CIP / ISBN Ⅰ Ⅱ Ⅲ Ⅳ G634 CIP ISBN /G http / /cbs pku edu cn pku edu cn

Transcription

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2 CIP / ISBN Ⅰ Ⅱ Ⅲ Ⅳ G634 CIP ISBN /G http / /cbs pku edu cn zyl@pup pku edu cn A

3 # 9 29 A B 3 A B A B A A B 1

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7 a 10 n 1 a < 10 n 0 1 π 槡 9槡 3-8 槡

8 3 1 槡 p p q q p q q = 1 p q km 2 km mm mm a 10 n 10 n 1 n 0 a 10 - n 10 n n a 5 a = 2

9 2 n n n + 1 n A 1-5 A 1 5 B 5 C A B 1 3 D - 5 C - 3 D A B 槡 3 C - 3 D 3 4 A 0 B C 槡 2 D 槡 m 3 A m 3 B m 3 C m 3 D m 3 6 a b a b A a b B - a b C a - b D - a - b

10 < B 1 a = 槡 6 a A B C D 2 a a = 0 a 槡 3 A B B A C C

11 A 1 8 B 1 2 C 1 4 D 3 4 C a a ( 3 ) 0 + ( 1 ) 槡 = = 4 2 = = 4 3 a b a b = b = b 3 2 = =

12 2003= 2006 A 1 4 C + 4 C 18 C A - 22 C B - 18 C C 22 C D 18 C 2 a b A ab > 0 B a > b C a - b > 0 D a + b > A 125 B 5 C ± 5 D 槡 A - 9 B 5 C - 5 D A 1 B 0 C - 1 D A - 2 A 3 B B A 1 B 5 C - 5 D mm 2 mm 槡 ( 1 2 ) 槡 槡 槡

13 ( 1 ) 槡 槡 槡 槡 6 B A 2 3 B 3 3 C 2 4 D a = 3 槡 b = 2 ab > 0 a + b A 7 B - 1 C 7-1 D a b c b + c > 0 2b - c < 0 3a + c < 0 4ab > ac A 1 B 2 C 3 D

14 A 50 B - 50 C 60 D aδb = ab - a - b + 1 3Δ4 = Δ5 5Δ- 2 < = > 6 a b a + b = 6 a b 7 R P U P = U2 R ~ A A B C D A B 3 4 C 3 3 D

15 A B C D ± 3 A 0 B 1 C 2 D 3 5 A B C D A > - - 2> B > > C - - 2> > D - - 2> > A = - 9 B = 3 C = - 6 D 5-3 = A 7 B - 7 C 0 D a a < x = 1 2= 2 1 = = = 6 4=

16 13 ( ) ( ) 槡

17 < a b c 1-2 O a b c cm AB 2 CD 3 EFGH 5 11

18 B A 2 B - 2 C 1 2 D ABC A 0 B 1 C 2 D 3 3 A - a a B - a a C 1 a aa 0 D - a a A 1 B - 1 C D % % A B C D π A 1 2 B 2 C π - 1 D 7 x A x < - 2 B x < 0 C x > 2 D x = 0 12

19 a a b 8 c d b c d - 1 = ad - bc A - 17 B 17 C - 7 D ab cd 槡 a + b + 槡 3 cd = 10 m = 3 n = 1m + n = ~ % 槡 ( ) 15 槡 槡 π + 槡 a 1-6 槡 4a 2-4a a

20 ABCD DAE = CBE = 45 AD = 2 ABE O 1 m 2 m A 2 3 m A 3 5 m A 4 8 m A 5 A 6 O A 1 14

21 x + a x + b= x 2 +a + b x + ab 1 # ax 2 + bx + ca 0 ax 2 + bx + c = 0 x 1 x 2 ax 2 + bx + c = ax - x 1 x - x A 3x 2 + 2x 3 = 5x 5 3 B a C a = 1 a 3 2 a = a D - x 5 - x 3 = - x x 2 2x A a a = a = 13 6 a B a = a - 1 = 1 a C - x 5 - x 3 =- x 2 = x 2 15

22 D ab2ab 2 + 3ab 22x 5 - x x 2 3-2x 3 2a - 3b 2b + 3a 4 x + 2 x x a 30% 8 A a B 0 8a C 1 04a D 0 92a % a = 1 04a 30% 8 4 3y 2 3-2y y2 - y + 1 A 1 B 2 C 3 D 4 3y 2-2y = y2 - y = 1 2 B 5 x x + y - 3 = 0 3xy + x 2 y - 2xy 2 x x + y x x + y - 3 = 0 x + 2 = 0 x + y - 3 = 0 x = - 2 y = 5 16

23 = = = x 3-12xy 2 2a 2 - b 2 + 4a + 4 3x 2-2x - 3 # 4x 2 - x - 1 # 52x 2-4x = 3xx 2-4y 2 = 3xx + 2y x - 2y 2 =a b 2 =a - b + 2 a + b =x - 3 x x 2 1 ± - x - 1 = 0 x = 槡 5 2 = ( 1 + x - 槡 ) ( x - 槡 5 2 ) 5 2x 2-4x - 2 = 0x = 1 ± 槡 2 = 2x 槡 2 x 槡 2 7 4x - 3 4x 2 + 5x + a a A - 6 B 6 C - 9 D 9 4x - 3 4x 2 + 5x + a x = 3 4 4x x 2 + 5x + a 0 a A A km 17

24 1 km 1 4 s km s > 3 A s B C 1 4s D s A a 10 a 5 = a 2 B 3a - 2a = a C a 3 - a 3 = 1 D a 2 3 = a % A 3 7 B 7 3 C A 2a 2 + a = 3a 3 B 2a - 1 = 1 2a D C - a 3 a 2 = - a 6 D - a 2 - a 2 = - 1 # 5 A 15a 2 + 5a = 5a3a + 1 B - x 2 - y 2 = - x 2 - y 2 = - x + y x - y C kx + y+ x + y =k + 1 x + y D a 2 - ab + ac - bc =a - b a + c 6 5 a x 7 7 1a 3 + 2a 2 b + ab 2 2x 4-16 # 32x 2 + 6x - 1 4x 2 - y 2-5x - 5y 5x 2 + 2x xy3x 2 y - x 2 y - 3xy 9 mm - 1+m 2 - m m - 1 6x 2 + 5x x = 2 y = 1 2 x + y x - y+x - y 2 - x 2-18

25 3xy B n n n 2 m + n = 9mn = 14 m 2 - mn + n 2 = 3 4x 2 + Q + 1 Q 4 x 2 + px + q = A x + 3 x - 4 C x - 3 x - 4 B x - 3 x + 4 D x + 3 x a b a > b

26 A a + b 2 = a 2 + 2ab + b 2 B a - b 2 = a 2-2ab + b 2 C a 2 - b 2 =a + b a - b D a + 2b a - b= a 2 + ab - 2b km 7 3 km 1 km km 1 km 19 x km x 7 4 cm 1 cm 2 cm 1 cm 1 x 2-4x + 3 x x 2-3x + 2 x x 2-4x + 3 x 2-3x + 2 x 2-3x + 2 = 0 x = 1 x = 2 x 1 x 2 x2-4x + 3 = 0 { x = 3 x 2-3x

27 2 1 x2 + 9x x 2 + 3x + x 2-9 x 2 + 6x a - b a + 2b a 2 - b 2 a 2 + 4ab + 4b 2 1 = x + 9 x x - 3 x + 3 = x x - 3 = 2x + 6 x + 3 x + 3 = 2 a - b 2 = 1 - a + 2b a + 2b 2 a + b a - b = 1 - a + 2b a + b = a + b - a + 2b = - a + b b a + b 3 x - 3 x 2-1 x2-2x - 3 x 2 + 2x x - 1 x = 槡 x = x x x + 1 x - 1 x x - 1 x - 3 = x + 1 x - 1 x + 1 x x - 1 = 1 x x - 1 = 2 x x = 槡 = = 槡 2 槡 x + y + z x = 2y z = 3xx 0 3x + 2y - z x = 2y z = 3x z = 32y = 6y x = 2y z = 6y x + y + z 2y + y + 6y = 3x + 2y - z 6y + 2y - 6y =

28 A x + y 1 x - y x y 3 A B 3 1 C 3 2 2x x x - 2 A 1 x + 2 B 1 x D 6 C 3x - 2 x 2-4 D 3x + 2 x A 1 a + 1 b = 2 a + b B a 3 2 = a 3 a a 2 + b 2 C a + b = a + b D a - 3 a 2-6a + 9 = 1 a u v f 1 u + 1 v = 1 u = 12 cmf = 4 cm f v 5 A 8 cm B 6 cm C 4 cm D 2 cm x x 2 - xy = 1 = 2y - x = - y - x 1 6 x 2x - 1 m = m - 1 m - 3 m 2-3m a = 2 3 a 2-2a - 3 a 2-7a + 12 x 8 x x + 1 = 22

29 x x x = 10 - a 2 b 11 x 12 2 ( ) a 3 ( 2 b ) - ( 1 3 ab) = 槡 x + 1 x 2 - x - x ( x 2-2x ) ( x - y + 4xy x - y ) ( x + y - 4xy x + y ) a + 1 a ( ) x 13 a 2-2a + 1 a a - 1 a a 3 b + a 2 b ab - a 2 + 2ab + b 2 1 b = 槡 5-1 a 2 - ab a b a = 槡 5 + B 1 1 m x x 2-2x + m A m 1 B m > 1 C m 1 D m < 1 2 x x x 2 + x + 1 x = 0 x + 1 x A 1-2 B C 1 D R 1 R 2 U I A R 1 > R 2 B R 1 < R 2 C R 1 = R 2 D ( ) 4 a a D 2a + 5 a 2 a + 3 a + a - 6 a A 1 B 5 C 2a

30 5 y = x2-2x + 1 x2 - x x 2-1 x x + 1 x y 槡 a 2 = a 槡 a 0 a 0 槡 a 槡 b = 槡 aba 0 b 0 槡 a 槡 b = a 槡 b a 0 b > 0 a 槡 2 = a a 1 槡 x x A x 3 B x 3 C x > 3 D x < 3 1 槡 a a x 3 - x 0 x > 3 C 2 x 12x 槡 槡 1 3x

31 3槡 - 4x 2-4x - 1 4x 槡 2-2x x x x x + 7 > 0 x > x 2-4x x x = x 2-2x + 2 =x > 0 x 槡 槡 槡 2 2 槡 3 - 槡 槡 3 ab 3 ( 槡 ab - ) 槡 ab - b a + 槡 ab a - b 槡 槡 3 3a 4 2 < x < 4 槡 x x < x < 4 x - 2 > 0 x - 4 < 0 = x x = 2 槡 a 2 槡 a 2 = { aa 0 - aa < m = 2 + 槡 3 1-2m + m2 - 槡 m 2-2m + 1 m - 1 m 2 - m 1 m = = 2 - 槡 3 < 槡 3 m m m - 1 mm - 1 = m = = 2 - 槡 槡 3 = m mm - 1 = m m 25

32 A 1 槡 3 3 A 槡 24 B 槡 12 C D 槡 2 槡 18 2 槡 a - 1 A a < 1 B a 1 C a 1 D a > 1 3 獉獉 A 槡 2 槡 3 = 槡 6 B 1 槡 2 = 槡 C 2 槡 槡 2 = 5 槡 2 D 槡 槡 2 - 槡 3= 槡 2 - 槡 A 槡 8 槡 2 = 2 B 2 槡 槡 2 = 5 槡 6 C 槡 = - 6 D 5 槡 3 5 槡 2 = 5 槡 6 5 槡 8 - 槡 2 槡 A - 2 B 槡 2-2 C 2 D 4 槡 a = 5b 槡 2 = 3 ab > 0 a + b A 8 B - 2 C 8-8 D y 7 槡 15 槡 槡 23 x 槡 槡 A 1 B 2 C 3 D 4 8 槡 槡 2-1= 9 槡 2 10 x + y 槡 x = 0 3x + 2y = 11 x = 槡 3-1 x - 1 x - 1 x ( x ) 26

33 B x - 槡 x 2-8x A x B 1 x 4 C x 1 D x 4 2 a 1 槡 1 - a x - 5 x A a - 1a 槡 - 1 B 1 - a1 槡 - a C a 槡 a D 1 - aa 槡 a 0 槡 3a 2 = 4 ( 1 x x 2-3x + 2 ) 1 - x 2 x = 2 + 槡 3 5 x = 槡 ( x + 1 x 2 - x - x x 2-2x + 1 ) 1 x ( ) 1 6 x - y - 1 x + y 2y x 2-2xy + y 2 x = 1 + 槡 2y = 1 - 槡 A a b 2 A 2a - b B 2a - b C a - 2b D 2a - 2b 2 A a +b - c + d= a - b + c - d B a - b - c + d= a - b - c + d C a - b - c + d= a - b + c - d 27

34 D a - b - c + d= a - b + c + d 3 A x 2 x 3 = x 6 B - 2x 2 2-4x 2 = - x 2 C x 2 3 = x 8 D 3xy 3 = 9x 3 y 3 4 3xy 2 A xy 2 B 2xy C - x 2 y D 3x 2 y 2 5 a 2-4 A a - 2 a + 2 B a + 4 a - 4 C a D a A C x 6 x 2 = x3 B x + y x + y = 0 x 2 + y 2 x + y = x + y D - x + y x - y = xy 2a 3x 2 y 3 xy 2 A xy B 3xy C x 2 y 2 D 3x 2 y 2 8 槡 3 A - 槡 3 B 槡 12 C 槡 18 D 槡 3 9 a 10% 10 2x 2-4xy + 2y 2 = 11 x = 2 12 a 槡 a a 2 b 2 +8a 6 b 2-2a 2 14 a + b 2 - a - b 2 15 ( ) 2x x x x + 3 x x

35 16 槡 18 - 槡 20 + 槡 槡 5 槡 x 2-3y 2 + 5x 2 +4y 2 + 7xy x = - 1 y = 1 - 槡 = = = = = = x - 3 x x = x - 3 x + 1 x x - 1 x - 3 = x + 1 x - 1-3x + 1 3x + 1 x - 1 = x - 3-3x = - 2x

36 B a b a b A 10b + a B ba C 100b + a D b + 10a ABCD AB = a AD = b LMPQ RSTK LM = RS = c A bc - ab + ac + b 2 B a 2 + ab + bc - ac C ab - bc - ac + c 2 D b 2 - bc + a 2 - ab 槡 x - 1 x - 2 x A x 2 B x 1 C x 1 x 2 D x > 2 4 x 3 = y 4 = z 5 3x + 4y - z x - y A 12 B - 12 C 20 D a + 2 a a A 0 B 1 C - 1 D 2 a a 2 =- 5 2 b 3 =- 5 3 a + b A 0 B - 10 C 0-10 D x 7 x = 槡 2 x - 1 A 4 + 槡 2 B 6-3 槡 2 C 槡 2-1 D 槡

37 8 a < 0a 槡 2 b A a 槡 b B - a 槡 b C a 槡 - b D - a 槡 - b = = = = n n 10 2x m - 1 y 2 - x 2 y n - m n = 11 4a b = < x < 3 槡 x x a - 3b 2-2a + 3b 2a - 3b+2a + 3b 2 a = ( ) x 2 + 2x 1 + x x - 2 x + 1 x = 槡 槡 3 = 2 2 槡 槡 8 = 3 3 槡 8 34 槡 4 15 = 4 4 槡 槡 5 24 = 5 5 槡 ax 5 + bx 3 + cx + 9 x = x = 1 31

38 17 x + 1 x = 槡 5 2x2 x 4 - x 槡 = 2S 1 = 槡 1 2 槡 = 3S 2 = 槡 2 2 槡 = 4S 3 = 槡 nn 2 OA 10 3 S S2 + 2 S S a7 < a

39 x x = 3 - x x x= 18-2x - 1 3x x = 18-2x + 2 3x - x + 2x = x = 22 1 x =

40 1{ 2x + y = 4 3x - 2y = 13 2x + 1-3y - 1= 10 2{ 1 2x y - 1= 20 2 { x + y + z = x - y = 7 2 y = 3z 3 x = 3 1 { y = y - 1= 10 y = 2 y = 2 1x = 11 2 { x = 11 2 y = x - 3z = x + 3z + z = 35 5 x - 3z = { x + 4z = 35 5 x = 19 { z = 4 x = 19 z = 4 1 y = 12 { x = 19 y = 12 z = % A B 34

41 C D 1 a 0 75a 8 = 6a a + 0 7a 7 = 5 9a a + a + 0 7a 6 = 5 95a B B 4 1 y xkm 2 km y x y = kx + b x = 10 y = 26 x = 20 y = 46 10k + b = 26 { 20k + b = 46 { k = 2 b = 6 y x y = 2x m km/h n km/h { 1 m - n= 16 = 20 2 m + n= 16m { 3 n = 4 35

42 20 km/h 4 km/h A 1 A ac = bc a = b C a 2 = b 2 a = b B a c = b c a = b D x = 6 x = x = 3 A 3 B - 3 C D = x x A B C D x k - 2x + 1 = 0 x = - 1 k = 5 x = - 1 mx - ny = 5 { y = 2 { 2mx + 3ny = - 20 m = n = % CaCO 3 CaO CO { x - 4y = - 1 2x + y = 16 { x 22 - y = 1 3x + 2y = 10 B 4x + 3y = 1 1 { ax +a - 1 y = 3 x y a 36

43 A 4 B 10 C 11 D 12 2 x - y = 4 x + y = 7 x + y A ± x B ± 11 C ± 7 D ± x + 4y = 16 { 5x - 6y = 33 x - 2y = y 4 x k + b x 1 1 x x x y x + z - 3 = 0 x + y + z { y = x 7 1 z = 2x x + y + z = 4 { x + y = 3 2 y + z = 1 z + x = 4 4x - 5y + 2z = 0 3 { x: y: z x + 4y - 3z =

44 % = 20% 10 A H km 180 H A B C D E F G H H km B E = A F % 30%

45 1 y - 3y y y - 73y y y - 21y y y - 21y + 4y y y 10 2 { 2x + 5 3x + 21 x - 1 < x x x < 3-1 x <

46 3x - 2 2x x x - 2 2x x x x - 2 2x x 1 y x y = 150 6x x = - 400x x 20 2 y = - 400x x x = 20-5 = A 1 a < b 1a + 3 b + 3 2a - 5 b a 2b 4- a - b 5b - a a 2 - b 7 2 7x - 3x - 8< x 2 40

47 A 1 B 2 C 3 D % A 6 B 7 C 8 D 9 x > 3 4 { x > a x > a a A a < 3 B a = 3 C a > 3 D a 3 x + 2y = 1 5 { x - 2y = k x y 1 k A - 3 < k < 1 B - 3 k < 1 C - 3 < k 1 D - 3 k 1 - x < 0 6 { 2x - 1 < x x x x < 1 - x { 1-2x < 3 8 2x - 1 5x B 1 2a - 3< 2 - a ax - 4 < x - a 3 5 A x < 1 5 B x < a - 5 a C x < a 5 - a D x > a 5 - a 2 15 A 2 B 3 C 4 D 5 41

48 x + y = 3 3 { x - 2y = a - 3 a 2x - a < 1 4 x - 2b { > 3-1 < x < 1 a + b - 1 { x + 2 < 0 5 x - 4 < 0 x + 6 > % 20 xx > 20 x = 8 10 A B A B / / /

49 10 ax 2 + bx + c = 0a 0 Δ = b 2-4ac Δ > 0 Δ = 0 Δ < 0 ax 2 + bx + c = 0a 0 x 1 x 2 x 1 + x 2 = - b a x 1x 2 = c a x 1 x 2 1 x 2 - x 1 + x 2 x + x 1 x 2 = x = 16 23x = x5 - x 3 2x = 42x + 1 4x 2 + 5x + 3 = x = 16 9 x - 2= ± 4 3 x 1 = x 2 = x xx - 5= 0 x - 5 4x - 15= 0 x 1 = 5x 2 = x x = 0 2x = 0 x 1 = x 2 =

50 4Δ = = 13 > 0x = - 5 ± 槡 x 1 = 槡 13 x 2 2 = 槡 13 2 x = - 5 ± 槡 13 2 x 2 + kx - 1= 1 1 k 2 k x 1 x 2 x 2 + kx x 1 x 2 = 7-3x 1 + x 2 k 1 x 2 + kx - k - 1 = 0 Δ = k 2 + 4k + 4 = k k x 2 + kx x 1 x 2 = 7-3x 1 + x 2 x 1 x 2 x 2 + kx 1 1 = k + 1x 1 + x 2 = - kx 1 x 2 = - k - 1 k k - 1= 7 + 3k k = - 2 k > 0 k 3 x a 2-1 x 2 - a + 1 x + 1 = 0 a 1 x 1 x 2 x 1 x 2 = a 2-1 = 1 a 2-1 = 1a 2 = 2 a = ± 槡 2 a = 槡 2 x 2 - 槡 x + 1 = 0 Δ = 槡 = 2 槡 2-1 > 0 a = - 槡 2 44

51 x 2 + 槡 2-1 x + 1 = 0 Δ = 槡 = - 2 槡 2-1 < 0 a = 槡 2 a a x = 16 x 1 = 0 2 = 20% x 2 = % 4 = % = A 1 5x 2-7x + 5 = 0 A B C D 2 x 2 + 8x + 7 = 0 A x = 9 B x = 9 C x = 16 D x = 57 3 x 2-3x + 2 = 0 x 1 x 2 x 1 + x 2 45

52 A - 2 B 2 C - 3 D x x 2 + px + q = 0 x 1 = 3 x 2 = 1 6 4x 2-4m + 1x + m 2-1 = 0 0 m = 7 1 x - 3 = 4 22x 2 = 3x 3x 2 + 6x + 9 = 0 4x 2-4x - 3 = 0 53x 2 + 2x - 1 = 0 1 ( ) 6x x = 2 8 x 2 + x - 1 = 0 x 1 x 2 1 x x x 1 - x 2 B 2 x 2 + x 1 x 1 x 2 1 a b c ABC c - b x 2 + 2b - a x + a - b = 0 A B C D 2 3x 2-4x = - 1 x 1 x 2 + x 1 x 1 x x 2-3x + m = 0 m 46 x 2

53 5 x x 2 - k + 1 x - 6 = 0 2 k 6 x x 2-2a - 1x - b = 0 1 a b 3 2 a b # 47

54 # 1 1 x 2x - 5 = x 2x + 1 x x 2-1 = 1 # 3 6 x x - 1 = 1 1 x = 2x x = 0 x = 0 2 x = x 2-1 2x = 2 x = 1 x = x + 1= x 2-1 x 2 + 3x - 4 = 0 x 1 = 1 x 2 = - 4 x = 1 x = { y = x x 2 + y 2 = 5 2 2{ x + y = 10 1 xy = x 2 +x = 5 x 1 = 1 x 2 = - 2 x 1 = 1 x 2 = - 2 1y 1 = 2 y 2 = - 1 x 1 = 1 x { 2 = - 2 y 1 = 2 { y 2 = x = 10 - y y y = - 24 y 1 = 12y 2 =

55 y 1 = 12y 2 = - 2 3x 1 = - 2x 2 = 12 x 1 = - 2 x { 2 = 12 y 1 = 12 { y 2 = - 2 2x + a 3 x - 2 = - 1 a 2x + a = - x + 2 3x = 2 - a x = 2 - a a > 0 a < 2 3 2x + a a < 2 x - 2 = - 1 x = 2 - a 3 x = 2 - a 3 x = 2 - a = 2 x = 2 = 2 - a 3 3 2x + a = - x + 2 x = 2 - a 3 x = 2 - a > 0 x = 2 - a a < 2 a - 4 a < 2 a m 25% 20 x m x x = 20 #

56 x 2x x + 1 2x - 10 = 1 12 x 1 = 3 x 2 = 20 2x - 10 = y 12y + 12y - 150= y = = = < A 1 2x - 5 x x A B 5 3 C 7 3 D x A C 80 x - 5 = 70 x 80 x + 5 = 70 x B D 80 x = 70 x x = 70 x - 5 x + a 3 x - 1 = a a A - 1 B 1 C ± 1 D - 2 x - y = 1 4 { x 2 - y 2 = 3 50

57 x = 2 x = - 1 x = 3 x = 1 A { B y = 1 { C y = - 2 { D y = 2 { y = 2 5 x + 1 x 2-3 = 1 x x = y = 2x { y 2 = 4x x x - 1 = 2 x x x x - 2 = 2 x x - 1-2x + 10 x 2-6x = - 2x + 10 x 2-4x x 2-6x + 8 = 1 x 2-4x x 2-6x + 8 = x 2-4x x = x = x x = x 2-7 x + 2 = 1-3x x ( ) 3 x x = 2x + 2 x 4x - 1 x 2-14 = 5x - 5 x km 51

58 154 km h B x x x - 1 = m x - 1 m A - 1 B - 2 C 1 D 2 2 x k x = x x k 3 x x - x 2 + 2x = 1 4 x 2-3x + m - 1 = 0 1 m km 480 km 45 km/h 6 4 m 3 5m 3 5m 3 2 5m 3 /m x x 52

59 A x x + 2 A x > 2 B x < 2 C x 2 D x 2 2 m > - n A n < - m B m - n < 0 C m + n > 0 D a 2 m < a 2 n 3 x x 1 = 1 x 2 = 2 A x 2 + 3x - 2 = 0 B x 2-3x + 2 = 0 C x 2-2x + 3 = 0 D x 2 + 3x + 2 = x x 2 - x = 1 x - 2 A x= 1 B x= 1 C x= x - 2 D x= x A x 2 + x + 1 = 0 B x 2 + 2x + 1 = 0 C x 2-2x - 1 = 0 D x 2 - x - 2 = g A

60 A 2 g B 3 g C 2 g 3 g D 2 g 3 g 7 x 2 + 2x - 5 = 0 A 2 5 x + y = 7 # 8 xy x = 2 A { B y = 5 B { = 12 x = 6 x = 4 { C y = 2 { D y = 3 C x = D x 2-2x - 1 = 0 x = - 3 { y = x 3x 2 + mx + m - 6 = 0 0 m = x > x + 2y = 2 13 { 2x + y = 0 x > x x - 5 x x x

61 5 x x x x B 3 24 x + 5 > x { 1 2x + 7 > 3x { x A 2 < x < 8 B 2 x < 8 C x < 8 D x 2 x + 9 < 5x { x > 2 m x > m

62 A m 2 B m 2 C m 1 D m > 1 4 x - 2 2x - 3 = 2 3-2x A x = 0 B x = 1 5 C x = 4 D 5 x x 2-2x + a = 0 a A a 1 B a < 1 C a - 1 D a 1 6 x 2x 2-2x + 3m - 1 = 0 x 1 x 2 x 1 x 2 > x 1 + x 2-4 m A m > B m 1 2 C m < D < m x x 2 + 2k - 1 x + k 2 = 0 k A k < 1 2 B k 1 2 C k > 1 2 D k % A 106 B 105 C 118 D x 9 2x x - 3 x = 5 x 2x - 1 = y y x + 2y = p x { 4x + 3y = p - 1 x > y p

63 x 2-2x = x x - 2 { x - 3x x > x a - x 15 x = bx - 3 x = 2 a 0 b 2 3 a 0 b - b a #

64

65 ABCD A AB y B C D AB y B A AB x E AE = 1BE = AB - AE = 3 B 59

66 3 AB y x B = x A = - 1 B- 1 3 C3 3 D3-1 x y Px y x y y x x 1y = - 3x - 1 3y = 槡 x + 2 x - 3 2y = 槡 4 - x 4y = x + 3 x 2 + 5x x 4 3x - 2 x 3 4x - 2 x

67 0 ~ C 24 C x y y x y x y = { 2xx x - 4 x > 4 C 61

68 A A B C D A B C 1-3 D ABCD A- 1 3 B- 1-2 C4-2 D A C 4 3 B 4-3 D A1 2-1 A' AA' A x B y C D Ax 5 y = 1 x + 1 x A x - 1 B x > - 1 C x 1 D x 0 6 s t 62

69 A 8 14 B C D Ax y x y4 xy < 0 Bx y 9 a b x V a b x 10 A B C D 63

70 A 0 05 / B 50 / 0 02 / 1 y x 2 20 B 1 獉獉 A y = x B y = - x C y = x 2 D y = 1 x O 0 ~ 90 ABC S n S n

71 獉獉 A 13 B 14 C 23 D ABC 3 6 A 1 B 1 C 1 A 1 B 1 C 1 B

72 90 A 2 B 2 C 2 A 2 B 2 C 2 C 2 2 A 3 B 3 C C C 1 C 2 C C 1 C OABC AOC = 60 OC = 3 CB = 2 OABC

73 V 3 t A B C

74 y = kx + bk x y > 0 2 x y = 0 3 x > 0 y y = x x > - 1 y > 0 2 x = - 1 y = 0 3 x > 0 y > x 0 x 0 x 0 y 0 y 0 y ABC AB = 6 AC = 4 D E AB AC ADE = C AD = x CE = y 1 y x

75 2 1 A = A ADE = C ADE ACB AD AC = AE AB AE AD = AB AC = 6 4 = 3 2 AD = x AE = 3 2 x CE = y y = x y 0 x 8 3 x 0 < x km/h 4 h 4 km/h 1 km/h y 2 3 x 25 h ykm/h xh 1 2 km 4 h 4 2 = 8km/h 4 km 10-4h = 32km/h 69

76 = 32h + 25 = 57h y = kx + b { 25k + b = 32 57k + b = 0 { k = - 1 b = 57 y = - x x ~ x x10 x 25 y 1 y 2 y 1 = x y 1 = 150xy 2 = x - 1 y 2 = 160x y 1 = y 2 150x = 160x x = 16 y 1 > y 2 150x > 160x x < 16 y 1 < y 2 150x < 160x x > ~ 25 x = x x A B C x A y B y x x A B C 70

77 W W x A B C A B C A B C 1 A x B y C 20 - x - y 2 2x + 2 1y x - y= 42 y = - 2x + 20 A x B - 2x + 20 C 20 - x - - 2x + 20= x x 2-2x { 2 x 9 x x 2 W= 6 2 2x x x W = x Wx x = 2 W W= = A 2 B 16 C 2 1 x 2 x 9 x 2 k > 0 x y k < 0 x y A 1 y = x + 1 A B C D 71

78 2 y = kx + b x < 0 y A y > 0 B y < 1 C - 2 < y < 0 D y < cm 5 cm ycm xh 4 y = kx + 2 y x y = - 2x km 3 km 3 km km 1 km x 3km y 72

79 h d 1 h d d cm dcm hcm B 1 y = kx - k y x A B C D 獉獉 h t 73

80 3 y = ax + b ab 0 < > = 4 y = x - 1 A B C ABC C A2 0 B0 4 1 = 2 C A 20 B 0 t S y = - 4 x + 4 x 3 y M N 1 M N 12 2 P P 5 y = x + 4 P

81 A0 4 B2 0 x y C D DB = DC CD ABCD A 0 2 y = x + t l t l l S 1 t S = 3 2 S t 75

82 y 1 = kx + b y 2 = m x A- 2 1 B1 n 1 2 x 1 A y = m x m = = - 2 B1 n y = - 2 x n = y = = - 2 A- 2 1 B1-2 y = kx + b 1 = - 2k + b { - 2 = 1k + b { k = - 1 b = - 1 y = - 2 y = - x - 1 x 2 x < < x < 1 Am n y = k x m n k x y 2 pkpa Vm m kpa 76

83 1 p = k V A p = k V k = = 96 p = 96 V V= 1 m 3 p = 96 1 = 96kPa 3 p 140 kpa kpav > V 0 V m3 3 y = ax 2 + bx + c a b c A a < 0 b < 0 c > 0 B a < 0 b < 0 c < 0 C a < 0 b > 0 c > 0 D a > 0 b < 0 c > a < 0 y b c > 0 - < 0 a < 0 2a b < 0 A y = ax 2 + bx + c a y c b x b 2-4ac AB OC

84 O OC y y = ax OC = 0 6 AC = 0 6 A y = ax 2 a = 5 3 y = 5 3 x2 D 1 D y = 5 3 x2 D 1 D 2 y 1 = y 2 = C 1 D 1 = = 0 53C 2 D 2 = = 0 33 y 2C 1 D 1 + C 2 D 2 + OC = m 1 xm ym 2 y x x 2 x 78

85 xm y = x18 - x x 0 < x < 18 2 y = - x x = - x x = 9 0 < x < m 2 - b a = - 1 < 0y x = - 2a = = 9 0 < x < 18 y = 4ac - b2 4a = = 81m2 x 6 x 1 x 2 x x 2 - kx + k - 1 = 0 y =x 1-2x 2 2x 1 - x 2 y = 2x 2 1-4x 1x 2 - x 1 x 2 + 2x 2 2 = 2x2 1 + x2 2-5x 1x 2 = 2x 1 + x 2 2-9x 1 x 2 x 1 + x 2 = kx 1 x 2 = k - 1 y = 2k 2-9k - 1= 2k 2-9k + 9 = 2 k - k = ( ) Δ = - k 2-4k - 1= k > 0 k = 9 4 y

86 m x 0 01 ABDC AB = CD = 2x7x + 4y + πx = 15 y = 15-7x - πx S = πx xy y = 15-7x - πx 4 S = πx x15-7x - πx = - 3 5x x b x = m 2a x S 4 02m 2 y S x y 1 m m 6 m 1 Sm 2 xm 2 x 3 x ABC AD BCBC = 8 m AD = 6 m EFGH HG AD D' EF = HG = x m S EFGH = Sm 2 80

87 AD' HG BC AHG ABC AD = HG BC AD' 6 = x 8 AD' = 3x 4 HE = D' D = AD - AD' = 6 - S = HEEF = x 6 - ( ) 3 4 x = x 3 4 x2 + 6x 2 EF BC x 0 < x < 8 3 S = x2 + 6x = - 3 x x = m 2 A 1 1 y = - x A2m m A - 2 B 2 C y =x A x = - 1 C x = - 2 B x = 1 D x = 2 D y = x 2 2 A y = x 2-2 B y =x C y = x D y =x y = x y

88 y = ax 2 + bx + c A B C 1 A B C 2 7 y = x 2 + bx + c x A2 0 1 b c 2 y B O OAB B 1 2 ABC x y y x y = ax 2 + bx + c a + b + c < 0 2a - b + c > 0 3abc > 0 4b = 2a A 4 B 3 C 2 D

89 3 y = ax + c y = ax 2 + c 83

90 ( ) ( ) ( ) 4 M y N y P y 3 y = k x k < 0 y 1 y 2 y 3 A y 2 > y 3 > y 1 B y 2 > y 1 > y 3 C y 3 > y 1 > y 2 D y 3 > y 2 > y A C y = 1 x AB y x B CD y x D ABCD S A S = 1 B 1 < S < 2 C S = 2 D S > y x 7 y = k x k > 0 x y x y 12 8 y = ax 2 + bx + c y

91 ym 2 Rm y = - 5 x A2 2 y A x

92 y x y x 2 z x = - - x OABC O Ax C y D DC B C OD D DE OD AB E OE CD t 1 t = 1 3 DE COEB s S t 86

93 A P- 1 x A B C D 2 y = - x - 1 A B C D 3 y = k x A - 2-3B 3 2 C 3-2 D y =x A x = - 3 C x = - 2 B x = 3 D x = a b 135 b < a 135 b = a y t Ax 1 y 1 Bx 2 y 2 y = kx + b k < 0 x 1 > x 2 y 1 y 2 A y 1 > y 2 B y 1 < y 2 87

94 C y 1 = y 2 D y 1 y 2 7 ABCD P Q AB AD APQ = 45 APQ y AP x A y = x 2 B y = 1 2 x2 C y = x D y = x P y = 1 x 4-2 PA x A OAP S S A S = 1 2 B S = 1 C S > 1 2 D 1 2 < S < y = x y x y x 11 a A2a a a = M C t M = t 3-5t t = 0 12 t = C km y x km/h 88

95 y = kx + b A B x C 1 2 AOC 15 x 2-6x + 4 = - 1 y = x 2-6x y = ax 2 + bx + c x A1 0 B3 0 y x

96 y C x y 2 1 y x B y = ax 2 + bx + c A a > 0 B c < 0 C D x 2 y = x 2 - bx + 8 x 4-7 b A 4 槡 2 B - 4 槡 2 C ± 2 槡 2 D ± 4 槡 2 90

97 3 y = kx + b y = 1 x A k < 0 b < 0 C k > 0 b < 0 B k < 0 b > 0 D k > 0 b > 0 x 4 x 1 y 1 x 2 y 2 x 3 y 3 y = - 3 x 1 < 0 < x 2 < x 3 A y 1 < y 2 < y 3 B y 2 < y 3 < y 1 C y 3 < y 2 < y 1 D y 1 < y 3 < y t h y = ax 2 + bx + c a < 02 b > 03 c < 04 b 2-4ac > 0 A 1234 B 123 C 14 D ABCD DAB = 60 AB = 5BC = 91

98 3 P D DC CB B P x P AD AP y y x y x 8 y = x 2 + bx + c 3 2 y = x 2-3x + 5 A b = 3 c = 7 C b = 3 c = B b = - 9 c = - 15 D b = - 9 c = 獉獉獉 10 Pm n y = - 2 x > 0 x y = - x - 2 m n 11 y = x 2 + 2x y = x 2 + bx + c 4-11 y < 0 x m 2 m y = x

99 1 4 m 2 m O A c α βoa= 1 km tanα = 9 28 tanβ = 3 8 O 5 km 3 D C 3 km 4 km E C y x x 20 y x x

100 16 hm h = - 4 9t t ts 1 t = 1 t = t t = 0-4 9t t = OABC O Ax C y OA= 5 OC = AC 2 M AC BO M y = x2 + kx k 3 CE B x D D AB CD x B D AD BC E A- 2-6 C1-3 1 E y 2 A E C 3 AB DC kk > 0 AD BC E' 4-17 AE' C S k 94

101

102 #

103 % 80%

104 % 49% % = 20% % 360 = % 31% % 360 = % 49% 49% a b c

105 0 ~ ~ 69 5 a ~ b 79 5 ~ c = 0 02 c c = 2 = 100a = = b = 25 = = 68% A 1 A B C D A 48 B 52 C 52 D

106 A B C D A 12% B 13% C 16% D 20% % 10% 30% 50%

107 2 B x

108 % % % % % 1 102

109 ~ ~ ~ ~ ~ M 4 71 ~ 80 5 A PA 1 P = 1 0 P = 0 A 0 < PA<

110

111 % P = 1 2 P = % ~ P = ~ % 105

112 A 1 3 A 1 6 B 1 3 C A 0 34 B 0 17 C 0 66 D A B C 0 D A B 1 17 C A B C D D D

113 B 1 95% kg kg A 1 2 B

114 A A B C D A 3 5 B 3 C 0 5 D m 2 30 m 2 30 m 2 40 m 2 30 m A B 108

115 C D 4 A B C D A 12 B 3 C 4 8 D 13 6 A B C 1% 100 D 30% 30% 7 A B C D A 1 5 B 2 5 C D 2 3

116 # cm 1: 3: 5: cm 160 cm A B C D 110

117 A B C D : 3: 1 1: 4: % 10 kg /kg 1 1 /kg kg

118 ~ B A 2005 B C D 112

119 A B C D A B C D 4 x 1 x 2 x 3 x n x 珋 x x x n + 8 A 珋 x B 珋 x + 8 C 8 珋 x D 珋 x A B 7 12 C D A 1 6 B 1 3 C A C B D D P 1 P 2 A P 1 = 2P 2 B P 1 = P 2 C P 1 = 3P 2 D P 2 = 2P 1 x 2 113

120 ~ A B C A 50 B 40 C mm 6 mm

121 A B C A 40 69% B 30 57% C 22 12% A B C A B C A B C A B C A

122 # AOC = BOC = 90 AOC BOC 116

123 AB CD EF 1 = 2 AB CD 1 = 2 1 = 3 2 = 3 AB CD ABC D E AB AC CD BE CD BE DE DBCE DB EC BD CE A CD BE CD BE 117

124 A 1 A A B C AB B AB C D C AB 2 A B C D 3 60 A B C D # 4 A B C D # 7 a = b a = b #

125 B ABC AD ABC AE = AD 2AB = AC 3OB = OC 4 B = C 119

126 B AC D E AB BC 1 2 AC = 20 EC = 4 AD A B C D E AD AB = AC - BC AB AD E BC BC = 2EC = 8 AC = 20 AB = AC - BC = 20-8 = 12 D AB AD = 1 AB = 6 2 AB BA n

127 n = = = = n AB CD APC PAB PCD APC + PAB + PCD = APC = PAB + PCD 3 APC = PCD - PAB 121

128 4 APC = PAB - PCD A 1 OC AOB OC AOB A AOB = 2 AOC B AOC = BOC C AOC + BOC = AOB D AOC = 1 2 AOB AB CD OEO CD O AOE DOB A B C D l 1 l 2 l 3 l 1 l A 1 = 2 B = 180 C = 90 D = A 15 B 75 C 145 D AB CD O OE AB

129 A= 48 A AOD = 127 BOC = AB CD ABE = 120 ECD = 25 BEC = = 50 2 = 50 3 = B AOB' = 50 B' OG =

130 OA n O AB OD BOC OE AOB 1 AOC = 70 EOD = 2 AOC EOD DC AB 1 = B DE BC l 1 l

131 SAS ASA AAS SSS cm 6 cm 5 cm 3 cm cm 21 cm 125

132 A C BE BD AC EC AD CAD + ACE + B + D + E = 180 ECD BCE ECD = B + E CAD + ACE + D + ECD = 180 ECD BCE ECD = B + E ACD CAD + ACE + D + ECD = 180 CAD + ACE + B + D + E = 180 ECD BCE ACD ABC B C E E DF BC AB D AC F AB = 7 ADF ADF DE = DB EF = FC ABC AC = AB = 7 BE ABC DBE = EBC DF BC DEB = EBC DBE = DEB DE = DB EF = FC = 14 ADF = AD + DF + AF = AD + DB + FC + AF = AB + AC 126

133 ABC A= 2 B CD ACB BC = AC + AD CD ACB CACD A CB E DE = BE CB CD B CA BC CE = CA { CA= CE ADC EDC ACD = ECD CD = CD ACD ECD DA= DE DEC = A A= 2 B DEC = 2 B DEC BED DEC = B + BDE B = BDE EB = DE DA= DE DA= EB BC = BE + EC = AD + AC = ABC H AD BC ABC = 45 BH = AC BH = AD ADC BDH AD ABC ADB = ADC = 90 ABC = 45 ABC = BAD = 45 BD = AD BE ABC BEC = 90 CAD + C EBC + C = 90 CAD = EBC 127

134 { EBC = CAD Rt BDH Rt ADC ADB = ADC BD = AD Rt BDH Rt ADC BH = AC ABC D E BC AC BD = CE AD BE F 1 BFD 2 B AD BG BF GF BFD ABF BFD = ABF + BAF ABF = DAC BFD BF GF 1 FBG = A 1 7 x x A 1 < x < 14 B 0 < x < 14 C 3 5 < x < 14 D 0 < x ABC A= 90 B C P BPC A 105 B 120 C 135 D

135 A 1 B 2 C 3 D AD BCD BC A ABD ACD B ABC C B = C D AD ABC ABC A 3 B 2 C 2 3D AB = AC 129

136 α ABC A = 50 B = 70 CD C DE AC CDE = CDB = DE BE = CF ABC DEF 9 18 cm 4 cm E C BF AB = 2 3 = 4 ED = EC

137 A C A C B A B C ABC AB = AC A = 36 BD ABC DE BC AB E ABC BD CD ABC ACF A= α D ABC A= 54 B = 78 C ABC ABC AB = AC A = 120 AB BC D BD DC BD DC 131

138 ABC D E AC AB BD CE O 1 EBO = DCO2 BEO = CDO3 BE = CD4 OB = OC 1 ABC 2 1 ABC CE = ABC CE AB AD BC BE = 1 AE = DE Rt ABC BAC = 90 AB = AC B C A L BD CE D E 1 DE = BD + CE 2 A BAC Rt ABC AB = AC A = 90 E F AB AC AE = CF M BC EF EM 132

139 FM MEF C AB ACM CBN AN = BM 1 C AB ACM CBN AN = BM 2 CBN C 90 ACM CBN AN = BM

140 # 1 n n n = n = = = 27 n 1 nn E F AC AE = CF 1 BFDE ABCD ABCD ABCD BFDE BFDE BD 134

141 BFDE ABC D E F ABBCAC ADEF 1AB = CD 2 ABC = 90 ADEF D E F AB BC AC DE AC EF AB ADEF ADEF ABCD AC BD O P BC P B C PF BD AC F PE AC BD E PE + PF = OB 2 ABCD PE + PF = OB PE + PF = OB OEPF BEP PF = OE PE = BE PF BD PE AC PFOE PF = OE ABCD AC = BD OB = 1 2 BD OC = 1 2 AC OB = OC OBC = OCB PE AC EPB = OCB EPB = OBC EB = PE PF = OE OB = BE + OE = PE + PF 135

142 ABCD AB = 6 BC = 8 BD A E DE BC F 1 BFD 2 BF 3 BFD AD BC ADB = DBC ADB = BDF DBC = BDF BF = DF BFD BF BF = x DF = x FC = 8 - x Rt DFC x 2 B D GH ABCD AD BC AD = 6 cm BC = 10 cm AC BD DBC = 45 ABCD D DG AC BC G DE BC E AC BD BD DG AD BC AC DG ACGD AC = DG AD = CG ABCD AC = BD = DG 136

143 BDG DBG = DGB = 45 DE = BE = 1 2 BG S ABCD = S DBG = 1 2 BG1 2 BG = = 64cm2 # ABCD AB CD = 8 CD = E F AC BC EF 2 A 1 A 2 AD A 1 A 2 AB BC B 1 B 2 A 1 B 1 + A 2 B 2 3 A 1 A 2 A 10 AD A 1 A 2 A

144 AB BC B 1 B 2 B 10 A 1 B 1 + A 2 B A 10 B 10 1 EF EF = 1 AB + CD= ABCD A 1 A 2 B 2 B 1 A 1 B 1 + A 2 B 2 = AB + CD = 12 A 1 B 1 + A 2 B A 10 B 10 = 60 EF ABCD A 1 A 2 B 2 B 1 A 1 B 1 + A 2 B A n B n = 6n ABCD AB = 6 cm BC = 12 cm P A AB B 1 cm/s Q B BC C 2 cm/s P Q B C PBQ 8 cm 2 2 t APQCD S cm 2 S t t 3t S S 1 t PBQ 8 cm x 2x= 8 2 x 1 = 2x 2 = PBQ 8 cm 2 2 S = t 2 2t = t2-6t < t < S = t 2-6t + 72 =t t = 3 S S 63 cm 2 138

145 A 1 72 A 6 B 5 C 4 D 3 2 ABCD A ABCD A = 50 B = 50 C = 130 D = 130 B ABCD = 5BC = 10CD = 5AD = 9 C ABCD A= 52 B = 128 C = 50 D ABCD = CD = 5BC = AD = 10 3 ABCD A AB = CDCD = DA B AB CDAD = BC C AB CD A= C D A= B C = D 4 A B C D A B C D 139

146 ABCD AC BD O OE DC BC E AD = 6 cm OE A 6 cm B 4 cm C 3 cm D 2 cm a A 1 4 a 2 B 1 3 a 2 C 1 2 a 2 D a 2 8 ABCD A = 70 BC = 5 cm B = AD = cm 9 ABCD 64 cmab: BC = 3: 5 CD = cm ABCD AC BD O AB = 8 cm AC = 16 cm AE BD E BD = cmbe = cm ADB = BAE = 11 6 cm 8 cm cm cm 5 cm cm ABCD E F AB CD DE BF F DEBF DE ABCD ADC EF AD DC 1 AEFD 140

147 2 B = 120 DE = 5 cm AEFD ABCD E F G H AB BC CD DA EFGH ABCD O E F G H OA OB OC OD A B C D E F G H O B ABCD AEFC S 1 S 2 141

148 S 1 S 2 S 1 S 2 < > = cm 1: ABCD AE BC E AF CD F EAF = 60 D = BAF = BE = 2 cmdf = 3 cmab = cmad = cms ABCD = cm ABCD DCE DCF BED = cm 8 cm 6 24 cm cm 7 ABCD AC BD O 5 1 AB CD2 OA= OC3 AB = CD4 BAD = DCB5 AD BC ABCD 142

149 ABCD ABCD C A EF 1 AECF 2 AB = 6 cm BC = 8 cm EF ABCD AC BD O AC O BC AD E F 1 OE = OF 2 AOB = 60 AC BEDF ABC a b c A 1 B 1 C 1 l 1 A 1 B 1 C 1 A 2 B 2 C 2 l 2 143

150 1 a b c n A n B n C n l n 2 5 A 5 B 5 C 5 l 5 3 ABC S S n A n B n C n S n ABCD AD BC EF 2 A EF A' BM 3 MA' MN 2 BMN ABCD AD BC B = 90 AD = 24 cm BC = 28 cm P A AD 1 cm/s D Q C BC 3 cm/s B P Q A C t t PQCD ABCD E F AD BC ABFE EF V 1 A' B' FE 144

151 2 A= 63 B' FC A AB CD O OA EOC DOB = 35 EOC A 70 B 50 C 55 D A B C D 3 A 3 B 4 C 5 D 6 4 ABCD AB = AD DC = BC B 145

152 A A B A C C D D C D 5 ABCD AD BC ABCD A A+ C = 180 B B + D = 180 C A+ B = 180 D A+ D = A B C D 7 4 A B C D 8 3: 4 24 A 2 B 4 C 6 D = cm 2 6 cm cm 12 ABCD AB CD AB CD ABCD AB = 4 cmbc = 10 cmae BAD DF ADC AEFD 146

153 cm 1 = A B B = 30 DE = 6 BC ABCD AD BC AB = CD DE BC EAC = BC BF AC F BF 6-6 BF = 17 ABC A 3 1 BC x B C B C m 0 n 0 m n 147

154 2 BC x y B C B C m 0 0 n m n ABGH BCFG CDEF ADEH AE BG CF P Q AB = 6 BP 2 ACQ B ABC D E AC BC ADB EDB EDC C A 30 B 60 C 15 D a b c d a c a 2 + b 2 + c 2 + d 2 = 2ab + 2cd A B C 148

155 D ABCD AP BD P E F AB AD ABCD 18 cm AEPF A 36 B 18 C 9 D cm 3 cm A 18 cm B 20 cm C 22 cm D 20 cm 22 cm cm 10 A 400 cm 2 B 500 cm 2 C 600 cm 2 D cm Rt ABC ACB = 90 BC = 6 cmac = 8 cme AB CD AB CE AD AE ADCE A 4 8 cm B 5 cm C 6 4 cm D 10 cm AEF ABCD A AEF E F ABCD BC 149

156 CD BAD A 100 B 120 C 135 D A B C D x 2-6x + 8 = 0 10 ABCD 30 cm AC BD O AOB BOC 5 cm AB = ABCD E F AD DC BF CE M AB = 4 AM = ABCD AD BC AB = AD = DC = 3 cm B = 60 EF = cm 13 ~ ABCD AB = 4 AD = 2 M CD 1 ADM BCM 2 AM ABM ABCD CE BD BE = BD BE DC F 1 BEC = 30 2DE = DF 150

157 ABCD M AB E AB MN DM CBE N 1MD MN 2 M AB M AB MD = MN ABCD 6-18 AB = 2 BC = 4Q DC P P x y 1 P BC AQP S x 2 x AQP P

158 ABCD AD = 4 cm A = 60 BD AD P A 1 cm A B C P PM PM AD 1 P 2 PM AD E APE 2 P 2 Q A A B C AB 1 cm BC 2 cm Q QN QN PM Q x 0 x 10 PM QN ABCD S cm 2 1 S x 2 S cm

159 a b = c d ad = bc d b = c a a c = b d # # A 1 A BB 1 CC 1 AB = 8 BC = 4 A 1 B 1 = 6 B 1 C 1 # AB CD AD BC O A AB/CD = OA/AD B OA/OD = OB/BC C AB/CD = OB/OC D BC/AD = OB/OD 153

160 ABCD AC BD O BC AB CD E F 1 2 AD = a BC = b a b EF A ABC EO BC OE BC = AO AC A X AD BC AD BC = AO OC H AD EF BC AE BE = DF FC ABCD EF BC AB CD E F AD = a BC = b EF EF 154

161 EF A 1 a b c d ab = cd A a: d = c: b B a: b = c: d C d: a = b: c D a: c = d: b 2 1: cm km A B 125 C 12 5 D : 100 1: 500 A 25 B 5 C a = 3b = 4c a: b: c = 5 1: cm m ED BC AE EB = 1 3 ED BC = D ABC DE BC AB = 15 AC = 10 AE = 4 AD = BD = 8 a b c d a = 1 cmb = 3 cmc = 2 cm d = 155

162 B D BC E AD CE AB F FE EC A 1 2 B 1 3 C 2 3 D ABC DE BC EF AB 1 AE EC = BF AD 2 FC BF = AB EF 3 BC AB = DE CE 4 BC CF = EA BF A 4 B 3 C 2 D ABCD E AB F BC BF: FC = 1: 2 EF BD P FP: PE ABCD EF ABDC EF CB AE: EB = 2: 3 AD = 4 EF = 24 5 BC 156

163 # 1 157

164 DE BC 2 A= D 3 DAB = CAEAB AD = AE AC ADE = 4 ABP = CDP PACD = 5 Rt ABC ACB = 90 CD AB D 6 ABC = 90 ACB = 30 AD = 2AC CD = 2BC D = ABC AC = 9 BC = 6 AC D ABC BDC CD CBA CBD = A AC D C ABC BDC BC: AC = CD: BC CD CD = 4 158

165 AB DB B CD DB D AB = 6 CD = 4 BD = 14 DB P C D P P B A P P CDP BPA D B C P A 1 CDP ABP CD: AB = DP: BP DP = CDP PBA CD: = DP: AB DP = D ABC AC D DE E ABC D E ABC ABC DE PB D DE 1 BC AB E 1 ADE 2 = B AB E 2 D DE 3 AB BC E 3 CDE 4 = B BC E ABC BC = 8 AD BC AD = 159

166 12E F AB AC B C EF BC EF ABC EFGH 1EF 1: 2 2EF EFGH G H BC 11 EF: FG = 1: 2 EF = x FG = 2x AK EF BC AD = AE AB EF BC = AE AB AK AD = EF BC FG BC AD BC EF BC KD = FG = 2xAD = x BC = 8AK = 12-2x 12 = x 8 x = EF = 7 AK 2 EF: FG = 2: 1 EF = 2x FG = x AD = EF CB 12 - x = 2x 12 8 x = 3 EF = x 12 S AK 2 EFGH EF = FG = x AD = EF CB = x 8 x = EF = 5 S ABC = S AEF + EH EBCF AD + EF BC = 1 160

167 ABCD = 12 cm AB = 8 cmp Q AB BC P A 1 cm/s AB Q B 2 cm/s BC P B Q BDC x PBQ BCD PBQ = BCD = 90 PB 1 1 = 2 DC = BQ BC 8 - x = 2x 24 x = PB 2 1 = 3 BC = BQ DC 8 - x 12 = 2x 24 x = PBQ BCD BD CE ABC ADE ABC ADE ABC A A ADE ABC BD CE ABC AEC = ADB = 90 AD A= A AEC ADB AB = AE AC A ADE ABC AD AB = AE AC 161

168 BD EC O A A 90 B 80 C 45 D 40 3 ABC 槡 2 槡 6 2 A' B' C' 1 槡 3 x ABC A' B' C' A' B' C' A 槡 2 B 槡 2 2 C 槡 6 2 D 槡 AB B 1 6 m D 1 4 m BD 0 55 m m A 3 85 B 4 00 C 4 40 D

169 5 9: 25 A 9: 25 B 3: 5 C 81: 625 D = 2 ABC ADE A D = B B E = C C AD AB = AE AC D AD AB = DE BC 7 D ABC AB D DE BC AC E AD: DB = 1: 2 BC: DE A 1: 3 B 2: 3 C 3: 1 D 2: ABC ACB = Rt CD AB D AD = 5 BD = 20 CD = AC = ABCDA E F B C F FCE ABCD A ABCD AB' C' D' B' C' D'

170 ABCD E F BC CD AEF = Rt ABE ECF OABC O A C B 2 C CD AB D OABC 1: 3 CD 3 2 y E C D E B C D E AB = A B AB AB C AC BC AC BC M N MN = 20 m AB = 2 20 m = 40 m 1 AB AC D CD = 1 2 AC BC E CE = 2 AB AB

171 B 1 O A1 1 x P AOP P A 4 B 3 C 2 D ACB = ADC = 90 BC = aac = bab = c ABC CAD CD A b 2 c B b 2 a C ab c D a 2 c cm 50 cm 60 cm 30 cm 50 cm A 1 B 2 C 3 D ABCD AC BD O O 165

172 E F OE: A 4 B 5 C 7 D 8 OF 5 ABCD = 2 5 AD = 1 5 AD AB AE AED DE AE BC F CF A 0 5 B 0 75 C 1 D ABCD EF ABDE: EF = 4 CD A 16 3 B 8 C 10 D 16 EA = 2: ABCD E F AB BC AF DE O AO DO = A B 槡 ABC B =25 AD BC AD 2 = BDDC BCA C D 1 2

173 Rt ABC BAC = 90 D AC ABD = C EF D BA F EF BC E 1 ABD AC 2 AB = t t ADF EDB ABC 1 y 3 2 y 3 A 2 AB' C' A B' C'

174 ED AB 1 AB ED BC = 2 4 DF = 7 2 AB 2 h AB 獉獉獉 m n α β 2 AB ABCD A = 60 B = D = 90 AB = 20 CD = ABC AB = 3 AC = 2 AC A C D D DE AB BC E E EF AC AB F FD ABC 1 D 168

175 α sin α cos α tan α cot α # sina= cos90 - A cosa= sin90 - A tana = cot 90 - A cota= tan90 - A 1 1 Rt ABC C = 90 sina= cosa tanb 2 Rt ABC C = 90 3a = 槡 3b sinacotb 1 C = 90 sina = a = 12kc = 13kb = 5k cosa= b c = 5 13 tanb = b a = C = 90 3a = 槡 3b a = 槡 3kb = 3k 2 ABC C = 90 a b c A B C 169

176 1 A= 30 b = 2 cosb a 2 tana= 3 b = 2 4 c sinb ABC B B- 1 槡 3 S = 槡 A 1 Rt ABC C = 90 A b = ccosa B a = btanb C a = csina D b = acota 2 A tan45 < sin30 < cot45 B sin30 < cot60 < cos45 < tan45 C cot60 < sin30 < cos45 < tan45 D tan30 < sin30 < cot45 < cos45 3 EFG G = 90 EG = 6 EF = 10 cote = A 3 4 B 4 3 C 3 5 D ABC A= 105 B = 45 tan C A 1 2 B 槡 3 3 C 1 D 槡 3 5 ABC C = 90 sina= 2 5 sinb A 2 3 B 2 5 C 4 5 D 槡 ABCD ABC = 60 AC = 4 BD A 8 槡 3 B 4 槡 3 C 2 槡 3 D 8 170

177 Rt ABC C = 90 b = 2 c = 3 sina Rt ABC C = 90 cota = 7 4 b = 2 a = ABC B = 45 C = 60 AD = 槡 3 BC = ABC AB = 槡 3 AC = 槡 6 A = 45 = S ABC tan D ABC C = 90 BAC = 30 AD = AB B ABCD AB CD C = 90 D = α AD = 171

178 b DC = a AB = A a - bcosα B a + bcosα C a + bsinα D a - bsinα ABC C = 90 cosb = 4: 5 AB: BC: CA= A 3: 4: 5 B 3: 5: 4 C 5: 4: 3 D 4: 3: i = 2: A 7 B 9 C 12 D Rt ABC CD AB BD = 8 AD = 2 tana A C B 2 D 槡 m 2 A 150 B 75 槡 3 C 9 D 7 6 α cosα = 槡 3 2 α = m 8 ABC C = 90 a + b = 2 A= 60 c OB = OC = 4 BOC = 120 B BC 172

179 ABC CD AB A = 30 CD = 3 BC = 2 槡 3 AB ABC ACB = 90 CD AB DAC = 6 槡 3 BD = 3 1 cosa CD AB ACB = 90 AC = cosa = ACcosA AC = 6 槡 3BD = 3 6 槡 3 = ABcosA = AD + BD cosa = 6 槡 3cosA + 3 cosa t = cosa t > 0 2 槡 3t 2 + = 0 cosa= t = 槡 BC ABC ABC AB = 2 槡 3 AC = 2 BC 173

180 AD = 槡 BC 2 AB AC BC ABC AC = BC ACB = 90 ABD D C AB CD DEC E A DC AE = 1 CD 1 A C AC B C BC C CD AB Rt ADC Rt BDC CAD = 45 CD = AD B = 30 CD BD 槡

181 A D AB BC B A 60 C B 45 C D AB = 20 m BC = 40 m AD 0 01 m B BE AD BF CD E F AD CD BFDE BF = ED Rt ABE AE = ABcos EAB Rt BCF BF = BCcos FBC AD = AE + BF = 20cos cos45 = 槡 2 2 = 槡 = 38 28m BC 10 CAB 45 D

182 Rt ABC BC = 10 CAB = 45 AC = 10cot45 = 10 10cot30 Rt DBC CDB = 30 DC = = 10 槡 3 DA= DC - AC = 10 槡 3-10 = DA > A 1 1: A 30 B 10 C 30 槡 10 D 10 槡 BC AB = 2 m AD = 3 m CE = 8 m BC A 7 m B 33 3 m C 7 16 m D 5 16 m m m m 2 m 8 m 176

183 m 30 m B A C 12 m BAC = 48 BC 0 1 m 7 55 m 4 8 m α = 30 β = 47 AB B D 200 AB = BD = Rt ABC AB 12 m 45 1: 1 5 AD DB A 15 槡 2 km/h km/h 177

184 2 h C 75 B 1 C A 200 m B C ABC = 60 ACB = 45 B BC 5 AB 13 AB A 1: 3 B 1: 2 6 C 1: 2 4 D 1: ABCD AD BC AC BD O AD: BC = 1: 3 A S COD = 9S AOD B S ABC = 9S ACD C S BOC = 9S AOD D S DBC = 9S AOD 3 8 cm 10 cm

185 A 80 cm 2 B 40 cm 2 C 56 槡 3 cm 2 D 65 槡 3 cm a b a + b 2 A 13 B 19 C 25 D xoy A2-2 B0-2 P AOP AOB P MAa 75 NB 6 45 AB cm A B C D cm m 15 m 20 m

186 AB CD AB BD B CD BD D A C α = 30 D β = 60 AB = 24 m CD A 35 m C P B B 30 A P 45 A B a b c α β 180

187 A A> 45 sina A 槡 2 2 B 槡 2 2 C 槡 3 2 D 槡 ABC C = 90 cota = 槡 3 B A 30 B 45 C 60 D 75 3 a b Rt ABC 槡 3a - b = 0 tana A 槡 3 3 B 槡 3 C 槡 AD Rt ABC AE AD CB E 181 D 1 2

188 A AED ACB B AEB ACD C BAE ACE D AEC DAC 5 ABC C = A a = btanb B a = ccosb C b = acotb D b = asinb # 6 α cos90 - α A cosα B sin90 + α C sinα D cos90 + α DE C CD = 30 m DC A AC = 5 m A AB DE EC B AB = 6 m DE A 25 m B 30 m C 36 m D 40 m A 150sin52 B 150 sin C 150tan52 D 150cot52 9 Rt ABC C = 90 tana= 5 12 cosa= E ABCD CD AE BD O ADE 6 182

189 11 ABC A0 2 B3 3 C2 1 B 7-4 ABC D E ABC AB AC DE BC AB = 8 cm AC = 12 cm BD = 3 cm AE = EC = 13 ~ BC 1 8 AD = : 2 BC AB AC EH EF A C D CD = 100 C BD AB A A km B 65 BC 400 km A 183

190 A B AB BC CD BD AD CD AD E A B E D A B E C B A AB = 4 槡 3 BC = 10 CE = 6 BDC = 45 ABD = 15 2 / 4 / 1 AD CD 3 184

191 B A B 35 C 100 D A C 30 D 45 CD A 14 B 17 C 20 D ABCD AD = 8 cm AB = 4 cm D B DE EF A 3 cm 2 槡 5 cm B 5 cm 2 槡 5 cm C 3 cm 槡 5 cm D 5 cm 槡 5 cm 4 ABC C = 90 tanb = 槡 2 sina A 槡 2 2 B ± 槡 sin60 > sin59 C 槡 D ± 槡 2 2

192 2 sin cos 2 29 = 1 3 槡 cos = cos30-1 = 槡 tan17 5 = cot72 30' A 4 B 3 C 2 D ABC 7 ABC DEF A D 1 A= D 2 A= E 3 AB BC = DE EF 4 B = E A 1 B 2 C 3 D ABC DE BC EF AB 1 AE EC = BF FC 2 AD BF = AB BC 3 EF AB = DE BC 4 CE CF = EA BF 7-14 A 4 B 3 C 2 D 1 186

193 Rt ABC AB AC 3 cosa = tana = 10 D E ABC AB AC AED ABC AB i = 1: 槡 3 α = 12 sin15 cos15 = 1 2 sin30 sin20 cos20 = 1 2 sin40 sin30 cos30 = sin ~ ABC AB = 4 AC = 6 D E AB AC ADE = C AD = y CE = x y x x ABC AB = 7 AC = BC = 8 BC 2 BA x ABC y 187

194 y x A4 0 B0 2 C x C A B O C AOB C 16 ABO A- 1 3 B- 4 1 O OA 1 B 1 1 OAB 2 A 1 B AB- CD P CD C D P B E 1 BPC 2 P CD BPC Rt ABC C = 90 AB = 10 cm AC = 8 cm M AC A C M MP AB P 1 AM = x cm PBCM y cm y x x 2 PBCM ABC 188

195 90 # O AB = CD 1 AOB = COD ) ) 2AB = CD 3 AOD = COB ) ) 4AD = BC 189

196 A 1 B 2 C 3 D B O AB C D AB = 10 cm CD = 6 cm AC O OE AB E AE = BE CE = DE ABC AB = AC AB AC D BC E DE BC = 2DE AE AE BC BE = EC BAE = CAE BE = DE BC = 2DE BE = CE BD Rt BDC E BC BC = 2DE O AB CD G F 190

197 CD AF O E AC 2 = AEAF AC 2 = AEAF ACE AFC CE AD AB CD CD AC = AD ADC = ACD AEC = ADC AEC = ACD CAE = FAC ACE AFC AE AC = AC AF AC2 = AE AF A 1 A B C D 2 O 5 A O 3 A A 4 B 6 C 8 D AB O BAC = 32 D AC DAC A 32 B 25 C 29 D # A B C D O BOD = 100 DAB A 50 B 80 C 100 D

198 AB O OC AB D AB = 4 槡 3 cm OC = 4 cm OD A 3 cm B 2 5 cm C 2 cm D 1 cm ) ) AB AB AB CD AB ) C AB D AD EF AB E AB ) F DB GH AB G AB H A AC = CB ) ) B EC = CG ) ) ) ) C EF = GH D AE = EC 7 O 10 AB 8M AB OM O AB AC OD AB OE AC D E = 2 cm O cm cm 5 cm 192

199 cm cm O 2 槡 3 cm AB AOB AD ABC O A B C AE O ABAC = ADAE O APC A B C D PO APC B D = α ABC = x ACF = β F = y 1α = x - y 2β = x + y 3x = 1 α + β 2 4y = 1 2 β - α A 4 B 3 C 2 D ABCD O BC ABC + ) DCB = 120 AD 193

200 AB C D AB = 4 CD = 2 AB H T D D C O A D OBA = 60 D 0 2 A C # ABCD AD BC E F BD DE CDF 1 AB = AC 2 AC = 3 cm AD = 2 cm DE 194

201 ABC AB = AC D BC E AD ABC 1 AB 2 = ADAE 2 D BC A A A A A A cm r r cm 2 1 cm r r cm 195

202 3 2 cm 1 r r cm cm # AOB = 30 P OA OP = 5 cm P r OB r cm 5 - A 5 B 槡 3 2 C D 槡 3 2 P PC OB C P OB PC = r AOB = 30 PC = 1 2 OP = 5 2 cm C A = 60 AC = 8 AB = 10 O AB AC O AB E 1 O y EA x 196

203 x O ABC O 3 O ABC x 1 OEOA O AB AC A = 60 OAE = 30 OE AB Rt AEO OE = AEtan EAO = 槡 3 3 x O y = π C CD AB D Rt ADC ACD = = 30 AD = 1 AC = 4 2 BD = 6 CD = 槡 = 4 槡 3BC = 槡 = 2 槡 21 S ABC = 1 2 CDAB = 1 OEAB + BC + AC 2 4 槡 3 10 = OE 槡 OE = O y = 34-6 槡 21π 3 槡 3 - 槡 7 3 O ABC 槡 3 3 x = 3 槡 3-197

204 槡 7x = 9 - 槡 21 0 < x 9 - 槡 ABC O B C D O E BC OE BC FDE AC G ADG = AGD 1 AD O # 2 AB = 2 AD = 4 EG = 2 O D O OD OD AD ADG = AGD OEG = ODG OE BC ADG + ODG = 90 AD O AD 2 = AB AC = 8 AD = AG = 4 EG GD = BG CG DG = 4 AG = DG = AD AGD = 60 = EGF = 30 O ED OE A 1 O 5 cm OA= 4 cm A MN MN O A B C D 2 A B C D 3 A B C D 4 O 8 O l 6 l O 198

205 AD ABC EAC AD ABC D DBC 6 3 cm 4 cm 5 cm 7 ABC O 1 O AB ACB C AB D CD AB ABC CBD ACD ABO OA= OB O AB C OA OB E F AB O P 2 18 B 1 AB O O 3 P O P AB 199

206 A 3 B 6 C 0 D 3 槡 2 # O AB CD E AC DB P A CECD = BEBA B CEAE = BEDE C PCCA= PBBD D PCPA= PBPD O PAB O A B PA = 7 cm AB = 2 cm PO = 10 cm O cm P O PA PB O A B PA= PB = 4 cm APB = 40 C AB C O ) PA PB D E PDE DOE = 5 ABC ABC AC O A CB O D B AC = 6 BD = 5 AD AB 1 CAD CBA 2 DC 200

207 AB O BC O D O AD CO 1 ADB OBC 2 AB = 2 BC = 槡 2 AD M y M x A B AD M D M x C A C B CD 2 D DE BA M E DB AE 201

208 # A 0 3 A 1 B x 1 B 4 0 B 3 A B 2 B M2 0 A B # A B 13 cm 7 cm AB = 15 cm A B EF Rt ABC EF 202

209 O 2 AB C D COD = 60 AC = CD = DB 1 # 2 AE F AE CO = DO COD = 60 COD CD M OM OM CD CO = 2 OM = 槡 3 2 CO = 槡 3 AO Rt AOM AM = 3 CD = 3 2 AO = OM 2 2 槡 + AM = 槡 = 2 槡 3 2 槡 3 2 OF AE F OF AE AF AE AE = 2AF AF 2 = ACAD = CD = 2 AD = 2CD = 2 槡 2 AE = 2AF = 4 槡 ABCD AB = 20 cmbc = 4 cm P A ABCD 4 cm/s Q C CD 1 cm/s P Q A C D ts P Q 2 cm 3 cm t P Q 2 t 203

210 P AB Q CD P Q PQ = 5 cm Q QM AB AB M QM = 4 cm Rt PQM PM = 3 cm AP + PM + CQ = 20 4t t = 20 t = AP - PM + CQ = 20 4t t = 20 t = P BC Q CD 3 P CD Q CD t 1 = 17 5 t 2 = 23 5 t 3 = 19 3 t 4 = 23 3 t 5 = 29 3 t 6 = 25 3 P Q 204

211 A 1 O O' R R' OO' = 5 R = 3 0 < R' < 2 O O' A B C D # 2 A 4 B 3 C 2 D 1 # 3 6 cm 5 cm 6 cm cm # ABCD E F AB CD O 1 O 2 EF O 1 ABCD DA AB BC O 2 O 1 O 2 DC F O 1 O 2 4 cm 2 cm ABCD a b a b a b < = > O 1 O 2 T AB CD T O 1 A C O 2 B D 1 AC BD 205

212 2 O 1 O 2 T O 1 O 2 A B O 2 O 1 O 1 D C O 1 O 2 C = 40 D B P O 1 O 2 3 cm O 1 A O 2 B AC O 2 C PC PC A 2 槡 3 cm B 3 槡 2 cm C 3 cm D 4 5 cm O 1 O 2 O 3 l O 1 O 2 O 3 4 cm O 1 A 24 cm B 20 cm C 18 cm D 16 cm AD ABC AD ABC O E CD E AC F O 1 206

213 EF DF 1 AEF FED AD = 6 DE = 3 EF # 3 DF BE ABE AO O 1 O 1 O E AO O B C O G O GF AO D AE F 1 AE O 2 AB = 2 AE = 6 ODG AB O 1 O 2 B CD O 1 C O 2 D BAD AM O 1 E CD F O 2 M 1 DM CE DFM DFM # 2 CD = 12 CB = 5 DF = 4 AF = 3FM EF O 1 O 2 A B O 1 AC O 2 C EF B O 1 E O 2 F 207

214 EF AC D 1 AE CF 2 EF AC D 2 DADF = DCDE 3 EF AC # 208

215 ABC 2 π B B C BC 120 A AB π 2 4π 3 # n M N O ABC ABCD ABCDE n ABCDE AB BC BM = CN OM ON MON 2 2 MON 3 MON 209

216 3 MON n n 1 OB OC OBM OCN MON BOC MON MON = 360 n = OB OC ABC O OBM = OCN = 30 BOC BM = CNOB = OC OBM OCN BOM = CON MON = BOC = 120 OA OB ABC O AB = AC OAM = OBN = 30 AOB = 120 BM = CNAM = BN OA = OB AOM BON AOM = BON MON = AOB = MON = 360 n ABC O ODE B ODE O ABC 1 ABC

217 ABC ABC OA OB OD AB F OE BC G AOF = BOF BOG = BOF AOF = BOG AOF BOG 1 OFBG = AOB = ABC cm 30 cm 2 28 cm 2 5 cm 1 x r l r l = 2πr l l = nπr 180 x 2 R 28 cm 2 R 1 x r l r = 槡 = 50 l = 2π 40 = 80π l = πxr 180 x = 180l πr = 18080π 50π = 288 S = π = 2 000πcm = 2 000πcm 2 S 2 R 2πR 2 + 2πR5 = 28π R 2 + 5R - 14 = 0R 1 = - 7 R 2 = 2 = 20πcm 2 S = 2πR ABC B = 60 BA = 5 槡 3 BC = 8 槡 3 O 211

218 ABC BA BC D E OB = x y 1 y x 2 x 1y = S BEOD - S ODE 2 BC AC ABC R R R x x A 1 72 A B C D 2 a a A 1 2 B 2 3 C 1 3 D Rt ABC AB = 5 AC = 3 BC A 8π B 12π C 15π D 20π A A A 3 A 6 槡 3 B 槡 C 3 槡 3 D 3 # cm cm # 6 60 a 212

219 # Rt ABC C = 90 AC = 2 AB = 4 AC BC a B # 1 a A a cos20 B a sin20 C a 2cos20 D a 2sin20 # 2 C 3 C 4 C 6 A C 3 > C 4 > C 6 B C 6 > C 4 > C 3 C C 3 > C 6 > C 4 D C 4 > C 6 > C OA OB AOB = O 2 π m 8 m 213

220 # ABC AD = BE = CF ADBECF ABC- DEFG

221 A O 5 AB 8 C AB OC A 3 B 6 C 9 D AB O CD AB = 10 CD = 6 A B CD A 6 B 8 C 10 D ABCD A: B: C = 1: 2: 5 D A 60 B 120 C 140 D PA PB O A B PO O C AB DOC DC A 3 B 4 C 5 D 6 5 O AB CD M AB = 8 cm M AB CM: MD = 1 : 4 CD =

222 A 12 cm B 10 cm C 8 cm D 5 cm A B C D C D AB π CD 3 A C π 6 2π 3 B D π 3 3π 4 + 槡 A 5: 4 B 4: 3 C 3: 2 D 2: MN AB AB O BD = OB CAB = 30 AO = OB = BD O 6 cm d C O 3 cm d O 12 O P O A PBC O O B C PB = BC = 2 PA 216

223 PA PB O A B AC AB BC OP PAB O CD O CD AB D C CF O F CB 2 = CFCE ABCD AB = 1 ABC AB ABCD AB BC ABCD AB 8-9 = 4 AD = 3 AP AA A BE O A BE PD BE C OD AOD = APC 1 AP O 2 OC: CB = 1: 2 AB = 9 O sina 217

224 M x A B y C D M 1-1 槡 5 1 AB CD 2 A B C D 3 D M B PA PB O A B C O P = 50 ACB A 40 B 50 C 65 D ABC AB = 9 BC = 5 AC = 6 ABC O AB BC AC D E F AF A 5 B 10 C 7 5 D 4 218

225 槡 3 ABC ABC A 槡 3 B 槡 3 C 槡 3 D 槡 3 4 O 10 cm AB CD = 8 cm CD = 6 cm 8-15 AB CD A 1 cm B 7 cm C 1 cm 7 cm D 8 cm A2 0 B6 0 C1 槡 3 x CD C D AB CD E F CE + FD A 2 B 4 C 5 D ABCD BD BC DC E BD = 2 9 A 槡 3-4π C 槡 3-2π 6 9 B 槡 3-2π 6 21 D 槡 3-4π r R 219

226 A R = 2r B R = 9 r C R = 3r D R = 4r O AB OC P PAPB x 2-12x + 24 = 0 A 8 槡 2 B 6 槡 2 C 4 槡 2 D 2 槡 P O0 0 A0 2 B2 0 P O B OPB = 10 x A B A B PAB O A B PCD O C D PA= PC PB = 3 cm PD = cm

227 13 ~ P AB PA= 2 PB = 6 CD P PC: PD = 2: 3 PC PD OAB OCD AC BD 1 AOC BOD 2 OA= 3 OC = Rt ABC C = 90 BE ABC AC E D AB DE EB 1 AC BDE 2 AD = 6 AE = 槡 2 BC ABC a D E AB AC DE BC 1 O 1 O 2 ABC O 1 O 2 B C DE DE BC M N P Q 1 O 1 O 2 2 O 1 x O 1 O 2 y y x x 3 O 1 O 2 x 4 2 D E AB AC O 2 221

228 O 1 ABC 2 ABC O 1 O ABCD BC BC = 2 cm EF B A E BA 1 cm / s A F ADC 2 cm/s C E B ts t EF BC < t < 2 t EF 3 1 t < 2 EF AC P E F P AP: PC 222

229

230 9 1-1 B 獉獉 D D A B y O CD EF x O C E D F π π 2 224

231 A A 1 B 2 C 3 D A 1 B 2 C 3 D 4 3 A B C D

232 P Q P AB Q P AB A O 1 B O 2 C O 3 D O A 1 B 2 C 3 D = 226

233 ABCD 1 ABCD 2 2 EFG EFG ABCD 227

234 A B A l P B P B 1 A B C D 2 A B 60 C D 3 A B 228

235 C D 4 10 m 12 m 3 m 1 2 m A 1 B 2 C 4 D 5 ABCD AC ACB = 25 DOC A 50 B 40 C 30 D A 1 B 2 C 3 D ABCD MN A C MN AC 獉獉獉獉

236 ABCD l A 1 B 1 C 1 D L

237 ABC AB = AC = 5 BC = 3 BD C AB E AED ABCD 1 A 1 B 1 C 1 D 1 A 1 B 1 C 1 D 1 ABCD MN 2 A 2 B 2 C 2 D 2 A 2 B 2 C 2 D 2 ABCD O 3 A 1 B 1 C 1 D 1 A 2 B 2 C 2 D 槡 槡 槡

238 A m 30 m 232

239 A 600 m 2 B 551 m 2 C 550 m 2 D 500 m = 551m 2 B ABC AB = BC = AC = 3 O O ABC 180 A' B' C' ABC A' B' C' 3 A 槡 3 2 C 槡 3 2 A 3 B 槡 3 4 D 6 槡 ABC EFG 4 1 EFG G ABC O EFG O α 0 < α < 90 CHGK 2 1 BH CK CHGK 233

240 2 HK BH = x GKH y y x x 3 2 GKH 5 ABC 16 x BH = CK CHGK CG ABC OG CG = BG CG AB ACG = B = 45 BGH CGK BGH = CGK BGH CGK + 4 BH = CK S BGH = S CGK S CHGK = S CHG + S CGK = S CHG + S BGH = 1 2 S ABC = = 4 CHGK 4 2 AC = BC = 4 BH = x CH = 4 - x CK = x S GKH = S CHGK - S CHK y = 4-1 x4 - x 2 y = 1 2 x2-2x 0 < α < 90 0 < x <

241 1 2 x2-2x + 4 = x 1 = 1 x 2 = 3 5 x = 1 x = 3 GHK ABC 16 A DEF ABC A AB EF B AB DF C B E D A F ABC A' B' C A C 90 B C 90 C B 30 D B 90 3 A B C D 4 O ABC AOB O BOC 235

242 A 60 B 120 C 240 D N 2 A 1 1 B 1 2 C 2 1 D

243 A 88 mm B 96 mm C 80 mm D 84 mm ABC A' B' C' ABC DEF AD = 4 cm BE = MN = cm CF = cm cm M AB N DE O ABC 5 A 1 B 1 C 1 ABC O 90 A 2 B 2 C 2 2 O 1 A 2 B 1 237

244

245 ABC AB AC ADEB ACGF DC BF ADC ABF 2CD BF 3CD BF B

246 A 9 B 18 C 36 D ABC 6 cm A cm B B A C O 獉獉獉獉 ABC BC P ABC ABP A ACP' AP = 3 PP' Rt ABC ACB = 90 AC = 槡 3 BC = 1 Rt ABC C 90 Rt A' B' C Rt A' B' C B' 240

247 Rt A"B' C' A C B' A" A A" 8 O0 0 A- 1 1 B- 1 0 ABO O 135 A B A 1 B 1 A 1 B cm B 4 槡 3 3 cm AC AC A' PC 1 cm 2 AA' cm Rt ABC C = 90 ABC = 60 ABC C A' B' C' B A' B' A' C AB D BDC a b P ABC a DEF DEF b GHI ABC GHI 2 2 a b P 60 ABC a DEF b GHI 241

248 ABC GHI ABCD AEFG A G E AD AB 1 1 DF BF AEFG A DF BF 2 AEFG A DG DG

249 A B C D A B D C C 2 1 cm A 36 cm 2 B 33 cm 2 C 30 cm 2 D 27 cm

250 6 6 cm 2 6 cm = 36 cm 2 36 cm C C

251 9 3-5 A

252 A B C D AC BC CD

253 ABCD EF A G D H GH B E C F BC ABCDA 1 B 1 C 1 D 1 B 1 C AB 1 C 247 AB 1 AC

254 ABCD M N AD BC BC C MN P BQ PBQ = B A 7 B 6 C 5 D 獉獉獉 248

255 A 1 2B 1 3C 1 4D A B C 249

256 D cm 5 cm cm A B C

257 x y z mm x y z 獉獉獉 a b c d = e = 1 f = 2 251

258 A ABCD-A 1 B 1 C 1 D 1 A 1 B 1 = A 1 D 1 = 2 DD 1 = 1 DB 1 A 2 槡 2 B 3 C 3 槡 2 D 2 252

259 ABC A' B' C' A BC = B' C' B C = C' C A= A' D AB = A' C' A C A A= C B A> C C A< C D A C 253

260 7 A B C D 8 A B C D O ABCDE BOC AGA' H GA' H 254

261 ABCD O A' B' C' D' ABCD A' B' C' D' O ABC 5 A 1 B 1 C 1 ABC 255

262 O 90 A 2 B 2 C A 2 B 2 C ABC BAC = 140 AB AC BC D E DAE ABCD E BC F AB FDE = 45 DEC DGA DEC 2 GDF B

263 A 1 B 2 C 3 D 4 257

264 AB = CD AB CD O AOC = 60 CE AB AC + BD AB A AC + BD < AB B AC + BD = AB C AC + BD AB D ABCD = 6 AD = AB AD AE AEB BE AE DC F CEF A 4 B 6 C 8 D A A A 2 B 3 C 4 D B 258

265 A 3π 2 B 4π C 4 D 2 + 3π ABCD E AD BE ABE A CD F FDE 8 FCB 22 FC AOB = 9-26 ) 120 OA6 cm C D AB cm

266 n n ABCD EF D B C C' BFE = 60 DEF AEB Rt ABC C = 90 BC = 4AC = 4 ABC CB A' B' C' 1 3 ABC A' B' C' 2 x0 x 4 ABC A' B' C' 260

267 y y x 17 A B 25 C D DA AB A CB AB B DA = 15 CB = 10 km AB E 1 C E D 9-30 E A 2 C D E E A A 獉獉 1 C BB 1 E AE EC 1 A E C A C 1 1 / C 1 C A 2 / 1 C

268 A 3 4 B A 2-2 = - 4 B = 3 5 C 4 3 D C 槡 槡 2-1= 1 D x 8 x 4 = x 2 3 P1-2 y A - 1-2B 1 2 C D x a - 1 x 2 + x + a 2-1 = 0 0 a A 1 B - 1 C 1-1 D 5 y =x + 2 x + k x 4 A x = 4 B x = - 4 C y D x = - 4 y x x - 1 = m x - 1 m A - 2 B - 1 C 1 D

269 A B C D # 7 10 x 5 84 A C x x B D 10x x x < 2 槡 x A x - 2 B - x + 2 C x + 2 D - x cm 4 cm A 24π cm 2 B 12π cm 2 C 6π cm 2 D 12 cm A 8 65 B C 8 63 D a b = a + b + 1 槡 3 - 槡 3 A 1 B - 3 C - 2 D y = k 1 x y = k 2 x y = k 3 x x k 1 k 2 k 3 263

270 1-1 A k 1 > k 2 > k 3 B k 2 > k 3 > k 1 C k 3 > k 2 > k 1 D k 3 > k 1 > k a 3-4a 2 + 4a = 6 16 x + 6 x + 5 = [ ] x x - 2 x x - 2 x = 槡 y = 12 x y = kx - 7 Pm

271

272 1 y x x x - 1 x = x 1 = 2 x 2 = x - 1 x = x 1 = 3 x 2 = x - 1 x = x 1 = 4 x 2 = x - 1 x = x 1 = 5 x 2 = x = 10 x # x m 2 x 2 +2m + 1 x + 1 = 0 m 266

273 y = - 2x + 2 x y A B AB Rt ABC BAC = 90 C CD x D 1 A B AD 2 B A D K / 50 / a1 a < 5 5 a < 10 / /

274 π - 2 槡 4 cos 槡 2 0 A 2 B 3 C 4 D 5 2 A x 3 x 3 = x 6 B 3x 2 + 2x 3 = 5x 2 C x 2 3 = x 5 D x + y 2 2 = x 2 + y 4 3 A 4 槡 a B 4 P1 - m a 4 C a 槡 4 槡 D 槡 a 4 m A 0 < m < 1 B m > 0 C m > 1 D m < A x 2-2x + 3 = 0 B x 2 + 2x + 3 = 0 C x 2 + 2x - 3 = 0 D x 2-2x - 3 =

275 A 200 cm 2 B 300 cm 2 C 600 cm 2 D cm 2 # A 0 5 B 0 05 C 0 95 D 槡 x = x - 3 x A x > 3 B x 3 C x < 3 D x 3 8 a x 2 + 4x + a =x a A 5 B 4 C 3 D 2 9 y = kx y = m x A C A 1 3 C A 1-3 B C - 1-3D ± 0 1 kg 25 ± 0 2 kg 25 ± 0 3 kg A 0 8 kg B 0 6 kg C 0 5 kg D 0 4 kg A 182 B 189 C 192 D v t

276 獉獉獉獉 = - 6 = # ~ 槡 = 槡 槡 5 + 槡 3 = 槡 5 - 槡 3 2 槡 7 + 槡 5 = 槡 7 - 槡 5 ( 槡 槡 3 + 槡 槡 5 + 槡 = 槡 槡 S a b a = S S b S 0 ) 槡 12 - 槡 槡 cos x x - 1 = x x x x x

277 x x x 2-2x + k - 3 = 0 6 k # x y x 12 y x

278 : 4: 6: 3: ~ y = kx + b A B x C AB AOC x x 2 - kx - 2 = x 1 x 2 2x 1 + x 2 > x 1 x 2 k 272

279 a a < b a c x y 1 0 < x a y = x > a y = b a b c a b c y x y = x 2 +2n - 1 x + n 2-1n 1 2 A 1 x Ax D AB x B DC x C 1 BC = 1 ABCD 2 ABCD A 273

280 a b c 1 A 2 B 3 C 4 D A 1 B 2 C 3 D E C BF 獉獉 ABC DEF A AB = DE AB DE BE = CF 274

281 B AB DE BE = CF AC DF C AB DE AC = DF AC DF D AB = DE AC DF BE = CF D E AB AC F G DB EC 獉獉獉 A DE = 1 BC B BC = DE + FG 2 C DE = 2 3 FG D BC = 4 3 FG 6 ABC A B 1 槡 2 槡 3 C D 1 槡 A 6 B 5 C 4 D 3 8 ABCD A B C D AD O C = 30 DAC A 40 B 50 C 60 D

282 ABC C AB M A 1 B π C 槡 3 2 π D 槡 3 3 π O EF 10 cm AB CD 6 cm 8 cm AB EF CD A 25 2 πcm2 B 25 3 πcm2 C 75 8 πcm2 D πcm2 276

283 α β α = 36 12' β = ABCD A CD F CB E AECF ABC BDC BED AB = 2 DE = ABCDE