________________________________________________

c Two lengths of timber are in the ratio 4 : 7. If the longer length is 154 cm,

find the shorter length. ______________________________________________________

5

d If a car travels 60 km in 3 hours, find the average speed. ___________________________

e Change 10 m/s into km/min __________________________________________________

3 Complete the tables below.

y

44

a x+ y =2

b 2x - y = 1

33

x -1 0 1 2

x -1 0 1 2

22 11

y

y

?x ??44 ??33 ??22 ??11 00 11 22 33 44 x

??11

c Draw the graph of each line from parts a and b on the number plane.

??22 ??33

5

d Find the point of intersection. _________________

??44

?y

4 Plot and label the following coordinates on the number plane.

a A(?1, 2) B(2, 2) C(5, ?3) D(?3, ?3) b Join the points together A B C D A c Name the shape. _________________________ d What is the ratio of the lengths of the parallel sides?

___________________________________________

y

66 55 44 33 22 11

?x ??66 ??55 ??44 ??33 ??22 ????1111 00 11 22 33 44 55 66 x

??22

??33

??44

??55 ??66

5

?y

Total marks achieved for PART C Total marks achieved for PART C

CChhaapptteerr 55:: RRaattiioo,, rraatteess aanndd tthhee nnuummbbeerr ppllaannee

Ratios, rates and the number plane Mathletics Instant Workbooks ? Series I Copyright ? 3P Learning

20 20

6v3

12 4x + 1 13 7x + 10 14 8x cm 15 3x + 5y + 2

PAGES 47 & 48 1 A 2 D 3 A 4 D 5 B 6 D 7 A 8 C 9 D 10 D 11 B 12 D 13 B 14 C 15 C

PAGE 49 1 ?2y 2 6a3 3 7(x + 2y) 4 x = 44

5 6x2 ? 15xy 6 5 7 6x

5a 8 9a4b2 9 7x 10 24m3 11

4x +5 12

9

4

13 3 14 8 15 7a + 8b ? 12

Anunmswbeerrs p?laRanetios, rates and the PAGE 50 1 a 48 b ?40 c 160 d ?36

4 e ?16 2 a 3a b a + 15 c ?15a ? 24b d a

31x e 35 3 a 6x ? 15 b x

3ab c 8 ? x d ?3x + 6y e ?4a ? 14b 4 a x(3 ? x) b 3pq(p + 4q) c x = 3 d 5p3q6 e

10

PAGE 151 1 a 1:2 b 1:3 c 1:3 d 1:6 e 1:7 f 1:12 g 1:9 h 1:8 i 1:9 j 1:4 k 1:5 l 1:9 2 a 5:13 b 1:3

c 1:3 d 2:19 e 1:13 f 2:21 g 2:9 h 1:13 i 3:14 j 2:11 k 2:15 l 4:9 3 a 1:3:5 b 3:1 c 9:16 d 3:4 e 1:5

f 5:1 g 1:3 h 5:7 i 6:13 j 5:6 k 12:1 l 1:5 4 a 4:21 b 4:15 c 1:6 d 2:5 e 3:4 f 1:7 g 8:25 h 2:3 i 5:2

j 4:5 k 10:1 l 5:4 5 a 6:25 b 1:15 c 5:18 d 3:1 e 7:18 f 8:1 g 5:7 h 7:8

PAGE 522 1 a 20 kg, 160 kg b $10, $35 c $168, $672 d $300 e $800 2 a 25 cm b 15 c 40? , 60? , 80? d 16:25

e 9 3 a 28 m b $36, $60 c 3:10 d $1200, $1600, $2000

PAGE 353

1 a 80 km/h

b $20

c

5

1 3

L / min

d $7.95

2 a 1 b 960 c 3600 d $300

e 1800 f 0.6?

3 a 80 km/h b 108 km c 48.6 L 4 a 2.5 km/min b 0.027 km / s c 136 5 a 168.75 km/h b 2.58 m/y c 37

PAGE 454 1 a 1:1500 b 1:200 c 1:30 000 d 1:5000 e 3:500 f 1:40 g 1:30 000 h 3:10 i 1:8000 2 a 1 m

b 4 m c 6 m d 50 cm e 70 cm f 2 km g 60 cm h 80 cm i 1.5 km 3 a 4 m b 100 m c 8 km d 75 m e 9.3 km

f 23.45 km g 9 m h 15.2 km i 48.25 km 4 a 6 cm b 7 cm c 13.8 cm d 0.5 cm e 50 cm f 39.65 cm

5 a 4.8 m ? 5.6 m b 0.58 m

y

PAGE 555 1 a

5 4

b yes c see diagram d y = x + 1 2 a y = 2x + 1

b (?1, ?1),

3

2

1

?x ?5 ?4 ?3 ?2 ?1?1 0 1 2 3 4 5

x

x -1 0 1 2 2 y -1 1 3 5 5

?2

?3

?4

?5

?y

y

5

4

(0, 1), (1, 3), (2, 5) c

3 2

1 ?x

?5 ?4 ?3 ?2 ?1?1 0 1 2 3 4 5

Answers

?2 ?3 ?4

?5

?y

d yes

x

y

5 4

B

3

3 a

?x

2

A1

C

?5 ?4 ?3 ?2 ?1?1 0 1 2 3 4 5

b

x

right-angled triangle

c 3 units

d 4 units

?2

?3

?4

?5

?y

148 e 5 units f 12 units g 6 units2 4 a (0, 5), (1, 6), (2, 7), (E3X,CE8L)ESSbEN(T?IA1L,SK1IL)L,S:(Y0E,A3R)8,M(1AT,H5EM),A(TI2C,S 7RE)VIScIO(N?A1N,D?E5X)A,M(0W,O?R2K)B,O(O1K, 21?)E,X(T2EN, S4IO)N PAGE 656 1 a (?1, 1), (0, 2), (1, 3), (2, 4) b (?1, ?3), (0, ?1), (1, 1), (2, 3) c (?1, 3), (0, 1), (1, ?1), (2, ?3) 2 a (?1, ?1),

(?1, 0), (?1, 1), (?1, 2) b (?1, 2), (0, 2), (1, 2), (2, 2) c (?4, ?1), (?4, 0), (?4, 1), (?4, 2) 3 a (?1, ?2), (0, 0), (1, 2), (2, 4);

(?1, 2), (0, 0), (1, ?2), (2, ?4); the point of intersection is (0, 0) b (?1, 0), (0, 2), (1, 4), (2, 6); (?1, 1), (0, 2), (1, 3), (2, 4); the

point of intersection is (0, 2)

1a

y 5

1b

y 5

4

4

3

3

2

2

1

1

?x ?5 ?4 ?3 ?2 ?1?1 0 1 2 3 4 5

x

?x ?5 ?4 ?3 ?2 ?1?1 0 1 2 3 4 5

x

?2

?2

?3

?3

?4

?4

?5

?5

?y

?y

2c

y

3a

y

5

4

3

2

1

?x ?5 ?4 ?3 ?2 ?1?1 0 1 2 3 4 5

x

?2

?3

?4

?5

5

4

3

2

1

?x ?5 ?4 ?3 ?2 ?1?1 0 1 2 3 4 5

x

?2

?3

?4

?5

?y

?y

1c

y 5

4 3

2

1

?x ?5 ?4 ?3 ?2 ?1?1 0 1 2 3 4 5

x

?2

?3 ?4

?5

?y

3b

y

5

4 3

2

1

?x ?5 ?4 ?3 ?2 ?1?1 0 1 2 3 4 5

x

?2

?3 ?4

?5

?y

2a

y 5

4 3

2

1

?x ?5 ?4 ?3 ?2 ?1?1 0 1 2 3 4 5

x

?2

?3 ?4

?5

?y

2b

y

5

4

3

2

1

?x ?5 ?4 ?3 ?2 ?1?1 0 1 2 3 4 5

x

?2

?3

?4

?5

?y

PAGE 757 1 a (3, ?1), (3, 0), (3, 1), (3, 2); (?1, 1), (0, 1), (2, 1), (3, 1); the point of intersection is (3, 1) b (2, ?1), (2, 0),

(2, 1), (2, 2); (?1, ?1), (0, ?1), (1, ?1), (2, ?1); the point of intersection is (2, ?1) 2 a (?2, ?5), (?1, ?2), (0, 1), (1, 4); (?2, ?5),

(?1, ?3), (0, ?1), (1, 1); the point of intersection is (?2, ?5) b (?1, ?1), (0, 1), (1, 3), (2, 5); (?1, ?1), (0, ?2), (1, ?3), (2, ?4); the

point of intersection is (?1, ?1)

1a

y

1b

y

5

4

3

2

1

?x ?5 ?4 ?3 ?2 ?1?1 0 1 2 3 4 5

x

?2

?3

?4

?5

5

4

3

2

1

?x ?5 ?4 ?3 ?2 ?1?1 0 1 2 3 4 5

x

?2

?3

?4

?5

?y

?y

2a

y

5 4

3

2

1

?x ?5 ?4 ?3 ?2 ?1?1 0 1 2 3 4 5

x

?2 ?3

?4 ?5

?y

2b

y

5

4

3

2

1

?x ?5 ?4 ?3 ?2 ?1?1 0 1 2 3 4 5

x

?2 ?3

?4 ?5

?y

PAGE 58 1 a (?3, 10), (?2, 5), (?1, 2), (0, 1), (1, 2), (2, 5), (3, 10) b (?2, ?8), (?1.5, ?3.375), (?1, ?1), (?0.5, ?0.125),

(0, 0), (0.5, 0.125), (1, 1), (1.5, 3.375), (2, 8) 2 a (8, ?3), (3, ?2), (0, ?1), (?1, 0), (0, 1), (3, 2), (8, 3) b (?3, 8), (?2, 3), (?1, 0), (0, ?1), (1, 0), (2, 3), (3, 8) Mathletics Instant Workbooks ? Series I 2 Copyright ? 3P Learning

1a

y

10

8

6

1b

y

10

8

6

2a

y

3

2

2b

y

8

7

6

5

(2, 1), (2, 2); (?1, ?1), (0, ?1), (1, ?1), (2, ?1); the point of intersection is (2, ?1) 2 a (?2, ?5), (?1, ?2), (0, 1), (1, 4); (?2, ?5),

(?1, ?3), (0, ?1), (1, 1); the point of intersection is (?2, ?5) b (?1, ?1), (0, 1), (1, 3), (2, 5); (?1, ?1), (0, ?2), (1, ?3), (2, ?4); the

point of intersection is (?1, ?1)

1a

y

1b

y

2a

y

2b

y

5

Ans432wers

?

5

R432 atios,

5

ra432tes

and

the 5 4 3 2

1

1

number plane ?x ?5 ?4 ?3 ?2 ?1?1 0 1 2 3 4 5

x

?2

?3

?x ?5 ?4 ?3 ?2 ?1?1 0 1 2 3 4 5

x

?2

?3

1

?x ?5 ?4 ?3 ?2 ?1?1 0 1 2 3 4 5

x

?2

?3

1

?x ?5 ?4 ?3 ?2 ?1?1 0 1 2 3 4 5

x

?2

?3

?4

?4

?4

?4

?5

?5

?5

?5

?y

?y

?y

?y

PAGE 858 1 a (?3, 10), (?2, 5), (?1, 2), (0, 1), (1, 2), (2, 5), (3, 10) b (?2, ?8), (?1.5, ?3.375), (?1, ?1), (?0.5, ?0.125),

(0, 0), (0.5, 0.125), (1, 1), (1.5, 3.375), (2, 8) 2 a (8, ?3), (3, ?2), (0, ?1), (?1, 0), (0, 1), (3, 2), (8, 3) b (?3, 8), (?2, 3),

(?1, 0), (0, ?1), (1, 0), (2, 3), (3, 8)

1a

y

10

8

6

4

2

?x ?5 ?4 ?3 ?2 ?1 0 1 2 3 4 5 x

?2 ?4 ?6 ?8 ?10

?y

1b

y

10

8

6

4

2

?x ?2 ?1

0 1

2x

?2

?4

?6

?8

?10

?y

2a y 3

2

1

?x ?4 ?3 ?2 ?1 0 1 2 3 4 5 6 7 8 x

?1

?2

?3

?y

2b

y

8

7

6

5

4

3

2

1

?x ?3 ?2 ?1 0 1 2 3 x

?1

?2

?3

?4

?y

PAGE 959 1 a 3: 4 b 4:7 2 a 4:5 b 5:4 3 80 km/h 4 $240, $320 5 a 4:9 b 3:8 6 120 km/h 7 30 cents

8 3:4 9 $4000 10 30? , 60? 11 25 kg/s

PAGES 1600 & 1611 1 D 2 B 3 D 4 C 5 B 6 B 7 C 8 C 9 B 10 B 11 D 12 C 13 D 14 B 15 B

PAGE 1622 1 4:5 2 1:6 3 2:7 4 $65

5 50 m 6 1:4 7 12:7

8

33

1 3

m/s

9 13 h 20 min 10 256 m, 384 m

11 $54.60 12 p:2q 13 4.8 14 22.8 L 15 40?

PAGE 1633 1 a 1:25 b 98 c $30 d 4 h 40 min e $138.40 2 a 10 b 1:13 c 88 cm d 20 km/h e 0.6 km/min

3 a (?1, 3), (0, 2), (1, 1), (2, 0) b (?1, ?3), (0, ?1), (1, 1), (2, 3) c see diagram d point of intersection is (1, 1) 4 a see

diagram b see diagram c trapezium d 3:8

3

y

4

3

2

1

?x ?4 ?3 ?2 ?1 0 1 2 3 4 x

?1 ?2 ?3 ?4

?y

4

y

5

4

A

3 2

B

1

?x ?5 ?4 ?3 ?2 ?1?1 0 1 2 3 4 5

x

?2

D

?3 ?4

C

?5

?y

Answers

149

Mathletics Instant Workbooks ? Series I 2 Copyright ? 3P Learning

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download