Tài liệu Thiết kế bài giảng hình học nâng cao lớp 10 -tập 1

TRAN VINH JI1 HINH HOC TAP M O T ^ NHA XUAT BAN DAI HOC SU PHAM TRAN VINH ^ ^ s, THIET KE BAI GIANG HINH HOC -^ /v NANG CAO - TAP MOT NHA XUAT BAN OAI HOC SLT PHAM L0I NOI DAU Bat d^u tir nam hoc 2006 - 2007, hai bo sach giao khoa toan mdi : Co ban va Nang cao da duoc su dung tren toan qudc Viec thay sach luon gkn lien v6i viec ddi mdi phuong phap day hoc. Bo sach Thiet ke bai giang Toan 10 - nang cao ra doi nham phuc vu viec ddi mdfi do. Bo sach duoc bien soan dua tren cac chuong, mitc ciia sach giao khoa, bam sat noi dung cua sach giao khoa, tir do hinh thanh nen cau triic mot bai giang theo chuong trinh m6i: Lay hpc sinh lam trung tam va hd trp cua cac phuong tien day hpc hien dai. Phan dai sd gom 2 tap. Tap 1: gdm cac chuong I, chuong II va chuong III. Tap 2 : gdm cac chuong IV, chuong V va chuong VI. Phan hinh hpc gdm 2 tap. Tap 1: gdm chuong I va bai 1, bai 2 chucmg II. Tap 2: phan con lai Mdi chuong dupe thiet ke cong phu, dua ra cac cau hdi va tinh hudng thii vi. Trong cac hoat dong chung toi cd gang chia lam 2 phan: Phan ciia giao vien (GV) va phan ciia hpc sinh (HS), df mdi phan co cac cau hoi chi tiet va hudng din tra ldi. Thuc hien xong mdi hoat dong, la da thuc hien xong mot don vi kien thiic hoac ciing cd don vi kien thiic do. Sau mdi bai hpc chiing toi co dua vao ph^n cau hpi trie nghiem khach quan nham de HS tu danh gia dupe miic dp nhan thiic va miic dp tiep thu kien thiic cua minh. Sau mdi bai chiing toi cd gang co nhirng phki bd sung kien thiic danh cho GV va HS kha gioi. Phan phu luc trong dai sd, la phan danh cho giao vien, nham sii dung cac phdn mdm ciia toan hpc lam chu kidn thiic, lam chu cac c«n sd can tinh toan tir do neu len dupe each day moi chii dong va sang tao. Day la bp sach hay, dupe tap the tac gia bien soan cong phu, iing dung nhidu thanh tuu khoa hpc mdi trong tinh toan va day hpc. Chiing toi hy vpng dap iing dupe nhu cau ciia giao vien toan trong viec ddi mdi phuong phap day hpc. Trong qua trinh bien soan, khong the tranh khoi nhung sai sot, mong ban dpc cam thong va chia se. Chiing toi chan thanh cam on su gop y cua cac ban. 1 ac gia Chi/oiMq I VECTO PHAN 1 NHONG VXN 9 E CUA CHLfONG I. NOI DUNG Chuong I nham cung ca'p cho hpc sinh nhirng kien thiic co ban vd vecto, cac phep toan vd vecto va cac tinh chat cua vecto. Hpc xong chuang nay yeu cau hpc sinh nam viing nhirng van dd sau: 1. Dinh nghia vecto: Gia ciia vecto, hai vecto cimg phuong, hai vecto cung hudng, hai vecto ngupc hudfng. 2. Hai vec to bang nhau, vecto-khong. 3. Tdng cua hai vecto: Quy tac hinh binh hanh va Quy tac ba diem. 4. Hieu cua hai vecto. 5. Tich cua vecto va mot sd. 6. Toa dp trung diem, toa dp vecto, toa dp trpng tam, dp dai vecto va dp dai doan thang. II. MUC TIEU 1. Kien thijrc Nam dupe toan bp kidn thiic co ban trong chuong da neu tren. - Hieu khai niem vecto. - Hidu y nghia cac phep toan vd vecto. - Bidt dupe phep toan cua mot vecto va mot sd thuc. - Nam dupe toa dp ciia vecto, toa dp cua diem, toa dp trung diem va toa dp trpng tam. 2. KT nang - Xac dinh nhanh mot vecto khi bidt mdt doan thang. - Xac dinh dupe dp dai vectP. - Chirng minh ba didm thang hang dua vao vecto. - Tfnh dupe dp dai dudfng trung tuyen, chu vi tam giac,... 3. Thai do - Hpc xong chuong nay hpc sinh se lien he dupe vdi nhieu van de thuc te sinh dong. Lien he dupe vdi nhiing va'n 6i hinh hpc da hpc b ldp dudi, md ra mdt each nhin mdi vd hinh hpc, tir dd cac em cd the tu minh sang tao ra nhiing bai toan hoac nhung dang toan mdi. >^ PHAN 2 CAC BAI SOAN §1. Cac dinh nghia (tiet 1, 2) - ^ ^ j I. MUC TlfiU 1. Kien thurc HS nam dupfc: 1. HS hieu khai niem vecta, vectcf-khdng, dp dai vecta, hai vecta cilng phuong, hai vecta cung hudng, hai vecta bang nhau. 2. HS biet duoc vecta-khong ciing phuong va cung hudng vdi mpi vecta. 3. HS biet chiing minh hai vecta bang nhau ; biet xac dinh mot vecta bang vecta cho trudc va cd diem dau cho trudc. 2. KT nang • Xac dinh nhanh chdng dupe vecto khi biet mot doan thang. • Xac dinh dupe hai vecto ciing chidu, hai vecto ngupc chidu. • Xac dinh dupe hai vecto bang nhau. 3. Thai do • Lien he dupe vdi nhidu van 6i cd trong thuc te vdi van dd vecta. • Cd mdi lien h6 chat che giua vecto va doan thang. • Cd nhidu sang tao trong hinh hpc. II. CHUAN BI CUA GV VA HS 1. Chuan bi cua GV: - Hinh ve 1, 2 trang 4 SGK - Tranh ve gidi thieu lire trong vat li. - Thudc ke, phaii mau,... 2. Chuan bi ciia HS : - Dpc bai kl a nha, cd the dat ra cac cau hoi \ e mot van de ma em chua hieu. in. PHAN PHOI THOI LUQNG Tiet 1: Tiir dau den het muc 2. Tiet 2: Phan con lai va hudng dan bai tap. IV. TEN TDiNH DAY HOC n. DAT VA'N D€ Cau hoi 1. Tren mot doan dudng AB (ta gia sir day la mot doan thang) Ban Thao di tir A den B. ban Hidn di tir B den A. a) Quang dudng hai ban di cd bang nhau khdng? b) Hudng di ciia hai ban cd ciing nhau khdng? GV cho HS tra ldi va hirdng den khai niem vecta. Cau hoi 2. Hai dtd di tren hai doan dudng thang song song vdi nhau. (a) Hai dtd ludn ludn di cimg chidu. (b) Hai dtd ludn di ngupc chieu. (c) Hai dtd cd the di ciing chieu, cd thd ngupc chidu. (d) Ca ba kdt luan tren deu sai. Hay chpn khang dinh diing. 0. am MOI HOAT DONG 1 1. Vectd ia gi ? a) Muc dich: Giiip HS Mid dugc vecto Id gi'. b) Hudng thitc hien - Niu vi du trang 4 SGK. Thite hiin ? 1 - Niu cdc dudi nglua. - Gidi thieu ki hiiu vecto. - Gidi thieu vecto-khong c) Qud trinh thitc Men • Thuc hien 1 GV : Thu'c hien thao tac nay trong 3'. Hoat dong cua GV Cdu hdi 1 Chide tau dang chay theo hudng nao? Cdu hdi 2 Vay cd the giai dupe bai toan khdng? Cdu hdi 3 Em cd the tra ldi cau hdi ciia bai toan khdng ? Hoat dong cua HS Ggi y trd ldi cdu hdi 1 Hien nay bai toan dat ra chua biet hudng ciia tau. Ggi y trd ldi cdu hdi 2 Khdng the giai dupe. Ggi y trd ldi cdu hdi 3 Khdng the tra ldi dupe. GV ket luan cac van de: - De tra ldi cau hdi cua bai toan, phai bidt hudng chuyen ddng cua tau. ~ Biet van tdc chuyen ddng cua tau. Sau d6 dung hinh 2 (trang 4 SGK) de d i n dat HS di den khai niem vectd. B B A a) /?) Hinh 2 • Neu dinh nghTa Vecto Id mdt dogn thdng ed hudng, nghia Id trong hai diim miit cda dogn thdng, dd ehi rd diim ndo Id diem ddu, diem ndo la diem cudi. Ki hieu Neu vecta cd diem dau la M va diem cudi la A^ thi ta ki hieu vecto dd la MN. GV : Thu'c hien thao tac nay trong 3'. Hoat dong ciia GV Hoat dong cua HS Cdu hdi 1 Mdt doan thang AB cd dp dai khac khdng, cd the xac dinh dupe bao nhieu vecto ? Ggi y trd ldi cdu hdi 1 Cdu hdi 2 Ggi y trd ldi cdu hdi 2 Mdt doan thang AB cd dp dai khac khdng cd thd xac dinh dupe hai vecto: AB va BA. Vecto AB \a BA cd cac diem dau Sai, vi didm dau ciia vecto AB \a trung nhau, cac diem cudi triing nhau. A, diem dau ciia vecta BA la B. diing hay sai ? Tuong tu dd'i vdi cac diem cudi. 10 • GV gidi thieu cac ki hieu vecto : Nhidu khi de thuan tien, ta cung ki hieu mdt vecto xac dinh nao dd bang mdt chu in thudng, vdi mui ten d tren. Chang han vecta a, b, x, y,.... • Vecta-khong GV dat van de de di den khai niem vectd khong bang cac cau hoi sau: Cho hai diem A vd B. HI. Khi A triing B thi AB cd do ddi bdng bao nhiiu? H2. Vecto AB vd BA khdc nhau khi ndo? Ggi 2 HS trd ldi vd di din khdi niim vecto-khong. Khdi niem Vecto ed diem ddu vd diem cudi trimg nhau ggi Id vecto-khong. GV thi/c hien thao tac nay trong 3' Hoat dong ciia GV Cdu hdi 1 Hoat dong cua HS Ggi y trd ldi cdu hdi 1 Mot doan thang AB cd dp dai tuy y. cd Mdt doan thang AB cd dp dai khac khdng cd the xac dinh dupe the xac dinh dupe bao nhieu vecta ? vaJs. 4 vecta :JB.'BA,'AA Cdu hdi 2 Trong cac vecto dd, vecto nao la vecto khdng? Gtyi y trd ldi cdu hdi 2 AAwaBB. 11 HOAT DONG 2 2. Hai vectcf cung phiTdng, cung hirdng a) Muc dich: Ddn dat HS hieu dugc khdi niim : Hai vecto cUng phuong ; Hai vecto cdng hudng. b) Hudng thitc Men Ddy Id khdi niim mdi, do dd G\^ niu vd cho HS thdo ludn nhieu ve ede van de : - Gid eiia recto ; Hai vecto cimg pliUOng ; Hai vecto cimg hifdng. - Phdn biet duge cdc khdi niim vecto ciing phuong, cdng hifdng. c) Qud trinh thuc Men • Gia cua hai vecta GV sir dung hinh 3 (trang 5 SGK) va cho HS tra ldi cac cau hoi HI. Mdt vecta AB khac vecto-khong cd bao nhidu dudng thang di qua hai diem A va B? H2. Mdt vecta AB bang vecto-khdng cd bao nhieu dudng thang di qua A va B? Sau do GV ket luan: Vdi mdi vecto AB (khdc vecto-khdng), dudng thdng AB dugc ggi la gid eua vecto AS. Cdn ddi vdi vecto-khdng A A thi mgi dudng thdng di qua A deu ggi Id gid ciia nd. M Hinh 3 12 • Hai vecta ciing phuang GV dat van de : HI. Tren hinh 3, cac vecto A6, DC, EF cd gia quan he vdi nhau nhu the nao? H2. Tren hinh 3, cac vecto MN, QP c6 gia quan he vdi nhau nhu thd nao? GV cho HS tra ldi va neu khai niem hai vectd cung phu'dng Cdc vecto AB, DC, EF cd ciing phuong, hay don gidn Id ciing phuong. Hai vecto MN vd QP cd gid cdt nhau. Ta ndi hai vecto dd khdng cung phuong. Hai vecto ggi Id cung phuong ne'u chung cd gid song song hodc triing nliau Rd rdng vecto-khdng cung phuong vdi m.gi vecto. Be cung co GV thi/c hien thao tac sau trong 3' Cho hinh binh hanh ABCD Hoat dong cua GV Cdu hdi 1 Hay chi ra vai cap vecto ciing gia. Hoat dong ciia HS Ggi y trd ldi cdu hdi 1 AB va BA ; AD va DA; Cdu hdi 2 Hay chi ra vai cap vecto ciing phuong Ggi y trd ldi cdu hdi 2 nhung khdng cimg gia. AB va CD ; AD va BC,... Cdu hdi 3 Ggi y trd ldi cdu hdi 3 Hay chi ra vai cap vecto khdng ciing JC va BD, JB va AD,... phuang. • Hai vecto cung hudng GV sir dung hinh 4 trang 6 SGK de thao tac di den khai niem : Hai vectd cung hirdng. 13 B D C Hinh 4 GV di/a ra cac cau hoi sau: HI. Hai vecto AB va CD ciing phuang hay khdng? va cd hudng nhu the nao? H2. Hai vecto MN va PQ ciing phuang hay khdng? va cd hudng nhu the nao? GV di den dinh nghTa Ni'u hai vecto ciing phuong thi hodc chung cilng hudng, hodc chung ngugc hudng. De cung co GV tht/c hien thao tac sau trong 3'. Cho hinh binh hanh ABCD Hoat dong cua GV Cdu hdi 1 Hay chi ra vai cap vecto cung hudng. Cdu hdi 2 Hay chi ra vai cap vecto cung hudng nhung khdng ciing gia. Cdu hdi 3 Hay chi ra vai cap vecto cimg phuang nhung khdng ciing hudng. 14 Hoat dong cua HS Goi y trd ldi cdu hdi 1 AB vaDC ; AD va BC; Ggi y trd ldi cdu hdi 2 ABvaCD ; AD vaBC,... Ggi y trd ldi cdu hdi 3 ABvaCD, AD waCB,... GV neu chu y Ta quy udc rdng vecto-khdng eiing hudng vdi mgi vecto. HOAT DONG 3 3. Hal vectd bing nhau a) Muc dich: Cho HS ndm dugc khdi niim hai vecto bdng nhau. b) Hudng thuc Men - GV: Niu khdi niim do ddi dogn thdng vd do ddi vecto. - Thitc Men\?_1\, \?3\ trang 7SKG. - Niu dinh nghia hai vecto bdng nhau. - Cung CO khdi niem bang' 1 trang 7 SGK. - Cling CO khdi niim bang • 2 trang 8 SGK. c) Qud trinh thuc Men • Thuc hien ?1 GV thirc hien thao tac nay trong 3'. Hoat dong cua GV Cdu hdi 1 Vecto-khdng cd dp dai bang bao nhieu? Cdu hdi 2 Hai doan thang AB va CD bang nhau thi dp dai cac vecto AB va CD cd bang nhau khdng? Vi sao? Hoat dong cua HS Ggi y trd idi rdu hdi 1 Bang 0. Ggi y trd ldi cdu hdi 2 Bang nhau. 15 • Thuc hien [Til. Dua vao hinh 5, trang 7 SGK. GV thu'c hien thao tac nay trong 3'. Hoat dong ciia GV Hoat ddng ciia HS Ggi y trd ldi cdu hdi 1 Cdu hdi 1 Khdng bang nhau do khdng Hai vecto AB va AD tren hinh 5 cd cung hudng. bang nhau khdng? Ggi y trd ldi cdu hdi 2 Cdu hdi 2 Gang dp dai va ciing hudng. Hai vecto AB va CD tren hinh 5 cd dp dai va hudng nhu the nao? • Neu dinh nghTa Hai vecto ggi Id bdng nhau ni'u chiing ciing hudng vd ciing do ddi. Ni'u hai vecto a vd b bdng nhau thi ta viii a = b . GV thi/c hien thao tac nay trong 3', de cOng co khac sau khai niem. Cho hinh binh hanh ABCD. Hoat dong cua GV Cdu hdi 1 Hay chi ra cac cap vecto nao bang nhau? Cdu hdi 2 Hoat dong cua HS Ggi y trd ldi cdu hdi 1 AB va DC ; AD va BC ; Ggi y trd ldi cdu hdi 2 Hai vecta AB va CD cd bang nhau AB va CD khdng bang nhau vi khdng? vi sao? chiing ngupc hudng. 16 • Thuc hien thao tac ^ 1 (trang 7 SGK) GV thirc hien thao tac nay trong 3'. Hoat dong ciia HS Hoat dong ciia GV Ggi y trd ldi cdu hdi 1 Cdu hdi 1 Hay chi ra cac vec to nao bang nhau? JE = IC ; AF = 7B; BD=DC; Cdu hdi 2 Ggi y trd ldi cdu hdi 2 Neu G la trpng tam tam giac ABC thi cd the viet AG = GD hay khdng ? Vi sao ? • Thuc hien thao tac ^ AGva GD khdng bang nhau vi AG = 2 GD. 2 (trang 8 SGK) GV thirc hien thao tac nay trong 3'. Hoat dong ciia GV Cdu hdi 1 Hay chi ra diem A. Hoat dong cua HS Goi y trd ldi cdu hdi 1 Qua 0 dung dudng thing A // d (d la gia cua a), tren A la'y A sao cho OA ciing hudng vdi a, va OA = a Cdu hdi 2 Cd bao nhieu diem A nhu vay ? 2- TKBGHiNHHQC10/1 (NC) • Ggi y trd ldi cdu hdi 2 Cd mot diem A nhu vSy. 17 TOM m B^i hpc 1. Vecta la mdt doan thang cd hudng, nghia la trong hai diem miit ciia doan thang, da chi rd diem nao la diem dau, diem nao la diem cudi. 2. Vecta cd diem dau va diem cudi triing nhau gpi la vecto-khong. 3. Vdi mdi vectP AB (khac vecto-khdng), dudng thang AB duoc gpi la gid cua vecto AB. 4. Hai vecta gpi la ciing phuang neu chiing cd gia song song hoac triing nhau. Rd rang vecto-khdng cung phuomg vdi mpi vectP. 5. Neu hai vecto ciing phuang thi hoac chiing ciing hudng, hoac chiing ngupc hudng. 6. Hai vecto gpi la b4ng nhau neu chung cung hudng va ciing dp dai. Neu hai vectP a va b bang nhau thi ta viet a - b . HOATDONG 4 HCrPNG D^N Bfll T^P SGK a) Muc dich: Ciing cd cac khai niem trong bai hpc, ren luyen ki nang giai toan. b) Hudng thuc Men: Cac bai tap ddu hudng dan vd nha. c) Qud trinh thitc Men Bai 1. Hudng ddn - HS xem lai dinh nghia vecto va tra ldi. Vecto la doan thang dinh hudng, nghia la cd phan biet diem dau va diem cudi. Doan thang khdng cd hudng nghia la hai d^u doan thang cd vai trd nhu nhau. Bai 2. Hudng ddn 18