vo HCrU BiNH (Chu bien) NGUY~N XUAN BiNH >AM HIEU CHIEN 861 DUONG ~ --.!!!"/ TCJJA~ TAP MOT NHA XUAT BAN GIAO Dl,JC vu;r NAM

vo HCrU BiNH (Chu bien) NGUY~N XUAN BiNH >AM HIEU CHIEN 861 DUONG ~ --.!!!"/ TCJJA~ TAP MOT NHA XUAT BAN GIAO Dl,JC vu;r NAM

{[[W+bz0FkV43GmRt7u4DpvuYxd]]} PH N CONG BIEN SO~N vu Hftu Binh (Chu bien) Dam Hieu Chien : Phan D9i 56 Nguyen Xuan Binh : Phan Hinh Hr;>c

Nham dem den cha h<?c sinh m(>t cuon sach Toan chat h.tc;tng ve n<)i dung va d~p ve hlnh thuc, cac tac gia da bien soc;in b<) sach B6i dllang Toan 7 g6m hai t~p. Day la b<) sach dllc;tc bien soc;in theo djnh hllong phat trien nang h/c, giup cung CO, nang Cao kien thltc Va boi dllong h<?c sinh Vlldn len kha Va gioi, khoi gc;ti niem yeu thfch m6n Toan va giup h<?c sinh biet them nhieu ung d1:mg cua Toan h<?c trong cu<)c song. N<)i dung b<) sach barn sat Chuong trlnh va Sach giao khoa Toan hi n hanh, moi chllong g6m nhieu chu de, moi chu de g6m nhieu m1:1c : M1:1c Kien thuc can nha h thong cac kien thuc dlloi dc;ing so do, vua giup de nho kien thuc m<)t each tn/c quan, vua giup cac em nam chac h thong cac kien thuc Cd ban. M1:1c Hoi ctap nhanh g6m nhung cau hoi ngan g9n yeu cau h<?c sinh tra loi nhanh de cung co cac kien thuc Cd ban va tranh nhung sai lam de mac. Trang cac bai t~p trac nghi m c6 nhieu phllong an A, B, C, D, neu kh6ng c6 chi th! gl, ta quy lloc ch9n phllong an dung. M1:1c H9c giai Toan g6m cac vf d1:1 dien hlnh W ca ban den nang cao nham hlnh thanh phllong phap giai toan cha h<?c sinh. Ben cc;inh tu yen chf nh la cac loi giai dllc;tc trlnh bay mau mlfc nhll m<)t bai lam hoan chinh, con c6 tuyen phl,j g6m cac gc;ti y, nh~n xet, lllu y, loi blnh, cac ghi nho, ket lu~n va ma r<)ng kien thuc voi sv tham gia cua m<)t so nhan v~t hoc;it hlnh nham tang tf nh hap dan cha cu on sach. M1:1c Bai t~p ccmg g6m hai loc;ii co ban va nang cao, cac bai t~p dllc;tc ch9n l9c giup h<?c sinh nang cao dan ki nang giai toan va nang life tll duy de vllon len kha, gioi trong m6n Toan, m~t khac con giup h<?c sinh thay duc;tc nhieu ung d1:1ng thlfc te cua Toan h<?c. M1:1c Em co biet? mang den cha h<?c sinh nhieu thu vj, g6m nhung bai toan VUi, nhltng CaU do, nhltng thong tin ve cac nha toan h<?c CO lien quan den chu de dang h<?c, nhung ung dl,lng ho~c the hi n cua Toan h9c trong doi song. M1:1c E>i xa han cung cap them nhung kien thuc nang cao de c6 the hieu sau hon van de dang h<?c.

Cu6i sach la m1,1c Huang dan giai - >ap so giup h<;>c sinh kiem tra l9i bai giai c~a mlnh de rut ra nhung kinh nghi~m trong giai toan. Vai nhung doi m6'i cave n i dung Ian hl nh thuc, dap ung yeu cau ve tfnh khoa hqc, tfnh SU ph9m, tfnh thlfc tien, tfnh hap dan, cac tac gia hi v9ng rang cu6n sach se la m t an pham thiet thlfc va bo fch kh6ng chi cho cac em h9c sinh, ma con cho cac thay co giao, cac b~c cha m~ h9c sinh, cac nha quan If giao dl,ic va tat ca nhung ai quan tam den Slf nghi~p doi m6'i giao d1,1c. Cac tac gia chan thanh cam on b9n OQC da SU d1,1ng cu6n sach nay va mong nh~n duqc nhung g6p y cua b9n d<;>c de cu6n sach ngay cang hoan thi~n hon. MQi y kien g6p y xin gui ve : Ban bien t~p sach Toan.:... Tin, Nha xuat ban Giao d1,1c Vi~t Nam, 187B - Giang Vo - Dong Da - Ha N(>i. CACTACGIA 801 DUONG TOAN 7 I T~P 1

{[[W+bz0FkV43GmRt7u4DpvuYxd]]} PHAN A.' DAISO PHAN B~I SO

CBdd I San bong c6 chieu dai tu 1 oom den 120m, chieu r ng tl164m den 75m. Khung thanh c6 chieu dai 7,3m va chieu cao 2,44m. so huu ti Cac phep tinh ve so huu ti Luy thita cua m<}t so hftu ti Ti I~ thuc. Day ti so bang nhau So VO ti. So thl/c Bbl DUaNG TOAN 7 I T~P 1

56 HO'UTi KIEN THO'C CAN NHO 1. f>!nh NGHiA So hu'u ti 56 hctu ti la s6 c6 the viet du6'i d~ng m(>t phan s6. I a b la m(>t phan so khi: a, b E z va b :;e o. T~p hf1p so hu'u ti duqc kf hi~u la Q. a x E Q => x = b ; a, b E Z; b :;e 0. M t s6 khong the viet auqc duai dc;mg ~ m t phan s6 thi kh6ng la s6 hctu tl. ~ 2. BIEU Dl~N TR~N TRl)C S6 ~ 1 3 2,275-2 - 1 0 2 3 Moi s6 huu ti deu bieu dien bai m(>t diem tren tn,jc s6. Tren true s6, diem bieu dien s6 huu t.i x duqc g9i la diem x. Neu x, y E Q thi x ~ y, ho~c x < y. 3. SO SANH HAI S6 HO'U Tf Bu'6'c 1. Viet cac s6 hctu ti x va y dl16'i d~ng m(>t phan s6 c6 mau s6 duang. Bu'6'c 2. Quy dong mau s6 cac phan s6. Bu'6'c 3. So sanh cac tu s6 (so sanh cac s6 nguyen). PHAN D~I SO

XE Q x>o x la so huu ti dudng. 56 huu ti ducmg x = O x khong la so huu ti dudng va cling khong la so huu ti am. T~p hqp Q 560 x<o x la so huu ti am. 56 h[lu ti am HOI t>ap NHANH 1. Dung dien D, sai dien S: Khang dinh a) - 0,7 E Z b) - 0,7E Q 2 c) - - ~ Z 7 2 d) - - ~ Q 7 e) N c Z DIS 2. Dien so thich hqp vao cho cham (.. ~ : 1 1 a) -=- - 2 b) -~ =~ - 3 c) - ~= --=-- 7-7 3. Ket lu~n dung la: (A) - 10 > - 7-15 - 14 d) - 7 = -?_ 11... 3-3 e) -= - - 5... f) - 11 = - 11 (B) _ 9_ < - 11-27 33 Vi d\i f)z E Q HQC GIAI TOAN (C) - 34 > _22_ 51 57 (D) - 46 < - 27 69 54 So sanh hai s6 huu ti sau: ' 8 x=-0,8 va y = -. - 9 Cdch 7: So sdnh theo ba btjac. Cdch2: Xet tong cua moi so vai 7. each 1 Bllac 1. Viet cac so huu ti thanh phan s6 c6 mau so dudng. - 4 8-8 X= - 0,8=- Vay=-=-. 5-9 9 Buac 2. Quy dong mau so cac phan so. - 4-36 ' - 8-40 x=-=-- va y=-=--. 5 45 9 45 Buc]c 3. So sanh cac tu s6. - 36-40 - 36 > -40, nen - - > - -, suy ra x > y. 45 45 801 DUONG TOAN 7 I T~ P 1

- 4-4 1 Cach 2 X= - 0 8=-=? x + l = - + 1= - ;, 5 5 5 V1 1 1 A 1 1 1 - > -, nen x + > y + =? x > y. 5 9 8-8 - 8 1 y=-= - =? y + l = - + 1= -. - 9 9 9 9 Vid1:1 Loi giai dung hay sai? B~n BEE so sanh hai so - 13 ' 11 x=-va y = - nhusau: 15-13 - 13 11-11 Bliac 7: x = -va y = - = -. 15-13 13-13 - 11-11 B110c2: - < - < - (vl-13 <-11 15 15 13 va 15 > 13). - 13 11 Suyra: - < -. 15-13 Lai giai eta cho sai. C A ' 11 11-11 11 o-< -,nen-> -. 15 13 15 13 Do d6 kh6ng ket lu~n duqc x < y. S, I. C' 13 2, Ila a1. o x + l = - + 1=- va. 15 15 11-11 2 y + l = - + 1=-+ 1= -. - 13 13 13 M a ' - 2 < - 2 =? x+l < y+ 1 =? x<y 15 13 13 11 =} - <-. 15-13 Hay chi ra m9t so ho'u ti nam gio'a hai so ]_ va 0,5. 3 O<a<b 1 1 =} - > a b, 1 1 1 1 1 1 Co - < - < - =? - < - < - 3 2,5 2 3 ~ 2 1 2 1 2 =} - < - < -. 3 5 2 Suy ra so huu ti phai tlm la 3.. 5 C6 v6 so so ho'u ti nam gio'a hai so ]_ va ]_. V1 2 < 2,5 < 3 nen 3_ la mot so can 3 2 5. tlm. Nhung gio'a 2 va 3 con v6 van so ho'u ti no'a, ch~ng h~n v6'i so 2,4, ta c6 : 1 1 1 1 1 1, 5 2 < 2,4 < 3 =} - < - < - =} - < - < -, do do - cung la so ho'u ti can tlm. 3 2,4 2 3 ~ 2 12 5 PHAN D~I SO

Vi dl:i TI so giua so do chieu cao va so do vong eo cua m9t nguoi dan 6ng (cling m t don v! do) cho biet sue khoe cua ngvoi c16. Neu nguoi dan ong c6 ti s6 c16 nho hon 2 la sue khoe c6 van de. Ong A cao 1,72m, vong eo 88cm ; 6ng B cao 1,56m, vong eo 72cm. Theo bc;in th1 sue khoe cua ai kem hon? Gii~ --------- f) ~ t cp(c) la ti s6 gio'a s6 do chieu cao va s6 do vong eo cua 6ng c. Ta c6: <p (A) = 172 = 1.3..!_ < 2; 88 22 <p (B) = 156 = 2_!_ > 2. 72 6 V~y sue khoe cua 6ng A kem hon. Vai nam giai tr11tmg thanh, vong eo cang Ian thi sue khoe cang kem. Hlnh vu6ng kfch thll6'c 3x3 (c6 9 6) dvqc gqi la HINH VUONG DUQC SAP khi cac 6 dvqc dien cac s6 huu ti tang dan theo hang tu trai sang phai, tang dan theo c t Wtren xu6ng dv6'i. Hlnh sau cho ta m(>t vf dt,1 Ve hinh vuong dli<!c sap. 1 3 4 2 6 7 5 8 9 Cho B = {-_!_.~.!_. i._1 - _!_. - ~ } 3 ' 4 ' 4'5 ', 6' 7 Dien cac s6 huu ti thu(>c t~p B vao cac 6 vu6ng con khuyet cua hlnh vu6ng B de duqc "hlnh vu6ng dvqc sap": 0 Sap xep: 5 1 1 1 3 4 B: - 1<--< - - < - - < - - < - < - 7 3 4 6 4 5 Ta c6 ket qua nhv sau: 1-1 - - 0 3 5 1 3 -- -- - 7 4 4 1 4-0,3 -- - 6 5 Hlnh vu6ng B -0,3 Hlnh vu6ng B Sap xep eek s6 dii cha tu nho den Ian, sau <16 dien s6 vao eek 6 vu6ng. ---------------Ut "-"- - II.Ii) 801 DUONG TOAN 7 I T~P 1

Vi dy Sa do sau bieu dien d9 cao cua cac vi trf so vai mlfc nuac bien. Hay dien cac so do la cac s6 hctu ti (don vi la ki-16-met) vao cac diem tlfc1ng ung: 82. 226. 124. 28. - 145. 0. 132 91' - 339 1 23 '19'174' '21" c Ml/c nuac bien la diem H ung vai s6 0. Cac diem E va G la cac diem duai mljc nlfac bien va ung vai cac s6am. B A E G H So sanh cac s6 hvu ti am: -145-5 - 4-2 - 226 226-145 226 - - =-< - = -=- - = --::::} --< - - < 0. 174 6 6 3 339-339 174-339 So sanh cac so hctu ti duang: 82 < 1 < 28 < 38 = 2 = 124 < 124 < 132 < 132. 91 19 19 62 23 23 21 Suy ra: V~y: - 145 < 226 < 0 < 82 < 28 124 132 174-339 91 19 < 23 < 21 H ~ O (km) A 82 km D 124 km Truac Mt hiiy sap xep ccic s6 huu 91 23 ti do cho theo thu ti/ nho den Ian. Q ~ 28 km -145 B E --km 0() ~;... (~ ' ( 19 174. ~) ~ \'-, 226 132 km ' c G km 21-339 PHAN B~I SO

Vidy So sanh cac so ho'u ti sau: 12 ' 13 a ) - va - b) 17 18 1 84 ' -337 -va--. - 83 331 a) C6: ~ < 1 I nen ~ < 12 + 1 = 2i. 17 17 17+1 18 b) C6: - 337 < 1, 331. -337-337+ 1 nen - - <--- 331 331 + 1 h 84-337 ay - 83 >331. -336-84 332 83 Truong hqp: a, b E z va b > 0 N eu,, a < b t h' a a+ 1,,, b h' a a+ 1 1 - < -- va neu a > t 1 - > --. b b+ 1 b b + 1 Truong hqp: a, b, C, d E z va b, d > 0,, a c h' a a+ c c Neu - < - t 1-<--< -. b d b b+d d BAIT~P A 8 CO BAN 1.1. f)ung dien ), sai dien s: Khang dinh f>/s Khang dinh f>/s a)-0,25 E Q d) 226 EN b) - 0,25 c Q e) 226 ~ Z c){ - 0,25} c Q 1.2. Khang dinh nao sai? - 22 33 (A) - > - 9-7' f) 226 ~ Q (B) ~ < -28; - 48 35-8 - 4 6-20 - 36 (C) - < - <-; (D)- < -. 24 28-30 35 63 1.3. M~ mua banh nuong nhan dip Tet Trung thu. Bo cat m(>t chiec lam 4 phan bang nhau va an 3 phan. M~ cat m(>t chiec lam 8 phan bang nhau va an 7 phan. Hoi neu con cat m(>t chiec lam 6 phan bang nhau th) con can an may phan de phan con lc;ii cua con trong khoang hai phan con lc;ii cua bo va m~? 1.4. f)ien cac so ho'u ti thfch hqp vao cho cham (... ) : 1 1 - - <... <... <... <... < - -. 5 8 801 ouang TOAN 7 I w 1

{[[W+bz0FkV43GmRt7u4DpvuYxd]]} NANG CAO 1.s. nm s6 nguyen t6 a, biet: 8 10 8 - < - <-. 17 a 11 1.6. Nguoi ta viet cac so huu ti: 1 1 1 1-12, -,,, - 10 tren m<?t vong tron theo chieu kim dong ho. Sau d6 theo chieu kim dong ho, dau tien xoa s6 (-1 ), roi b6 qua m<?t s6 xoa s6 tiep theo. Cu lam Ian luqt nhu the den khi chi con lc;ii m<?t s6. H6i s6 con lc;ii la s6 nao? 1.7. nm s6 hctu ti c6 dc;ing? biet gia tr! a 8 8 cua ' no ' I' an h an - - va ' n h o ' h an - -. 11 13 1.8. C6 bao nhieu s6 huu ti viet duoi dc;ing m<?t phan s6 c6 tli s6 bang 9 ma gia tri cua s6 huu ti d6 Ion hon - 3 va. 5-4 nh6 hon -? 9 1.9. nm s6 nguyen a, sao cho: a ) - 3 - I' a so,, nguyen. 2a - 5 b) 3 - - I' a so " tun h" 1en. 7-3a EMCOBIET? Trong toan hqc, s6 huu ti la thuong cua m<?t phep chia hay la m<?t s6 duqc viet duoi dang mot phan s6 ~ voi a, b la cac.. b s6 nguyen (b khac O). Moi s6 nguyen deu la m<?t s6 huu ti voi b = 1. T~p hqp s6 huu ti duqc kf hi~u la Q (hay Ql), trong d6 Q chu cai dau cua tlt quoziente (tieng Y, nghia la thuong). PHAN ll~i s6

cac PHEP TiNH VE s6 HO'U Ti KIEN THO'C CAN NHO 1. GIA TR! TUY~T f>61 CUA M()T s6 HO'U Ti Gia trj tuy~t doi cua x duqc kf hi~u la Ix!- -xlas6a6icuax. ~ lxl la khoang each tu diem x toi aiem o.!xi V x E Q: lxl= jx, ne~ x ~ O - x neu x < O!xi lxl ~ O lxl=l-xl lxl~x... - x 0 x 2. PHEP T[NH C()NG, TRCJ', NHAN VA CHIA cac s6 HO'U Ti Neu x I y E Q thl x = ~ va y =!::... voi a, b, C, d E z va b, d :;e 0. ) b d a c ad+bc x+y= - + -= bd b d Cc}ng x-y=x+(-y) Tru I so huu ti x, y a c ac x.y= -. - =- Nhan b d bd Chia 1 x:y=x. y (voi "#- O) 3. QUY TAC CHUY~N V~ I x+y=z chuyen ve doi dau l x=z-y Phep c ng va phep nhan so hclu tl c6 ccic tf nh chat cua phep c ng, phep nhan phan s6. BUI DUONG TOAN 7 I T~P 1

HOI OAP NHANH 1. Dung dien D, sai dien S: Khang djnh a) x < O =? Jxl < x 1 b)x >O=?- <X x c)-x la so am d) x<o => lxl= -x D/S 2. Cho a = - x + y - z. Voi x = 1, y = 2 va z = 3 thl iai bang (A) -2 (B) 0 (C) 2 (D) 4 HQC GIAI TOAN Vi d1,1 Dien s6 thfch hqp vao 6 tr6ng: 1-1 2 2 Chia khoa: Tu 6 thu ba, s6 can dien la tong cua cac s6 thu c hai 6 lien truck Vf d1,1: 56 a 6 thu ba la tong cua hai s6 a 6 thu nhat va 6 thu hai..!.+ - l = 0. 2 2 Vi d1,1 Thl,l'c hi~n phep tf nh: s6cr6thuba:..!.+ - 1 = 0. 2 2 S oaot "''' h utu: ' -+0-1 = - - 1 =-0,5. 2 2 Cu tiep t1,1c nhu v~y ta c6: -1 2 2 0-0,5-0,5-1 - 1,5-2,5-4 - 6,5 a) A= - 90 + 45 _ 75 189 84 126 bl B=112- + 8~ - 10~ 21 24 35 c) C = 37.~ - 32}+-2.-: l~ - ~: 120 43 29 41 2 58 37 29 21 Khi thlfc hi~n cac phep tf nh voi s6 huu ti, luu y: Rut g9n de quy dong mau s6 de hon. Tach hon s6 thanh phan nguyen va phan s6 (nh6 hon don vi). Nh6m cac s6 hc;ing m t each thfch hqp. Sud1,mg tinh chat phan ph6i giua phep nhan va phep c ng. PHAN B~I SO

a) A= - 10 +~ - 25 = - 40+ 45-50 21 28 42 84-45 15 = - =-- 84 28 1 2 3 b) B= ll-+8--10-3 3 5 ( 1 2 3) = (11 + 8-1 0) + -+--- 3 3 5 = 9 +( 1 - ~ )= 9 + % = 9%. = -.-- -. - = --- = - = - 43 58 41 58 58 58 58 29 Vi d\i Dien tiep vao cac 6 con tr6ng cua hai hlnh KIM Tl/THAP, biet chla khoa a hang cu6i. - - 100 1 1 1 1 - - - - -- 2 2 3 3 H rn 0,01-0,l 10 _@_ rn - 1 - -- 3 100 1 1 -- -- 10 10 6 6 1 0 -- 0-0,1-100 6 1 1 1 1 - -- - -- O,Ql - 10 10 2 2 3 3-0,1-0,Ql Cho A= lxl+ x. a) Rut g<;>n A. b) Tfnh gia trj cua A biet x E {~ 1 ; ~ 1 ; 0 ; ~ ; ~} c) nm gia tr! nh6 nhat cua A. d) nm x biet gia trj cua A bang - 0,4; O; ~. a) Ta xet hai tn.tong hqp: Truong hqp 7: x ~ 0 ::::} lxl,= x ::::} A= x + x = 2x. Truong hqp 2: x < O::::} lxl =-x :::} A = -x + x = O. V~y : A= 2x I neu x ~ 0 va A = 0, neu x < 0. 801 DUONG TOAN 7 I T~P 1