2002 2005 11

!!!!!!!!!!!!!!!!!!!!!!! 1 1!!!!!!!!!!!!!!!!!!!!!!! 1 2!!!!!!!!!!!!!!!!!!!!!! 3 3!!!!!!!!!!!!!!!!!! 6 4!!!!!!!!!!!!!!!!!!!! 8!!!!!!!!!!!!!!!!!!!!!! 10 5!!!!!!!!!!!!!!!!!! 10 6!!!!!!!!!!!!!!!! 13 7!!!!!!!!!!!!!!!!!!!! 17 8!!!!!!!!!!!!!!! 20!!!!!!!!!!!!!!!!!!!!!! 23 9!!!!!!!!!!!!!!!!!! 23 10!!!!!!!!!!!!!!!!!! 25 11!!!!!!!!!!!! 28 12!!!!!!!!!!!!!!!!! 31!!!!!!!!!!!!!!!!!!!!!! 34 13!!!!!!!!!!!!!!!!! 34 14!!!!!!!!!!!!!!!!!!! 37 15!!!!!!!!!!!!!!!!!!!! 40 16!!!!!!!!!!!!!!!!!!! 43!!!!!!!!!!!!!!!!!!!!!! 45 17!!!!!!!!!!!!!!!!!!!! 45 18!!!!!!!!!!!!!!!!! 48 19!!!!!!!!!!!!!!!!!! 52 1

20!!!!!!!!!!!!!!!!!!!! 56!!!!!!!!!!!!!!!!!!!!!! 59 21!!!!!!!!!!!!!!!!! 59 22!!!!!!!!!!!!!!!!!!! 62 23!!!!!!!!!!!!!!!! 65 24!!!!!!!!!!!!!!!!!!!! 69 A!!!!!!!!!!!! 75!!!!!!!!!!!!!!!! 75 9 1!!!!!!!!!!!!!!!!!!!! 75 9 2!!!!!!!!!!!!!!!!!! 79 9 3!!!!!!!!! 83 9 4!!!!!!!!! 85 9 5 91!!!!!!!!!! 9 6 94!!!!!!!!!!!!!!!!!!!!!!!!!!!! 101 9 7!!!!!!!!!!!!!!!!!!! 101 9 8!!!!!!!!!!!!!!!!!!! 105 9 9!!!!!!!!!!!!!!!!!!!! 108!!!!!!!!!!!!!!!!!!! 111!!!!!!!!!!! 120 10 1!!!!!!!!! 121 10 2!!!!!!!!!!!!!!!!!!!! 123 10 3!!!!!!!!!!!!!!!!!!!! 126 10 4!!!!!!!!!!!!!!!!! 130!!!!!!!!!!!!!!!!!!! 134!!!!!!!!!!!!!!!!!!! 142 11 1!!!!!!!!!!!!!!! 143 2

11 2 147!!!!!!!!!! 11 3!!!!!!!!! 150!!!!!!!!!!!!!!!!!! 154 B!!!!!!!!!!!! 159!!!!!!!!!!!!!!! 160 9 1!!!!!!!!!!!!!! 160 9 2!!!!!!!!! 164 9 3!!!!!! 168 9 4!!!!!!!!!!!!!! 173!!!!!!!!!!!!!!!!!!! 177 9 5!!!!!!!!!!!!! 177 9 6!!!!!!!!!!!! 185!!!!!!!!!!!!!!!!!! 190 9 7!!!!!!!! 190 9 8!!!!!!!!!!!!!!!!!!! 195!!!!!!!!!!!!!!!! 200 9 9!!!!!!!!!!!!!!!! 200 9 10!!!!!!!!!!!!!!!!!!!! 207!!!!!!!!!!!!!!!!!!! 209!!!!!!!!!!! 216 A Unit 11 Scientific achievements!!!!!!!!!!! 217 Unit 12 Fact and fantasy!!!!!!!!!!!!!! 221 Unit 13 The water planet!!!!!!!!!!!!!! 225 3

Unit 14 Freedom fighters 230!!!!!!!!!!!!!! Unit 15 Destinations 234!!!!!!!!!!!!!!!! Unit 16 The United States of America 238!!!!!!!! Unit 17 Disabilities 243!!!!!!!!!!!!!!!!! Unit 18 Inventions 246!!!!!!!!!!!!!!!!! Unit 19 The Merchant of Venice 251!!!!!!!!!!! Unit 20 Archaeology 256!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 260 260 262 263 265 266 268!!!!!!!!!!!!!!!!! 273 273 275 277 279!!!!!!!!!!!!!!!!! 284 285 288 289 291!!!!!!!!!!!!!!!!! 298 298 299 300 301 303!!!!!!!!!!!!!! 308 309 311!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 4 314 314 317 319

321!!!!!!!!!!!!!!!! 323!!!!!!!!!!!!!!!!!!!! 325!!!!!!!!!!!!!!!! 325!!!!!!!!!!!!!!!!!!!!!! 329!!!!!!!!!!!!!!!!! 329!!!!!!!!!!!!!!!! 330!!!!!!!!!!!!!!!!!!! 332!!!!!!!!!!!!!!!!!! 335!!!!!!!!!!!!!!!!!!!!!! 337!!!!!!!!!!!!! 338!!!!!!!!!!!!!!! 339!!!!!!!!!!!!!!! 341!!!!!!!!!!!!!!!!!!! 343!!!!!!!!!!!!!!!!!! 344!!!!!!!!!!!!!!!!!!!!!! 347!!!!!!!!!!!!!!!!!! 347!!!!!!!!!!!!!!!!! 348!!!!!!!!!!!! 348!!!!!!!!!!!!!!!!!!!!! 357!!!!!!!!!!!!!! 364!!!!!!!!!!!!! 371!!!!!!!!!!!!! 376!!!!!!!!!!!!!! 383!!! 5

!!!!!!! 384!!!!!!!!!!!!!!! 387!!!!!!!!!!!!!! 388!!!!!!!!!!!!!!! 392!!!!!!!!!!!!! 394!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 395 409 410 418 6

殞 檶檶檶檶 殞 檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶 殞 殞 1 1 2 3 1

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殞 檶檶檶檶 殞 A 檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶 殞 殞 1 1 2 3 4 5 6 2 1 2 3 9 1 7 1 79

A 1 C 1 A 1 B BC 1 α β γ 1 A 1 α B 1 2 A β B 3 A / α B α C 1 β A 1 α A 4 α β = A 1 B 1 β γ = α D 1 β B 1 γ B α β γ α γ = 1 2 3 / / 4 BB 1 B 1 C 1 2 3 1 4 1 A α B α 2 l α m α 3 α β l 4 l α P α Q 5 l α β m α l m P 1 A α B / α 2 l α m α 3 α β = l 4 P / α Q α P l Q l 5 α β = l m α l m = P 9 1 7 1 80 1 3 2 1 2

3 A A BD ABC BCD ABD BD ABC ABC ACD = = BC / AC ABC BCD 3 4 1 P α β 2 l α β 3 l m P 4 α β l P l 5 l α P l α 1 P α P / β 3 l m = P 5 P l P α l α 2 l α l β 4 α β = P l 5 1 3 A 1 B 3 C D 0 2 a b c 2 A 1 B 3 C 0 D 6 3 a b c 3 A 0 B 1 C D 0 1 4 4 3 A 0 B 3 C 4 D 1 C 2 B 3 D 4 C 6 4 3 4 3 A B C D 81

3 A l B l C l D / l D l α A α B α C α D α A B C D 7 1 ABC AB AC = A, AB α AC α B AB C AC, B α C α BC α α 2 ABCD AB DC, AB α DC α, A α B α C α D α, AD α BC α 7 1 α 7 2 8 1 1 9 l 1 l 2 l 3 l 1 = A l 3 l 2 = B l 1 l 2, l 1 l 2 α l 1 α l 2 α A l 1 B l 2, A α B α A l 3 B l 3, l 3 α l 1 l 2 l 3 α 9 10 82 A / B l C l D l AB AC AD

A / l, A l α A α B l α, AB α AC α AD α, AB AC AD 11 10 9 2 11 1 4 1 2 2 AA' BB' CC' BB' = AA' CC' = ABC A' B' C' BB' = AA' A' A, BB' A' A, AB = A' B' BC = B' C' AC = A' C', ABC A' B' C' 3 A - BCD 4 ABC ACD ABD BCD E F G AB AC AD EF BC FG CD EFG BCD EF BC FG CD 3 83

, EF BC = AF AC = FG CD EFG = BCD, EFG BCD 14 1 1 2 1 2 2 3 1 2 3 3 4 ABCD - A 1 B 1 C 1 D 1 1 AC B 1 D 1 2 BC 1 B 1 D 1 1 A 1 C 1 AC A 1 C 1 A 1 C 1 B 1 D } AC B 1 D 1 2 BD B 1 D 1 BD, 1 DBC 1 C 1 D C 1 D = BD = BC 1, DBC 1 = 60, BC 1 B 1 D 1 60 9 2 14 1 84 4

1 a b a b A B C D 2 AA 1 AA 1 A 1 B 2 C 3 D 4 3 a b a b A B C D 4 OA O' A' OB O' B' AOB A' O' B' A B C D 1 D 2 C 3 D 4 C 2 1 a b c d 4 a b b c c d a d 2 a b α β a α b β a b 1 2 3 A 1 C 1 P P CD P A 1 B 1 C 1 D 1 l C 1 D 1 C 1 D 1 CD, l CD 3 4 4 AE = A 1 E 1 AF = A 1 F 1 EF = E 1 F 1 E 1 E FF 1 85

AE = A 1 E 1 AA 1 E 1 E AA 1 = EE 1 AF = A EF 1 F 1 AA 1 F 1 F AA 1 = FF } = E 1 F 1 1 5 E F G H AB- CD AB BC CD DA EFGH E H AB AD, EH = 1 2 BD FG = 1 2 BD 5, EH = FG, EFGH 6 1 a b a h b a b = a b 2 a b c a b a c α b c 3 AA 1 AA 1 4 a b c a b 1 2 α 3 8 4 2 7 a b c a b c b c c a b, b h c b c =, b c 8 AB CD AC BD A B C D AB CD 86 9 1 a b c a c b 2 a c b c a b

1 2 10 2 槡 3 cm 2 cm 1 BC A' C' 2 AA' BC' 3 A' B' DD' B' C' CD 1 A' C' B BC B' C', BC A' C' 10 A' B' = B' C' A' B' C' = 90, A' C' B = 45 BC A' C' 45 2 AA' BB', AA' BC' B' BC' BB' = 2 B' C' = 2 槡 3 BB' C' = 90, B' BC' = 60 AA' BC' 60 3 A' D' A' B' A' D' A' B' = A' A' D' DD' A' D' DD' = D', A' B' DD' A' D' = 2 槡 3 cm B' C' CD CC' = 2 cm 9 3 19 1 2 AB AB 2 3 3 α β γ a b c a b a c b 87

c a b a β a c b c 9 3 19 1 α β = AB P α P l l β P α l AB AB AB β l β, l β l 2 1 a b a b a b 1 2 a α a α a α 3 a b α a α b α a b 4 a b α a b a α b α b α 1 2 3 4 3 ABCD E F G AB BC CD EFG BD EFG AC EF AC AC EFG} EFG AC EFG BD 3 4 4 a b α a α b α P a P b' b' b a b' = P, a b' α α a α b α 88 5

5 AB α AC BD C α D α AC = BD CD AC BD, AC BD β C α D α, β α = CD AB α, AB CD, ACDB, AC = BD 6 α β = CD α γ = EF β γ = AB AB α CD EF a b c AB α AB β β α = CD, AB CD AB EF, CD EF 7 α β = a b α c β b c b c b α c α } c α c β } β α = a c a b c } a b c 6 7 8 8 a b a α = A b α b α b α b α b α a α a b, a α a α = A b α b β α = b' b b' a b, a b' a α, a α a α = A b α 9 4 23 1 1 l α l α 89

2 m α n α l m l n l α 3 l m m n l α n α 4 l m m α n α l n 1 2 3 4 2 m l = O, m l α n m n l, n α 2 3 3 α P PQ α Q R α R Q QR PQ QR Rt PQR PQ < PR 4 A B α α AB α A B AA' α A' BB' α B' AA' = BB', AA' B' B, AB A' B' AB α, AB α 25 1 l 1 l 2 α l 1 l 2 l 1 l 2 l 1 l 2 α 2 l 1 l 2 90

2 AB = 2a AC α BD α C α D α CD = a AB α AC α BD α, AC BD, ABDC AB α E E CD AEC AB α B BF CD AC F AEC = ABF Rt ABF BF = a AB = 2a, ABF = 60 AEC = 60 AB α 60 27 1 ABCD - A 1 B 1 C 1 D 1 AC 1 BD AC AC BD CC 1 AC AC 1 BD 2 O ABC PO ABC A O AO BC PA BC AO AO BC PO ABC, PA BC 1 2 3 3 V- ABC VO ABC O CD VA= VB AD = BD CD AB AC = BC VA= VB AD = BD } VD AB VO } ABC DO AB O CD} CD AB AD = BD} AC = BC 9 4 28 91

1 1 l α m α l m 2 m α n α m n l m l n l α 3 l α m α l m 4 l m l α m α 1 2 3 4 2 l α m α l m l β α = l' m α, m l', m l l α, l l' 3 Rt ABC D AB AC = 6 cm BC = 8 cm EC ABC EC = 12 cm EA EB ED CD = 1 2 AB = 1 2 10 = 5 EA = 6槡 5 cm EB = 4 槡 13 cm ED = 13 cm 4 BC AD B C D AD AD 3 AD BD AD CD BD α CD α BD CD = D, AD α 4 5 5 AB = 5 cm BC AB BD AB BC BD α E BE = 7 cm 1 EB AB CD AB 2 AE 1 CD AB 90 92 AB α EB α CD α, EB AB CD AB EB AB

2 AE = AB 2 2 槡 + BE = 槡 74 cm 6 8 m 10 m 6 m 6 2 + 8 2 = 10 2 7 α β = AB PC α PD β C D AB CD PC α AB α } PC AB PD AB } AB PCD CD PCD} AB CD 7 8 8 m n l 1 l 2 m n l l 1 l 2 1 = 2 m n, m n α l 1 m l 1 n, l 1 α l 2 α, l 1 l 2 l l 1 l 2, 1 = 2 9 l 1 l 2 α 1 l 1 α l 1 α l 2 α l 2 α l 1 l 2 α 0 2 l 1 α l 2 α l 1 l 2 α 90 9 93

3 l 1 α l 2 α A 1 A 2 l 1 l 2 B 1 B 2 B 1 α B 1 C 1 α C 1 B 2 C 2 α C 2 A 1 C 1 A 2 C 2 B 2 A 1 B 1 A 2 B 2 B 1 C 1 B 2 C 2, A 1 B 1 C 1 = A 2 B 2 C 2 B 1 C 1 A 1 = B 2 C 2 A 2 = 90, B 1 A 1 C 1 = B 2 A 2 C 2 l 1 l 2 α 10 D DA DB DC DA = a BDA = CDA= 60 BDC = 90 BC DA α, DAB = DAC = 90 DA= a BDA= CDA= 60, DB = DC = 2a BDC = 90 10, BC = BD 2 2 槡 + DC = 2槡 2a 11 AOB O P PC OA C PD OB D POD = POC PC = PD PE AOB E OE EC = ED ED OB EC OA, OE AOB 94 11 12 12 E E

C E C 1 E E C 1 E l l CE 13 α O 2 cm OH α = 4 cm H AB OC AB C HC HO AOB, HC AB, HC H AB HC = 槡 ( ) 槡 OH 2 + OC 2 = 4 2 + 槡 3 2 2 = 槡 19 cm OB HB H B HB = 槡 OB 2 + HO 2 = 2 2 2 槡 + 4 = 2槡 5 cm 9 5 32 2 13 1 1 m α n α m β n β α β 2 α β m α n β m n 3 α β l α l β 4 α β α β 1 m α n α α β = m n l m β n β 2 m α n β m h n 3 α β α β = l α } l β = l β 4 α a b a β b β, α β 2 α β AB CD α β AB CD γ γ α = AC γ β = BD α β, AC BD AB CD, AB = CD 9 5 32 1 ABC - A' B' C' AB' 1 + 2 = 180 95

BC' 3 + 4 = 180 ABC A' B' C' 1 + 2 = 180, A' B' AB, A' B' ABC B' C' ABC A' B' B' C' = B', A' B' C' ABC 1 2 2 ABC - A' B' C' ABB' = A' B' B = CBB' = C' B' B = 90 AC' AC A' C' BB' A' B' BB' A' B' C' BB' B' C' } ABC A' B' C' BB' } ABC A' C' AC 3 1 2 1 β 2 α γ β γ l γ l α l β α 4 1 A B C AA' = BB' = CC' ABC A' B' C' 96

2 AA' BB' CC' O AO = A' O BO = B' O CO = C' O ABC A' B' C' 1 AA' = BB' =, A' C' ABC B' C' ABC CC', A' C' AC B' C' BC A' C' B' C' = C', ABC A' B' C' 2 AO = A' O BO = B' O AOB = A' OB', AOB A' OB', OAB = OA' B', A' B' AB B' C' BC A' B' ABC B' C' ABC A' B' B' C' = B', ABC A' B' C' 4 1 4 2 5 α P β γ β α γ α β α γ α β γ P β γ, β γ = l P l β γ 6 90 α β l α l β l α β l α l P l' α 6 7 97

l' β l' AA' l' BB' AA' BB' l l' AA' BB' PAA' = PBB' 7 12 cm 60 A AC β C ABC = 60 AC = 12 12 BC β, AC BC AB = = 8 sin 60 槡 3 cm 8 1 a b a α b α b β a β α β 8 1 8 2 2 b P P a γ γ β = c a β a γ γ β = c, c a, c α b α b c b β c β, α β 9 α β γ a b α β γ AB A B C D E F BC = DE EF HE CF AF β = H AD BH α β, AD EH, AB BC = AH HF AB BC = DE EF DE EF = AH HF 9 6 9 98

36 1 3 90 2 α β γ α β = l α γ = a β γ = b l γ α-l-β β a b α-l-β l a l b a α b 2 3 3 α-l-β 30 P α P β h P l P PR β R PQ l Q RQ PQR = 30 RP = h PQ P l PQ = 2h 4 ABCD - A 1 B 1 C 1 D 1 ABC 1 D 1 AD 1 BC 1 90 4 45 38 1 2 99

1 2 3 α β α β = l AB α AB l BC β DE β BC DE AC DE α β } α β = l AB β AB α BC DE AC DE AB l } DE β 9 6 39 3 1 1 V- ABC V-AB-C 2 V- ABCD ABCD V-AB-C 100

1 1 1 2 1 AB D VD DC AB VD AB CD VDC V-AB-C 1 VD = CD = 槡 3 2 VC = 1 VCD cos VDC = 1 3 V-AB-C arccos 1 3 2 O O EF AB AB CD E F VE VF VEF 1 VE = VF = 槡 3 2 EF = 1 VEF cos VEF = 槡 3 3 VEF = arccos 槡 3 3 101

1 1 1 2 2 3 45 40 m 14 14 m BC α C CD l D BD BD AD BD = AB sin 45 = 20 槡 2 sin BDC = BC BD 1 2, BDC 30 30 3 4 4 V V 40 mm 20 mm 5 α-l-β 45 P α P β h P l 102

α-l-β P α PA β A AB l B PB PB l Rt PAB PA AB PA = h PB = PA = sin 45 槡 2h P l 槡 2h 6 P PQ α Q PR β R PQ AB PR AB, AB PQR S QS RS AB QS AB SR, QSR α-ab-β PQSR Q = R = 90, P QSR 6 7 ABCD O AC BO DO B-AC-D B-AC-D 60 B D BO OB AC OD AC BOD B-AC-D BO DO B-AC-D 90 OB = OD BOD = 60 BOD BD = BO 8 1 7 2 1 α a a β α β 1 a γ α = a' a α, a a' a β, a' β a' α, α β 103

1 2 8 2 α β α γ β γ 2 α α γ a α γ, a γ α β, a β 1 β γ 9 α γ β γ α β = l l γ l P P l' γ P α α γ, l' α l' β, l' = α β = l, l γ 10 1 2 1 a b c a b α a c β c a c b c α } a b α c β } α β l α β γ γ α 2 9 11 α l β α β = a α l' a α β, l' β l β, l l' l α, l α 12 104

1 α γ β γ α β 2 α β β γ α γ 3 α α 1 β β 1 α β α 1 β 1 1 2 α β γ β α γ 3 α α 1 α β } α 1 β β β } α 1 β 1 1 13 1 α β α β = l A α B β AB = a AB α β θ 1 θ 2 A B l A' B' 13 1 13 2 2 A α AA' l A' A' B AA' β, ABA' = θ 2 B β BB' α B' AB' BAB' = θ 1 AA' β, AA' A' B BB' AB' Rt AA' B AA' = asin θ 2 Rt AB' B AB' = αcos θ 1 Rt AA' B' A' B' = acos θ 1 2 2 - asin θ 2 槡 = a 槡 cos 2 θ 1 - sin 2 θ2 Rt A' BB' A' B' = a 槡 cos 2 θ 2 - sin 2 θ1 14 V - ABC VAB = VAC = ABC = 90 VAB VBC VAB VBC 14 105

VA AB VA AC } VA ABC VA BC AB BC} BC VAB VAB VBC VA ABC BC AB } VB BC AB BC} BC VAB 9 7 43 1 1 2 3 4 5 1 2 3 ABB' A' 1 3 1 4 4 AC' BCC' B' ABB' A' 106

5 2 2 cm 4 : 3 2 槡 26 cm 4a cm 3a cm a > 0 2 2 + 4a 2 + 3a 2 = 2 槡 26 2, a = 2 cm 8 cm 6 cm 45 1 2 9 7 45 1 2 ABCD - A' B' C' D' AA' 5 cm B' D A' C 9 cm 15 cm AC BD O AC = 槡 A' C 2 - A' A 2 = 槡 15 2-5 = 10槡 2 cm BD = 2 槡 14 cm OA = 5槡 2 cm OB = 槡 14 cm 2 2, AB = 槡 OA 2 + OB 2 = 8 cm S = 4 8 5 = 160 cm 2 3 4 cm BC 30 AA' D AD BCD S ABC = S DBC cos 30 S DBC = 8 cm 2 AD = tan 30 AD = 2 cm 2槡 3 4 1 3 2 1 ABCD-A' B' C' D', ACC' A' AB' C' D 107

AC' A' C O AC' B' D O', O O' AC' O O', AC' A' C B' D O O BD' O O 2 AC' = A' C BD' = B' D, ACC' A' BB' D' D, AA' AC BB' BD AA' BB', AA' BD, AA' ABCD, ABCD-A' B' C' D' AD ABB' A' AD AB ABCD 4 1, ABCD-A' B' C' D' 4 2 5 a b c x 1 x 2 x 3 x 2 1 + x 2 2 = a 2 x 2 2 + x 2 3 = b 2 x 2 3 + x 2 1 = c 2, 2 x 2 1 + x 2 2 + x 2 3 = a 2 + b 2 + c 2 l l 2 = x 2 1 + x 2 2 + x 2 3 1, l = 槡 2 a2 + b 2 + c 2 = 1 2 6 槡 2 a 2 + b 2 + c 2 7 1: 2: 3 48 cm 3 x cm 2x cm 3x cm x 2x 3x = 48, x = 2 2 cm 4 cm 6 cm 8 a C D 1 ABCD 2 ABCD 108

1 CD = 1 2 EF = AB, CD = 1 2 AB, ABCD 2 AD = BC = 槡 a 2 + 1 4 a, ABCD 2 = 槡 5 2 a DH AB H AH = 1 2 AB - CD = 1 2 槡 2a - 槡 2 ( a 2 ) = 槡 2 4 a, DH = 槡 AD 2 - AH 2 = 5 1 4 a2-8 a 2 3 = 槡 2 4 a 槡 ( ), ABCD = 1 2 槡 2 2 a 3 + 槡 2a 槡 2 4 a = 9 8 a2 8 9 a b 45 h S V h = bsin 45 = 槡 2 2 b S = 6 1 2 a 槡 3 2 a = 3槡 3 2 a2 3 V= Sh = 槡 6 4 a2 b 10 30 cm 10 x cm 槡 2x = 20 x = 10槡 2 V 1 = π 10 2 30 = 3 000π cm 3 V 2 = 30 10槡 2 2 = 6 000 cm 3 = V 1 - V 2 = 3 000 π - 2 cm 3 11 109

V = Sh = 1 a + b 2 ch = 1 ah + bh 2 c = 1 2 S 1 + S 2 c S 1 S 2 CC 1 D 1 D ABB 1 A 1 c 9 8 49 11 1 1 2 3 4 1 2 3 4 2 h l S ABCDEF S O AO = OA= 槡 l 2 - h 2 SH AB H AH = 1 2 AB = 1 2 槡 l 2 - h 2, SH = 槡 SA 2 - AH 2 = 1 2 50 槡 3l 2 + h 2 2 cm 槡 6cm 1 2 cm ABCD O 110 2 SO ABCD SO = 2 cm 50

3 SA SB SC SD SA= SB = SC = SD = 槡 6 cm 51 1 2 9 8 52 1 2 a h 1 2 3 1 S - ABC S O AO BC D SD AD BC SD BC D BC OA= 槡 3 3 a OD = 槡 3 6 a SO = h, 1 SA= 槡 3 a2 + h 2 = 1 3 槡 3a 2 + 9h 2 1 SD = 槡 12 a2 + h 2 = 1 6 槡 3a 2 + 36h 2 2 1 2 2 2 OE BC E SE SE BC, OA= 槡 2 2 a OE = 1 2 a SO = h 111

, 1 SA= 槡 2 a2 + h 2 = 1 2 槡 2a 2 + 4h 2 1 SE = 槡 4 a2 + h 2 = 1 2 槡 a 2 + 4h 2 3 AB S O OM AB M SM SM AB OA= a OM = 槡 3 2 a SO = h, SA= 槡 a 2 + h 3 SM = 槡 4 a2 + h 2 = 1 2 槡 3a 2 + 4h 2 3 4 cm 2 2 3 槡 3 cm S - ABCD O SO OB BC = 4 cm SB = 2 槡 3 cm OE BC E SE SE BC SEO OB = 4 槡 2 2 = 2 槡 2 cm 槡, SO = 2 槡 3 2-2 槡 2 2 = 2 cm OE = 1 2 4 = 2 cm 3 tan SEO = 2 2 = 1 SEO = 45 4 1 2 1 2 1 2 1 5 3 112

1: 9 6 A - BCD EFGH AB EFGH CD E F G H AC BC BD AD EFGH EF AB HG EH CD FG, EF HG EH FG, EFGH 7 8 4 A - BCD 6 a a 3 ( ) V= 1 3 1 2 a 2 a = 1 6 a3, V A BCD = a 3-4 1 6 a3 = 1 3 a3 V A BCD 9 n 8 1 1 n 1 2 n n 1 5 n 3 1 2 n 10 1 x x 2 : 1 x: 1 x 3 : 1 = 1: 2, x = 槡 3 2 1: 槡 2 3 113

9 9 62 R 1 R 2 d 2 d 2 = R 2 R - ( 2 ), d = 槡 3 2 R 2 A B 60 6 370 km 1 O AOB = π 3 OA= OB = 6 370 km, AB = 6 370 π 3 ) 6 671 km 65 1 2 8 2 2 8 2 4 cm 2R 2R = 槡 4 2 + 4 2 2 + 4 = 4槡 3 cm V= 4 3 πr3 = 32槡 3π cm 3 67 1 6 370 km S = 4πR 2 = 4 6 370 2 π 5 099 10 8 km 2 2 100 cm 3 4 75 3 πr3 = 100, R = 槡 π cm, S = 4πR 2 = 20 槡 3 45π cm 2 9 9 67 3 1 114

,, 2 O 1 O 2 r 1 r 2 r 1 = r 2 OO 1 OO 2 O, OO 1 = R 2 2 槡 - r1 OO 2 = r 1 = r 2, OO 1 = OO 2 槡 R 2 2 - r2 R 3 13 cm A B C AB = 6 cm BC = 8 cm CA = 10 cm ABC ABC O O 1 AB = 6 cm BC = 8 cm CA= 10 cm, CA 2 = AB 2 + BC 2, CA O 1 OO 1 O ABC Rt OAO 1 OO 1 = OA 2 2 槡 - AO 1 = 槡 13 2-5 2 = 12 cm 4 O R A B AOB = θ π A B A B Rθ 5 O R r h = 2 OO 1 = 2 槡 R 2 - r 2 V = 2πr 2 槡 R 2 - r 2 5 6 6 ABCD - A 1 B 1 C 1 D 1 O R a 115

2R 槡 3a 2R = 槡 3a, R = 槡 3 2 a 7 O 1 O 2 O 3 1: 8: 27 R 1 R 2 R 3 4 3 πr3 1 : 4 3 πr3 2 :, R 1 : R 2 : R 3 = 1: 2: 3 4 3 πr3 3 = 1: 8: 27 8 R 2R V = V - 2 V = πr 2 2R - 2 1 3 πr2 R = 4 3 πr3 = V 8 9 4 10 O 1 O 2 125 O 1 10 cm 116 O 2 R S 4 3 π 103 = 4 3 πr3 125 R = 2 cm, S = 4πR 2 = 16π cm 2 A 75 1 O 2

1 l 1 l 2 l 3 = P l 1 l 2 l 3 2 l 1 l 2 l 3 l 1 l 2 l 3 3 l 1 l 2 = P l 2 l 3 = Q l 3 l 1 = S P Q S 3 l 1 l 2 l 3 1 l 1 l 2 α l 3 α P l 3 α 2 l 1 l 2 α l 3 α α 3 l 1 l 2 = P, l 1 l 2 α Q l 2 S l 1, Q α S α Q l 3 S l 3, l 3 α l 1 l 2 l 3 2 1 2 1 2 1 1 l 1 l 2 l 3 = P P / l 4 l 1 l 4 = A l 2 l 4 = B l 3 l 4 = C l 1 l 2 α l 4 α l 3 α 2 l 1 l 2 = A l 1 l 3 = C l 2 l 3 = B l 1 l 4 = F l 2 l 4 = D l 3 l 4 = E l 1 l 2 α l 3 α l 4 α 2 l 1 l 2 l 1 l 2 α l 3 B l 3, l 1 l 3 = A l 2 l 3 = B, l 3 α l 4 α A α B α A 2 2 3 1 a b a c b c 117

2 3 1 2 3 4 1 A B C D 2 a b a α b β α β = l A l a b B l a b C l a b D l a b 3 l 1 l 2 A l 1 l 2 B l 1 l 2 C l 1 l 2 D l 1 l 2 1 B 2 D 3 D 5 l 2 1 l 1 l 2, l 1 l 2 α α l 1 2 l 1 l 2 l 1 β l 2 β, l 2 β 1 2 6 1 α β = m n α n β m n 118

6 1 6 2 2 δ n δ m δ δ α = l n α, n l γ n γ m γ γ β = q n β, n q l q l α α β = m q β l q, l m n l m n m 7 1 l α l γ α β β γ 2 δ l δ α δ = l 1 β δ = l 2 l α l l 1 α β l 1 l } l l 2 2 l γ } l 2 γ β γ l 2 β} 7 1 7 2 8 1 ABC C ABC P PC = 24 cm P AC BC PD PE 6 槡 10 cm 1 P ABC PF 2 PC ABC 119

8 1 8 2 2 EF FD 1 PE BC PF ABC } EF BC } FCE = FCD = 45 DF AC Rt PEF Rt PDF EF = DF CF ACB EF = EC = PC 2 2 槡 - PE 2 FC = 槡 2EF = 12槡 3, tan PCF = PF FC = 槡 3 3, PCF = 30 = 6槡 6 PF = 槡 PE 2 - EF 2 = 12 cm 9 α β = a β γ = b γ α = c a b a b a b a b c a b = P P a α P b γ P γ α = c a b c = P a b b γ a γ a γ a α c α γ α = c a c 10 AC α AC l C l BD β l D l AC = 3 BD = 4 AB = 槡 17 CD = 2 α-l-β EC BD BE CD CE BE = E AE CDBE AE BE 120 AB = 槡 17 BE = CD = 2, AE = 槡 17-4 = 槡 13 10

ACE AC = 3 CE = 4 AE = 槡 17 cos ACE = 1 2, ACE = 60 AC l CE l ACE α-l-β 60 11 4 3 ABCD AC B D 11 BE AC E BE = 12 5 AE = 9 5 DE DE 2 = 193 25 BD = 槡 337 5 n - 2 180 12 n n n n - 2 180 13 a b S ABC ABC O OA OA= 槡 3 3 a 1 3 槡 SO Rt SOA = b 2-1 3 a 2 = 槡 9b 2-3a 2 V= 1 3 槡 3 4 a2 1 3 槡 3 36 a2 槡 9b 2-3a 2 槡 9b 2-3a 2 = 13 121

14 cos ACB = n2 + p 2 - m 2 2np = c2 np > 0 ACB ABC 14 15 A BCD A H BH AH BH BO AC O DO DO AC BOD a OB = OD = 槡 3 2 a BD = a BOD cos BOD = 1 3, BOD = arccos 槡 a 2-1 3 15 Rt ABH AH = 槡 AB2 - BH 1 3 a 2 = 槡 6 a 3 槡 6: 3 16 a r R a 3 = 2πr 3 = 4 3 πr3 S 1 S 2 S 3 S 1 = 6a 2 S 2 = 6πr 2 S 3 = 4πR 2, S 1 > S 2 > S 3 B 77 1 P a b c l a b c a b α b c β α β P l α β 122 2 α-l-β 120 2 =

A α B β A B l 2 4 AB = 10 AB l AB β CE = 4 AC l BD l CE DB BE CE E AC = 2 BD = 4 ACE = 120 ACE AE = 2槡 7 AE BE 2, sin ABE = 槡 7 10 = 槡 7 5, AB l ABE = arcsin 槡 7 5 ACE β ACE β = CE AH CE H AH β BH ABH AB β AH = AC sin60 = 2 槡 3 2 = 槡 3 AB = 10, sin ABH = 槡 3 10, ABH = arcsin 槡 3 10 3 ABCD - A 1 B 1 C 1 D 1 1 B 1 D A 1 C 1 B 2 B 1 D A 1 C 1 B H A 1 C 1 B 1 B 1 D 1 B 1 D 1 A 1 C 1 D 1 D A 1 B 1 C 1 D 1 B 1 D A 1 C 1 B 1 D BC 1 A 1 C 1 BC 1 = C 1 B 1 D A 1 C 1 B 2 1 B 1 D A 1 C 1 B = H HA 1 HB HC 1 A 1 B 1 = B 1 C 1 = B 1 B HA 1 = HB = HC 1 A 1 C 1 B H A 1 C 1 B 123

3 4 4 AB a b a α b β α β = l AB l A b' b a b' δ AB b b' b } AB b' AB a } AB δ a α l α } a l AB l b β l δ b' b b' l } l β 5 1 60 124 A BCD BC E AE DE AE BC DE BC, BC ADE AH DE AEH = 60 AH BCD EH = 槡 3 6, AH = 槡 3 6 槡 3 = 1 2 ( ) AE 2 = 槡 3 6 2 + ( 1 ) 2 2 = 1 3 5

1, AB = 槡 3 + 1 4 = 槡 21 6 CO AB O DO DO AB CO = DO COD 2 AB CO = BC AE CO = DO = 槡 7 7 COD cos COD = 1 8, COD = arccos 1 8 1 2 槡 21 6 arccos 1 8 6 F n 1 n 2 n 3 n F E = 1 2 n 1 + n 2 + + n F E n 1 + n 2 + + n F F 7 R x h = 槡 R 2 - x 2 πr 2, S = f x = 2πx 槡 R 2 - x π x 2 + R 槡 2 - x 2 2 = πr 2 2 7 x = 槡 R 2 - x 2 x = 槡 2 2 R 8 h V 1 V 2 ( h) V 1 = 1 3 π 槡 3 3 2 h = 1 9 πh3 125

3 槡 225h ( ) V 2 = 1 3 π 3R 槡 3 3 V 1 = V 2, 2 3R - R 1 15 槡 225h 4 3 πr3 = 5 3 πr3 1 9 πh3 = 5 3 πr3, R = 1 15 3 8 1 1 2 3 2 1 2 3 10 1 82 1 1 2 5 1 4 2 1 126

2 A B 3 B C 2 A B C 1 5 + 4 = 9 2 3 2 = 6 2 3 5 4 1 1 2 3 1 1 3 + 5 + 4 = 12 2 3 5 4 = 60 3 a 1 + a 2 + a 3 b 1 + b 2 + b 3 + b 4 c 1 + c 2 + c 3 + c 4 + c 5 3 4 5 = 60 4 0 9 10 10 10 10 10 = 10 000 5 5 1 1 5 1 5 4 1 4 5 4 = 20 10 1 83 1 4 7 1 4 + 7 = 11 2 2 3 4 2 2 3 + 4 2 = 14 3 1 5 9 13 4 2 127

4 8 12 16 4 4 4 = 16 4 1 1 4 2 5 3 3 9 2 4 13 1 4 + 3 + 2 + 1 = 10 4 A B A B 3 3 1 2 2 3 + 1 + 2 2 = 8 5 1 A= 0 2 3 4 5 2 B = 1 3 5 7 y C = 2 4 6 8 1 6 6 = 36 2 4 4 = 16 6 1 4 1 3 4 4 3 2 3 5 1 3 5 5 3 1 3 4 3 3 3 3 3 = 3 4 128 2 5 3 5 10 2 90 1 1 4 a b c d 2 2 5 a b c d e 2 1 ab ac ad ba bc bd ca cb cd da db dc 2 ab ac ad ae ba bc bd be ca cb cd ce da db dc de ea eb ec ed 2

1 A 4 15 2 A 7 7 3 A 4 8-2A 2 8 4 A8 12 A 7 12 1 A 4 15 = 15 14 13 12 = 32 760 2 A 7 7 = 7 = 5 040 3 A 4 8-2A 2 8 = 8 7 6 5-2 = 1 568 4 A8 12 = 5A7 12 = 5 A 7 12 A 7 12 4 3 n 2 3 4 5 6 7 8 n n 2 3 4 5 6 7 8 n 2 6 24 120 720 5 040 40 320 4 1 18 17 16 9 8 A A 8 18 B A 9 18 C A 10 18 D A 11 18 2 n A A n n B 1 n + 1 An + 1 n + 1 C A n n + 1 D na n - 1 n - 1 1 D 18-8 + 1 = 11 2 C A n n + 1 = n + 1 n 2 n 5 1 A m n = na m - 1 n - 1 2 A 8 8-8A 7 7 + 7A 6 6 = A 7 7 1 = na m - 1 n - 1 = n n - 1 n - 2 n - 1 - m - 1 + 1 = n n - 1 n - 2 n - m + 1 = A m n = 2 = A 8 8-8A 7 7 + 7A 6 6 = A 8 8 - A 8 8 + A 7 7 = A 7 7 = 6 A7 n - A 5 n = 89 n A 5 n 129

A 5 n n - 5 n - 6 - A 5 n = 89 n - 5 n - 6 = 90 = 10 9 A 5 n, n - 5 = 10 n = 15 n - 5 n - 6 90 = 10 9 n - 5 n - 6 = 90 7 5 3 A 3 5 = 5 4 3 = 60 8 4 3 3 A 3 4 = 24 130 10 2 91 1 1 5A 3 5 + 4A 2 4 2 A 1 4 + A 2 4 + A 3 4 + A 4 4 1 5A 3 5 + 4A 2 4 = 5 5 4 3 + 4 4 3 = 348 2 A 1 4 + A 2 4 + A 3 4 + A 4 4 = 4 + 4 3 + 4 3 2 + 4 3 2 1 = 64 2 1 A n + 1 n + 1 - A n n = n 2 A n - 1 n - 1 n + 1 2 k - n n - k + 1 = n k - 1 k k n 1 = A n + 1 n + 1 - A n n = n + 1 A n n - A n n = na n n = n 2 A n - 1 n - 1 = n + 1 2 = k - n n + 1 = - k n n - k + 1 = n k - 1 k k = 3 n 1 A 3 2n = 10A 3 n 2 A5 n + A 4 n = 4 A 3 n 1 A 3 2n = 10A 3 n 2n 2n - 1 2n - 2 = 10n n - 1 n - 2 4 2n - 1 = 10 n - 2 n = 8 2 A5 n + A 4 n = 4 A3 n n - 3 n - 4 + A 3 n n - 3 = 4 A 3 n A 3 n n - 3 n - 4 + 1 = 4 n - 3 = 2 n = 5

4 1 A m 10 = 10 9 5 m = 2 9 = 362 880 A 7 9 = 3 A 2 n = 56 n = 4 A 2 n = 7A 2 n - 4 n = 1 10 - m + 1 = 5 m = 6 2 A 7 9 = 1 9 = 181 440 2 3 n n - 1 = 8 7 n = 8 4 A 2 n = 7A 2 n - 4 n n - 1 = 7 n - 4 n - 5 ( ) n = 7 n = 10 3 5 8 4 1 A 4 8 = 1 680 6 4 1 A 4 4 = 24 A 1 4 = 4 A 1 3 4 3 2 1 = 24 7 1 2 3 4 5 2 1 3 4 5 13 000 1 A 1 5 + A 2 5 + A 3 5 + A 4 5 + A 5 5 = 325 1 2 3 4 5 2 1 2 3 4 5 1 3 4 5 4A 4 4 + 3A 3 3 = 114 2 1 2 A 5 5 - A 3 3 = 114 8 1 7 2 7 2 3 7 3 4 4 7 3 4 1 A 6 6 = 720 131

2 5 A 2 2 A 5 5 = 240 3 3 4 = 144 4 A 3 7 A 4 4 = 5 040 A 7 7 = 5 040 9 11 1 1 4 2 5 7 10 3 3 6 9 2 4 8 4 3 2 = 288 10 1 A 5 7 + 5A 4 7 = A 5 8 2 A m n + ma m - 1 n = A m n + 1 1 A 5 7 + 5A 4 7 = 3A 4 7 + 5A 4 7 = 8A 4 7 = A 5 8 2 A m n + ma m - 1 n = 10 3 95 n m n + = n n - m + 1 + m n - m n - m + 1 n - m + 1 = n n + 1 = A m n + 1 n - m + 1 1 4 1 2 1 2 2 A B C D 4 3 3 132 ABC ABD ACD BCD 3 1 5 a b c d e 2 2 5 a b c d e 3 1 ab ac ad ae bc bd be cd ce de 2 abc abd abe acd ace ade bcd bce bde cde

4 3 1 5 a b c d e 2 ab ac ad ae bc bd be cd ce de ba ca da ea cb db eb dc ec ed 5 1 C 2 6 2 C 3 8 3 C 3 7 - C 2 6 4 3C 3 8-2C 2 5 1 C 2 6 = 6 5 2 1 = 15 2 C3 8 = 8 7 6 3 2 1 = 56 3 C 3 7 - C 2 6 = 35-15 = 20 4 3C 3 8-2C 2 5 = 3 56-2 10 = 148 6 C m n = m + 1 n + 1 Cm + 1 n + 1 m + 1 n + 1 Cm + 1 n + 1 = m + 1 n + 1 n + 1 n = = C m n m + 1 n - m m n - m 99 1 1 C 17 20 2 C 98 100 1 C 17 20 = C 3 20 = 1 140 2 C 98 100 = C 2 100 = 4 950 2 C 5 12 + C 6 12 = A C 5 13 B C 6 13 C C 11 13 D C 7 12 B 2 3 1 C 3 7 + C 4 7 + C 5 8 = C 5 9 2 C 0 5 + C 1 5 + C 2 5 + C 3 5 + C 4 5 + C 5 5 = 2 5 1 C 3 7 + C 4 7 + C 5 8 = C 4 8 + C 5 8 = C 5 9 2 C 0 5 + C 1 5 + C 2 5 + C 3 5 + C 4 5 + C 5 5 = 2 C 0 5 + C 1 5 + C 2 5 = 2 1 + 5 + 10 = 2 5 4 6 1 C 2 6 = 15 5 6 3 C 3 6 = 20 6 3 5 7 11 C 2 4 = 6 10 3 100 133

1 1 C 3 15 2 C 197 200 3 C 3 6 C 4 8 4 C n n + 1 C n - 2 n 1 C 3 15 = 455 2 C 197 200 = C 3 200 = 1 313 400 3 C 3 6 C 4 8 = 2 7 4 C n n + 1 C n - 2 n = C 1 n + 1 C 2 n n - 1 n = n + 1 = 1 2 2 n n2-1 2 1 C m n + 1 = C m - 1 n + C m n - 1 + C m - 1 n - 1 2 C m + 1 n + C m - 1 n + 2C m n = C m + 1 n + 2 1 C m - 1 n + C m n - 1 + C m - 1 n - 1 = C m - 1 n + C m n = C m n + 1 2 C m + 1 n + C m - 1 n + 2C m n = C m + 1 n + C m n + C m - 1 n + C m n = C m + 1 n + 1 + C m n + 1 = C m + 1 n + 2 3 10 1 2 2 3 1 C 2 10 = 45 2 C 3 10 = 120 4 1 2 n 1 C 2 5-5 = 5 2 C 2 n - n = n n - 3 2 5 1 C 1 4 + C 2 4 + C 3 4 + C 4 4 = 15 6 1 8 4 3 2 10 4 4 1 C 3 8 = 56 2 C 4 10 = 210 7 1 3 5 3 2 5 3 3 3 5 3 1 134

4 A m B n 1 1 C 3 5 = 10 3 3 5 = 243 2 C 3 5 A 3 3 = A 3 5 = 60 4 C 1 m C 1 n = mn 8 1 4 3 2 3 2 3 2 1 1 4 3 C 3 4 2 3 2 C 2 3 3 2 1 C 1 2 C 3 4 C 2 3 C 1 2 = 24 9 5 4 4 1 4 2 2 3 1 4 4 1 C 2 5 C 2 4 = 60 2 C 2 7 = 21 3 C 4 9 - C 4 7 = 91 4 C 4 9 - C 4 5 - C 4 4 = 120 10 6 C 1 6 + C 2 6 + C 3 6 + C 4 6 + C 5 6 + C 6 6 = 63 11 200 2 5 1 2 2 1 3 4 1 1 C 2 2 C 3 198 = 1 274 196 2 C 1 2 C 4 198 = 124 234 110 3 C 5 198 = 2 410 141 734 4 1 C 3 198 + C 1 2 C 4 198 = 125 508 306 2 C 5 200 - C 5 198 = 125 508 306 12 1 3 5 7 9 3 2 4 6 8 2 135

1 3 5 7 9 3 C 3 5 2 4 6 8 2 C 2 4 5 A 5 5 C 3 5 C 2 4 A 5 5 = 7 200 13 5 1 5 5 A 1 3 A 1 3 A 3 3, A 1 3 A 1 3 A 3 3 = 54 A 1 3 4 A 1 3 A 4 4 - A 3 3 = 54 10 4 106 1 p + q 7 p + q 7 = p 7 + 7p 6 q + 21p 5 q 2 + 35p 4 q 3 + 35p 3 q 4 + 21p 2 q 5 + 7pq 6 + q 7 2 2a + 3b 6 3 T 3 = C 2 6 2a 4 3b 2 = 2 160a 4 b 2 3 3b + 2a 6 3 T 3 = C 2 6 3b 4 2a 2 = 4 860b 4 a 2 4 槡 3 n 1 x - ( 2 ) 槡 3 x r T r + 1 = C r n 槡 3 1 x n - r - ( 2 ) 槡 3 = x r + 1-1 r 3 2 r C r nx n - 2r T r + 1 = C r n - 1 槡 x 2 槡 3 x 5 x 3 + 2x 7 4 4 136 r 3 ( ) n - r 1 4 C 3 7 = 35 4 C 3 7 2 3 = 280 r

6 x - 1 10 6 A C 6 10 B - C 6 10 C C 5 10 D - C 5 10 D T 5 + 1 = C 5 10 x 10-5 - 1 5 = - C 5 10 x 5 109 1 1 C 5 15 = a C 9 15 = b C 10 16 = 2 a + b 9 3 C 1 11 + C 3 11 + + C 11 11 = 4 C0 n + C 1 n + C 2 n + + C n n = C 0 n + 1 + C 1 n + 1 + C 2 n + 1 + + C n + 1 n + 1 1 C 5 15 = C 10 15 = a C 9 15 = b, C 10 16 = C 9 15 + C 10 15 = a + b 2 C 4 9 = C 5 9 = 126 3 C 1 11 + C 3 11 + + C 11 11 = 1 2 211 = 2 10 = 1 024 4 = 2n 2 = 1 n + 1 2 2 C 0 n + C 2 n + C 4 n + + C n n = 2 n - 1 n C 0 n + C 1 n + C 2 n + + C n n = 2 n C 0 n + C 2 n + + C n n = C 1 n + C 3 n + + C n - 1 n n, C 0 n + C 1 n + C 2 n + + C n n = C 0 n + C 2 n + + C n n + C 1 n + C 3 n + + C n - 1 n = 2 C 0 n + C 2 n + + C n n = 2 n, C 0 n + C 2 n + + C n n = 1 2 2n = 2 n - 1 n 3 10 4 109 1 1 0 < p < 1 p + 1 - p n 2 1 n ( 2 + 1 2 ) 1 p + 1 - p n = C 0 np n + C 1 np n - 1 1 - p + C 2 np n - 2 1 - p 2 + + C r np n - 1 r - p r + + C n n 1 - p n 2 1 n ( 2 + 1 2 ) = C0 n 2 + C1 n n 2 + C2 n Cnn n n + + 2 2 n 137

2 1 a + 槡 3 b 9 7 2 槡 x 2-2 ( ) 槡 x 1 a + 槡 3 b 9 = a 9 + 9a 8 3 槡 b + 36a 7 3 槡 b 2 + 84a 3 b 2 + 36a 2 b 2 3 ( ) 2 槡 x 2-2 槡 x 224x - 5 2-128x - 7 2 7 槡 b + 9ab 2 = 1 128 x 7 2-3 1 1 + 槡 x 5 + 1 - 槡 x 5 3 b 槡 2 + b 3 2 2x 1 2 + 3x - 1 2 4-2x 1 2-3x - 1 2 4 1 1 + 槡 x 5 + 1 - 槡 x 5 = 2 + 20x + 10x 2 3 槡 b 2 + 84a 6 b + 126a 5 b 槡 3 b + 126a 4 b 7 32 x 5 2 + 21 8 x 3 2-35 2 x 1 2 + 7 0 x - 1 2-168x - 3 2 + 2 2x 1 2 + 3x - 1 2 4-2x 1 2-3x - 1 2 4 = 192x + 432x - 1 4 1 1-2x 15 4 2 2a 3-3b 2 10 8 3 槡 x 3 + 3 12 ( ) 槡 x 4 x槡 y - y槡 x 15 1 1-30x 420x 2-3 640x 3 2 T 8 = C 7 10 2a 3 3-3b 2 7 = - 2 099 520a 9 b 14 6 3 T 7 = C 6 槡 x 12 ( 3 ) 3 6 ( ) = 924 槡 x 4 T 8 = C 7 15 x槡 y 8 - y槡 x 7 = - 6 435x 11 y 11 槡 x 138 T 9 = C 8 15 x槡 y 7 - y槡 x 8 = 6 435x 11 y 11 槡 y 5 10 ( ) 1 ( 2 ) 1 1 1-2x 2 2x 3-2x 1 x 5 10

1 T r + 1 = C r 10 - ( ) = C 5 1 10-2x 5 = - 63 8 1 x 5 ( ) 1 2x r 1 ( ) = - 1 x - 63 5 8 2 T r + 1 = C r 10 2x 3 ( 2 ) 10 - r - 1 2x 2 r r C r 1 10 x 1 r x 6 T 5 6 T 6 = C r 102 10 - r - 1 ( ) 2 r x 30-3r - 2r, 30-5r = 0 r = 6 7 T 7 1 ( ) 6, T 7 = C 6 102 10-6 - 2 6 1 n + 1 n - 1 n 2 2 99 10-1 1 000 1 n + 1 n - 1 = n n + C 1 nn n - 1 + C 2 nn n - 2 + + C n - 2 n n 2 + C n - 1 n n + 1-1 = n n + C 1 nn n - 1 + C 2 nn n - 2 + + C n - 2 n n 2 + C 1 nn = n 2 n n - 2 + C 1 nn n - 3 + C 2 nn n - 4 + + C n - 2 n + 1, n + 1 n - 1 n 2 2 99 10-1 = 100-1 10-1 = 100 10 - C 1 10100 9 + C 2 10100 8 + + C 8 10100 2 - C 9 10100 = 1 000 10 17 - C 1 1010 15 + C 2 1010 13 + + C 2 10 10-1, 99 10-1 1 000 7 2n 1 1 x ( - x ) - 2 n 1 3 5 2n - n = 105 2 2 1 + x 2n 1 T r + 1 = C2nx r 2n - r 1 - x 1 3 5 2n - 2x n n ( ) r = C2n - r 1 r x 2n - 2r 2n - 2r = 0 n = r 139

T n + 1 = - 1 n C n 2n = - 1 n 2n n n = - 1 n 2n - 1 2n - 2 2 1 = - 1 n 1 3 5 2n - 1 2 4 6 2n n n = - 1 n 1 3 5 2n - 1 2n 1 2 3 n n n = - 2 n 1 3 5 2n - n 2 1 + x 2n 2n + 1 n + 1 T n + 1 T n + 1 = C2nx n n = 2n n n xn = 1 3 5 2n - 1 2n n x n n n 8 = 1 3 5 2n - 2x n n 9 1 + x n 4 8 C n n C 3 n = C 7 n C 3 n = C n - 3, n - 3 = 7 n = 10 C 3 10 C 7 10 120 10 2 n - C 1 n 2 n - 1 + C 2 n 2 n - 2 - + - 1 2-1 n = 1 n n - 1 C n - 1 n 2-1 n = C 0 n2 n - C 1 n2 n - 1 + C 2 n2 n - 2 + + - 1 2 n - C 1 n2 n - 1 + C 2 n2 n - 2 + + - 1 A 114 n - 1 C n - 1 n 2 + - 1 n = 1 n - 1 C n - 1 n 2 + - 1 n = 1 1 1 a 1 + a 2 + + a m b 1 + b 2 + + b n C m n 2 = a = C m n' A m n A m n' 2 + - 1 n 3 7 3 6 2 4 6 140

1 mn 2 a 3 C 3 7 C 2 6 = 525 4 C 1 4 A 5 5 = 480 2 1 5 4 1 A 5 4 B 4 5 C 5 4 3 2 D 5 4 3 2 4 2 5 4 1 A 5 4 B 4 5 C 5 4 3 2 D 5 4 3 2 4 3 A 12 11 B 2 12 9 C 12 11 D 12 9 2 4 1 + x 2n n N A n 2 + 1 B n C n + 1 D n n + 1 1 D C 4 5 = C 1 5 = 5 2 B 4 5 4 5 3 B 1 C 2 12 12 C 2 12-12 = 12 9 2 2 C 1 12 9 C 1 9 C 1 12 C 1 9 = 12 9 2 2 4 C 1 + x 2n 2n + 1 n + 1 3 1 2n 2 n n = 1 3 5 2n - 1 2 1 + 2 2 + 3 3 + + n n = n + 1-1 n n = n + 1 - n 141

1 2n 2 n n = 2n - 1 3 2 1 2 n n = 1 3 5 2n - 1 2 4 6 2n 2 n n = 1 3 5 2n - 1 2n n 2 n n = 1 3 5 2n - 1 2 k k = k + 1 - k k = k + 1 - k k N +, 1 + 2 2 + 3 3 + + n n = 2-1 + 3-2 + + n + 1 - n = n + 1-1 1 1 7 4 1 - = C m C m 5 C m 6 10 C m 8 7 C m - 1 n 2 = Cm n 2 3 = Cm + 1 n 4 n m 1 m 5 - m 5 - m 6 - m 6 = 7 m 7 - m 10 7 10 6 m 5 - m 10 6-10 6 - m = 7 - m 6 - m m 2-23m + 42 = 0, m = 2 m = 21 C m 8 = C 2 8 = 28 { C m - 1 n = Cm n 2 3 1 2 C m n 3 = Cm + 1 n 2 4 n n 1 = 2 m - 1 n - m + 1 3m n - m 2 n - m + 1 = 3m 2n - 5m + 2 = 0 3 n n 2 = 3 n - m = 4 m + 1 3m n - m 4 m + 1 n - m - 1 3n - 7m - 4 = 0 3 4 n = 34 m = 14 5 1 2 3 4 5 6 2 1 3 4 5 6 500 000 142 4

1 1 2 3 4 5 6 A 1 6 + A 2 6 + A 3 6 + A 4 6 + A 5 6 + A 6 6 = 6 + 30 + 120 + 360 + 720 + 720 = 1 956 2 500 000 5 6 C 1 2 A 5 5 = 240 6 1 8 3 2 5 1 2 3 4 1 C 3 8 = 56 2 C 1 5 + C 2 5 + C 3 5 + C 4 5 = 1 + 1 5 - C 0 5 - C 5 5 = 2 5-2 = 30 7 10 6 2 2 C 4 8 2 C 6 8 C 4 8 + C 6 8 = C 4 8 + C 2 8 = 98 8 1 n 2 n 1 n 2 C 2 n n - 1 n = 2 2 C 2 n = n n - 1 2 9 100 97 3 5 1 5 2 5 2 3 5 2 1 C 5 97 = 64 446 024 2 C 2 3 C 3 97 = 442 320 3 C 2 3 C 3 97 + C 3 3 C 2 97 = 446 976 10 4 5 3 A 4 4 A 5 5 A 3 3 1 3 A 3 3 A 3 3 A 4 4 A 5 5 A 3 3 = 103 680 ( ) 11 n = 1 2 3 4 1 + 1 n n 143

( ) 3 1 ( 1 + ) 2 ( ) = 9 4 ( 1 + 1 ) 1 1 1 n = 1 1 + = 2 n = 2 1 + = 2 25 1 2 n = 3 = 64 4 2 370 n = 4 = 625 2 441 3 27 4 256 e 12 1 1-2x 5 1 + 3x 4 x 3 18 1 2 9x - ( 3 ) 槡 x 3 1 + 槡 x n 9 10 11 n 4 1 + x + x 2 1 - x 10 x 4-26x 2 - r - 1 = C 0 5 1 5 C 0 4 1 4 = 1 = 1 C 1 4 3x + C 1 5-2x 1 = 2x = 1 C 2 4 3x 2 + C 1 5-2x C 1 4 3x + C 2 5-2x 2 1 = 2 T r + 1 = C18 9x r r 2 = 0 r = 12 T 13 = - 1 ( ) 3 18 - r - 12 r 1 ( 3 ) = C189 r 18 - r - 槡 x 3 9 6 C 12 18 = 18 564 3 2C 9 n = C 8 n + C 10 n 1 ( ) 2 n n n = + 9 n - 9 8 n - 8 10 n - 10 r x 18 - r - r 2 18 10 n - 8 n 2 10 n - 8 = 10 9 + n - 8 n - 9 n 2-37n + 322 = 0, n = 14 n = 23 4 T' r + 1 1 - x 10 r + 1 x 4 T' 4 + 1 T' 3 + 1 T' 2 + 1 C 4 10-1 4 + C 3 10-1 3 + C 2 10-1 2 = C 4 10 - C 3 10 + C 2 10 = 135 144 13 55 55 + 9 8 55 55 + 9 = 56-1 55 + 9 55 55 + 9 = 56-1 55 + 9 = 56 55 - C 1 55 56 54 + + C 54 55 56-1 + 9 =

56 55 - C 1 55 56 54 + + C 54 55 56 + 8 8 55 55 + 9 8 14 1 + x 2n x n 1 + x 2n - 1 x n 2 1 + x 2n x n C n 2n 2n = n 2n - n = 2n n 1 + x 2n - 1 x n C n 2n - 1 2n - 1 = = 2n - 1 = n 2n - 1 - n n 2n n - 1 2n 2 n = 1 2 Cn 2n, C n 2n = 2C n 2n - 1 ( ) 15 槡 x + 1 n 3 a + b 2n 槡 x 240 1 槡 x + 1 n 3 ( ) 3 2 a + b 2n 槡 x 2 n = 2 2n - 240, 2 n 2-2 n - 240 = 0 2 n - 16 2 n + 15 = 0 2 n > 0, 2 n = 16 n = 4 ( ) 1 槡 x + 1 4 3 3 槡 x T 3 = C 2 4 槡 x 2 1 2 3 ( ) = 6 槡 3 x 槡 x 2 a + b 8 T 5 = C 4 8 a 4 b 4 = 70a 4 b 4 B 116 1 1 C n - 1 n + 1 = 21 n = 2 6 4 2 3 A= a 1 a 2 a 3 a 4 B = b 1 b 2 b 3 A B B A 4 2 4 2 145

1 C n - 1 n + 1 = C 2 n + 1 n + 1 = n = 21 n 2 + n - 42 = 0 n = 6 2 2 A 1 4 A 1 2 A 4 4 = 192 3 A B A B A 4 3 A B 3 4 = 81 B A 4 3 = 64 card A = m card B = n A B n m B A m n 4 A 2 26 10 4 = 6 500 000 146

2 1 A C 1 8 C 3 7 B C 4 8 C C 4 8-6 D C 4 8-12 2 1-2x n A 1 B 2 n C - 1 D 1-1 1 D 8 4 C 4 8 4 4 6 4 AD' C' B 6 D 2 D 1-2x n x = 1-1 n 1-2 n = - 1 n = { 2 1 1 n 3 n - 1 n 1 1 2 3 n = 3 4 2 5 3 n n - 2 2 C m n - 1 + C m n - 2 + C m n - 3 + + C m m + 1 + C m m = C m + 1 n n 1 1 2 3 n - 1 n = 3 4 5 n n - 1 n 4 5 n n n n = n 3 4 2 5 3 n n - 2 2 C m + 1 n = C m + 1 n - 1 + C m n - 1 = C m n - 1 + C m n - 2 + C m + 1 n - 2 = C m n - 1 + C m n - 2 + C m n - 3 + C m + 1 n - 3 = = C m n - 1 + C m n - 2 + C m n - 3 + + C m m + 1 + C m + 1 m + 1 = C m n - 1 + C m n - 2 + C m n - 3 + + C m m + 1 + C m m 4 0 1 2 3 4 5 1 2 201 345 1 0 2 3 4 5 1 3 5 A 1 3 4 A 1 4 4 A 4 4 A 1 3 A 1 4 A 4 4 = 288 2 1 1 A 1 4 A 5 5 201 345 201 345 1 A 1 4 A 5 5-1 = 479 147

201 345 2 0 1 2 3 4 5 201 345 4 1 3 A 1 2 A 2 2 2 A 1 3 A 3 3 A 1 4 A 4 4 A 1 3 A 5 5 1 + A 1 2 A 2 2 + A 1 3 A 3 3 + A 1 4 A 4 4 + A 1 3 A 5 5 = 479 5 1 m n 2 m n l 1 C 2 m C 2 m m - 1 n n - 1 mn m - 1 n = = n - 1 2 2 4 2 C 2 m C 2 n C 2 l = 1 8 mnl m - 1 n - 1 l - 1 6 5 1 2 1 A 1 4 A 4 4 = 96 2 A 2 3 A 3 3 = 36 ( 4 ) 7 1 x槡 x + 1 x n 3 2 44 x 2 1 + x 3 + 1 + x 4 + + 1 + x n + 2 x 2 1 C 2 n - C 1 n n - 1 n = 44 - n = 44 n = 11 n = - 8 2 ( 4 ) x槡 x + 1 x 148 11 r + 1 T r + 1 = C r 11 x 3 2 11 - r x - 4 r = C r 11 x 1 2 33-11r 1 33-11r = 0 r = 3 2 x T 4 = C 3 11 = 165 2 1 1 + x 3 + 1 + x 4 + + 1 + x n + 2 =

1 + x n + 3-1 + x 3 x 3 x 2 x C 3 n + 3 - C 3 n + 3 3 = n + 2 n + 1-6 6 = n n2 + 6n + 11 6 2 1 + x 3 1 + x 4 1 + x n + 2 x 2 C 2 3 C 2 4 C 2 5 C 2 n + 2 x 2 B 3 2 C 2 3 + C 2 4 + C 2 5 + + C 2 n + 2 = C 3 n + 3 - C 2 2 = n n2 + 6n + 11 6 8 1 C 0 n 2 + C 1 n 2 + + C n n 2 = 2n n 1 + x n 1 + x n = 1 + x 2n x n 2 C 1 n + 2C 2 n + 3C 3 n + + nc n n = n 2 n - 1 1 1 + x n 1 + x n = 1 + x 2n x n, C 0 nc n n + C 1 nc n - 1 n + C 2 n C n - 2 n + + C n nc 0 n = C2n n C 0 n 2 + C 1 n 2 + + C n n 2 = 2n n n 2 k C k n = k n n n - 1 = = nc k - 1 k n - k k - 1 n - 1 - k - 1, C 1 n + 2C 2 n + 3C 3 n + + nc n n = nc 0 n - 1 + nc 1 n - 1 + nc 2 n - 1 + + nc n - 1 n - 1 = n C 0 n - 1 + C 1 n - 1 + + C n - 1 n - 1 = n 2 n - 1 n - 1 1 1 2 n k 149

2 1 2 3 11 1 122 1 1 a b a + b = b + a 2 1 3 4 5 6 7 8 9 10 10 4 3 4 60 15 5 50 6 1 2 3 4 5 6 2 n 10 20 50 100 200 500 m 8 19 44 92 178 455 m n 1 2 m 1 0 8 0 95 0 88 0 92 0 89 0 91 n 150 2 1 0 9 3 1 2 3 4

5 544 9 607 13 520 17 190 2 883 4 970 6 994 8 892 1 3 2 1 0 520 0 517 0 517 0 517 2 0 517 127 1 2 1 2 1 1 3 1 1 4 2 2 1 1 1 3 1 1 3 1 2 2 1 2 1 2 4 2 1 1 2 3 1 1 P = 2 4 = 1 2 4 1 1 2 2 1 2 4 + 1 4 = 1 2 1 1 1 3 2 3 3 1 1 3 2 3 1 A 3 3 = 6 2 A3 3 2 = 3 3 P = A 3 3 2 A 3 3 = 1 2 151

3 40 12 30 mm 1 30 mm P = 12 40 = 3 10 4 1 3 5 8 1 3 P = 2 4 = 1 2 5 A B C P = 1 6 11 1 128 1 1 20 2 1 2 4 3 4 1 000 1 4 A 1 A 2 A 3 3 B 1 B 2 2 A 2 B 1 1 1 2 20 = 1 10 2 1 3 4 4 1 000 = 1 4 1 250 3 2 = 1 6 2 100 1 100 1 1 7 2 7 1 7n 100 n n = 1 2 3 14 100 1 100 1 7 14 152

2 7 P = 14 100 = 7 50 3 3 2 1 1 2 3 C 1 2 C 1 2 C 1 2 = 8 2 3 1 3 2 1 8 3 2 1 8 4 10 3 2 10 6 10 3 C 3 10 3 2 10 6 C 3 6 + C 2 6 C 1 4 P = C3 6 + C 2 6 C 1 4 = 2 C 3 3 10 2 3 5 1 3 2 2 2 3 1 5 2 5 1 1 2 1 C 1 5 C 1 5 C 1 3 C 1 2 P = C1 3 C 1 2 = 6 C 1 5 C 1 25 5 6 365 C 1 365 C 1 365 C 1 C 1 365 365 P = = 1 C 1 365 C 1 365 365 7 80 50 20 10 3 1 3 2 2 1 3 1 153

1 80 3 C 3 80 3 C 3 50 P = C3 50 = 245 1 027 C 3 80 2 P = C2 50 C 1 20 = 1 225 C 3 4 108 3 P = C1 50 C 1 20 C 1 10 = 125 80 C 3 1 027 80 8 A 3 3 2 P = 2 A 3 3 = 1 3 9 7 0 9 10 7 7 0 9 10 10 7 7 A 7 10 P = A7 10 10 = 189 7 3 125 10 5 1 2 5 A 5 5 1 A 4 4 P = A4 4 = 1 5 2 A 2 2 A 3 3 P = A2 2 A 3 3 = 1 A 5 10 5 11 1 2 3 4 5 3 1 5 2 3 400 A 5 5 1 P = A2 4 = 1 A 3 5 5 5 A 2 4 154

2 P = C1 2 A 2 4 = 2 A 3 5 5 2 4 C 1 2 A 2 4 3 P = C1 2 A 2 4 = 2 4 5 C 1 A 3 2 A 2 4 5 5 11 2 131 1 2 2 1 1 2 2 1 3 1 1 4 1 1 2 3 4 2 A B C 3 1 A B 2 A C 3 B C 1 A B 2 A C 3 B C 3 m 8 10 10 12 12 14 14 16 16 18 0 1 0 28 0 38 0 16 0 08 1 10 16 m 2 8 12 m 3 14 18 m 1 P = 0 28 + 0 38 + 0 16 = 0 82 2 P = 0 1 + 0 28 = 0 38 11 2 132 3 P = 0 16 + 0 08 = 0 24 1 1 30% 50% 155

2 1 0 42 0 28 1 30% + 50% = 80% 2 1-0 42-0 28 = 0 30 2 A B C D B 3 1 2 45 g 0 22 2 50 g 0 20 2 45 2 50 g P = 1-0 22-0 20 = 0 58 4 10 9 8 0 24 0 28 0 19 1 10 9 2 8 1 P = 0 24 + 0 28 = 0 52 2 P = 1-0 24 + 0 28 + 0 19 = 0 29 5 9 1 2 9 2 1 1 A 2 1 P A = C1 5 C 1 4 = 5 9 B 2 2 P B = C2 5 = 5 C 2 18 C 9 2 1 A B C = A+ B P C = P A+ B = P A + P B = 5 9 + 5 18 = 5 6 2 A 2 B 2 1 156 A B P A = C2 4 = 1 6 C 2 9 C 2 9

P B = 1 - P A = 5 6 6 10 000 1 5 10 1 1 2 1 1 P 1 = 10 000 5 P 2 = 10 000 = 1 2 000 P 3 = 10 10 000 = 1 1 000 1 2 P = P 1 + P 2 + P 3 = 10 000 + 1 2 000 + 1 1 000 = 1 625 m n i a i i = 1 2 n i P i = a i i = 1 m 2 n P = P 1 + P 2 + + P n = a 1 + a 2 + + a n m 11 3 136 1 2 2 1 A 3 1 B A B 1 2 1 1 B 3 2 1 1 B 2 3 A B A B 2 96% 97% 1 157

1 A 1 B 2 A B A B P A B = P A P B = 96 100 97 = 93 12% 100 3 0 2 0 3 1 2 3 A B 1 P A B = P A P B = 0 2 0 3 = 0 06 2 P A B = P A P B = 1-0 2 1-0 3 = 0 8 0 7 = 0 56 3 1 - P A B = 1-0 56 = 0 44 4 1 0 9 4 2 3 1 2 3 4 A 1 A 2 A 3 A 4 A 1 A 2 A 3 A 4 P A 1 A 2 A 3 A 4 = P A 1 P A 2 P A 3 P A 4 = 0 9 3 1-0 9 = 0 072 9 138 1 0 04 4 1 2 1 1 158 P 4 1 = C 1 4 0 04 1-0 04 3 0 14 2 P 4 2 = C 2 4 0 04 2 1-0 04 2 0 009 1 P 4 0 + P 4 1 0 96 4 + 0 14 0 85 + 0 14 = 0 99

2 4 4 3 2 1 0 0 9 + 0 1 4 P 4 4 = C 4 4 0 9 4 1-0 9 0 P 4 3 = C 3 4 0 9 3 1-0 9 1 P 4 2 = C 2 4 0 9 2 1-0 9 2 P 4 1 = C 1 4 0 9 1-0 9 3 P 4 0 = C 0 4 0 9 0 1-0 9 4 0 9 + 0 1 4 11 3 139 1 1 1 5 1 4 2 0 8 0 7 1 P = 1 5 1 4 = 1 2 P = 0 8 0 7 = 0 56 20 2 1 1 4 1 5 1 3 A 20 B 1 5 C 2 5 D 9 20 1 2 1 3 1 1 2 1 5 6 A 2 B 2 C 2 D 2 1 159

1 1 ( )( 1 - ) 1 C 1-1 - = 2 4 5 5 1 2 C 1-2 1 3 = 5 6 3 5 5 1 1 5 5 5 1 2 5 1 ( 2 ) = 1 32 4 0 04 0 05 1 1 A B A B P A = 0 04 P B = 0 05 P = P A B + P A B = 0 04 1-0 05 + 1-0 04 0 05 = 0 086 5 9 1 3 000 0 99 3 000 9 P = 0 99 9 0 91 6 4 1 1 0 79 2 0 79 3 0 80 4 0 81 4 P = 0 79 0 79 0 80 0 81 0 40 7 3 100 1 1 1 3 1 2 3 1 3 1 1 3 P = 1 = 0 01 100 1 3 1 P 3 1 = C 1 3 P 1 - P 2 ( ) = 3 1 100 99 100 160 2 0 03 2 3 1 1-1 - P 3 = 1 -

0 99 3 0 03 1 8 2 3 2 2 2 1 3 2 C 2 3 ( 1 2 ) 1 ( 1-2 ) = 3 8 2 3 8 9 95% 4 3 4 3 P = P 4 3 + P 4 4 = C 3 4 0 95 3 1-0 95 1 + C 4 4 0 95 4 1-0 95 0 0 99 10 1 90% 5 1 4 2 2 1 5 4 P 5 4 = C 4 5 0 9 4 1-0 9 1 0 33 2 5 2 3 P 5 3 = C 3 5 0 9 3 0 1 2 0 07 11 0 6 3 0 1 2 3 0 1 2 3 0 064 0 288 0 432 0 216 A 146 1 1 1 2 5 2 3 161

8 2 4 1 3 3 3 80% 70% 4 90% 5 4 1 P = C1 2 C 1 2 C 1 3 2 1 = 1 C 3 4 64 6 3 P = 1-1 - 0 8 1-0 7 = 0 94 4 P 5 4 = C 4 5 0 9 4 1-0 9 = 5 0 9 4 0 1 0 328 = 2 5 2 P = ( ) 2 1 2 2 2 A 1 B 1 1 C 1 2 D 1 1 2 2 2 1 A 1 4 B 1 3 C 1 2 D 3 4 1 C 1 2 2 C 1 P 2 1 = C 1 2 ( 1 ) ( 1 ) 2 2 1 = 1 2 3 1 0 1 2 0 3 3 0 4 4 0 1 4 4 4 P = 0 1 + 0 3 + 0 4 + 0 1 = 0 9 4 5 3 162

5 A 5 5 3 2 A 2 2 A 3 3 P = A2 2 A 3 3 = 1 A 5 10 5 5 1 2 3 5 8 1 2 23 000 1 2 3 5 8 A 5 5 1 3 5 C 1 3 A 4 4 P = C1 3 A 4 4 = 3 5 2 23 000 1 A 4 4 2 1 A 3 3 P = A4 4 + A 3 3 = 1 4 6 1 3 5 7 9 cm 3 5 3 C 3 5 3 3 3 5 7 3 7 9 5 7 9 3 P = 3 = 3 C 3 10 5 7 1 2 3 4 5 6 1 2 1 6 2 6 P = 6 6 = 1 2 6 2 P = C1 3 C 1 3 6 6 = 1 4 1 1 - P = 1-4 = 3 4 1 1 6 A 5 5 A 5 5 163

1 1 6 1 6 2 3 4 5 6 1 6 1 6 1 ( 6 1 6 ) 6 = 1 6 2 1 2 1 2 1 2 1 1-2 1 2 = 3 4 8 1 0 9 2 0 8 3 0 7 1 P = 1-0 9 0 8 0 7 = 0 496 9 m P m m m 1 - P m 1-1 - P m 10 0 7 0 6 3 2 3 2 P 1 = C 2 3 0 7 2 1-0 7 1 3 2 P 2 = C 2 3 0 6 2 1-0 6 1 2 P = P 1 P 2 = C 2 3 0 7 2 0 3 C 2 3 0 6 2 0 4 0 19 B 147 1 1 27 1 2 2 5 4 5 2 164 1 P = 12 27 = 4 9 2 P = C2 5 C 3 4 + C 3 5 C 2 4 = 50 C 5 63 9 2 8 2 8 4

1 8 A B 4 C 4 8 C 1 2 C 2 6 P = C1 2 C 2 6 = 3 7 C 4 8 2 2 2 2 A 2 B 2 A 8 4 2 P 1 = C2 6 2 B 8 4 P 2 = C4 6 C 2 P = P 4 1 + P 2 = C2 6 + C4 6 = 3 8 C 4 8 C 4 7 8 3 2 2 1 2 1 8 4 C 1 2 C 3 6 1 2 1 - C1 2 C 3 6 C 4 8 = 1-4 7 = 3 7 C 4 8 3 52 13 4 4 4 4 P = C1 4 C 4 13 = 44 0 01 4 165 4 P = C1 13 4 0 11 4 m n n m 1 1 1 P = m m + n m m + n + n m + n n m + n = m2 + n 2 m + n 2 5 3 1 p C 4 52 C 4 52 C 4 8 165

p 3 1 - p 3 2 1 - p 3 2 2 1 P = 1-1 - p 3 2 = 2p 3 - p 6 P = 2 1 = P 2 1 2 1 2 = p 3 p 3 + p 3 1 - p 3 + 1 - p 3 p 3 = 2p 3 - p 6 166

殞 檶檶檶檶 殞 B 檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶 殞 殞 1 1 2 3 4 5 6 7 8 2 1 2 3 167

9 1 5 1 2 3 AB α AB α 1 AB α 4 l α l α 1 5 9-3 6 1 α β 2 3 4 5 6 1 2 3 4 5 6 7 168 7

169

3 7 1 1 l l A A l A l 2 1 2 2 3 1 A α B α 2 l α 3 α β l 1 A α B α 2 l α 3 α β = l 4 2 3 2 a b a b a b A a b A B C 3 A B C α A B C α 4 1 a b α α a b a b A B C 3 A B C a b 170 3 10 1 1 2 3 1 2 3

2 ABC A' B' C' ABC BC A' M' B' C' M' A' M' 3 1 4 cm 2 2 3 cm 3 5 cm 4 cm 3 cm 9 1 11 1 2 1 2 3 1 2 3 3 A B C AB BC CA X Y Z BC CA AB AX BY CZ ABC ABC 1 4 3 5 6 171

3 3 6 7 8 8 9 4 cm 3 cm 2 cm 172

9 9 2 13 1 4 4 1 2 2 AA' BB' CC' AA' BB' AA' = BB' BB' CC' BB' = CC' ABC A' B' C' AA' BB' AA' = BB' } AA' B' B AB = A' B' BC = B' C' AC = A' C' 14 1 2 173

3 1 2 3 3 4 1 ABCD A' B' C' D' 4 1 4 2 1 AA' 2 AB = 槡 3 AA' = 1 BA' CC' 2 1 C' D' B' C' CD BC AA' 2 AA' CC', AA' B BA' CC' AB = 槡 3 AA' = 1, tan AA' B = 槡 3, AA' B = 60, BA' CC' 60 9 2 15 1 A' C' P P BC 174

A' C' P B' C' 1 2 1 2 1 AE = A' E' AF = A' F' EF = E' F' 2 EE' FF' AEE' A' AFF' A' E' E = A' A = F' F, EE' F' F, EF = E' F' 3 a b c 2 2 a c a b c A B α a b β 3 4 4 a b c a b b c c a 5 AB CD AC BD 175

AB CD AC BD AB CD AC BD AC BD A B C D, AB CD AB CD,, AC BD 6 2 cm 7 4 cm 1 BC A' C' AA' BC' 2 AA' BC AA' CD AA' CC' 176 1 BC A' D', D' A' C' BC A' C' A' D' = D' C' = 4 cm, cos D' A' C' = 槡 2 2, BC A' C' 槡 2 2 AA' BB', B' BC AA' BC' BB' = 2 cm B' C' = 4 cm, cos BBC' = 2 槡 20 = 槡 5 5, AA' BC' 槡 5 5 2 AA' BB' BB' BC, AA' BC 90 AA' CC' CC' CD, AA' CD 90 7

AA' CC', AA' CC' 0 177

9 3 17 1 ABCD AB AB AB CD CD AB 2 1 AB 2 AA' 3 AD 1 A' C' C' D 2 BC' C' D 3 A' C' BC' 3 2 BA' CD' 2 CD' AD = BC A' D' = AD } A' D' = BC A' BCD' BA' CD' BA' CD' 4 1 2 1 2 5 AB α AC BD AC BD α C D AC = BD AC BD AC AD AB α α AD = CD, AB CD AC BD, ABDC, AC = BD 5 178

19 1 1 2 1 π b 1 b 2 b 1 γ b 2 γ π γ 2 2 α β β γ α γ α β β γ α γ 1 1 ρ π α β γ a 1 b 1 a 2 b 2 a 3 b 3 1 1 α β, a 1 a 2 b 1 b 2 β γ, a 2 a 3 b 2 b 3, a 1 a 3 b 1 b 3, α γ 3 α β γ l m A B C D AB E F BC = DE EF AF β M BM CF β γ, BM CF, AB BC = AM MF DE EF = AM MF, AB BC = DE EF 179

3 4 4 α β P α β PAB PCD α β A B C D 1 AC BD 2 PA= 4 cm AB = 5 cm PC = 3 cm PD 1 2 PD = 27 4 cm 9 3 19 1 1 2 1 2 3 180 1 2

3 3 α β = l a α b β a l b l a b b β a β, a β a α α β = l, a l b l 3 4 1 4 α β = l a α a β a l 2 a γ δ α β b c a α, a b a β, a c, b c, b β α β = l, b l, a l 4 2 5 5 a b b α a b A β a A a b 181

β A c a α b c c α c a a α, a α 6 AB α AB α a b c AB α α a, AB a AB b AB c, a b c a b c 6 7 α β P α β P PA PB PC α A B C β A' B' C' ABC A' B' C' 7 8 α β, AB A' B', AB A' B' = PA PA' AC = PA A' C' PA' BC = PB B' C' PB' AB A' B',, 182 AB A' B' PA = PB PA' PB' = AC = BC A' C' B' C', ABC A' B' C' 8 ABC P PA PB PC

A' B' C' PA = PB PA' PB' PA PA' = PC PC' ABC A' B' C' = PB APB = A' PB', PAB PA' B' PB', PAB = PA' B', AB A' B' BC B' C', ABC A' B' C' 9 4 22 1 2 3 A a 3 A a A a A a α β A a α β = l A a γ α γ = b β γ = c 183

a α a β, a b a c γ A b c a A a 4 5 ABC l AB l AC l BC l AB l AC, l ABC, l BC 6 a b a α b α α m n 6 a α, a m a n a b, b m b n, b α 7 AB C AB AB α C α P α PA= PB PC AB α, AB PC AC = BC, PC AB, PA= PB 24 7 1 O ABC BC OP ABC PA BC 184 OP ABC, AO PA ABC O ABC, AO BC PA BC

2 PD ABC AC = BC D AB AB PC PD ABC, CD PC ABC AC = BC D AB, CD AB PC AB 2 3 3 ABCD PA AC PB PC PD PA AC, PA AB PA AD, PAB PAD AB BC, PB BC, PAB PAD 9 4 25 1 BB' A' C' BB' A' BB' C' BB' A', BB' A' B' BB' C', BB' B' C', BB' A' C' BB' A' C' 1 2 185

2 AB = 5 cm BC AB BD AB BC BD α E BE = 7 cm 1 EB AB CD AB 2 AE 1 AB BC AB BD BC BD = B, AB α EB α CD α, AB EB AB CD, EB AB 90 CD AB 90 2 AB α BE α, AB BE, AE = AB 2 2 槡 + BE = 槡 25 + 49 = 槡 74 cm 3 ABCD = AC DB = DC BC AD BC E AE DE AB = AC, AE BC BD = DC, DE BC, BC ADE, BC AD 4 α β = CD EA α A EB β B CD AB EA α CD EA EB β CD EB} CD EAB CD AB 4 5 5 E E C E C' E E l C' E l 6 186 ABC α P α PBA= PBC PQ α Q α QBA= QBC

PR AB PS BC R S PRB = PSB = 90 PB = PB PBR = PBS, Rt PRB Rt PSB, PR = PS PQ α = PQ, Rt PQS Rt PQR, QR = QS, Rt RBQ Rt SBQ, QBA= QBC 9 5 27 6 1 1 ABCD AC BD M G BC CD 1 AB + BC + CD 2 AB + 1 2 BD + BC 3 AG - 1 2 AB + AC 1 1 1 2 2 1 AB + BC + CD = AD 2 AB + 1 2 BD + BC = AG 3 AG - 1 2 AB + AC = MG 187

2 ABCD - A' B' C' D' E F A' C CD' x y 1 AC' = x AB + BC + CC' 2 AE = AA' + x AB + y AD 3 AF = AD + x AB + y AA' 1 x = 1 2 x = y = 1 2 3 x = y = 1 2 2 30 1 1 A B C ABC O P Q R S 1 OP = OA + 2 AB + 2 AC 2 OQ = OA - 3 AB - 2 AC 3 OR = OA + 3 AB - 2 AC 4 OS = OA + 2 AB - 3 AC 1 1 1 2 2 2 A B C ABC O M A B C 1 OM = 1 3 OA + 1 3 OB + 1 3 OC 188 2 OM = 2 OA - OB - OC 1 OA + OB + OC = 3 OM, OA - OM = OM - OB + OM - OC

MA = BM + CM MA = - MB - MC M A B C 2 M A B C M A B C x y AM = x AB + y AC ABC O OM = 1 - x - y OA + x OB + y OC OM = 2 OA - OB - OC 1 - x - y = 2 x = - 1 { y = - 1 x y M A B C 32 1 a b c a b c p = a + b q = a - b c a + b a - b c a + b a - b c a b 2 a b a b 3 O A B C OA OB OC O A B C 4 OABC M N OA BC OA = a OB = b OC = c a b c MN MN = ON - OM ON = 1 2 OB + OC = 1 b + c 2 OM = 1 2 OA = 1 2 a, MN = 1 2 b + 1 2 c - 1 2 a 189

5 OABC O' A' B' C' OA = a OC = b OO' = c a b c 1 OB' BA' CA' 2 OG G BB' C' C 1 OB' = OB + BB' OB = OA + AB = OA + OC = a + b BB' = OO' = c, OB' = a + b + c 5 BA' = BA + BB' BA = - OC BB' = OO', BA' = OO' - OC = c - b CA' = CA + AA' CA = OA - OC = a - b AA' = OO' = c, CA' = a - b + c 2 OG = OC + CG = OC + 1 2 CB' 1 = b + 2 a + c = 1 2 a + b + 1 2 c 35 1 AB BD α BD AB AC α AB = a BD = b AC = c C D 1 1 1 2 190

2 AC α, AC BD AC AB BD AB, AB BD = 0 AC AB = 0 BD AB = 0 CD 2 = CD CD = CA + AB + BD CA + AB + BD = CA 2 + AB 2 + BD 2 = a 2 + b 2 + c 2, CD = 槡 a 2 + b 2 + c 2 2 ABCD a M N AB CD MN AB MN CD MN AB AC AD = MN AB = AN - AM AB [ ] 1 2 AC + AD 1-2 AB AB = 1 2 AC + AD - AB AB = 1 2 a2 cos 60 + a 2 cos 60 - a 2 = 0, MN AB, MN AB MN CD 2 3 OABC OB = OC AOB = AOC = θ OA BC OA BC = OA OC - OB = OA OC - OA OB 4 ABCD A' B' C' D' CD' DC' O AO AO CD' AB = a AD = b AA' = c a = b = c = a a b = b c = c a = 0 a b c AO CD AO = AD + 1 2 DC' 1 = b + 2 a + c = 1 2 a + b + 1 2 c 4 191

1 CD' = 2 CD 1 + CC' = - 2 a + 1 2 c ( ), AO 1 CD' = 2 a + b + 1 c - 2 AO CD' = - 1 4 a2 + 1 4 a2 = 0 ( c) 1 2 a + 1 2 5 ABCD A' B' C' D' AB = 5 AD = 3 AA' = 7 BAD = 60 BAA' = DAA' = 45 AC' ABCD A' B' C' D' AC' = AA' + AD + AB 5, AC' = 槡 AA' + AD + AB 2 = AA' 2 + AD 2 + AB 2 + 2 AA' AD + 2 AD AB + 2 AA' AB 槡 = 49 + 9 + 25 + 2 7 3 槡 2 2 + 2 3 5 1 2 + 2 7 5 槡 2 槡 2 槡 = 98 + 56 槡 2 13 3 9 5 35 1 ABC A' B' C' AA' = a AB = b AC = c M BC' N B' C' a b c AM AN 192 1 AM = AB + BM = AB + 1 2 BC' BC = AC - AB = c - b = AB + 1 2 BC 1 + CC' = b + 2 a + 1 2 BC, AM = b + 1 2 a + 1 2 c - b = 1 2 a + 1 2 b + 1 2 c 2 AN 1 = AA' + A' N = a + A' C' + C' N = a + AC + C' B' 2 = a + c - 1 1 B' C' = a + c - 2 2 BC = a + c - 1 c - b 2

= a + 1 2 b + 1 2 c 1 2 2 ABCD A' B' C' D' AB = a AD = b AA' = c P CA' M CD' N C' D' Q CA' CQ: QA' = 4: 1 a b c 1 AP 2 AM 3 AN 4 AQ AC AD' 1 AP = 1 2 AC 1 + AA' = 2 AB + AD 1 + AA' = a + b + c 2 2 AM = 1 2 AC 1 + AD' = 2 AB + 2 AD 1 + AA' = 2 a + b + 1 2 c 3 AN = 1 2 AC' 1 + AD' = 2 AB + AD + AA' + AD + AA' = 1 2 AB + 2 AD 1 + 2 AA' = 2 a + b + c 4 AQ = AC + CQ = AC + 4 5 AA' 1 - AC = 5 AB + 1 5 AD + 4 5 AA' = 1 5 a + 1 5 b + 4 5 c 3 ABCD a E F G AB AD DC 1 AB AC 2 AD DB 3 GF AC 4 EF BC 3 193

5 FG BA 6 GE GF 1 AB AC = AB AC cos 60 = 1 2 a2 2 AD DB = AD DB cos 120 = - 3 GF AC = GF AC cos 180 = - 1 2 a2 ( a) ( a) ( a) 1 2 a2 GF = 1 2 AC = 1 2 4 EF BC = EF BC cos 60 = 1 4 a2 EF = 1 2 BD = 1 2 5 FG BA = FG BA cos 120 = - 6 GE GF = ( GC + CB + 1 2 BA ) 1 2 CA = ( ) 1 2 DC + CB + 1 2 BA 1 2 CA = 1 4 DC CA + 1 2 CB CA+ 1 4 BA CA 1 4 a2 FG = 1 2 AC = 1 2 = 1 4 DC CA cos 120 + 1 2 CB CA cos 60 + 1 4 BA CA cos 60 = 1 4 a2 4 1 ABCD A' B' C' D' a 1 A' B B' C 2 A' B AC' 4 1 4 2 194

2 Dxyz a A' a 0 a B a a 0 B' a a a C 0 a 0 1 A' B = 0 a - a B' C = - a 0 - a, A' B =, A' B B' C, cos A' B B' C = a 2 2 槡 + a = 槡 2a B' C = a 2 2 槡 + a = 槡 2a = 0 a - a - 0 - a = a 2, A' B B' C 60 A' B B' C = a2 A' B B' C 2a = 1 2 2 2 A' B = 0 a - a A a 0 C' 0 a a, AC' = - a a a A' B AC' = 0 a - a - a = a 2 - a 2 = 0, A' B AC' 5 195

1 PO α BC OA BC α PA BC PO α, PO BC PO BC = 0 OA BC, OA BC = 0 PA BC = PO + OA BC, PA BC = PO BC + OA BC = 0 5 1 BC α BC PA PO α OA BC 2 PO α, PO BC, PO BC = 0 5 2 PA BC, PA BC = 0 OA BC = PA - PO BC = PA BC - PO BC = 0, OA BC 9 6 38 1 2 A 0 0 B 2 0 C 2 0 D 0 2 0 A' 0 2 B' 2 0 2 C' 2 2 D' 0 2 2 A 2 0 B 1 3 0 C 2 3 D 0-3 3 B A 3 4 5 xoy OB 196 OB = 槡 3 2 + 4 2 + 0 = 5 4 O - xyz 1

1 x y z 2 P 2 3 4 3 P 1 5 1 yoz x xoz y xoy z 2 P xoy yoz xoz 2 3 0 0 3 4 2 0 4 3-1 - 3-5 5 1 i + 2j + 3k 2 - i + 5j - 4k 3 8i + 3k 4-5i - 2j 5 3j 1 3 2-1 5-4 3 8 0 3 4-5 - 2 0 5 0 3 0 6 a = - 3 2 5 b = 1 5-1 1 a + b 2 a - b 3 6a 4 a b 1-2 7 4 2-4 - 6 3-18 12 30 4 2 7 a = 2-3 1 b = 2 0 3 c = 0 2 1 a b + c 2 a + 6b - 8c 1 a = 2-3 1 b + c = 2 3 + 0 2 = 2 0 5, a b + c = 2-3 1 2 0 5 = 4 + 5 = 9 2 a + 6b - 8c = 2-3 1 + 6 2 0 3-8 0 2 = 14-3 8 1 2-2 - - 4 2-2 3 5 16-24 40 1 a = 1 2-2 b = - 2-4 b = - 2a, a b 2 c = - 2 3 5 d = 16-24 40 16-2 = - 24 3 40 5, c d 9 ABCD A 1 B 1 C 1 D 1 BB 1 D 1 B 1 EF DA 1 ( ) ( ) E 1 1 2 F 1 2 1 2 1 E F 9 197

( ), EF 1 = - 2-1 2 1 2 A 1 1 0 1 D 0 0, DA 1 = 1 0 1, EF A 1 1 D = - 2-1 ( 2 1 2 ) 1 0 1 = 0, EF DA 1 10 ABCD A' B' C' D' DB' ACD' DB' AC = 0 DB' AD' = 0 42 1 1 a = 2-3 槡 3 b = 1 0 2 a = - 1-1 b = - 1 0 1 1 a = 2-3 槡 3 b = 1 0, a = 槡 2 2 + 3 2 + 3 = 槡 16 = 4 b = 1 a b = 2 1 = 2 a b, cos a b = = 2 a b 4 1 = 1 2 198 2 a = - 1-1 b = - 1 0 1, a = 槡 1 + 1 + 1 = 槡 3 b = 槡 1 + 1 = 槡 2 a b = - 1-1 + 1 1 = 2 a b 2, cos a b = = a b 槡 3 槡 2 = 槡 6 3 2 1 A 1 0 B 1 1 2 C - 3 1 5 D 0-2 3 1 A 1 0 B 1 1, AB = 0 1, AB = 1 A B 1 2 C - 3 1 5 D 0-2 3, CD = 3-3 - 2 10, CD = 槡 9 + 9 + 4 = 槡 22 C D 槡 22 3 A 1-2 11 B 4 2 3 C 6-1 4 ABC

A 1-2 11 B 4 2 3 C 6-1 4, AB = 3 4-8 AC = 5 1-7 BC = 2-3 1, AB = 3 2 + 4 2 2 槡 + 8 = 槡 89 BC = 槡 4 + 9 + 1 = 槡 14 AC = 槡 25 + 1 + 49 = 槡 75, AB 2 = 89 BC 2 + AC 2 = 14 + 75 = 89, AB 2 = BC 2 + AC 2 ABC 4 1 A 1 0 1 B 3-2 1 2 A - 3 2 B 1 0-2 1 C x y z A B AC = x - 1 y z - 1 BC = x - 3 y + 2 z - 1 AC = BC, x - 1 2 + y 2 + z - 1 2 = x - 3 2 + y + 2 2 + z - 1 2 x - y = 3 x - y = 3 2 A B C x y z AC = x + 3 y - 2 z - 2 BC = x - 1 y z + 2 AC = BC x + 3 2 + y - 2 2 + z - 2 2 = x - 1 2 + y 2 + z + 2 2 2x - y - 2z + 3 = 0 2x - y - 2z + 3 = 0 5 ABCD A 1 B 1 C 1 D 1 M AB DB 1 CM DA DC DD 1 x y z D 0 0 B 1 1 1 1 ( ) 1 ( 1 - ) M 1 1 2 0 C 0 1 0 DB 1 = 1 1 1 CM = 2 0 5 199

DB, cos DB 1 CM = 1 CM DB 1 CM = 1-1 2 + 0 槡 3 1 + 槡 1 4 = 槡 15 15 200

9 6 42 1 a b c x y z a x 0 b y 0 c z 0 2 a x 0 a a yoz - 28 3 a = 3-2 4 b = - 2 5-3 a + b a - b 3a - 5b a b a + b = 1 3 1 a - b = 5-7 7 3a - 5b = 19-31 27 a b = 4 1 a = 2-1 - 2 b = 6-3 - 6 2 a = 0 1 b = 0-3 1 b = 3a 2 b = - 3a 5 a = 2-1 3 b = - 4 2 x a b x a b, a b = 0-8 - 2 + 3x = 0 x = 10 3 6 A 3 5-7 B - 2 4 3 AB BA AB AB = - 5-1 10 BA = 5 1-10 AB M OM = 1 2 OA + OB = ( ) 1, M 2 9 2-2 ( ) 1 2 9 2-2 7 A 4 1 3 B 2-5 1 C 3 7-5 AB BC CA AB = - 2-6 - 2 AB = 2 槡 11 BC = 1 12-6 BC = 槡 181 CA = 1-6 8 CA = 槡 101 8 3 P x y z 3 x 2 + y 2 + z 2 = 9 9 ABCD A 1 B 1 C 1 D 1 M N A 1 A B 1 B 201

CM D 1 N DA DC DD 1 x y z O xyz C M D 1 N ( ) ( ) ( ) 1 ( 1 - ) D 1 N C 0 1 0 M 1 0 1 2 D 1 0 0 1 N 1 1 2 D 1 N =, CM = 1-1 1 2 CM = 3 2, cos CM D 1 N 2 3 = 2 = 1-1 -, sin CM 4 D 1 N = 槡 5 9 9 4 1 4 = - 1 9 9 9 7 44 1 AB = l AB α θ AB α 1 l = 6 θ = π 3 3 l = 8 θ = π 2 2 l = 10 θ = 0 4 l = 8 θ = 72 1 3 2 10 3 0 4 2 472 1 2 45 45 60 3 P PA PB PA= PB PA PB PA PB 202

DC' OP OA OP OB PA= PB OP = OP, OAP OBP, OA= OB PAO = PBO OP OA OP OB OA= OB PAO = PBO, OAP OBP, PA= PB 4 3 A C AA' α CC' α BA' AB CD AA' CC' AA' B = CC' D = 90, ABA' = CDC' 4 5 5 PD β D α B α β, PD α, PAB PCD PC α β 46 1 2 203

3 90 A B AC BD AB = 5 cm AC = 3 cm BD = 8 cm CD α β α β = AB AC AB AC α, AC β BD β, AC BD, AC AB = 0 AC BD = 0 AB BD = 0, CD = CA + AB + BD = AC 2 + AB 2 + BD 2 = 98, CD = 7槡 2cm 9 7 46 2 1 AB α A' B' AB α 1 AB = 8 A' B' = 4 3 AB = 4 A' B' = 4 2 AB = 8 A' B' = 4 槡 3 4 AB = 2 A' B' = 0 1 60 2 30 3 0 4 90 2 OAB OBC OAC O AOB = BOC = COA= 60 OA OBC OB OC OE = OF = 1 ED OA D DF EF G OG DG DH OG H ODF ODE, ODF = ODE = 90 OD DF, OD DEF DG EF DEF, OD DG OD EF OE = OF EG = GF, OG EF, EF ODG, DH EF DH OG, DH OEF, DOG OA OBC 3 2 204

Rt ODG OD = sin 30 OF = 1 2 OG = sin 60 = 槡 3 2, cos DOG = 槡 3 3, DOG = arccos 槡 3 3, OA OBC arccos 槡 3 3 3 4 2 BC AC α β = l AB = 2BC BC β AC Rt BAC sin BAC = 1 2, BAC = 30 B-l-C 30 4 B-l-D 150 30 150 5 1 ABC DBC AB = BC = BD CBA = DBC = 120 1 AD BCD 2 AD BC 3 A-BD-C 5 1 5 2 205

2 1 A BC E ED ABC BCD, AE BCD AB = BC = BD ABC = CBD = 120, AE = ED = AC 2, ADE = 45 2 1 AD BC = 0 AD BC = BD - BA BC = BD BC - BA BC 2 D EC C ED F 1 EDFC DF DE, DF AD BC AD 3 E EG BD G AG AG BD EG BD = BE ED EG = 槡 3 4 BD AE = 槡 3 2 BD Rt AEG tan AGE = 2 AGE = arctan 2, A-BD-C π - arctan 2 6 BC AD ABD ACD BD CD BAC = 60 BAD ACD BD AD, BD ACD, BD CD, cos BAC = cos BAD cos CAD = 槡 2 2 槡 2 2 = 1 2, BAC = 60 7 206 OA OC OA OB OC OB = O OB OC γ, OA γ OC β OB α OA α OA β OC α, α γ β α γ β 7

8 α β γ α β = m α γ = l β γ = n α γ α β, AOB A-n-B, AOB = 90 l m l n m n 8 207

9 8 49 1 2 α 3 cm α α 3 cm 3 α β 4 cm α β α β α β 2 cm α β 4 α-l-β 45 A α A l a A β OB AO β O AB l B AB = a ABO = 45, AO = sin 45 AB = 槡 2 2 a A β 槡 2 2 a 4 5 Rt ABC α D AB AC = 6 BC = 8 EC α EC = 12 cm EA EB ED EA = 6 槡 5 cm EB = 4 槡 13 cm ED = 13 cm 5 6 1 ABC O 2 cm OH ABC OH = 2 cm H 208

6 1 6 2 2 AO BC D AD = 槡 3 OD = 槡 3 3 BC OD, BC DH = 槡 OH 2 + OD 2 = 槡 39 3 cm H AB AC 槡 39 cm 3 9 8 50 1 α β A α B β AB = 6 cm AB β 3 cm AO β O α β, AO OB OB β, AO OB, AO = AB 2 2 槡 - OB = 3槡 3 cm 1 3槡 3cm 2 ABCD - A' B' C' D' 1 A' B' BC 2 AB CC' 3 AD BB' 4 DC B' C' 1 BB' 2 BC 3 AB 4 CC' 3 1 OABC 1 D E 209

OA BC DE 1 DE OA BC 2 DE 3 O ABC OH 1 2 1 BD CD BD = CD, DE BC DE OA DE OA BC 2 DBC DE = 槡 BD 2 - BE 2 = 槡 2 2 3 1 3 2 210 3 O OF AB F OF = 槡 3 2 FH = 1 3 FC = 槡 3 6, OH = 槡 OF 2 - FH 2 = 槡 6 3 2 1 DE OA = 0 2 DE = OE - OD = - 3 OH = 1 3 OA + OB + OC 1 2 OA + 1 2 OB + 1 2 OC 4 ABCD - A' B' C' D' 1 DA' AC A' C' AC A' C' D A' D DC' DO' O OE

O' D E A' C' BB' D' D, A' C' OE OE O' D, OE A' C' D OE DA' AC Rt OO' D OE O' D = OD OO' OE = 槡 3 3 5 1 AB α 30 4 AC α 60 AB = 6 cm AC = 8 cm AB AC α AB' AC' BC 5 1 5 2 1 2 BC = BB' + B' A + AC' + C' C 2 AB' = 6cos 30 = 3槡 3 AC' = 8cos 60 = 4 B' C' = 槡 16 + 27 = 槡 43 B' BC CC' N B' N = BC C' N = CC' - BB' = 4槡 3-3 Rt NC' B' 槡 B' N = 槡 NC' 2 + B' C' 2 2 = 43 + 4槡 3-3 = 100-24槡 3 cm 6 1 α-pq-β 60 A B α β 槡 C PQ ACP = BCP = 30 CA= CB = a 1 AB PQ 2 B α 211

3 R CA BR α 45 CR 6 1 6 2 1 2 BN PQ N AN AC = BC = a ACP = BCP = 30, BCN ACN, AN PQ, AB PQ 2 α ABN B BH AN H BH α BN = a BNA= 60 2, BH = a 2 sin 60 = 槡 3 4 a 3 HR BH α BRH BR α x 2 DA 2 212 BRH = 45 BH = 槡 3 4 a BR = 槡 6 4 a CR = x CA RB = DB - DR = DB - 1 - x DC - x DA RH = DH - DR = 1 2 DA - 1 - x DC - x DA DA DC DB DC RB RH = 1 2 DA DB - 1 2 x DA 2 + 1 - x 2 DC 2 - x DA DB + BRH = 45 ADB = 60

RB RH = 3 16 a2 DA 2 = 1 4 a2 DA DB = 1 8 a2 DC 2 = 3 4 a2, 3 16 a2 = 1 16 a2-8x 2-14x + 5 = 0 1 8 xa2 + 3 1 - x 2 a 2-4 x = 1 2 a x = 5 4 a 5 4 a > a, CR = 1 2 a 1 8 xa2 + 1 4 x2 a 2 7 120 A B AC BD AB AB = 4 cm AC = 6 cm BD = 8 cm CD BD BA ABDE CE AC AB AE AB, CAE = 120, CE = 槡 AC 2 + AE 2-2AC AEcos CAE = 2槡 37 AB ACE DE AB, DE ACE, DE CE 7, CD = DE 2 2 槡 + CE = 2槡 41 cm 8 1 m 60 10 m l n AB l n AB = 1 m C l D n AC = BD = 10 m CD B m l CE m E DE AB m EBD = 60 120 AB m AB n CE AB, CE BED ED BED, CE ED BED BE = AC = BD = 10 m EBC = 60 120, ED = 10 m 10槡 3m CE = AB = 1 m, CD = 槡 CE 2 + ED 2 槡 101 m 槡 301 m 8 213

9 9 53 1 1 2 6 4 12 4 8 55 1 3 2 3 4 ABC - A 1 B 1 C 1 ACB = 90 CB = 1 CA M CC 1 BA 1 AM 214 1 ACB = 90, BC AC AC 1 CC 1 ABC, BC CC 1, BC AC 1 BC AM A 1 C Rt ACM Rt AA 1 C = 槡 3 AA 1 4 = 槡 6

, AM A 1 C, AM A 1 BC, BA 1 AM 1 2 BA 1 = BC + CA + CC' AM = AC + 2 CC' BA 1 AM = - CA 2 + 1 2 CC' 2 = - 3 + 3 = 0, BA 1 AM BA1 AM 57 1 2 1 2 1 2 3 3 4 4 AC' AC' BD' AC' = A' C = BD' = B' D AC' 2 = AB + AD + AA' 2 = AB 2 + AD 2 + AA' 2 215

1 3 BD' 2 = AA' + AD - AB 2 = AB 2 + AD 2 + AA' 2, AC' = BD' AC' = A' C BD' = B' D, AC' = A' C = BD' = B' D 5 a b c 1 a = 3 b = 4 c = 5 2 a = 7 b = 11 c = 4 1 槡 a 2 + b 2 + c 2 = 槡 3 2 + 4 2 + 5 59 2 = 5 槡 2 2 槡 a 2 + b 2 + c 2 = 槡 186 1 2 61 1 3 cm 4 5 2 6 cm 15 cm 62 1 5 2 9 9 62 1 2 ABCD - A' B' C' D' B' D A' C 9 cm 15 cm AA' 5 cm 216

AC = a BD = b 2 2 a b ( 2 ) + ( 2 ) = 槡 槡 a 2 2 + b 2 ABCD - A' B' C' D', Rt A 1 CA Rt B 1 BD 1 A 2 + a 2 = A 1 C 2 { B 1 B 2 + b 2 = B' D 2, 5 2 + a 2 = 15 2 {, 5 2 + b 2 = 9 2 a 2 + b 2 = 256 16 2 = 8 cm 3 1 4 BC 30 AA' D AD BCD 3 1 3 2 2 BC N AN DN BC AD BC AN, BC AND, DNA AB = 4 AN = 2槡 3 DNA= 30,, AD = 2, DN = 2AD = 4 AD AN = tan 30 = 槡 3 3, S DNC = 1 2 BC DN = 1 2 4 4 = 8, S BCD = 2S DNC = 16 4 217 4

AC 1 A 1 C B 1 D C 1 A D 1 B AC 1 AC 1 A 1 C 1 CA B 1 D 1 DB A 1 C B 1 D C 1 A D 1 B, A 1 C 1 CA B 1 D 1 DB CC 1 A 1 C 1 BB 1 B 1 D 1 BB 1 CC 1, BB 1 A 1 C 1, BB 1 A 1 C 1, A 1 C CB A 1 B BC AB, ABCD, A 1 C 5 ABC - A 1 B 1 C 1 2 1 M BC CC 1 N MN AB 1 AB AC AA 1 i j k CN 1 = xk AB 1 = i + 2k MN = j - i + xk 2 ( ) 1, AB 1 MN = i + 2k - 2 i + 1 2 j + x k = 0 x = 1 8 5 6 7 a h 1 2 3 槡 9h 2 2 + 3a 1 = 3 = 槡 36h 2 2 + 3a 6 2 = 槡 4h 2 2 + 2a = 槡 4h 2 2 + a 2 2 3 = 槡 h 2 + a 2 = 槡 4h 2 + 3a 2 218 2

8 4 cm 8 cm arccos 槡 5 5 9 a CD = CB = BD = a 219

S BCD = 1 2 a2 sin 60 = 槡 3 4 a2 C 1 D 1 1 = 2 CD B 1 C 1 1 = 2 BC, B 1 C 1 D 1 BCD, S B1 C 1 D 1 ( ) = C 1 D 1 S BCD CD, S B1 C 1 D 1 = 槡 3 16 a2 2 = 1 4 9 10 150 cm 2 54 cm 2 12 cm h, h = 30 cm 30 cm 54 cm 2 150 cm = h - 12 2 2 h 2 11 4 cm 2 5 cm 12 4 cm 8 13 13 14 220 15 a ABCDEF, BCDE 15

2, CE CE = 槡 2a = 槡 2a 16 2: 3 a 槡 6 a 3 2 槡 6 ( a 3 ) : a 2 = 2: 3 9 10 71 1 13 cm A B C AB = BC = CA = 12 cm 11 cm 2 25 cm 49π cm 2 24 cm 3 O 74 1 100 1 000 2 R ( 1 + 1 1 000) R, V = 4 3 πr3 [ ( ) R] ( ), V = 4 3 π 1 + 1 1 000 = 1 + 3 1 000 + 3 V 3 1 000 ( ) = 1 + 1 1 000 3 4 3 πr3 3 4 cm 221

,, 2r 2 = 4 2 + 4 2 + 4 2 r = 2槡 3 cm, V= 4 3 πr3 = 4 3 π 24槡 3 = 32槡 3π cm 3 4 2 S' = 2S S = 4πr 2 r' = 槡 2r V= 4 3 πr3 V' = 2槡 2V 2 槡 2 5 R = 6 370 km S = 4πR 2 = 4 3 14 6 370 2 = 5 096 10 8 km 2 9 10 74 1 2 R A B OA OB n n < 180 A B nπr 180 A B O AB ) 3 30 120 1 155 10 4 km 4 O R A B AOB = θ A B θr 5 1: 2: 3 3 222 R 2R 3R, V + V = 4 3 πr3 + 4 3 π 2R 3 = 12πR 3

V = 4 3 π 3R 3 = 36πR 3, V = 3 V + V 6 r = 2r S = 4πr 2, S = 4S 7 120 S = 120S S = 4πr 2, r = 2槡 30r V= 4 3 πr3, V = 240槡 30V 8 O 1 O 2 125 O 1 10 cm O 2 V O1 = 125V O2 V= 4 3 πr3, r O1 = 5r O2, r O2 = 2 cm, S O2 = 4πr 2 O 2 = 4π 4 = 16π cm 2 80 A 1 m α β γ = m α β = a γ α = b a b m α m β β α = a, m a m b, a b 1 2 2 AB O PA O C PAC PBC AB O, AC BC 223

PA O PC BC, BC PAC BC PBC, PAC PBC 3 P l PA PB PN l PA PB PN PA PB = P PA l PB l, l PAB P PN l PN PAB PN PA= P PN l PA l, l PAN 3 P l, PN PAB P l PAB PA PB PN 4 ~ 8 4 M N ABCD - A' B' C' D' BB' B' C' 1 MN CD' 2 MN AD 4 5 1 AB AD AA 1 CD' = - 1 0 1 AM = ( ) 1 1 2 1 MN = AN - AM = 224 ( ) 0 1 2 1 2 CD' 1 MN = 2 ( ) 1 1 0 2 AN =

, cos CD' MN =, CD' MN = 60 2 CD' MN = 1 2 MN CD' ( ) AD = 0 1 0 MN = 0 1 2 1 2, MN AD = 1 2 MN = 槡 2 2 AD = 1, cos MN AD =, MN AD = 45 MN AD MN AD = 1 2 槡 2 2 1 = 槡 2 2 5 ABCD - A' B' C' D' a M AA' O BD' OM AA' BD' 1 BD' = BA + AD + DD' AO = AB + BO = 2 AB + AA' + A' D' AM = 1 2 AA', MO = AO - AM = 1 2 AB + A' D' MO 1 BD' = 2 AB + A' D' BA + AA' + A' D' = 0, MO BD' MO 1 AA' = 2 AB + A' D' AA' = 0, MO AA', OM AA' BD' [ ] OM 2 2 = OM 2 1 = 2 AB + A' D' = 1 4 AB2 + 2 AB A' D' + A' D' 2 225

, OM = 槡 2 2 a = 1 4 a2 + 0 + a 2 = 1 2 a2 6 AB α B α B BC BD BE AB α BE = BC = BD AB BC BE BD 6, AB BE = AB BC = AB BD, AB BE - BC = 0 AB CE = 0, AB CE AB CD, AB α 7 30 α-l-β AC l C BD l D ABC = BAD = 30 AB = a AC = 1 2 a BD = 1 2 a AB = AC + CD + DB, AB 2 = AB AB = AC + CD + DB 2 7 226 a 2 = ( a) 1 2 = AC 2 + CD 2 + DB 2 2 + CD 2 + ( a) 1 2, CD 2 = 1 2 a2 CD = 槡 2 2 a 2 AB AB = AB AC + AB CD + AB DB a 2 = a a 2 cos 60 + a 槡 2 2 acos AB CD + a 1 a cos 60 2

, cos AB CD = 槡 2 2 AB CD = 45 8 ABCD - A 1 B 1 C 1 D 1 A 1 60 AC 1 AC 1 = AB + AD + AA' 2, AC 1 = AB + AD + AA1 2 = AB 2 + AD 2 + 2 AA1 + 2 AB AD + 2 AB AA1 + 2 AD AA1 = 1 + 1 + 1 + 2cos 60 + 2cos 60 + 2cos 60 = 6, AC 1 = 槡 6 9 15 cm 30 h = 15 sin 30 = 7 5 cm 7 5 cm 10 144 cm 2 14 cm 144 cm 2, 12 cm, 槡 12 2 + 12 2 + 14 2 = 22 cm 11 a β O ABC ABC, OAO' = β, AO' = 2 3 槡 3 2 a = 槡 3 3 a, tan β = OO' AO' OO' = 槡 3 atan β 3 槡 3a tan β 3 B 11 1 ABCD AC E F AD BC O ABCD EOF ( ) ( ) OB OC OD OE 1 = 0-2 1 2 OF 1 = 2 1 2 0 227

, OE = 槡 2 2 OF = 槡 2 2 OE 1 OF = - 4 OE OF, cos EOF = OE = OF, EOF = 120-1 4 槡 2 2 槡 2 2 = - 1 2 2 ABC S ABC α θ ABC α A' B' C' S' S' = S cos θ AB A' B' CD AB D C' D C' C α, CDC' = θ cos θ = C' D CD C' D = CD cos θ S ABC = 1 2 AB CD S ABC' = 1 AB C' D 2, S' = Scos θ 2 3 1 ABC - A' B' C' AB = BC = CA = a AA' = 槡 2a AB' AC' 3 1 3 2 228 2 B' D A' C' A' C' D AD AB = BC = CA= a AA' = 槡 2a

, B' D = 槡 3 2 a AB' = 槡 3a ABC - A' B' C', B' AD AB' AC' 槡 3 2 a, sin B' AD = 槡 3a = 1 2 B' AD = 30, AB' AC' 30 4 ABCD - A' B' C' D' ABCD a AA' b A' AB = A' AD = 120 AC' BD' AC 229

230 AC' = AB + AD + AA', AC' 2 4 = AC' AC' = AB + AD + AA' AB + AD + AA' = AB 2 + AD 2 + AA' 2 + 2 AB AD + 2 AB AA' + 2 AD AA' = a 2 + a 2 + b 2 + 0 + 2abcos 120 + 2abcos 120 = 2a 2 + b 2-2ab, AC' = 槡 2a 2 + b 2-2ab BD' = AD + AA' - AB AC = AB + AD, BD' 2 = BD' 2 = AD + AA' - AB 2 = AD 2 + AA' 2 + AB 2 + 2 AD AA' - 2 AD AB - 2 AA' AB = a 2 + b 2 + a 2 + 2abcos 120-0 - 2abcos 120 = 2a 2 + b 2, BD' = 槡 2a 2 + b 2 AC = 槡 2a BD' AC = AD + AA' - AB AD + AB = AD 2 - AB 2 + AA' AD + AA' AB = a 2 - a 2 + abcos 120 + abcos 120 = - ab ab b, cos BD' AC = = 槡 2a 2 + b 2 槡 2a 槡 4a 2 2 + 2b 5 7 cm 8 cm O O' AO' = 槡 2 8 = 4 2 槡 2 cm

槡, 4槡 2 2 + 7 2 = 9 cm 6 6 cm 8 cm 60 60, r 1 2 r 6 + 8 + 10 = 1 2 6 8 r = 2 cm tan 60 = h r, h = tan 60 r = 2槡 3 cm 5 7 P A B C O PA PB PC PA = PB = PC = 1 PA PB PC, PA 2 + PB 2 + PC 2 = 4r 2 4r 2 = 3 r = 槡 3 2, S = 4πr 2 = 3π V= 4 3 πr3 = 4 3 π 3槡 3 8 = 槡 3 2 π A 231

殞 檶檶檶檶 殞 檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶 殞 殞 Unit 11 Scientific achievements 1 solar mankind constitution man support daily achieve likely zone private institute grasp master perfect arrange rely failure valley base mark agency organ forward breakthrough march aim announce evolution battle set foot in have an effect on rely on come to life put forward aim at 2 1 If I got the money I would 2 My plan is to 3 I hope that 4 I d like to 5 I m thinking of 3 1 POST-READING 1 1 ABCD 2 D 3 C 4 B 5 D 2 232

LANGUAGE STUDY Word study 1 A 2 C 3 B 4 A 5 C 6 B 7 B 8 C Grammar Word Formation 1 1 2 construct construction connect connection attract attraction act action direct direction express expression invent invention product production protect protection suggest suggestion impress impression celebrate celebration communicate communication educate education graduate graduation pollute pollution contribute contribution combine combination admire admiration examine examination transport transportation explore exploration imagine imagination 3 invisible disagreement dishonesty impossibility non-conductor international illogical replacement disappearance misunderstanding enlargement reconsideration interaction unexpected unforgettable unsuccessful 4 showcases = show + cases breakthrough = break + through bioengineering = bio- + engineer + -ing outstanding = out + stand + -ing enable = en- + able strengthened = strength + -en + -ed PRACTISING Vocabulary indirectly = in- + direct + -ly 1 1 Mark 2 support 3 March 4 Master s 5 support 6 marks 233

7 marched 8 battle 9 masters 10 battle against 2 1 A private 2 B rely 3 C aim 4 D evolution 5 E base 6 F solar 7 G institute 3 1 constitution is the basic law of a nation 2 the Chinese government has set up more than 50 national economic zones of technology development 3 this house would be perfect 4 you will gain the seven-day free trip to Europe for two persons provided by the Youth Travel Agency 5 My baggage is very heavy 6 it was necessary to make a law to forbid the trade of human organs as soon as possible 7 we must rely on technology 8 he keeps putting forward new requests 9 aiming at improving the farmers standard of living Grammar 1 1mankind 2daily 3achievement 4failure 5arrangement 6researcher 7breakthrough 8likely 9announcement manned 1 1mankind 3achievement 4failure 5arrangement 6researcher 7 breakthrough 8likely 9announcement 2 2daily manned 2 telephone telegraph telescope television transaction transport transplant biochemistry bioengineering 3 1 S The prefix sub- means below or under in both words 2 D 3 S 234 The prefix im- in import means bring into while im- in impossible means not The prefix in- in indirect and im- in impolite all means not

4 D 5 S The prefix ex- in export means send out while ex- in ex-wife means former The suffixes -ed in both words is the symbol of adjective 4 hope hopeful hopeless help helpful helpless care careful careless use useful useless power powerful powerless meaning meaningful meaningless hope desire for sth to happen combined with the expectation that it will hopeful having hope giving hope promising hopeless most unlikely to improve succeed be settled etc causing despair incompetent care serious attention or thought caution to avoid damage or loss sympathetic concern worry anxiety careful taking care cautious giving serious attention and thought done with care careless not taking care inattentive thoughtless resulting from lack of care use employ sth for a purpose bring sth into service useful that can be used for some practical purpose serviceable or helpful useless not serving a useful purpose not producing good results weak or incompetent power ability to do or act particular faculty of the body or mind strength or energy behind or contained in sth control over others right possessed by or given to a person or group authority energy that can be harnessed and used to do work powerful of or having great power having a strong effect physically strong having great control or influence powerless without power or strength completely unable to do sth meaning what is conveyed or signified sense purpose significance meaningful full of purpose significant meaningless without sense or motive 5 1 different difference patient patience important importance absent 235

absence distant distance present presence independent independence silent silence 2 dark darkness blind blindness deaf deafness happy happiness willing willingness useful usefulness bitter bitterness lively liveliness great greatness careless carelessness fair fairness sick sickness 3 able ability active activity equal equality generous generosity popular popularity possible possibility disabled disability creative creativity personal personality curious curiosity similar similarity INTEGRATING SKILLS Reading 1 1 C 2 B 3 A 4 B electric electricity 2 1 made it possible for ancient humans to make fire and marked the beginning of modern society with the birth of the steam engine led to factories and cities and marked the beginning of public education and the modern branches of science make it easy for people to communicate whenever they want and wherever they are 2 The wheel of scientific development means on one hand scientific achievements lead to new discoveries and inventions on the other hand new technology in turn leads to future scientific achievements 3 Unit 12 Fact and fantasy 1 fiction belief league balloon botany apply applied servant whale hunter collision companion permanent guest voyage iron aboard lamp dislike prisoner gentle marble shore luggage brilliant phenomenon pl phenomena labour hesitate horrible cut up butcher 236

curtain lip make a living set out in public throw light upon 2 1 I believe 2 I suppose 3 I m sure that 4 I doubt 5 I m not certain 6 I can t imagine 7 It could be but 8 I can t believe my eyes 3 2 POST-READING 1 You could say Captain Nemo is someone you will neither like nor dislike You might think that he is a cruel man because he keeps Aronnax and the others as prisoners and destroy ships But at other moments you will find him gentle and weak as when he cries about the lost lives of people drowned in ships that have sunk 2 2 They try their best to survive and then they find themselves on the surface of the monster itself 3 accompany him forever LANGUAGE STUDY Word study 1 fiction 2 set out 3 voyage 4 belief 5 aboard 6 set out 7 voyage 8 aboard 9 escape 10 fiction 11 permanent Grammar Word Formation 2 1 1 E 2 F 3 B 4 C 5 D 6 A 7 G 2 1 2 3 4 5 6 7 237

PRACTISING Vocabulary 1 1 balloons 2 belief 3 voyage 4 permanent 5 butcher 6 brilliant 7 companion 8 shore 9 Botany 10 labour 2 1 You are not willing to work neither will you study then how can you make a living in the future 2 Tomorrow morning we will set out for a one-week sea voyage We are so excited for that 3 Don t hesitate If you don t take action you will miss the chance 4 It is a natural phenomenon that the rainbow appears after the rain 5 While dressing the baby you must be gentle Grammar 1 1 part-time long-term easy-going passer-by English-speaking film-maker check-out half-way man-made hard-working well-known pencil-box kind-hearted second-hand get-together so-called world-famous smoke-free best-seller overcoat 2 bedclothes bookmark boyfriend seaside firefighter greenhouse headache homesick armchair handshake birthday widespread daytime farmland sunrise courtyard overcoat underground friendship 2 assist assistant visit visitor act actor write writer 238

sing singer dance dancer paint painter piano pianist cycle cyclist journal journalist conduct conductor politics politician prince princess drive driver history historian music musician science scientist play player clean cleaner print printer direct director inspect inspector employ employer design designer dive diver explore explorer farm farmer foreign foreigner teach teacher lead leader speak speaker invent inventor serve servant sell seller travel traveler win winner work worker comedy comedian library librarian manage manager office officer own owner perform performer translate translator 3 dis- disappear disability disagreement dissatisfied in- im- ir- il- incapable inconvenient incorrect immature illegal irregular irresponsible impossible impolite non- nonsmoker nonlogical un- unlucky unfair unusual unexpected unwilling unhappy unfamiliar unfold unbelievable 4 1 extraordinary 2 retell 3 telecommunication 4 misunderstood 5 overseas 6 underwater INTEGRATING SKILLS Reading 1 Cavorite is a kind of material that will cut off the gravity of the earth 2 Material Property Application Glass Metal Cavorite Blocks heat but lets light pass through Blocks light but lets electrical energy and heat pass through Blocks the gravity from the earth 3 A flying machine and a new material - Cavorite Fire screen Conductor and pan Flying machine 4 The Cavorite applied to Mr Cavor s machine can block the gravity from the earth 239

below it So nothing above a layer of Cavorite weighs anything and everything a- bove it goes up into the air and leave the earth 5 The problem is how to prevent the flying machine from travelling in a straight line into space for ever Unit 13 The water planet 1 sailor transport range unique hydrogen atom oxygen relative freezing salinity density cubic float decrease substance centigrade absorb thus stable sensitive steady rust recreation all the way benefit from take advantage of give off call in a variety of 2 1 The water is being used to/for 2 We should /could 3 What will we do if 4 If we we can 5 It would be better to 6 Can you think a better way to 3 240

POST-READING 2 Property What is it What is it good for Chemical structure Density The water molecule is made up of two hydrogen atoms and one oxygen atom They form a polar molecule The density of pure water is 1 000kg/m 2 When water freezes its density decreases Because water is polar it can break down both solid and gases The chemical structure of water also make it different from almost everything else on earth Water is a liquid at room temperature and has a relatively high freezing point Marine animals and plants take advantage of the density of water With the right kind of body it is possible to float a- round in the ocean and let the water do the work Heat capacity The heat capacity of water is relatively high Water can absorb and give off a lot of heat without big changes in temperature thus creating a stable environment which made the ocean a safe and comfortable habitat The water in the ocean also keeps the temperature of the earth steady by absorbing and giving off heat 241

LANGUAGE STUDY Word study 1 1 atom 2 unique 3 solid 4 absorb 5 centigrade 6 pure 7 hydrogen 8 oxygen 9 mass 10 float 2 1 hydrogen oxygen 2 solid 3 absorb 4 relationship 5 raging 6 float Grammar 1 1 A 2 A 3 C 4 D 5 D 6 A 7 B 8 B 2 1 can 2 will 3 must 4 should 5 will 6 might 7 might 8 will 9 may 10 will 11 can 12 will John s problem is he is doubted by the manager that he is a thief and he does not know how to deal with this situation INTEGRATING SKILLS Reading 1 Because in estuaries animals can enjoy all the benefits of the ocean without having to face many dangers 2 The word density means the quantity of something 3 Estuaries absorb nutrients and pollutants from water coming from inland sources thus cleaning our water 4 Estuaries absorb pollutants from water coming from inland sources thus makes estuaries very sensitive to environmental pollution 5 Estuaries provide both recreation and education for human beings Most of us enjoy fishing swimming and having fun on the beach and scientists and students have endless opportunities to study a variety of life in the habitat Estuaries also contribute to the economy through tourism and fishing So estuaries are very important to human beings PRACTISING Vocabulary 1 1 unique 2 solid 3 float 4 decreasing 5 benefit 6 trust 242

2 A B C 3 1 2 3 4 5 3 6 Grammar 1 1 We must save the unnecessary water used to flush the toilets 2 When we are taking showers we need to limit the time so as to save water 3 We can turn off the tap while soaping up or shampooing 4 We could change the preference of taking high-flow showers because they use more water 5 We ought to use washing machines in a reasonable way When the clothes is not difficult to wash like underwear and socks we may wash them by hand When we have to use washing machines we had better make them full loaded The water that a washing machine has used would be used to mopping the floors 2 1 in the sea make sure it is a bathing place of the beach in the river make sure the water is not polluted and there is no dangerous float grass in the swimming pool it is more clean and safe 243

2 orange juice it can not satisfy your thirst cola it will make you excited purified water it may take some microelement away from your body mineral water it can not only satisfy your thirst but is good to your body 3 others there is no evidence of murder Reading 1 she must have stood on an ice to hang from the beam Depth Conditions Life forms How do the animals adapt About 200 metres deep There is sunlight Plants marine animals a variety of fish Become dark on the top and light on the bottom About 1 000 metres deep Some sunlight can reach this level Marine animals Be able to make light with their body About 3 000 metres deep Dark with marine snow Marine animals Turn out to be black or red Below 4 000 metres Cold dark with high water pressure Some small creatures sperm whale Slow the heart beat 6 000 meters deep Water pressure is Few creatures Some of the animals extremely high very little life do not have eyes no light 244

Unit 14 Fr eedom fighter s 1 freedom civil murder revolution slavery soul chorus arrest separation race marriage forbid vote political demand boycott lawyer racial discrimination act bill politics religion independence unconditional a- bolish prejudice chapter ridiculous join hands put in prison set an example to from then on start with regardless of at first sight 2 1 What happen first was that 2 happened as a result of 3 You could expect because 4 That led to 5 One of the reasons why is 6 is often followed by 3 POST-READING 1 Paragraph 1 In the summer of 1963 Martin Luther King made a famous speech I Have a Dream 2 I will put paragraph 1 before the paragraph which begins with the sentence It was during the 3 Martin Luther King want the black people to be treated with respect in the same way as other people 4 1 King led a boycott of the bus company For 381 days black people refused to take the city buses In the end the government lawyers in the capital said that 245

the bus company was wrong to separate blacks from whites 2 He led many non-violence demonstrations against racial discrimination and the Vietnam War One of these was in Birmingham Alabama 3 During the March on Washington DC in 1963 King gave the famous speech I Have a Dream to inspire people of all races to fight for equality 5 6 Why do you choose peaceful actions 7 What does the Nobel Peace Prize mean to you LANGUAGE ATUDY Word study 1 1 Slavery 2 forbidden 3 arrested 4 demanded 4 boycott 2 1 separate separate separation 2 politics political 3 races racial 4 law lawyer 5 freedom free Grammar Review the Passive Voice 1 1 Blacks were not treated as equal citizens in the southern states in the 1950s 2 Often blacks were not allowed into hotels schools or libraries at all 3 Black children were educated in separate schools 4 In 1964 a new Civil Rights Act was passed to give black people the right to vote 2 1 Flowers were painted on the cars in the street by a group of civil rights activities 2 Speeches were made in front of the city hall 3 A statement which said that the rules are unfair was read by one speaker 4 More than 100 demonstrators were arrested by the police 5 The civil rights activists were put into prison by the police 6 This day will never be forgotten by the people of the city 246

PRACTISING Vocabulary 1 adj n v n free freedom separate separation young youth employ employment political politics marry marriage independent independence sight sight racial race discriminate discrimination 2 chapter boycott prejudice revolution religion lawyer chorus ridiculous 3 1 vote 2 murdered 3 murderer 4 vote 5 demand 6 ordered 7 respect 8 arrested 9 demanded 10 arrest 11 order 12 vote 4 1 regardless of 2 join hands 3 in part 4 set an example 5 From then on 6 put in prison 5 1 The person who gets the most votes will win this election 2 In 1955 Martin Luther King led a boycott of a bus company to support a black woman 3 The reason of the break-out of the Civil War is that whether the slavery should be abolished or not 4 Some female graduates complain that they suffer from sexual discrimination in seeking jobs 5 July 4 is the Independence Day of the United States 6 Many inventions derive from ridiculous ideas 7 Have you read the novel Pride and Prejudice 8 The Chinese Constitution says that the citizens of the People s Republic of China have the freedom of religious belief 247

Grammar 1 1 Women should not be discriminated 2 He left school and was employed in a shoe factory 3 The famous poem Dying for a Just Cause was written in prison 4 Lei Feng was respected by the people all over China 5 Who is voted for a new monitor the most in the election 6 It is clear that he did not die in an accident but that he was murdered 2 1 Because begin is an intransitive verb which can not use the Passive Voice It should be School begins at 8 o clock 2 3 4 5 Because feel is used as a link verb in this sentence so it can not use the Passive Voice It should be The shirt feels soft INTEGRATING SKILLS Reading 1 In the western part of the world we can find the island republic now called Haiti 2 3 1 He joined the slaves in their struggle for freedom and soon became their leader He built up the state and the country repairing roads opening schools and restoring agriculture all over Haiti 2 When the revolution broke out he saved the family of his former owner and helped them to leave the country When he recognized that the new law did not really improve the situation of the slaves he decided to continue the fight for the rights of the black slaves 3 Lei Feng was a great man in China His story is well-known to the Chinese people He was always ready to help the others when they were in trouble He was a good example of serving the people with heart and soul 248

4 Because they were not recognized as full citizens and still subject to a number of discriminating laws 5 In 1801 when an independent republic was created in Haiti the racial discrimination in the island ended Unit 15 Destinations 1 upset airline fly n downtown avenue altitude guarantee gather feast dip gym analyse / analyze chat budget rate visa arrangement passport cheque / check currency look into every now and then get /be tired of cool off 2 1 I am sorry to say 2 I hate to say this but 3 Could you do something about 4 You really have to do something about 5 I will look into it immediately 6 Why don t you 7 What seems to be the problem 8 I ll do everything I can to help you 3 to POST-READING 1 249

2 Phrases / Sentences Kitzbuhel is a paradise for skiers a walk through downtown Rio is a history lesson a feast for the eyes should you have enough energy left Meaning Kitzbuhel is a wonderful place for people who like skiing A walk through the downtown Rio is a good opportunity to learn something about the history of Rio have many good things to see if you are not too tired 3 I would like to go to Rio de Janeiro because 1 Downtown Rio is the city s culture and historical heart 2 Rio de Janeiro has many beaches and I can go to visit the most famous one Copacabana 3 I can go to the famous festival Carnival which is one of the world s most famous and attracts visitors from all over the world I would like to go to Kitzbuhel because 1 Kitzbuhel is a paradise for skiers 2 Kitzbuhel is also home to one of the most challenging and exciting downhill slopes in the world 3 The town offers many shops cafes and a wide variety of entertainment A walk around Kitzbuhel is a feat for the eyes a lively mix of old village culture and the excitement of an international tourist area LANGUAGE STUDY Word study 1 1 altitude 2 avenue 3 gather 4 feast 5 dip 2 1 gather 2 downhill 3 Every now and then 4 gyms 5 has got tied of Grammar Review Nonfinite Verbs 1 1 1 The two Doings are used as subject and object respectively 2 Crossing is used as object complement 250

3 Rising is used as object complement 4 Not knowing is used as adverbial 5 Walking is used as adverbial 6 Playing tricks is used as subject 7 Tearing is used as object 8 Talking and laughing is used as adverbial 2 1 Being brave he went into the cave alone to look for his friend 2 Being quite ill she could not visit her friend in England 3 Being an experienced traveler he knows how to plan a trip 4 The girls attending the sick all come from the countryside 5 Hearing the music he began to miss his hometown 6 Seeing the flame on top of the mountain they knew that another war would begin soon 7 While driving to the airport he hit a boy on a bike 8 Married he lived separately from his parents 3 1 tiring tired 2 risen rising 3 unboiling unboiled 4 interesting interested 5 excited exciting 6 wait waiting INTEGRATING SKILLS Reading 1 According to the text reading about a destination is a good way to save money and avoid problems it can also be a lot of fun 2 In this text seasoned probably means experienced 3 To travel light means to carry less luggage while traveling 4 PRACTISING Vocabulary 1 1 cheque 2 cost 3 passport 4 visa 5 currency 6 airline 7 budget 8 arrangement 9 downtown 10 avenue The name of the place is Copacabana 2 2 airline 3 passport 4 lifestyle 5 downtown 3 1 When I was relaxing on the sofa the telephone rang 251

2 He was calling to ask me if I wanted to take a dip in the swimming pool 3 I told him I was tired of the life at the moment 4 It is good for you to go out for traveling sometimes 5 we chatted about his travel experience 6 the rate of this trip especially the hotel costs was reasonable 7 the beautiful natural scenery there was a feast for the eyes 8 the final destination of their trip 9 People gather to see 10 Don t worry I promise not to charge you more Grammar 1 1 to look into 2 cools off 3 Getting tired of 4 to guarantee 5 Gathering 6 to analyse 7 Rated 2 2 agree to bet á 20 000 on such a journey 3 decides to leave with his servant immediately 4 expect Mr Fix a police detective from the London office to follow him 5 Believing Phileas to be a wanted bank robber 6 threatens to arrest Phileas and take him back to London 7 is determined not to accept an arranged marriage 8 hopes to be taken with him 9 promises to marry her as soon as they get back to London 10 believe them to win the bet INTEGRATING SKILLS Reading 1 Because Vietnam is within easy reach and offers exciting adventures at a reasonable price 2 It refers to the Ho Chi Minh City 3 Whenever you go it is the best time to visit Vietnam 252

4 Day 1 Hanoi Day 2 Halong Day 3 Ho Chi Day 4 Mekong Arrive in Hanoi Bay Minh City River Afternoon Visit Morning Relax Morning Visit Morning Try hi- the famous Old on the beach and the museums king in the Quarter enjoy a good Afternoon Visit mountains meal in a restau- the parks gar- Afternoon Try rant in Halong dens and temples rafting on the City mighty Mekong Afternoon Take River a boat tour and explore the islands Unit 16 The United States of America 1 entry mental physical suffering greedy trader unemployment unrest sacrifice reconstruction former funeral vain eventually dawn overcome insist plain resist chief afterwards widespread rot wildlife supply chain willing in vain take a chance leave alone insist on as a result put out on sail in turn 2 1 How long/wide /high /tall /is 2 It s metres /feet long/wide /high /tall 3 There is in the north 4 It looks like 3 2 253

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POST-READING 1 1 B 2 C 3 D 4 E 5 A 2 1 Like other sister southern cities Atlanta has a history of suffering the suffering of the Native Americans who were killed or driven off their land by European settlers the pains of slaves brought from Africa by greedy slave traders the death and poverty of the Civil War the hardship of unemployment and civil unrest in the post-war years and the Great Depression the many sacrifices of the Civil Rights Movement Despite all the hardships Atlanta and other southern cities are trying to build a new South 2 Like many of its sister cities in the South Atlanta was burnt down in the Civil War The city was destroyed and there was no money for reconstruction The post-war years were hard and the people of Atlanta struggled to rebuild the city and create a new South where former slaves and slave-owners could live together 3 Advantages People from different background can learn from each other help each other share their different experience It s very helpful for people to learn different languages Disadvantages People should be more tolerant otherwise there will be unrest LANGUAGE STUDY Word study 1 1 heater Because heater is something while others are people 2 reconstruction Because the word reconstruction can only be used as a noun while the other words can be used both as nouns and verbs 3 moment Because the word moment is a single word while the other words are compound words and all have the suffix -ment 4 understand 5 entry Because the word understand has no negative meaning while the others have negative meaning 9 display Because the word entry is a noun while the others are adjective Because the word display has no negative meaning while the others have the negative meaning 2 adj n v n 255

hard hardship suffer suffering willing willingness begin beginning greedy greed destroy destruction poor poorness depress depression commercial commerce reconstruct reconstruction adj adv social economic rapid slow sure socially economically rapidly slowly surely 3 1 widespread 2 physical mental 3 former 4 greedy 5 chief Grammar Review Nonfinite Verbs 2 1 1 I expect to be told more about the south of the US 2 I don t want to be bothered by anyone 3 I don t mind to be said about bad things 4 I want to be left alone by other people 5 He insists to be showed respect 2 1 interested 2 knowing 3 to know 4 watching 5 to solve 6 looking 7 looking for 8 to put 9 to look 10 finding 11 checking 12 to interview 13 amazing INTEGRATING SKILLS Reading 1 1 F 2 F 3 T 4 T 5 F 256

PRACTISING Vocabulary 1 A 1 B 1 C 2 4 000 D 2 E 2 F 1 G 1 H 2 2 1 resist 2 insisted 3 insisted 4 resist 1 towards 2 afterwards 3 onwards 4 downwards 5 forward 3 1 The owners of the railways would not take a chance so they hired many hunters to shoot the bison insanely along the railways 2 The bison rotted slowly at the place where they fell down 3 As a result the insects which lived on these plants died out 4 This in turn reduced the food supply for birds prairie dogs and wolves 5 Thus the change in the number of bison had an effect on the whole wildlife chain of the plains 6 After being chased and hunted for nearly 90 years the bison are finally leave alone 7 These efforts are not in vain Grammar 1 1 I would like to be taken on a trip to the US 2 She asked more work to be given to do 3 It would be exciting for me to be introduced to a Native American chief 4 I don t want to be shown around the city 5 I don t like to be made fun of by other people 2 They would like /advise /hope /expect the heavily polluting factories to be moved a- way They would like /advise /hope /expect the buildings that date back to ancient times 257

to be protected They would like /advise /hope /expect a new road to be built They would like /advise /hope /expect old roads to be broadened They would like /advise /hope /expect a park in the city centre to be built They would like /advise /hope /expect public transportation to be improved My suggestion is to open up the parks free for the residents My suggestion is to control the air pollution and noise pollution caused by the building sites INTEGRATING SKILLS Reading 1 1 For thousands of years Native Americans lived as hunters in North America There were millions of people with many different cultures religions and languages 2 In 1838 the government began putting Cherokee men women and children in camps and made them walk a thousand miles The winter was cold and there was not much food 3 The Cherokees had built homes and farms developed a written language and made their own laws 4 Despite their hard work the Cherokees were not treated fairly When the government began driving the Native Americans away the Cherokees were among the last to go By the end of the nineteenth century only some 250 000 N- ative Americans had survived Their culture and way of life had been destroyed their land had been taken away from them and they were not given the rights most other Americans enjoyed 2 1 Native American were either killed or driven off their land and many died of diseases that the European settlers brought to the continent 2 Because the government decided to remove the Native Americans from their own land to make room for European settlers 3 Today Native Americans are beginning to receive the respect they deserve and their culture is recognized as an important part of American history 4 We should treat them equally and respect their traditional customs and culture help them develop the economy and education in their region 258

Unit 17 Disabilities 1 disability ability sidewalk waist fair potential guidance gifted assist sympathy encouragement visual adjust candy niece ceremony victory dignity participate conduct accessible get around get used to 2 1 I probably could t 2 I would not be able to 3 It would be difficult to 4 I m sure I would be able to 6 I could try to 7 If I I would be able to 8 I would need help to 3 POST-READING 1 Living with disability is frustrating and challenging Everyday activities are more difficult than they are for others It is also often disappointing to find that other people do not feel comfortable together with someone who is disabled 2 They not only learn how to assist disabled people but also learn the importance of cooperating to reach their goals in life 3 The aim of the special education college is to help disabled students understand that they can play a valuable role within society Blind children all over China read the magazine Literature of Chinese Blind Children and it has inspired many of them to believe that they can realize their dreams The articles in the magazine are often about disabled people who have overcome difficulties and learn to live a meaningful 259

and productive life 3 Today the disabled people are respected and most people believe that they can do many things and succeed 4 LANGUAGE STUDY Word study 1 1 waist 2 guidance 3 sympathy 4 fair 5 potential 6 gifted 7 visual 8 assist 9 disability 10 adjusted 2 1 frustrating 2 challenging 3 disabled 4 encouraging 5 disappointed 6 encouraged Grammar Review Direct and Indirect Object 1 1 Please try to find that book for me 2 I would like you to book a table by the window for me 3 I can t wait to show these photos to my parents 4 Has Mother left some food in the fridge for us 5 I forgot to send a birthday card to Alice 2 1 His mother bought him a computer 2 Please lend one yuan to me 3 Please give me the cheque 4 Tom asked me to bring him an umbrella 5 Could you tell me the time 3 1 This summer my grandpa bought some books for me 2 This summer my friends sent me short messages 3 This summer my aunt and uncle brought candy to me when they come to visit 4 This summer I taught her English INTEGRATING SKILLS Reading 1 Because it often seems as if the Olympic spirit is stronger at the Special Olympics than at the regular one winning is not about being the first one across the finish line or scoring the most goals but it is about being the best you can be 2 By preparing for and participating in the Special Olympics mentally disabled children and adults can develop their ability to move improve their health and gain 260

greater self-confidence The Special Olympics is also a good way to make friends 3 Because people have changed their view about the disabled People have realized that there is much they can do to help the disabled and holding and becoming interested about the Special Olympics is a way to show their respect and encouragement The answers may be various PRACTISING Vocabulary 1 1 disability 2 accessible 3 disability 4 abilities 5 encouragement 6 gifted 7 productive 8 guidance 9 participated 10 unfair 2 1 conducts 2 gifted 3 assist 4 potential 5 participated 6 ceremonies 7 self-confidence 8 candies 9 sympathy 10 victory 3 1 prefer to 2 get used to 3 lead to 4 Thanks to 5 make a contribution to Grammar 1 2 She taught me to swim 3 A local water recreation club offered me a job 4 it paid me 2 000 yuan a month 5 a customer told me that those who are disabled but skilled in sports could represent China at the Paralympic Games 6 I sent an e-mail to the local sports committee saying that I would like to go to the international games for the disabled 7 Then I wrote a letter to the National Sports Committee about the same thing 8 she showed some pictures of the big modern city 9 When someone asked the question why I wanted to do this 10 he brought a bottle of water to me 11 he gave every team member a swimming-suit 12 they gave me many prizes 2 Reading 261

1 1 Equal access means we must make sure that our streets and public buildings such as government offices schools hospitals cinemas and libraries are safe and accessible to all of us 2 Because every member of society has the right to education employment and a reasonable quality of life 3 The equal rights of the people with disabilities that they deserved will not be enjoyed 4 2 1 The interior of the apartment for people in wheelchairs has been designed properly in picture 2 2 In picture 1 the public telephone is out of reach from a wheelchair It should be placed lower The glass door at the entrance is not easy for the people with disabilities to pass through There should be an elevator so that the disabled persons can go upstairs 3 In picture 3 the path for the blind people is blocked by a newsstand It is not safe for the blind people to pass Unit 18 Inventions 1 vest heel patent officer petrol background reject possibility otherwise connection previous aware trial rider dusty pilot storage glue typewriter allow for get stuck break away from be aware of trial and error after all keep track of 2 1 This invention can help people 2 What dose it look like 3 This new invention will make it possible for people to 4 This is a new way of 5 How dose it work 262

6 How would people use it 3 POST-READING 1 1 F 2 T 3 F 4 F 5 F 6 T 7 T 2 1 Paragraph 3 4 Paragraph 2 LANGUAGE STUDY Word study 2 Paragraph 1 5 Paragraph 4 3 Paragraph 5 1 trial try v application apply v connect connection n produce productive adj fail failure n possible possibility n inspiration inspire v deep depth n awareness aware adj 2 1 of 2 from 3 of 4 for 5 by Grammar Review the Attributive Clause 1 1 fits on the desk 2 electricity is unavailable 3 business information is massive 4 patents are issued 5 they see similarities between their ideas and objects or system in the world 6 invent new things 7 can be eat 2 1 The wires with which the machines were connected were very old 2 Leonardo da Vinci who was interested in both literature and science painted the Mona Lisa 3 The pilot who we had dinner with told us stories about his travels 4 The four Chinese inventions which we are proud of have remained important in human history for thousands of years 5 Mozart whose music is popular all over the world showed his talent for music at a very young age 6 The photos are kept in the cupboard which our parents left to us ten years ago 7 The country that the news report is coming from is on the other side of the 263

world 3 1 who make Mickey mouse world famous 2 who discovered the Theory of Relativity 3 who invented one thousand and ninety three inventions all his life 4 who always took a stick in the film 5 who sang the famous song Country Road 6 who discovered the gravity of the earth 7 who was shot dead in the theater 8 who was created by the God 9 who wrote the novel 20 000 Leagues Under the Sea 10 who made the famous speech I Have a Dream 11 who was the president of South Africa 12 who was a deaf INTEGRATING SKILLS Reading 1 These scientific metaphors are familiar to us Using familiar words make it easier for us to understand and use a new tool but it may also make it more difficult for us to use the new invention in the best way 2 3 PRACTISING Vocabulary 1 officer writer farmer possibility connection awareness trial relativity involvement liberation storage 264 ability activity election question business illness material dial capacity quality instrument measurement correction function language baggage

1 He works hard during the period of trial in the company 2 How is the storage of memory in your computer 3 I m not aware that you are a good horse rider 4 The boy has dreamt of becoming an officer when he grows up 5 Is it possible to solve this problem 6 Einstein s theory of relativity has changed the course of physics 7 Don t involve me in your quarrel 8 It is necessary to raise the awareness of self-protection among the primary and secondary students 9 PLA is the abbreviation of the People s Liberation Army 10 To learn how to think you should learn to make connection at first 2 1 otherwise the conclusion will not be general 2 otherwise you will regret when you are old 3 otherwise I would forget it and be absent at the meeting 4 otherwise you won t know who call you 5 otherwise you may suffer from lung cancer 3 1 previous 2 attempt 3 was rejected 4 backgrounds 5 break away from 6 allowing for 7 get stuck 8 are aware of 9 trial and error 10 Keep track of Grammar 1 1 It is a type of fuel that can keep vehicles like cars buses or trucks moving petrol 2 It is the raised part of a shoe that supports the back part of the foot heel 3 He is a person who flies an aeroplane pilot 4 It is the highest title of teachers who teach in universities professor 5 It is a liquid which is used for joining things together glue 6 It is a machine that prints letters when you press its keys typewriter 7 He is a person who holds an important position in the army officer 2 1 I enjoy visiting the places where hotels are cheap and people are friendly 2 The person whom I was working with had to go home for a month 3 That is a subject which /that I know very little about 4 Some people whose lives are adventurous are usually interesting to talk to 5 Do you remember the national park where we were attacked by wild pigs 265

6 My cousin who likes singing and dancing studies the behaviour of animals 7 A Brief History of Time that /which is a best-seller was written by Stephen Hawking 8 The professor was Albert Einstein for whom she did research 9 The kind of insect that /which interests me most is the butterfly 10 My mother still remembers the winter of 1976 when a terrible earthquake 3 Report 1 happened I see many running creatures that are made of metal and glass Those creatures whose feet are round have four eyes two of which are red Those creatures inside which are soft shapes can move The running creatures are automobiles Report 2 In almost every tall building I see a square box that has a door beside which there are some buttons go up and down many times I see many creatures that move on two feet It is an elevator or a lift The creatures are human beings Report 3 At night the creature move back home where they sit in front of a small box for hours on one side of which there is a picture that moves and makes noises which the creatures can understand The box is a TV set and the creatures are human beings INTEGRATING SKILLS Reading 1 Invention Possible uses Invisible paint Very small robot 1 to make interesting clothes 2 to hide things that we do not want others to see to help doctors to cure patients with less risk 2 266

Unit 19 The Merchant of Venice 1 merchant crown deny mercy reasonable weakness judgement gentleman greeting envy troublesome accuse consequence fortune bargain bless legal deed surgeon requirement declare court justice therefore worthy kindness punish order sword complex pay back tear up go about as far as I know at the mercy of go down on one s kindness 2 1 Correct me if I m wrong but 2 You should t forget that 3 What should t be forgotten is 4 One of the most important facts is 5 You could for example 6 The way I would go about it 7 As far as I know 8 After all 9 But in this particular case 3 POST-READING 1 Portia is a lovely kind and intelligent girl 2 Shylock is a cruel and greedy businessman 3 Because he is so greedy and thinks that money is even more precious than his flesh 4 One I am willing to pay him back without reluctance 267

The other He may cut my whole heart away 5 6 Sentence Spoken by Spoken to I feel sorry for you You ve come to face an enemy with a heart of stone who knows neither pity nor mercy I don t have to give you answers that will please you Don t worry Before he can even take one drop of your blood he will first have to take my flesh blood bones and everything else Don t feel bad that a friend paid back the money you owed but feel bad that you lost him Portia Portia Bassanio The judge Antonio Shylock Antonio Shylock LANGUAGE STUDY Word study 1 after all 2 pay back 3 have mercy on 4 tear up 5 went about 6 As far as Grammar Review Direct and Indirect speech 1 Dialogue 1 BASSANIO I am in love with Portia a rich and beautiful lady and she loves me too ANTONIO Oh it s so great BASSANIO But I can t ask Portia to marry me because I had no money Could you lend me three thousand ducats ANTONIO I d love to help you but all my ships are at sea and I have no money Dialogue 2 at all Maybe I can borrow some money from Shylock ANTONIO Could you lend me three thousand ducats SHYLOCK OK I will lend you the money But there is one condition That is I 268

will have the right to have a pound of your flesh to be cut off from any part of your body if you do not pay the money back at the end of three months ANTONIO OK I will accept these terms BASSANIO No Antonio You can not accept these terms He is such a cruel man ANTONIO Don t worry my friend It is only a joke I will sign the agreement 2 Letter 1 Bassanio received a letter from Antonio In the letter Antonio said that his ships were all lost at sea and now he had to pay Shylock with a pound of his flesh according to their agreement Since paying Shylock will cost his life he wish to see Bassanio before he died If Bassanio s love for him was not enough to lead Bassanio there Bassanio could forget about the letter Letter 2 Doctor Bellario wrote in his letter that he was very ill When the letter reach him he had with him a learned young doctor from Rome He told the young doctor a- bout the quarrel between Shylock and Antonio They had studied many law books and the young doctor knew what he would say He ask the judge to let the young doctor stand in his place and pass judgment The doctor was young but he himself never knew so young a body with so wise a head PRACTISING Vocabulary 1 1 reason reasonable 2 merciful mercy 3 great greatness 4 judge judgement 5 punishment punish 2 1 merchant 2 enemy 3 gentleman 4 surgeon 5 sword 6 court 7 greeting 8 consequence 3 1 fortune 2 bargaining 3 legal 4 quarrel 5 justice 6 therefore 269

7 consequence 4 I am Bassanio The story I am telling happened ten years ago I fell in love with an intelligent and beautiful lady named Portia To propose to her was more troublesome than I had expected I had to ask my friend Antonio a merchant of Venice for help He was glad to help me but he had no money at that time He went to Shylock to borrow the money Shylock envied and hated Antonio but he agreed to lend Antonio the money on the condition that Antonio must pay back the money at the end of three months otherwise he would have the right to cut a pound of Antonio s flesh from any part of his body When Portia and I were getting married a letter arrived from Antonio saying that all his ships had been lost at sea and that he would have to give Shylock a pound of his flesh He wished to see me before he died I hurried to see him At the court my wife pretended to be a lawyer for this trial Shylock refused my offer to pay back the money and insisted on cutting one pound of flesh from Antonio When the judge declared the court allowed Shylock to cut a pound of flesh according to the agreement everybody thought that Antonio must die But the judge added If you let one drop of his blood fall you will be accused of trying to kill or murder the citizen of Venice and everything that you own will be taken away from you It was too late to regret for Shylock At last the judge ordered him to give half of his money to the city of Venice Grammar 1 1 pay off The wife asked her husband when should they be able to pay off the debt 2 pay back borrowed at once 3 go about 4 go ahead 5 have mercy on 6 at the mercy of then 7 tears up 8 be torn down 270 His father said that he wanted me to pay back the money I had I said that you just went ahead not to wait for me He begged to have mercy on him The judge told him that he was at the mercy of the Duck She asked who tore up the agreement The mayor declared that the old building would be torn down and a new one would be built in its place

9 After all child after all 10 above all 11 as soon as home 12 As far as take the bus The mother said that she would forgive him because he is only a He told us that he valued his freedom above all He promised her that he would give her a call as soon as he got He said to me that as far as he was concerned we could walk or 2 K King Lear G Goneril R Regan C Cordelia K I have decided to retire and spend the rest of my life in quite peace In order to divide my kingdom among you I would like to know how much you love me G I love you more than I can say as much as my own life in fact as much as any daughter can possibly love her father R I love you quite as much as Goneril and even more and that all my happiness lies in loving you and nothing else K Then how about you Cordelia C I had nothing to say To me words don t show real love at all K How can you say that You must know that nothing will come out of nothing Will you change your speech C I love you with all the love that I can give you no more and no less I obey you love you and honour you but I can not say like Goneril and Regan that I will always love you more than anyone else because it is not true K You are so heartless that I can no longer count you my daughter I will divide the third part of my kingdom between Goneril and Regan INTEGRATING SKILLS Reading 1 The names of the three women characters in Shakespeare s plays mentioned in the text are Juliet Portia and Cordelia Juliet in Romeo and Juliet is a character of passion and imagination Portia in The Merchant of Venice is a intelligent woman with sharp mind and debating skills Cordelia in King Lear is a devoted kind and honest lady 2 The quality of bravery marks Juliet The quality of intelligent marks Portia The quality of honesty marks Cordelia 3 4 Because she dared to use her life to gain her love 271

5 He asked his daughters how they loved him 6 Unit 20 Ar chaeology 1 decoration spear pot emperor pin clothing distinction centimeter clay arrow dozen cushion spare tend approximately average lorry link monument homeland status remote distant quantity mask accompany vast square triangle tend to in terms of in the eyes of serve as dig up 2 1 I wonder what /who 2 I m curious to/about 3 I really want to know 4 I d love to know 5 What I d really like to find out is 6 I d love to know more about 3 it POST-READING 272

2 3 Country or part of Europe Spain western France Europe Activity 1 Travel to Scotland 2 Construction of Stonehenge 3 Hunting 4 Trade with Europe 5 Making copper knives Material or object of trade Copper knives Copper knives gold jewellery Knowledge science inventions and tools needed Roads shoes The things that help transport and pull up the stones Arrow bow Roads something for trade ship Cushion stone copper fire LANGUAGE STUDY Word study 1 1 emperor 2 clothing 3 spear 4 pot 5 arrow 6 link 2 1 date dated 2 dress dressed 3 found find 4 transported transport 5 trade trade 6 pins pin Grammar Review the use of it 1 1 It is modern technology that makes it possible to find out more about the man in the grave 2 It is in central Europe that the tests on his teeth show that he spent his youth 3 In the Bronze Age it is tools of copper and bronze that people could make 4 It was from west Wales that the smaller blue stones came 2 1 It was said that it was an important archaeological discovery 2 It was reported that this man had a son who grew up in Scotland 3 It is believed that the two gold earrings found on the man are the oldest gold ever found in Britain 273

4 It is thought that European culture and techniques were brought to Britain through trade instead of war 5 It has been proved that the copper knives came from Spain and western France 7 It is unknown how these huge stones were transported over a distance of 380 kilometres PRACTISING Vocabulary 1 spear pot pin arrow cushion lorry monument mask crown triangle 2 1 ordinary 2 common 3 average 1 distant 2 vast 3 remote 1 clothing 2 cloth 3 clothes 3 1 In terms of 2 tend to 3 lend a hand 4 accompany 5 decoration 6 distinction Grammar 1 1 No It was a spear that Ben found in the room 2 No It is a monument that will be built here next year 3 No It is a book about Chinese emperors that Jack is reading 4 No It was in a pot that the rich man hid his gold 5 No It was on a cushion stone that ancient man worked metal 6 No It was a lorry that I saw passing at about ten o clock 7 No It is the rabbit mask that the little girl likes best 8 No It was a triangle that he drew on the paper 9 No It is his family that he misses most while studying in Auckland 2 Impersonal 1 2 3 4 6 8 9 10 12 Antecedent Emphatic 5 7 11 1 In this sentence it refers to the distance which is impersonal 2 In this sentence it refers to what he wants to do which is impersonal 3 In this sentence it refers to the time which is impersonal 274

4 In this sentence it refers to ten years which is impersonal 5 In this sentence it is used to emphasize the person who caught the big fish 6 In this sentence it refers to weather which is impersonal 7 In this sentence it is used to emphasize the person who the teacher was speaking to 8 In this sentence it refers to the fact which is impersonal 9 In this sentence it refers to the feeling which is impersonal 10 In this sentence it refers to the action which is impersonal 11 In this sentence it is used to emphasize the place 12 In this sentence it refers to talking to them which is impersonal INTEGRATING SKILLS Reading 1 1 China s archaeological treasures get damaged or lost 2 They should inform the police at once and protect the site 3 Because some people are afraid that they would make scientists come for nothing and some people are afraid that archaeologists work may influence their life or work 4 They must do field work very carefully Every find needs to be a written record about what was found where it was found and when and add photograph The outdoor work is followed by work in the lab cleaning restoring and identifying each artefact Finally when all is done an analysis must be written and published in a magazine or a book 2 1 C 2 D 3 C 4 D 5 D 275

殞 檶檶檶檶檶檶 殞 檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶 殞 殞 1 2 3 4 5 6 7 8 9 1 2 152 1 1 6 A 1 s 1 6 A 1 s q 260

= 1 6 C e = 1 6 10-19 C 1 s n = q e = 1 6 1 6 10 = 1 0-19 1019 2 v r e e T = 2πr v n = 1 T = v 2πr n I = ne = ve 2πr 3 10 ma 8 V 2 ma 50 V = U 2 50 V I 1 U 1 I 2 = U 2 I U 1 = 2 ma 50 V = 12 5 ma 1 8 V 10 ma < 12 5 ma 4 5 Ω 10 Ω 2 5 Ω I 2 4 5 R = U/I 261

154 1 100 m 1 mm 2 R = ρ l S = 2 9 10-8 100 Ω = 2 9 Ω 1 10-6 2 4 Ω 1 R = 4 Ω 4 1 Ω 1 2 2 R = 4 Ω 4 16 Ω 3 0 63 mm 2 200 m 8 A R = ρ l S = 1 7 10-8 200 Ω = 5 4 Ω 0 63 10-6 U = IR = 8 5 4 V = 43 V 4 A B C D P P A C P B A 4 P A C PA P B A 262

A D P B A B C P A B B D P A B 263

158 1 kw h 1 1 kw 1 h 1 kw h 1 kw h = 1 kw 1 h = 1 000 W 3 600 s = 3 6 10 6 J 2 220 V 40 W 100 W a b 110 V c 220 V b c a P = UI = U2 R 40 W R 1 = U2 = 220 2 Ω = 1 210 Ω P 1 40 100 W R 2 = U2 = 220 2 Ω = 484 Ω P 2 100 40 W b 110 V 40 W P 1 = U2 = 110 2 W = 10 W R 1 1 210 100 W P 2 = U2 = 110 2 W = 25 W 484 R 2 100 W c 220 V I P = I 2 R 40 W U 220 I = = A = 0 13 A R 1 + R 2 1 210 + 484 40 W P 1 = I 2 R 1 = 0 13 2 1 210 W = 20 W 100 W P 2 = I 2 R 2 = 0 13 2 484 W = 8 W 3 2 kw 2 kg 20 100 60% 4 2 10 3 J / kg K 264 2 kg 20 100 Q = cmδt t W= Pt η = 0 6 ηpt = cmδt

t = cmδt ηp = 4 2 103 2 100-20 s = 560 s 0 6 2 000 4 a P = UI b P = UI a n R 1 R 2 R n R R = R 1 + R 2 + + R n P 1 = I 2 1 R 1 P 2 = I 2 2 R 2 P n = I 2 n R n P = P 1 + P 2 + + P n = I 1 2 R 1 + I 2 2 R 2 + + I n 2 R n I = I 1 = I 2 = = I n P = I 2 R 1 + I 2 R 2 + + I 2 R n = I 2 R 1 + R 2 + + R n = I 2 R = UI b n R 1 R 2 R n R 1 R = 1 R 1 + 1 R 2 + + 1 R n P 1 = U 2 1 P R 2 = U 2 2 P 1 R n = U 2 n 2 R n P = P 1 + P 2 + + P n = U 2 1 + U 2 R 1 R 2 2 + + U 2 n R n U = U 1 = U 2 = = U n P = U2 + U2 + + U2 R 1 R 2 R n ( ) = U 2 1 + 1 + + 1 R 1 R 2 R n = U2 R = UI 5 U = 220 V 5 265

r = 5 Ω A R A = 100 Ω A B A A 220 V P A = U2 R = 2002 W = 400 W 100 A B A B R = 50 Ω A B U AB U 2r U AB U 2r = R 2r = 50 10 = 5 U AB + U 2r = 220 V U AB = 183 V P A = P B = 1832 W = 335 W 100 162 1 2 0 V 9 0 Ω 1 8 V I = U R = 1 8 A = 0 2 A 9 0 E = U + Ir r = E - U 2 0-1 8 = Ω = 1 0 Ω I 0 2 2 4 5 V 0 5 Ω 4 0 6 0 Ω 6 0 Ω 4 0 Ω I = E R + r = 4 5 A = 1 0 A 4 0 + 0 5 U = IR = 1 0 4 0 V = 4 0 V 6 0 Ω R = 2 4 Ω 266 I = E R + r = 4 5 A = 1 6 A 2 4 + 0 5 U = IR = 1 6 2 4 V = 3 8 V

6 0 Ω R = 10 Ω I = E R + r = 4 5 A = 0 43 A 10 + 0 5 U = IR = 0 43 10 V = 4 3 V 3 600 μa 30 μa E = 600 10-6 V I = E /r r r = E I - 6 600 10 = Ω = 20 Ω 30 10-6 4 10 2 0 V 0 04 Ω 3 6 Ω 4 E = 10 2 0 V = 20 V r = 10 0 04 Ω = 0 4 Ω I = E R + r = 20 A = 5 0 A 3 6 + 0 4 U = IR = 5 0 3 6 V = 18 V 5 4 1 5 V 1 Ω R 1 = 8 Ω R 2 = 8 Ω R 3 = 4 Ω R 1 R 2 R 3 E = 4 1 5 V = 6 0 V r = 4 1 Ω = 4 Ω R = 5 2 Ω I = 6 0 A = 1 0 A 6 I 1 = 0 25 A I 2 = 0 25 A I 3 = 0 5 A 164 267

1 R g = 120 Ω I g = 3 ma 6 V 3 A R g = 120 Ω I g = 3 ma U g = I g R g = 3 10-3 120 V = 0 36 V U = 6 V R R = U R R U g = U - U g 6-0 36 R g U g = 120 Ω = 1 880 Ω g 0 36 I = 3 A R R = I g R I g = I g R R I - I g = 3 10-3 - 3 120 Ω = 0 12 Ω g 3-3 10 2 2 1 2 3 2 4 6 2 2 1 2 3 2 4 6 3 150 V 20 kω 110 V 5 V I = U V 5 = R V 2 10 A = 2 5 10-4 A 4 268 U R = U - U V = 110 V - 5 V = 105 V R = U R 105 = Ω = 4 2 10 5 Ω I 2 5 10-4

4 R A = 0 03 Ω R V = 2 0 kω R 1 5 kω R 2 Ω 1 5 kω R R 2 Ω R R A 166 4 1 60 cm 0 5 mm 2 10 km 1 cm 2 l 1 R 1 = ρ 1 = 1 7 10-8 0 6 Ω = 0 02 Ω S 1 0 5 10-6 l 2 R 2 = ρ 2 = 2 9 10-8 10 103 Ω = 2 9 Ω S 2 1 10-4 10 km 10 2 R 1 2 R 12 = 0 5 R 2 3 R 23 = R 1 3 R 13 = 1 5 R 3 2 269

185 mm 2 400 A 5 cm R = ρ l S = 2 9 10-8 5 10-2 185 10-6 Ω 3 = 7 8 10-6 Ω U = IR = 400 7 8 10-6 V = 3 1 10-3 V 4 U 1 = 40 V I = 5 0 A U = 220 V R 1 = U 1 = 40 Ω = 8 0 Ω I 5 0 R 2 220 V R 2 R 2 = U I ( ) - R 1 = 220 5 0-8 0 Ω = 36 Ω 5 R 1 = 100 Ω 5 ma I = 1 A R 2 U 1 = 40 V I 1 = 5 ma = 5 10-3 A U 1 = I 1 R 1 = 5 10-3 100 V = 0 5 V U 2 = U 1 = 0 5 V I 2 = I - I 1 = 1-5 10-3 A = 0 995 A R 2 = U 2 = 0 5 Ω 0 5 Ω I 2 0 995 5 6 n R 1 R 2 R n R 270 1 R = 1 R 1 + 1 R 2 + + 1 R n 1 R > 1 R < R R i i 7

R R = R 1 + R 2 + + R n R 1 R R' 1 R' = 1 R 1 + 1 R 2 + + 1 R n R 1 R' 8 U = 220 V 20 R 807 Ω r 1 0 Ω 10 20 8 a 10 R = 1 807 Ω = 80 7 Ω 10 I = U R + 2r = 220 A = 2 66 A 80 7 + 2 1 0 P = IU = 2 66 220 W = 585 W ΔU = I2r = 2 66 2 1 0 V = 5 3 V ΔP = I 2 2r = 2 66 2 2 W = 14 2 W b 20 R = 1 807 Ω = 40 4 Ω 20 I = U R + 2r = 220 A = 5 19 A 40 4 + 2 1 0 P = IU = 5 19 220 W = 1 141 8 W ΔU = I2r = 5 19 2 1 0 V = 10 4 V ΔP = I 2 2r = 5 19 2 2 1 0 W = 53 9 W 9 2 271

a b 1 2 a 2 1 b 2 10 0 20 A 1 98 V 0 40 A 1 96 V E r E = I 1 r + U 1 = 0 20Ar + 1 98V E = I 2 r + U 2 = 0 40Ar + 1 96V 1 2 E = 2 V r = 0 1 Ω B 166 1 10 1 ab U = 10 V R 1 = 1 kω R 2 = 5 Ω R 3 = 2 kω R 4 = 10 Ω I ab 10 Ω I = U/R = 10 10 A = 1 A 2 1 2 2 R 1 R 2 272 a S

b R 2 R 1 /R 2 a S R 1 R 2 S R 1 R 2 S R 2 S R 2 b R 2 P 1 R 2 P 2 P 2 /P 1 = 2 R 2 I 1 I 2 R 1 R 2 = 槡 2-1 P 2 P 1 = I2 2 I 2 1 ( ) = R 1 + R 2 R 3 I R 1 2 2 = 2 a R 1 R 2 U b R 1 R 2 I 1 I 2 3 c a R 1 R R 1 R 2 U = IR I R 1 R 2 U b R 2 I 2 = U U R R 2 I 2 2 R 1 I 1 = I - I 2 I R 2 I 2 R 1 I 1 c P = UI I U P 4 ab 8 V 4 Ω 273 4

12 Ω 12 Ω 6 Ω 4 Ω 2 Ω 4 Ω R = 8 Ω a b U = 8 V I = U/R = 1 A P = IU = 8 W 274

1 2 3 4 5 6 1 2 3 173 1 N F 1 S F 2 F 1 F 2 1 F 1 F 2 2 275

1 2 3 3 276 4

4 176 1 1 2 15-3 I 1 I 2 I 1 B 1 I 2 F 2 I 2 B 2 I 1 F 1 I 1 I 2 2 277

I 1 B 1 I 2 F 2 I 2 B 2 I 1 F 1 3 A B C D D 4 B = F / IL B F I L IL F IL F / IL F IL 5 2 m 1 A B = 0 2 T F = ILB = 1 2 0 2 N = 0 4 N 6 4 0 10-2 T 8 cm ab ab 1 0 10-2 N F = ILB I = F LB = 1 0 10-2 - 2 A 3 1 A 0 08 4 0 10 6 b a 7 0 50 10-4 T 20 m 30 A F = ILB 278 F = 30 20 0 50 10-4 N = 3 0 10-2 N 3 0 10-2 N 179

1 1 2 Q A B Q - Q C B A B F = qvb - Q Q C F B 3 v = 3 0 10 6 m/s B = 0 10 T F = qvb = 1 6 10-10 3 0 10 6 0 1 N = 4 8 10-14 N 182 1 1 6 10 6 m/s B = 2 0 10-4 T v = 1 6 10 6 m/s B = 2 0 10-4 T r = mv qb = 0 91 10-30 1 6 10 6 1 6 10-19 - 4 m = 0 046 m = 4 6 cm 2 0 10 279

T = 2πm qb = 2 3 14 0 91 10-30 1 6 10-19 2 0 10-4 s = 1 8 10-7 s 2 B = 7 0 10-4 T 3 0 10-2 m r = mv qb v = qbr m = 1 6 10-19 7 0 10-4 3 0 10-2 0 91 10-30 m/s = 3 7 10 6 m/s 3 v 2v 4 A B C D B 3 5 p 1 H α 4 3 α 4 r = mv qb m H = 3m P m α = 4m P q H = e q α = 2e r H > r α > r P 280 5 6

r p : r H : r α = T p : T H : T α = 1: 3: 2 1: 3: 2 A 187 1 A A 2 2 3 4 1 2 m 5 0 A 1 8 N B = F IL = 1 8 T = 0 3 T 5 0 1 2 5 0 8 T 0 5 m 5 0 A 0 4 m F = ILB W= Fs W= ILBs = 5 0 0 5 0 8 0 4 J = 0 8 J 0 8 J 281

6 1 2 T 5 0 10 5 m/s F = qvb F = 1 60 10-19 5 0 10 5 1 2 N = 9 6 10-14 N 7 α E 1 α E 2 E 1 : E 2 A 4: 1 B 1: 1 C 1: 2 D 2: 1 B r = mv qb E = 1 2 mv2 E = r2 q 2 B 2 2m m 1 α m 2 q 1 α q 2 m 2 = 4m 1 q 2 = 2q 1 r 2 q 1 2 B 2 2m 1 E 1 : E 2 = = 1: 1 r 2 2q 1 2 B 2 2 4m 1 8 8 8 282

9 v B v 1 B v 2 v 1 B B v 2 B B B 188 1 abcd I I 2 10-2 kg bc F = ILB bc F bc bc 2F = 2 10-2 10 N = 0 2 N F = 0 1 N 2 A B 0 1 m A v 0 = 1 0 10 7 m/s a A B b A B 1 a r = mv qb 2 B = mv qr = 0 91 10-30 1 0 10 7 T = 1 1 10-3 T 0 05 1 6 10-19 b T = 2πm qb A B 283

t = T 2 = πm qb = 3 14 0 91 10-30 1 6 10-19 1 1 10-3 s = 1 6 10-8 s 3 E B v v 3 v = E B q F 1 = E q F 2 = qvb q F 1 = F 2 E q = qvb v = E B 4 a b α α a 4 a 4 a 284 b α m α m p 4 α q α

q p 2 m α = 4m p q α = 2q p E K α v α = 1 2 v p α tan φ p = q pul m p dv α 2 p tan φ α = q Ul α m α dv = 2 q pul 2 α m p du = 2tan φ 2 p α p 4 b E B v p v p = E B α v α = 1 2 v p α F α = q α v α B = q α B 1 2 v p = 1 2 q B E α B = 1 2 q E F = q E α α α α α 5 A B 5 B B 285

A A A B B A B A B A B 6 d E B 6 v 0 θ v W= ΔE K U = Ed qed = 1 2 mv2-2qed v = 槡 m + v 0 2 qu = 1 2 mv2-1 2 mv 2 0 1 2 mv 2 0 286 1 2 3 4 5

1 2 3 4 195 1 5 0 10-2 m 2 2 0 10-2 T Φ = BS = 2 0 10-2 5 0 10-2 Wb = 1 0 10-3 Wb 2 0 5 m 2 2 0 10-2 Wb Φ = BS B = Φ S = 2 0 10-2 0 5 Wb /m 2 = 4 0 10-2 Wb /m 2 = 4 0 10-2 T 3 3 4 4 287

5 OO' Φ = BS S OO' 6 1 5 2 1 6 7 ABCD I I B 7 288

8 8 9 A P A B A i t B 4 t 1 ~ t 2 B B A 9 B B 9 B 289

198 1 A B C D D 2 a 1 V = 1 Wb /s b 1 V = 1 T 1 m 1 m/s a E = n ΔΦ Δt 1 V = 1 Wb = 1 Wb /s 1 s b E = BLv 1 V = 1 T 1 m 1 m/s 3 0 4 T 25 cm 6 m/s 30 E = Blvsin θ = 0 4 0 25 6 0 5 V = 0 3 V 4 OO' L 1 L 2 ω B E = BSω S S = L 1 L 2 OO' 4 E = BLvsin θ v = ωr E = BL 2 L 1 ωsin θ S = L 2 L 1 θ = 90 E = BSω 5 1 000 0 4 s 0 02 Wb 0 09 Wb 10 Ω 290

990 Ω E = n ΔΦ 0 09-0 02 = 1 000 V = 175 V Δt 0 4 I = E R + r = 175 A = 0 175 A 990 + 10 6 20 5 km 4 6 10-5 T 7 6 km/s B = 4 6 10-5 T L = 20 5 km = 2 05 10 4 m v = 7 6 km/s = 7 6 10 3 m/s E = BLv E = 4 6 10-5 2 05 10 4 7 6 10 3 V = 7 2 10 3 V 7 1 2 A B 7 C D A D 203 1 7 7 291

A D C B 2 AB CD S CD AB CD AB 2 D C C D 3 CDEF AB ABCD ABFE AB CDEF AB ABCD 3 ABCD A B C D ABFE ABFE A B F E AB 4 M P a S P b M P c S P 4 d P P N 292

M B a S P b M P c S P d S P N S P N 5 A B A B A A B 5 A B A N A A A A A A B B B B 6 A A A g A A a a < g A 6 A A g A A A a < g A 211 1 v A 293

B C B 2 1 2 3 OO' OO' 3 4 a P 1 P 2 294

b c d B 1 5 T AB 10 cm BC 4 cm ω 120 rad /s P 1 P 2 4 ABCD a P 1 P 2 B C D A 90 A D C B 180 B C D A b c E = BSωsin θ d E max = BSω = 1 5 0 1 0 04 120 V = 0 72 V 5 ab cd ab cd cd cd cd 5 ab cd ab abdc a c d b cd cd cd ab cd cd 6 R ab = 0 1 Ω ab 295

R = 0 4 Ω B = 0 1 T ab L = 0 4 m v = 5 m/s a abcd 6 b E = V abcd I = A c ab F = N ab F' = N W d P' = F' v = W e P = EI = W f P 1 = W R P 2 = a ab a e 0 08 f 0 016 0 064 b 0 2 0 4 c 0 016 0 016 d 0 08 P = P 1 + P 2 P' = P 7 L = 0 1 m abcd m = 10 g h = 0 2 m ab cd L g 10 m/s 2 7 Q 296 Q = mg2l = 2mgL = 2 10 10-3 10 0 1 J = 0 02 J

B 212 1 2 abcd L ab R B ab PQ v ad bc PQ PQ L/3 ap 2 PQ R ap Pb R ap = 1 3 R R Pb = 2 3 R R PQ = R R' = R PQ + R ap R Pb R ap + R Pb = R + 1 3 R 2 3 R 2 1 3 R + 2 = R + 3 R 9 R = 11 9 R E I = E R' ap I ap = 2 3 I = 2E 3R' E = BLv R' = 11 9 R I ap = 6BLv 11R 3 A B A B S K D C C 297

S A B K D 3 4 4 5 ab E q m 3 /s d B q E 298 5

ba E = BLv L = d v q = πd2 4 v v = 4q πd 2 v E = Bdv E = Bd 4q πd = 4B 2 πd q q = πde 4B 6 A A L R v x B x F B A F 6 A 6 B 299

1 2 3 4 1 2 3 218 1 17-2 ab cd ab cd 2 17-1 ab 20 cm ad 10 cm B 0 01 T n 50 r /s 0 01 s E max = 2Blv E max = BSω 300

E max = 0 01 0 2 0 1 50 2π V = 6 28 10-2 V E = E - 2 max 6 28 10 = V = 4 44 10-2 V 槡 2 槡 2 n 50 r /s 0 01 s 3 400 V 314 rad /s 2 000 Ω e = 400sin 314t I max = E max /R = 400 /2 000 A = 0 2 A i = 0 2sin 314t 4 100 V 100 V 100 V U max = 槡 2U = 141 V 100 V 5 2 A I max = 槡 2I = 1 41 2 A = 2 82 A 6 0 2 s 6 5 0 Hz 10 A 221 1 1 301

2 2 224 1 2 36 V 220 V 1 140 40 W U 1 = n 1 n U 2 n 2 = U 2 n 2 U 1 1 U 1 = 220 V U 2 = 36 V n 1 = 1 140 n 2 = 36 1 140 = 186 5 187 220 P 2 = U 2 I 2 P 2 = 40 W U 2 = 36 V I 2 = P 2 = 40 A = 1 1 A U 2 36 302 I 1 U 1 = I 2 U 2 I 1 = U 2 I U 2 = 36 1 220 40 A = 0 18 A 36

3 400 220 V 55 V U 1 = n 1 n U 2 n 1 = U 1 n 2 U 2 2 U 1 = 220 V U 2 = 55 V n 2 = 400 n 1 = 220 400 = 1 600 55 4 17-16 17-17 17-16 17-17 5 I 1 U 1 = I 2 U 2 U 2 < U 1 I 2 > I 1 227 1 4 800 kw 110 kv 110 V P = UI I = P U P = 4 800 kw = 4 800 10 3 W 303

U = 110 kv = 110 10 3 V 4 800 103 I = A = 43 6 A 110 10 3 U = 110 V 4 800 103 I = A = 43 6 10 3 A 110 2 U 2 1 P = UI U = IR P = U 2 /R 3 P R P I ΔU P = IΔU ΔU = IR R ΔU = U - U' U 3 200 kw 0 05 Ω 110 V 11 kv ΔU = IR I = P U 1 2 3 ΔU = P U R P U 304 110 V 200 103 ΔU 1 = 0 05 V = 91 V 110 11 kv 200 103 ΔU 2 = 0 05 V = 0 91 V 11 10 3 4 220 V 11 kv

P U L S ρ P = I 2 R P = UI R = ρ L S P = P ( U ) 2 ρ L S = P2 ρl U 2 S P ρ L U S U 1 U 2 S 1 S 2 U 2 1 S 1 = U 2 2 S 2 ( ) S 1 = U 2 2 S 2 U = U 2 2 1 U 1 2 2 11 103 = ( 220 ) = 2 500 5 20 kw 400 V 0 5 Ω 250 V 400 V I = P 20 103 = A = 50 A U 400 P = I 2 R = 50 2 0 5 W = 1 25 kw P = P - P = 20 kw - 1 25 kw = 18 75 kw 20 103 250 V I = A = 80 A 250 P = 80 2 0 5 W = 3 20 kw P = 20 kw - 3 20 kw = 16 80 kw A 233 1 220 V 50 Ω I = U R = 220 A = 4 4 A 50 I max = I 槡 2 = 4 4 1 41 A = 6 2 A 305

P = I 2 R = 4 4 2 50 W = 968 W 2 120 4 V 0 1 A 220 V 4 0 1 W = 0 4 W 120 120 0 4 W = 48 W 48 W P = UI = 48 W I = P U = 48 A = 0 218 A 220 3 4 A B U 1 U 2 U 1 /U 2 C U 2 = n 2 U n 1 U 1 U 2 1 n 1 n 2 > 1 306 n 2 n 1

I 1 = I 2 P 1 = U 1 I 1 P 2 = U 2 I 2 P 1 /P 2 = U 1 /U 2 P 2 = n 2 P n 1 1 A B ΔΦ U 1 Δt n 1 = = n 1 U 2 ΔΦ Δt n n 2 2 C P 1 = P 2 U 1 I 1 = U 2 I 2 B 234 1 A 1 307

A A 2 A E U 1 2E U 2 + - 2 A U 2 B E U 1 B 0 ~ 1 U 1 E R U 2 U 1 B Oa U 1 E D 2 D 1 U 2 E B ab U 1 E D 1 U 2 U 1 B bc U 1 E U 2 U 1 E U 2 E 2 B 308

U 1 B 1 ~ 2 U 1 E U 2 U 1 B cd ef U 1 E D 2 - E B de U 2 3 n 2 U 1 U 2 = U 2 n 1 n 2 4 55% 0 03 m 3 20 m 80% 14 kw 20 kw 28 kw V= 0 03 m 3 h = 20 m mgh = ρvgh = 10 3 0 03 9 8 20 J = 5 880 J P = 5 880 W η = 55% = 0 55 P = P η = 5 880 0 55 W = 1 07 104 W η' = 80% = 0 80 P' = P 1 07 104 = W = 13 4 kw η' 0 8 14 kw 5 4 6 h 7 3 h U 1 U 2 309

45 000 kw 36 000 kw W W W = 4 45 000 10 3 6 3 600 J W W W = 7 3 600 10 3 3 3 600 J η = W /W = 0 70 = 70% 6 n 1 : n 2 : n 3 = 10: 5: 1 = 110 Ω R 3 = R 2 11 Ω n 1 220 V n 1 n 2 n 3 I 1 I 2 I 3 6 P 1 = P 2 + P 3 310 U 1 I 1 = U 2 I 2 + U 3 I 3 = n 2 U 1 n 1 U 2 U 2 = n 2 U n 1 = 5 220 V = 110 V 1 10 U 3 = n 3 U n 1 = 1 220 V = 22 V 1 10 I 2 = U 2 = 110 R 2 110 A = 1 A I 3 = U 3 = 22 R 3 11 A = 2 A U 1 U 2 U 3 I 2 I 3 1 110 1 + 22 2 I 1 = A = 0 7 A 220 1

1 LC 2 LC 3 1 LC 2 311

240 1 LC 1 t = 0 312

2 LC A B C D A C 3 LC 2 μh 7 5 MHz 1 f = 2π 槡 LC 1 C = 4π 2 f 2 L = 1 4π 2 7 5 10 3 2 2 10 F = 2 25 10-10 F = 225 pf - 6 4 300 pf 550 khz 30 pf 1 f = 2π 槡 LC 1 L = 4π 2 f 2 C = 1 4π 2 5 5 10 5 2 3 10 H - 10 = 2 79 10-4 H 30 pf 1 f = 2π 槡 LC = 1 2π 槡 2 79 10-4 3 10 = 1 74 10 6 Hz - 11 Hz 4 5 LC 313

244 1 3 84 10 5 km d c t t = 2d c = 2 3 84 108 3 0 10 8 s = 2 56 s 2 20 009 MHz 19 995 MHz 2 997 9 10 8 m/s λ = c f λ 1 = c 2 997 9 108 = m = 14 983 m f 1 20 009 10 6 λ 2 = c 2 997 9 108 = m = 14 993 m f 2 19 995 10 6 3 560 7 m 186 9 m f = c λ f 1 = c 3 0 108 = Hz = 5 35 10 5 Hz = 533 khz λ 1 560 7 f 2 = c 3 0 108 = Hz = 16 05 10 5 Hz = 1 605 khz λ 2 186 9 535 khz 1 605 khz 250 1 LC A B C D A D 314

1 f = 2π 槡 LC LC L L L C = εs 4πKd A D C L LC 2 4 MHz 12 MHz 1 f = 2π 槡 LC L f 1 = 4 MHz C 1 f 2 = 12 MHz C 2 f 1 f 2 = 槡 C2 槡 C1 C 2 = C 1 2 f ( 1 f ) 2 2 4 = ( 12 ) = 1 9 1 9 3 A B C D C 4 LC q t A t 1 B t 1 t 2 C t 4 2 t 3 D t 4 A C D LC 315

A C D 5 B q m LC L C 2πm qb = 2π 槡 LC LC = 2 m ( qb ) ( ) 2 m L C LC = qb 316

殞 檶檶檶檶檶檶 殞 檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶 殞 殞 1 2 1 2 3 77 1 2 3 4 1 molch 4 Cl 2 CCl 4 Cl 2 317

318 1 H H 2 CH 4 H C H H C H H H Cl 3 5 Cl C Cl Cl 4 4 1 A B C D 2 A B C D 3 A B 1 000 C D 4 A B C D 5 4 A CH 3 Cl B CH 2 Cl 2 C CHCl 3 D CCl 4 1 A 2 A B O 2

O 2 C D 3 CH 4 CH 4 CH 4 1 000 1 000 CH 4 C + 2H 2 CH 4 O 2 B CH 4 + 2O 2 CO 2 + 2H 2 O 4 H 2 + Cl 2 2HCl CH 4 Cl 2 CH 4 + Cl 2 CH 3 Cl + HCl HClO 2HClO 2HCl + O 2 CH 4 O 2 C 5 D 1 CH 4 H 2 CO CH 4 H 2 CO 2 11 2 L CH 4 + O 2 CO 2 + 2H 2 O 22 4 L/mol 1 2 11 2 L n CO 2 n H 2 O 319

V m V CH 4 = ν CO 2 n CO 2 n CO 2 = ν CO 2 V CH 4 V m = 1 11 2 L 22 4 L/mol = 0 5 mol n H 2 O = ν H 2 O V CH 4 V m = 2 11 2 L 22 4 L/mol = 1 mol CO 2 0 5 mol 1 83 1 1 2 1 CH 2 CH 3 3 CH 3 CH CH 320 3 CH CH 2 3 CH 3 CH 2 CH 2 CH 3 CH2 CH 2 CH 2 CH CH CH 3 2 1 C n H 2n + 2 n 1 14 3 2 CH 2 CH 2 CH 3 3 2 CH 3 CH CH CH CH 3 CH 3 CH 2 CH CH 3 CH CH 3 3 1 3

A CH 4 C 10 H 22 C C 2 H 6 C 4 H 10 B CH 4 C 2 H 5 OH D CH 3 COOH C 3 H 8 2 A B C D 3 A 2- B C D 1 CH 2 A C 2 5 D 3 4 2- Cl CH 3 C CH 3 CH CH CH CH 3 3 CH 2 3 Cl Cl CH 3 CH 2 CH 2 Cl CH 3 CH CH 3 CH 3 CH 2 CH 2 CH 2 Cl CH 3 CH CH 2 CH3 Cl CH 3 CH 2 Cl D 1 2 3 4 5 2-321

87 2-1 2 1-3 1 2 C n H 2n n 2 CH 2 = CH - CH 3 CH 2 = CH - CH 2 CH 3 3 1 322 A B C D 2 A C 2 H 4 B C 3 H 6 C C 5 H 12 D C 4 H 8 3 A CH 3 CH 3 CH 3 CH = CH 2 B CH 3 CH = CH 2 CH 3 CH 2 CH = CH 2 C CH 3 CH 2 CH 3 CH 3 CH = CH 2 D CH 3 CH 2 CH 2 CH 3 CH 3 CH 2 CH 3 4 A CH 3 CH 2 CH 2 CH 3 CH 3 CH = CH CH 3

B CH 3 CH = CH CH 3 CH 3 CH = C CH C CH 3 CH = CH CH 3 CH 3 C = CH 2 CH 3 3 CH 3 D CH 3 CH = CH CH 3 CH 3 CH 2 CH = CH2 5 A B C 2 1 D 6 A B C D 1 H 2 SO 4 CH 3 CH 2 OH H 2 SO 4 CH 170 2 = CH 2 + H 2 O H 2 SO 4 H 2 O H 2 SO 4 H 2 SO 4 C 2 KMnO 4 Br 2 C 3 CH 2 A B CH 2 C D B D 4 A B C D C D 5 C H Cl 2 Cl 2 CH 4 C 2 H 4 D 6 C D 323

CH 2 BrCH 2 Br CH 3 CH 2 OH幈幇 CH 2 = CH 2 CH2 - CH 2 n 1 CH 3 CH 2 OH H 2 SO 4 CH 170 2 = CH 2 + H 2 O 2 CH 2 = CH 2 + H 2 O CH 3 CH 2 OH 3 CH 2 = CH 2 + Br2 CH 2 Br - CH 2 Br 4 nch 2 = CH 2 CH 2 - CH 2 n CH 3 Cl CH 2 Cl 2 CHCl 3 CCl 4 HCl / CH 2 Br CH 2 Br CO 2 H 2 O CO 2 H 2 O 91 1 1 mol C 2 H 2 mol Br 2 2 6 C 8 H 16 C 9 H 16 C 15 H 32 C 17 H 34 C 7 H 14 C 8 H 14 1 2 324 2 C 15 H 32 C 8 H 16 C 17 H 34 C 7 H 14 C 9 H 16 C 8 H 14 1 A B C

D 2 CO 2 A B C D 3 1 mol 3 mol CO 2 2 mol H 2 O A C 3 H 4 B C 3 H 6 C C 3 H 8 D C 4 H 10 1 CO 2 H 2 O KMnO 4 HCl CH CH + HCl CH 2 = CH - Cl HCl CH 2 = CH 2 + HCl CH 3 CH 2 Cl D 2 CO 2 CH 4 = 12 = 75% 16 C 2 H 6 = 24 = 80% 30 = 24 28 = 85 7% = 24 = 92 3% 26 D 3 1 mol 3 mol CO 2 2 mol H 2 O 3 C 4 H A CH 3 - CH 3 CH3 CH 2 Cl CH 2 = CH2 CH3 CH 2 Cl CH CH CHBr = CHBr CHBr 2 CHBr CH 2 2 = CHCl CH2 CHCl 1 CH 3 CH 3 + Cl 2 CH 3 CH 2 Cl + HCl 2 CH CH + H 2 CH 2 = CH 2 3 CH 2 = CH 2 + HCl CH 3 CH 2 Cl 4 CH CH + Br2 CHBr = CHBr 5 CHBr = CHBr + Br2 CHBr 2 - CHBr 2 6 CH CH + HCl CH 2 = CHCl 7 nch 2 = CHCl CH 2 - CHCl n 325 n

CH 4 CH 2 = CH 2 CH CH 326

C n H 2n + 2 n 1 C n H 2n n 2 C n H 2n - 2 n 2 CH 3 CH 2 OH CaC 2 + 2H 2 O H 2 SO 4 CH 170 2 = CH 2 C 2 H 2 + Ca OH + H 2 O 2 CH 3 Br CH 2 Br 2 CH 2 BrCH 2 Br CHBr 2 - CHBr 2 CHBr 3 CBr 4 HBr 96 1 2 6 1 師 2 帪 庎 師 1 KMnO 4 A B C D 2 2: 1 A B C D 3 A 327

B C D KMnO 4 KMnO 4 1 C C KMnO 4 B 2 CO 2 H 2 O 2: 1 C H 1: 1 C D 3 C C C - C C = C B 1 2 3 1 庎 + Br 2 庎 Br + HBr H 2 SO 4 2 庎 + HO NO 2 NO 庎 2 + H 60 2 O 3 庎 + 3H 2 KMnO 4 328

102 1 A 1- B C D 1-2 A B C D 1 1-1- C 2 4 D 1 2 1 97% ~ 98% 2 C 4 C 5 ~ C 11 C 11 ~ C 16 C 15 ~ C 18 C 20 103 1 CH 3 CH 3 CH 3 CH = CH 2 CH 3 CH 2 C CH 3 C CCH 3 C 6 H 6 C 6 H 12 2 Cl 3 CH 3 CH = CH 2 CH 3 C = CHCl 3 C CH CH 2 = CHCHCl 2 329

4 1 mol C 2 H 6 1 mol C 2 H 4 1 mol C 2 H 2 1 CH 3 CH = CH 2 C 6 H 12 CH 3 CH 2 C CH CH 3 C CCH 3 2 2 2-4 Cl 3 CH 3 C = CHCl CH 3 C CH 4 C 2 H 6 C 2 H 6 1 A B C D 2 A B C D 3 A B C D 4 A B C D 1 A C 2 B D 3 KMnO 4 H + KMnO 4 H + B D 4 CO NO CO 2 A C 1 2 330

3 4 CH 2 CH 2 Cl Cl 5 6 1 2 3 4 5 6 1 2 1 H 2 C 2 H4 CH 4 KMnO 4 C 2 H 4 H H2 2 CH 4 CH 2 KMnO 4 5 5-130 1 2 3 4 4 331

5 6 1 CH 3 CH 3 + Cl 2 CH 3 CH 2 Cl + HCl CH 3 CH 2 Cl + Cl 2 CH 3 CHCl 2 + Cl 2 CH 3 CCl 3 + Cl 2 CH 2 Cl - CCl 3 + Cl 2 CH 3 CHCl 2 + HCl CH 3 CCl 3 + HCl CH 2 ClCCl 3 + HCl CHCl 2 CCl 3 + HCl CHCl 2 CCl 3 + Cl 2 CCl 3 CCl 3 + HCl 2 nch 2 = CH 2 CH 2 - CH 2 n 3 CH CH + Br2 CHBr = CHBr CHBr = CHBr + Br2 CHBr 2 - CHBr 2 H 2 SO 4 4 + HO - NO 2 NO 2 + H 60 2 O 5 + 3H 2 6 n 1 C n H 2n + 2 + 3n + 1 O 2 2 nco 2 + n + 1 H 2 O n 2 C n H 2n + 3n 2 O 2 nco 2 + nh 2 O n 2 C n H 2n - 2 + 3n - 1 O 2 2 nco 2 + n - 1 H 2 O n 6 C n H 2n - 6 + 3n - 3 O 2 2 nco 2 + n - 3 H 2 O 11 2 L 5 6 g C 2 H 4 ~ m 332 1 28 x 5 6 ( ) 11 2 0 2: - 0 2 = 2: 3 22 4

0 2 28: 0 3 30 = 28: 45 333

1 2 110 1 2 3 170 1 C 2 H 5 OH CH 3 CH 2 OH 2 75% 3 CH 3 CH 2 OH H 2 SO 4 CH 2 = CH 2 + H 2 O 170 1 A CuSO 4 5H 2 O B C D 2 32 g 11 2 L A CH 3 OH B C 2 H 5 OH C C 3 H 7 OH D C 4 H 9 OH 3 C 4 H 9 OH A OH 3 CH 2 CH 2 CH 2 OH B CH 2 = CHCH 2 CH 2 OH CH 334 3 C CH 3 CCH 3 D CH 3 CH 2 CHOH OH CH 3

1 B 2 C n H 2n + 2 O - 1 2 H 2 14n + 18 11 2 32 11 2, n = 1 CH 3 OH A 3 4 C CH 2 = CHCH 2 CH 2 OH B CH 3 CHO C 2 H 5 OH C 2 H 4 C 2 H 5 Br 1 2C 2 H 5 OH + O 2 2CH 3 CHO + 2H 2 O 2 C 2 H 5 OH H 2 SO 4 CH 170 2 = CH 2 + H 2 O 3 CH 2 = CH 2 + H - OH CH 3 CH 2 OH 4 CH 2 = CH 2 + HBr CH 3 CH 2 Br 8 96 10 4 m 3 99% 95% CH 2 = CH 2 + H - OH CH 3 CH 2 OH 22 4 L/mol 46 t 8 96 10 3 m 3 10 3 L/m 3 99% m C 2 H 5 OH 95% t m C 2 H 5 OH = 191 7 t 95% 191 7 t 113 1 H 2 2 3 1 8 g 5 4 g 335

1 2 Cu- SO 4 + 2NaOH = Cu OH 2 + Na 2 SO 4 HCHO + 2Cu OH 2 HCOOH + Cu 2 O + 2H 2 O CHO 3 CH 3 CH 2 CH 2 CHO 1 A B C D 2 CH 3 CHCH 2 OH CH A B C D CH 3 3 3 CH 2 = CHCH CHO A B KMnO 4 C 1 mol 1 mol Br 2 D 1 mol 1 mol H 2 4 A B C D 1 B 2 C D 3 CHO C = C CHO KMnO 4 H + H 2 C = C Br 2 H 2 1 mol 2 mol H 2 D 4 HNO 3 B 336

1 2 1 KMnO 4 H 2 2 HCHO + 2Ag NH 3 OH HCOONH 4 + 2Ag + 3NH 3 + H 2 O 2CH 3 CH 2 OH + 2Na 2CH 3 CH 2 ONa + H 2 11 6% 10 0 g 4 32 g C n H 2n O ~ 2Ag m = 58 m 216 10 11 6% 4 32 12n + 2n + 16 = 58, n = 3 CH 3 CH 2 CHO 119 1 2 1 CH 3 COOH CH 3 COO - + H + 2 1 CH 3 COOH A CH 3 COOH 337

B CH 3 COOH Na 2 CO 3 CO 2 C 1 mol /L CH 3 COONa ph 9 D 1 mol /L CH 3 COOH 2 CH 3 COOH 幈幇 CH 3 COO - + H + ph A H 2 O B CH 3 COONa C NH 3 H 2 O D H 2 SO 4 3 A B C D 4 KOH A B C D 1 CH 3 COONa CH 3 COOH CH 3 COONa ph 7 25 CH 3 COONa ph = 9 CH 3 COOH C 2 CH 3 COOH 幑幐 CH 3 COO - + H + CH 3 COOH ph H 2 O CH 3 COOH ph CH 3 COOHNa CH 3 COOH ph NH 3 H 2 O CH 3 COOH ph H 2 SO 4 CH 3 COOH ph D 3 B B 4 CH 3 COOC 2 H 5 + KOH CH 3 COOK + C 2 H 5 OH A C NaOH 338 1

2 3 1 NaOH 2 NaOH 3 NaOH A C 3 H 6 O 2 NaOH B B C B D D Cu OH 2 E 1 A B 2 B C 3 B D 4 D E 1 A B HCOOC 2 H 5 + H - OH NaOH HCOOH + C 2 H 5 OH 2 B C C 2 H 5 OH H 2 SO 4 CH 170 2 = CH 2 + 2H 2 O 3 B D 2C 2 H 5 OH + O 2 2CH 3 CHO + 2H 2 O 4 D E CH 3 CHO + 2Cu OH 2 CH 3 COOH + Cu 2 O + 2H 2 O OH O O C 2CH 3 CH C OH CH 3 CH CHCH 3 + 2H 2 O C O O O 1 339

2 1 2 A C H O 1 0 mol A 4 0 mol O 2 A A B 0 37 g B 25 ml 0 20 mol /L NaOH A B A B C n H 2n O 2 ~ NaOH m 1 0 37 0 25 0 2 m = 74 12n + 2n + 16 2 = 74 n = 3, A CH 3 CH 2 CHO B CH 3 CH 2 COOH 122 1 ph A B C D 2 A B C D 3 A B C D 4 HO CH 2 CH = CHCH 2 COOH A B C D 5 340 H H H 2 1 C C O H 3 4H H A 2 B 1 C 170 2 4

D Ag O 2 1 3 6 A C H 2 CH C H 2 C C H 2 3 C CH = CH C C CH3 2 CH3 = CH 2 CH 2 OH A A B A 3 C A D A 1 ph B 2 Mg + 2CH 3 COOH CH 3 COO 2 Mg + H 2 B 3 B 4 A 5 H 2 SO 4 1 170 2 4 Ag O 2 1 3 A 6 D A C H O A B C D E D 22 1 A B C D E F 341

2 A B B C A D D E A + E F 1 A CH 3 CH 2 OH B CH 2 = CH 2 C CH 3 CH 2 Br D CH 3 CHO E CH 3 COOH F CH 3 COOC 2 H 5 2 1 A B CH 3 CH 2 OH H 2 SO 4 CH 170 2 = CH 2 + H 2 O 2 B C CH 2 = CH 2 + HBr CH 3 CH 2 Br 3 A D 2CH 3 CH 2 OH + O 2 2CH 3 CHO + 2H 2 O 4 D E 2CH 3 CHO + O 2 2CH 3 COOH H 2 SO 4 5 A + E F CH 3 COOH + HOC 2 H 5 幑帯帯帯幐 CH 3 COOC 2 H 5 + H 2 O 1 5 0 g 1 35 L CH 3 COONa ~ CH 4 82 22 4 m = 4 94 m 1 35 5-4 94, 100% = 1 2% 5 2 2 3 20 g 2% CH 3 COOH ~ CH 3 COOC 5 H 11 60 130 1-2% m 2 3 20 342, m = 14 1 g

128 1 2 1 CHO 2 1 A C 6 H 12 O 6 B 6 C 6 H 2 O C D 2 A C 12 H 22 O 11 B C D 3 A B C D 1 B C 6 H 12 O 6 C 6 H 12 O 6 H 2 O B 2 343

C 3 CH 2 O CH 2 O CH 2 O C 12 H 22 O 11 D 1 2 1 180 40% 6 7% 180 40% 180 6 7% 180 53 3% C H O = 6 = 12 = 6 12 1 16 C 6 H 12 O 6 2 2 mol C 12 H 22 O 11 + H 2 O C 6 H 12 O 6 + C 6 H 12 O 6 1 180 180 344 2 x y, x = y = 360 g 132 1 A B C D 2

A B C D 3 A C 6 H 12 O 6 B C 12 H 22 O 44 C C 6 H 10 O 6 n D C 6 H 10 O 5 n 4 A C 6 H 10 O 5 n B C D 1 A C 2 n B 3 A B 4 n A 1 2 3 345

I 2 I 2 4 CHO 54% 2 0 t 85% 50% C 6 H 10 O 5 n nc 6 H 12 O 6 2nC 2 H 5 OH 162n 92n 2 0 54% 85% t m 50% m = 1 04 t 137 1 2 346 3 O R 1 C OCH 2 O 1 R 2 C OCH O R 3 C OCH 2 2 3 1 A

B C D 2 A B C D 1 C = C H 2 D 2 D 1 1 g 39 3 kj 17 2 /g 18 kj 2 A D E K 2 CO 2-3 + H 2 O 幑幐 HCO - 3 + OH - O R 1 C OCH 2 O CH 2 OH R 2 C OCH + 3NaOH 3R 1 R 2 R 3 COONa +CHOH O CH 2 OH R C OCH 3 2 11 5 t 85% 347

60% 348

C 17 H 35 COOCH C 17 H 35 COOC 2 CH 2 OH H + 3NaOH 3C 17 H 35 COONa +CHOH C17 H 35 COO C H 2 CH 2 OH 890 3 306 92 11 5 85% m C 17 H 35 COONa 60% m m C 17 H 35 COONa = 16 8 t m = 1 01 t 141 + 1 A Na 2 SO 4 B C D CuSO 4 2 A B C D 1 A 2 C 1 349

2 0 64% 2 2S = 0 64% M M = 2 32 = 10 000 0 64% 143 1 2 3 350 HgCl 2 4 1 CH 2 OH CHOH 4 CHO 2 3 4 1 A B C D 2 A B C D 3

A B C D CO 2 H 2 O 4 A B C D 5 A 1965 B C D 1 D D 2 D 3 H 2 CO 2 H 2 O C 4 CHO CHO O C H C D 5 B NH 4 2 SO 4 B 1 2 3 1 C 12 H 22 O 11 + H 2 O C 6 H 12 O 6 + C 6 H 12 O 6 2 C 6 H 10 O 5 n + nh 2 O H 2 SO4 nc 6 H 12 O 6 351

3 C 6 H 12 O 6 2C 2 H 5 OH + 2CO 2 C 17 H 35 COOCH C 17 H 35 COOC 2 + 3H OH H 2 SO4 CH 3C 17 H 35 COOH + 2 OH H CHOH C17 H 35 COO C H 2 CH 2 OH 1 50 t 80% 85% C 6 H 10 O 5 n + nh 2 O nc 6 H 12 O 6 162n 180n 50t 80% 10 3 kg t - 1 85% m C 6 H 12 O 6 m C 6 H 12 O 6 = 3 8 10 4 kg 3 8 10 4 kg 2 5 0 g 5 5 g C 6 H 12 O 6 ~ 2Ag 180 216 m 5 5 m = 4 58 g 4 58, 100% = 91 6% 5 3 95 6% 200 g 400 g 1 031 g/cm 3 C 12 H 22 O 11 ~ 4CH 3 CH 2 OH ~ 4CH 3 COOH 342 184 240 200 95 6% m n, m = 102 9 g n = 134 2 g 134 2 100% = 25 1% 400 + 134 2 352

134 2 60 400 + 134 2 100 1 031 ( ) = 4 32 mol /L 151 1 2 21 1999 1 5 1999 870 1 2 BaO 3 21 353

CO 3 155 156 1 A B C D A B C A C 3: 4 A B C D 1 A B C D 2 2 3 mx + n Y 幑幐 pz m + n = p X Z Y 4 A B C D aa + b B 幑幐 cc + dd C A n mol B n /2 mol C 3 /2n mol D n mol 354

A 1 a = b = c = d = 2 B D 3 5 0 2 mol /L 8 1 HNO 3 2 H 2 SO 4 3CH 3 COOH 4Ba OH 2 5NaOH 6CH 3 COONa 7KCl 8NH 4 Cl H + 6 KAl SO 4 2 12H 2 O ph 7 NH 4 2 SO 4 NH 4 NO 3 a L b mol NaOH a L c mol BaCl 2 NH 4 NO 3 8 1 mol C n H m O 2 a mol 1 C n + 1 H m + 2 O O 2 mol 9 C 4 H 8 O 10 1 1 CH 4 NH 3 H 2 O H H C H H 2 NH 4 HCO 3 NH 4 2 CO 3 2 NO 2 3 4 1 2 1 3 2 2 3 5 1 c Cl - > c NH + 4 > c H + > c OH - 2 2 < 1 < 3 < 8 < 7 < 6 < 5 < 4 6 KAl SO 4 2 12H 2 O K + 2 - + 2SO 4 + Al OH 3 + 3H + + 9H 2 O 355

7 356 b - 2c A 8 a + 1 5 9 2 10 1 A B C D 2 A NaBr B NH 4 Cl C KI D CaCl 2 3 A B C D 4 A B NaOH AlCl 3 C AlCl 3 D NaOH Fe 2 SO 4 3 5 A K + Na + HCO - 3 Cl - B Ba 2 + Na + AlO - 2 NO - 3 C NH + 4 Al 3 + NO - 3 Cl - D Na + Fe 3 + Cl - SO 2-4 6 A B C D 7 A C 3 H 8 B C 4 H 10 C C 4 H 8 D C 2 H 4 O 2 8 A B C D 9 A B C D 10 A B D 11

A B C D 12 A B C D 13 A B C D C n H 2 O m 14 A B C D 15 A 1: 2 B 1: 3 C 3: 2 D 1: 1 1 NaOH NaOH A D 2 NaBr NH 4 Cl KI CaCl 2 B 3 N 2 NaOH C 2 H 2 HCl A C 4 D 5 B 6 C 7 A 8 A B 9 D 10 A 11 C C 2 H 5 OH HCOOH C 3 H 7 OH CH 3 COOH B 357

B D 12 O 2 A 13 C H O C n H 2 O m C n H 2 O m H O 2: 1 C 6 H 12 O 5 C n H 2 O m CH 2 O C 2 H 4 O 2 A 14 4 1 2 3 4 C D 15 D 1 1 2 3 1 FeSO 4 Al + FeSO 4 = AlSO 4 + Fe 2 CH 2 = CH 2 + H 2 CH 3 CH 3 O O 3 CH 3 C OH O C 2 H5 幑帯帯帯幐 CH 3 C OC 2 H 5 + H 2 O 2 1 A 2 B 3 C 1 2NH 4 Cl + Ca OH 2 CaCl 2 + 2NH 3 + 2H 2 O 358

2 3 NH 3 3 A B C D AlCl 3 BaCl 2 FeSO 4 NaOH 1 A + B 2 B + D 3 C + D D 1 A B C D 2 B + D C D D 1 A BaCl 2 B FeSO 4 C AlCl 3 D NaOH 2 FeSO 4 + 2NaOH = Fe OH 2 + Na 2 SO 4 Al OH 3 + NaOH = NaAlO 2 + 2H 2 O 4 A 1 2 A 359

3 A B 4 B C 5 B NaOH D 6 A Ba NO 3 2 E 7 A A B C D E A KAl SO 4 2 12H 2 O B Al OH 3 C AlCl 3 360 D NaAlO 2 E BaSO 4 2 Al 3 + + 3H 2 O 幑幐 Al OH 3 + 3H + 3 Al 3 + + 3NH 3 H 2 O = Al OH 3 + 3NH + 4 4 Al OH 3 + 3H + = Al 3 + + 3H 2 O 5 Al OH 3 + OH - = AlO - 2 + 2H 2 O 6 Ba 2 + + SO 2-4 = BaSO 4 7 KAl SO 4 2 12H 2 O KAl SO 4 2 + 12H 2 O 5 1 2 CH 3 COOCH 2 CH 3 1 CaC 2 + 2H 2 O C 2 H 2 + Ca OH 2 C 2 H 2 + HCl CHCl = CH 2 nchcl = CH 2 CHCl - CH 2 n 2 CH 2 = CH 2 + H - OH CH 3 CH 2 OH 2CH 3 CH 2 OH + O 2 2CH 3 CHO + 2H 2 O 2CH 3 CHO + O 2 2CH 3 COOH CH 3 COOH + C 2 H 5 OH H 2 SO 4 幑帯帯帯幐 CH 3 COOC 2 H 5 + H 2 O 6

7 361

1 224 L NH 3 1 L 1 g/cm 3 c = n V = 224 L 22 4 L/mol 1 000 cm3 /L 224 L 17 g/mol + 1 000 g 22 4 L/mol 1 g/cm 3 = 8 5 mol /L 224 L w = m 17 g/mol m 100% = 22 4 L/mol 100% = 14% 224 L 22 4 L/mol 17 g/mol + 1 000 g 8 5 mol /L 14% 2 M 2MNO 3 2M + 2NO 2 + O 2 3 40 g MNO 3 NO 2 O 2 672 ml M 2MNO 3 2M + 2NO 2 + O 2 2 M + 62 2 + 1 = 3 3 40 g M = 108 672 ml = 0 03 mol 22 400 ml/mol M 108 3 1 L AlCl 3 FeCl 3 a mol NaOH NaOH NaOH b mol Fe 3 + FeCl 3 x AlCl 3 y 362 FeCl 3 3NaOH Fe OH 3 1 3 1 x 3x x AlCl 3 3NaOH Al OH 3 1 3 1 y 3y y

Al OH 3 + NaOH = NaAlO 2 + 2H 2 O 1 1 y y 3x + 3y = a 4a - 3b { x = mol y + a = b 3 c Fe 3 + = n 4a - 3b mol 4a - 3b = = mol /L V 3 1 L 3 Fe 3 + 4a - 3b mol /L 3 363

殞 檶檶檶檶 殞 檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶 殞 殞 1 357

2 3 358

1 1 2 2 3 1 2 3 359

4 5 2 1979 1992 6 1 2 360

7 8 + 1 2 9 1 2 3 1 1 2 361

3 2 1 1 2 3 2 1 2 3 1 1 2 3 2 1 2 362

3 1 2 1 2 363

1 2 3 1 2 3 4 4 5 6 1 1 2 2 1 000 500 500 1 2 3 4 5 1 364

2 3 4 365

1 1 2 3 2 1 2 3 366

3 4 5 1 1975 4 10 1983 1989 2 3 367

6 7 8 1 2 9 1 2 3 4 368

10 1 1 2 2 1 369

2 2003 1 2 1 1 2 3 2 1 2 1 1 2 2 370

1 2 371

1 1 2 3 372

2 3 1 2 3 4 1814 5 8 1 2 3 5 373

6 1 2 3 4 7 1 2 3 8 1 2 9 10 374

1 2 3 1 2 1 2 1 = 2 375

1 2 1 1 2 3 2 1 2 376

1 2 3 377

1 2 1 2 378

3 1 2 4 1 2 2 5 1 2 6 1 2 379

7 1 1 2 3 2 1 1 000 380

1 2 2 1 2 1 2 1 2002 8 15 5 381

2 1921 250 = 0 066 7 1 2 3 1 2 382

殞 檶檶檶檶 殞 檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶 殞 殞 7 1 D 2 D 1 2 3 4 15 1 D 2 D 383

21 ~ 22 1 D 2 B 3 C 4 B 1 1 2 3 4 2 11897 2 31919 41922 1 2 384

3 1921 1922 37 ~ 38 1 C 2 B 3 C 4 D 5 C 1 1929 1933 1 /3 2 /3 2 1 2 3 3 1935 1933 1936 385

4 1 2 5 1 2 44 ~ 45 1 A 2 C 1 20 30 2 1 2 1939 3 386

53 ~ 54 1 C 2 A 1 1939 2 3 30 1935 1939 9 1 60 ~ 61 1 A 2 D 1 1 2 387

2 1 2 3 4 5 67 1 A 2 D 1 388

2 1 2 1 2 74 ~ 75 1 A 2 D 1 1955 2 1973 1975 1 389

2 20 70 20 60 20 60 20 70 1987 84 1 C 2 D 1 2 1 /4 3 390 20 60

1968 1968 8 88 1 C 2 D 1 20 50 60 20 60 70 20 80 2 20 70 20 80 20 60 70 100 1 B 2 B 1 391

2 106 B 109 D 1 2 3 4 5 6 1 392

2 114 ~ 115 A 90 20 80 1992 393

125 1 A 2 D 1 2 1 2 3 394

殞 檶檶檶檶檶檶 殞 檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶檶 殞 殞 1 DNA 2 1 DNA 2 DNA 3 1 1 2 2 1 2 1 1 2 395

2 1 1 2 3 4 2 1 2 1 1 2 2 1 2 DNA 1 DNA 2 DNA RNA 1 DNA DNA 2 DNA 1 DNA 396

DNA 0 02% DNA DNA 1952 T 2 DNA 2 T 2 DNA DNA DNA DNA 1 DNA 4 A G C T DNA 4 2 DNA DNA ATP DNA DNA 1 DNA A + G / T + C = 1 2 DNA 1 DNA A DNA 4 B DNA C DNA D DNA D 2 1 1 DNA 1 A 4 DNA B 2 DNA C 2 DNA D 1 DNA 397 B

DNA 1 ~ 10 1 2 3 4 5 6 7 8 9 10 1 2 DNA ACGGATCTT DNA TGCCTAGAA DNA RNA UGCCUAGUU RNA RNA 398

1 A T G C 2 3 DNA 1 A B C D C 2 A DNA 3 B RNA 3 C RNA 3 D 3 C DNA DNA DNA DNA 1 2 3 1 A B 3: 1 C 1: 1 D 399

2 A B C D A B C B 1 B b 1 2 3 1 Bb Bb bb 2 P Bb Bb 1 2 B 1 2 b 1 2 B 1 4 BB 1 4 Bb F 1 1 2 b 1 4 Bb 1 4 bb 3 3 /4 2 R r 1 2 3 0 102 400 125 40 152 141

1 2 rr rr Rr Rr Rr rr 3 P Rr rr 1 /2R 1 /2r r 1 /2Rr 1 /2rr 3 1 Ⅱ 1 Ⅱ 2 Aa Aa 2 Ⅱ 1 Ⅱ 2 1 /4 3 Ⅲ 2 AA Aa 2 /3 4 5 401

1 F 2 1 4 /16 2 F 1 7 /16 2 AaBb 1 /2 3 CCEe CCEe 4 S aa SsAa ssaa 1 /8 1 A 9: 3: 3: 1 B C 1: 1: 1: 1 D D 2 A EeFf EeFf B EeFF eeff C EeFF EEFf D EEFf eeff C 1 2 R r T t 1 RrTt rrtt 2 Rrtt RrTt 1 402

2 1 RrTt rrtt Rr rr Tt tt 1Tt 1RrTt 1 1 1Rr 1 1tt 1Rrtt 1Tt 1rrTt 1 1 1 1 1rr 1 1tt 1rrtt 1 1 RrTt rrtt 1RrTt: 1Rrtt: 1Ttrr : 1ttrr 1 : 1 : 1 : 1 2 Rrtt RrTt 1RRTt: 1RRtt: 2RrTt: 2Rrtt: 1rrTt: 1rrtt : : : = 3: 3: 1: 1 P p R r F 1 PpRr PpRr PpRR pprr Pprr pprr pprr pprr 9 : 3 : 3 : 1 1 : 0 : 1 : 0 1 : 1 : 1 : 1 0 : 0 : 3 : 1 403

1 X h X H X H X H X h X h X h X H Y X h 2 1 /2 1 X Y 2 3 23 + X 23 + Y 1 X W w X w Y X W X w X W X w X W Y X w X w X W Y X w Y X W X w 2 X B X b A a 1 2 1 AaX B X b AaX B Y 2 404

AAX B X B AAX B X b AaX B X B AaX B X b AAX B Y AaX B Y 3 Ⅲ 3 Ⅰ 4 1 Ⅲ 3 X b Y Ⅲ 2 X B X b X B X B 2 Ⅰ Ⅲ 3 X b Y Ⅱ Ⅲ 3 X B X b 3 Ⅳ 1 1 /4 1 2 DNA 1 A B C 405

D D 2 AB CD B 3 A B C D B 4 A B C D A 1 DNA Dd dd 2 406 1 4

2 2 3 Ⅱ Ⅱ Ⅲ Ⅲ Ⅳ Ⅳ 4 Ⅹ Ⅹ 5 Ⅱ Ⅲ Ⅳ Ⅹ 1 A B C D B 2 A B DNA C D B 3 A B C D D 4 A B C D C 14 7 2 1 42 21 6 3 56 28 8 4 407

1 2 3 24 ~ 29 24 ~ 25 1 2 3 1 21 1 2 3 4 A 213 B 412 C 312 D 321 C 2 A B C D B h b X X 408

1 1 2 3 2 1 2 1 2 1 2 3 4 5 1 AA 409

18% Aa 78% aa 4% A a A 18% 82% B 36% 64% C 57% 43% D 92% 8% C 2 21 25 5 A B C D C 3 A B C D D 4 A B C D B 1 1 2 3 410

2 1 2 3 4 1 1 2 2 1 2 1 2 3 1 1 2 2 1 3 3 1 2 3 2 1 2 2 3 3 4 4 1 1 2 3 4 411

1 2 1 2 1 2 1 A B B B 412

2 1 2 1 2 1 2 3 4 413

5 6 1 80 ~ 81 2 1998 81 ~ 82 3 80 ~ 84 2 3 414 1 2 1 A B C D 2 A

A B C D C 3 A B C D B 1 A B C D C 2 1 2 3 A 1 < 2 < 3 B 1 > 2 > 3 C 1 = 2 = 3 D 1 = 2 + 3 3 2 1 B 1 8 7 10 4 J / m 2 a 1 4 10 4 J / m 2 a 1 2 100% 1 16% 2 100% 415

2 1 A B C D A 2 A B C D B 1 2 1 2 3 1 416

2 1 AB 2 BC 3 4 1 AB 2 BC NH + 4 3 4 417

1 1 2 2 1 1 2 2 1 2 1 2 3 418

1 2 3 4 5 A B C D D 419