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1 ( ) 1 1 ( ) 1!! Shinji Akematsu http://know-star.com/ info@know-star.com 1
2 (1) 1, 5, 13, 25,... 2 2 1,5,13,25,... 7 221 2
(2) (1) n (i) (ii) n 2 n = 2, 3, 4 n = 2 7, 1 + 3 + 5 + 7 = 16, n = 3 17, 1 + 9 + 13 + 17 = 40, n = 4 31, 1 + 19 + 25 + 31 = 76, n = 6 544 n = 26 (1) 5 2 2 5 = 2 2 + 1 2 2 13 2 13 2 = 3 2 + 2 2 3 25 = 4 2 + 3 2 3
4 1,5,13,25,... n 2 = 2 2 + 1 2 3 = 3 2 + 2 2 4 = 4 2 + 3 2 n n = n 2 + (n 1) 2. n = 7 7 = 7 2 + 6 2 = 85..8.5. 221 n 2 + (n 1) 2 = 221. n (n 11)(n + 10) = 0 n = 11, 10 n > 0 n = 11..1.1. (2) (i) (ii) = n 2!! n = 3 3 2 = 9 n = 4 4 2 = 16 n 2 m 2m 1 n 2 }{{} n 2 1 n 2 n = 6 2 6 2 1 = 71.7.1. 544 n = n 1, 2 4
n n 1 n 2 n 2 (n 1) n 1 n 2 2(n 1) n 2 ) 2n 2 1 (n 2 (n 1) ) 2 { n 2 (n 1) } 1 = 2n 2 2n + 1 (n 2 2(n 1) ) 2 { n 2 2(n 1) } 1 = 2n 2 4n + 3 1 544 (2n 2 1) + (2n 2 2n + 1) + (2n 2 4n + 3) + 1 = 544. (n 10)(n + 9) = 0 n = 10.1.0. 5
(n 2 n+1) 2(n 2 n + 1) 1 n 2 n + 1 26 6
3 1 2 O, O 2 A,B AD,CE O AB//CE (1) AE//CD a k DE DCE = 1 OAE = 2 1, 2 DCE = AE//CD 7
(2) 2 CA,DB F O, O 10cm, OO = 16cm AE = cm CF = cm AFD cm 2 8
AB//CE ( ) (1) 1 DCE = DCE DE DE. f. k. OAE OAE 2. e. i. DAE = CEA DCE CEA AE,CD AE//CD. c. H29 (2) AB O 2 H O AH AH 9
O AH AH 2 = 10 2 8 2 = 36. AH= 6cm BH= 6cm AB = AH + BH = 12cm O HO= 8cm BD CE I BI= 8cm AB//CE DO : DA = DI : DB 10 : 20 = DI : (DI + 8) DI = 8cm C A 12cm H O 10cm B 8cm I 8cm D E ODI OI = 6cm OE O OE = 10cm IE = OE OI = 10 6 = 4cm 10
C A 12cm H O 10cm 6cm B 8cm I 8cm 4cm D E BI AE G ABG EIG ( AB//CE ) AB : EI = 12 : 4 = 3 : 1 BG = 6, GI = 2 ABG AG 2 = 12 2 + 6 2 = 180 AG = 180 = 6 5cm AB : EI = 3 : 1 GE = 2 5cm AE = AG + GE = 6 5 + 2 5 = 8 5cm.8.5 CF CFI AB//CE C A 12cm 16cm F xcm B 8cm I (x + 8) : x = 16 : 12 x = 24cm ABF AF = 12 5 cm AF 2 = AB 2 + BF 2 = 12 2 + 24 2. 11
C A 12 p 5 cm 12cm 16cm F 24cm B 8cm I 24 : 32 = 12 5 : FC FC = 16 5cm.16.5 AFD AFD AFD A 12cm F 24cm B 16cm D AFD = 1 2 40 12 = 240cm2.240 H30 H29 1 12
!? 2...... H29 *1 1 (10 ) 2 (15 ) 3 (24 ) 1 ( ) 4 (15 ) 5 (15 ) 2 ( ) 6 (21 ) 3 ( ) 5 *2 *1 H28 1 16 3 18 *2 H30 13
H27 4 3 5 A: Mary is coming back from America today. Shall we go to the airport to see her? B: Do you know( plane arrive her time will what)? A: Yes. At 10:30. Do you know (what time will her plane arrive)? (SV ) *3 Do you know (what time her plane }{{} S will }{{ arrive } )? V ( when s,v,s,v ) (When s v), S V. s v S V SV S V (when s v). s v S V *3 S (Subject), V (Verb) O (Object), C (Complement) 14
when if, because (If s v), S V. S V (if s v). s v S V (Because s v), S V. S V (because s v). s v S V 28 6 When you take a trip through these states, you may see clocks that show two diffirent times. when, ( ) s,v,s,v (When s v), S V. s v S V you S (When you s may see V take a trip through these states), v clocks that show two diffirent times. 2 make O C (O C ) give give to buy buy for... 8 9 3 3 80 15
4 xkm 0.75 ym y x ym y x 2 x y 16
(1) 40km m (2) ym x y y = (3) ym x y y = x x 2 (4) 30km. m (5) 3.7m km 17
(1) x = 40 0.75 40[km/ ] [m/ ] 40[km/ ] 100 [m/ ] 9 100 9 75 100 = 75 9 = 25 3 m.25.3 (2) y x y = ax x = 40 y = 25 3 25 3 = 40a a a = 5 24 y = 5 24 x.5.24 (3) y x 2 y = ax 2 x = 60, y = 30 30 = a 60 2. a a = 1 120.1.120 (4) y x y = 1 120 x2 x = 30 y = 1 120 302 = 15 2 = 7.5 m.7.5 (5) = + x 3.7m 5 24 x + 1 }{{} 120 x2 = 3.7 }{{} 2 x = 12, 37 x > 0 x = 12.1.2 18
2 H28 3 H30 5 Takashi has a brother who goes to Hibari Elementary School. Takashi leaves home for school together with his brother every morning because his brother s school is on the way to Takashi s school. Takashi walks for twenty minutes, and his brother walks for fifteen minutes to go to school. Kenji usually leaves home for school at seven thirty-five, and arrives at seven fifty. Sayuri has a sister who goes to the same school as Takashi s brother. Her sister walks straight from their house to her school, and it takes twenty minutes. Mayumi usually laves home for school at seven thirty and she walks for the same number of minutes as Takashi. One Sunday, Takashi went to Kenji s house to play a new video game with him. He left his house at ten o clock. At one o clock in the afternoon, the two boys left Kenji s house because they had a plan to play tennis with Mayumi and Sayuri at their school. The two girls came from each of their own homes. When the boys arrived at the school, the two girls also arrived just at the same time. 19
A,B,C,D AC BD (1) Takashi s house is ( ) on the map..a.b.c.d (2) Sayuri s house is ( ) on the map..a.b.c.d (3) If Sayuri leaves home for school at 7:20, she arrives at..7:30.7:35.7:40.7:45 (4) When Takashi went to Kenji s house, he arrived at..10:15.10:20.10:25.10:30 (5) Mayumi left home at to play tennis with her friends..12:55.13:00.13:15.13:20 20
20 15 7 35 7 50 20 7 30 10 1 2 2 (1) Takashi leaves home for school together with his brother every morning because his brother s school is on the way to Takashi s school.. A (2) Sayuri has a sister who goes to the same school as Takashi s brother. Her sister walks straight from their house to her school, and it takes twenty minutes. 20 A.C 21
(3) 7:20 Sayuri has a sister who goes to the same school as Takashi s brother. Her sister walks straight from their house to her school, and it takes twenty minutes. 20 15. 7:35 (4) 22
One Sunday, Takashi went to Kenji s house to play a new video game with him. He left his house at ten o clock. 10 Kenji usually leaves home for school at seven thirty-five, and arrives at seven fifty. 7 35 7 50 A C D 152 + 20 2 = 25.10:25 (5) *4 *4 20 D 23
20 13:00 15 13:15 15 13:15 13:15 20 12:55.12:55 24