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II DIEN D A N KHAI THAC VA ill DUNC HIEU QUA THIET 61 DAY HOC TOAN 12 GOP PHAN DOI Mdl PHUONG PHAP DAY HOC Nguyen Huy Sim Tfl nam hpe 2007 2008, Vifc sfl dyng dyng cy him sd, liy dgo him bgc nhat, sic[.]
II DIEN D A N KHAI THAC VA ill DUNC HIEU QUA THIET 61 DAY HOC TOAN 12 GOP PHAN DOI Mdl PHUONG PHAP DAY HOC Nguyen Huy Sim Tfl nam hpe 2007 2008, sich giio khoa toin 12 ed sfl chpn Ipc cic ddn vj kien thfle ed bin, rf n ky nang thfle hinh, gin ly thuyet vio thfle tc, dim bio chat Ifldng dio tgo bgc THPT vi dip flng yfu cau ddi mdi Thiet bj dgy hpe (TBDH) rat can thiet, nhim ehdng dgy chay hpe chay, ehdng dpe chfp trpng cic trfldng phd thdng d nflde ta 1/ Tac dung cua TBDH toan 12 Vifc sfl dung cic logi tranh ve (hinh inh, ehfl viet, ky hifu) giflp eho HS khae siu kien thfle, ren luyfn tfl toin hpe dpc lip vi sing tgo Npi dung hmh inh minh hpa, cic djnh nghia, djnh ly, tinh chat, vi dy, quy tie, hf qui, ehfl y, ky hifu toin hpc( e thupc, vi chl khi, c nim trdng, ) Cac bing tdng ket dgng dd thj eua mdi logi him sd, bing nguyen him, dgo him eua him mu, logarit, luy thfla, can bgc n Cac inh ve chin dung, giflp eho HS hieu rd tieu sfl vi sfl nghifp, cdng trinh nghien cflu, nhflng phit minh ddng gdp cua cac nhi toan hpc ndi tieng tren the gidi den van cdn nguyen gia trj (anh La-grang, inh Nepe, anh Niu- tdn, inh Cic-dano, ) Vifc sfl dyng dyng cy thflde thing vi com pa de ve hinh di giiip HS tgp thdi quen vi ky nang ve dd thi vi cic logi hinh khdi khdng gian Vifc sfl dyng md hinh giup HS hieu dflde eie flng dyng thfle te eudc sdng eua eie khdi da difn vi biet phin tieh eie bp phin Giam tinh trfly tfldng eua toin hpe, tang cfldng sfl ghi nhd vi tfl hpe, giflp HS ehu ddng vi sang tgo hpe tip, phit trien tfl duy, hieu biet hdn ve the gidi xung quanh 2/ Khai thic vi sii dyng TBDH toin 12 Toin 12 gdm ed quyen li Giii tich vi Hinh hpc TBDH toin 12 di sfl dyng cic logi hmh dflgfc md ti bing cic bieu tfldng, qua ngdn ngfl ehfl viet vi ky hifu, eie chfl in dgm vi dflgic ddng khung tgo cho HS ghi nhd nhflng kien thfle ed bin nhat 2.1 Dung tranh ve trfle quan +Trong Giii Uch, vdi sfl ddng bien, nghjeh bien cua him sd, md dau bing hogt dpng 1, yeu ciu HS can phan bift khii nifm ve dogn, khoing, nfla khoing dflgfc xie djnh tren K GV phin tieh rd cic vi dy, tflng bflde xac djnh ve dieu kifn cua Nhdn bdi ngdy 1/2/2012 \l • TAP CHi THifTBIGlAO DUC-sd 78-2/2012 him sd, liy dgo him bgc nhat, lgp bing bien thien vi xet dau tfldddi den ket lugn ve sfl ddng bien vi nghjeh bien Vdi cflc trj cua him sd, GV cho hpc sinh nim dfldc khii nifm cflc dgi vi cflc tieu bang djnh nghia Vdi giatq nhd nhat vi ldn nhat, HS nhd quy tic, eich sfl dyng ky hify toan hpc min(nhd nhat), max(ldn nhat) Vdi dfldng tifm cgn, cd dfldng tifm cgn li dfldng tifm cgn ngang vi dfldng tifm can dflng qua cic hinh ve cua thj Ve khao sit sfl bien thien va ve thi cua him sd, HS hieu rd tflng bflde lim toin nhfl tip xac djnh, sfl bien thien, dd thj (tr.31) Mpt trfldng hgfp khic, dd la bang "Dgng dd thj cua ham sd bgcbay = ax^ + bx^ + cx + d(a5t 0)" dfldc tong ket giflp cho HS hieu gpn hdn ve cae dgng dd thi bgc ba Bing "Dgng eua thj him sd y = ax''+ bx^ + e (a ?;: 0)" tr.38, day li phfldng trinh trung phfldng ed nghifm phan bift vi nghifm Vdi luy thfla, qua mpt sd vi dy, HS biet tinh luy thfla vdi so mu nguyfn Vdi logarit, tfl dinh nghia, logait cd so a cua b cd ky^ hifu li log^b, tinh chat, djnh ly dflcfc ddng khung, yeu ciu HS phii DieN DAN ghi nhd de ap dung giai eae bii tip (tr.62) 2.2 Dung anh giio khoa Ai d i phit minh logarit? Muc bgn ed biet, vdi thdi gian ngan, GV dung inh chin dung in sich hoge d i dflde phdng to eua La-grang (1736 1813), ngfldi Phip, gidi thifu tdm tit tieu sfl vi sfl nghifp edng hien eho toan hpc eua dng(ve bii toin binh dpng eua Mat trang, ly giai vi ehuyen ddng Mgt trang ludn quay mat ve phia Trii dat, bii toin vit the, vit the, ) GV dung inh chin dung nhi toin hpc Nf-pe (15501617), ngfldi Xedt-len, da phit minh Idgarit Ldgarit dflde Nf-pe xem li sd trd giup de tinh ty sd cua sd Qua vifc quan sit bfle inh nay, GV gidi thifu ve tieu sfl, sfl nghifp v i cic ddng gdp cua dng cho toin hpc Muc bgn ed biet, GV dung anh Niu-tdn (1643 -1727), ngfldi Anh, dng rat ehiu khd dpe sich v i ghi chep can than nhflng dieu ly thfl Ong la mpt nhdm ngfldi da sing lip phep vi phin v i tich phin, phat minh ve diy so vd hgn, dinh ly mang ten dng gpi l i "Dinh ly nhi thfle Niu-tdn", djnh luit ve van vit hap dan, Ve flng dyng eua tich phin hinh hpc, tinh difn tieh hmh thang vudng dxigc gidi han bdi cac dfldng thing di tdi tinh the tieh eua vat the (tr 117) l i the tich khdi chop vi chdp cyt, the tich khdi trdn xoay Ve sd phflc: mdi bieu thfle dgng a + bi, dd a, b e R, i = -1 gpi li mpt sd phflc Ddi vdi sd phfle z = a + bi, ta ed a li phan thfle, b la phan io cua z Tren cd sd djnh nghia phdi hdp vdi mpt sd phep toin cd bin, dfla vio dfl lifu da cho, GV hfldng dan HS xac dinh gia trj cua phan thfle vi phan io eua mpt sd phfle Giio vien gidi thifu ve inh Cae-da-nd (15011576), ngUdi I-ta-U-a, dng cd tren 200 edng trinh ve toan hpe Trong quyen saeh "Nghf thuit ldn Clia phfp giai cae phUdng trinh dgi sd" dng trinh biy each giii phfldng trinh bic 3, bic vi de cgp tdi can bic hai cua sd im, sfl nghifn cflu sd phfle bit ngudn tfl cdng trinh II a li can dfldi, b la can tren, f(x)dx li bieu thfle dfldi dau tieh phan vi f(x) li him sd dfldi dau tieh phin PhUdng phip tinh tich phan bang ddi bien sd va tinh tieh phin tflng phan giup HS md rpng kien thfle, biet van dung djnh ly, bien ddi cdng thfle va each dat an phy + Trong Hinh hpc, die trflng eua hinh hpc la ve toan, xae djnh cic hinh khdi a Bing hinh anh Vdi khdi da difn (tr3), bang hinh anh eua khdi mudi an li tinh the cua hdp chat hda hpc tfl nhien, khdi ruble, hinh inh kim tfl thap d Ai Cap ed hmh dang li nhflng khdi chdp tfl giac deu GV gidi thifu ve Le-d-na-dd Da Vin-xi, 2.3 Dung ky hifu toan hpa sy thien tii ngfldi I-ta-U-a hoc Vdi nguyfn him, HS nam d i ve hinh 12 mat deu vi hinh dflde ndi dung djnh nghia v i 20 mat deu (tr.l6) GV cho HS di tdi djnh ly vi tinh chat cua eat bia theo mau (tri8), gap nguyen him Bang nguyen theo dudng ke rdi din cic mep h i m (tr 97) giup HS ghi nhd lgi de ed eie hinh tfl difn deu, eie dgng ed bin nhat de van hinh lip phUdng vi hinh bat dyng eie bii tip Vdi giac deu GV gdi y HS tim thay tich phin, tfl ndi dung bii toin eie hinh da difn deu tfl tinh difn tieh hinh thang cong nhien dfldi dgng tinh the eua vdi cic hinh ve, qua cic vi dy nhieu hdp chat HS nam dfldc cich ly lugn Vdi khdi chdp, the tieh trdng chflng minh de di tdi ket dflde tuih bang V =1/3 Bh(B li luin can tim Tfl dinh nghla difn tieh diy, h li chieu eao) tieh phin: Kim tfl thip d Ai Cap dflgfc xiy dflng vio khoing 2500 nam trfldc Cdng nguyen li mdt khdi chdp tfl giac deu ed chieu \f(x)dx = F{x)\ •' a eao 147m, cgnh diy dii 230m a (tr.24) = F(b) F(a) Vdi mat trdn xoay, xung dd: quanh ta ed nhieu vat the m i f l i dau tieh phin mat ngoii hinh dgng li nhflng TAP CHi THI^ BI GIAO DUC - Sd 78 - 2/2012 II DIEN DAN mgt trdn xoay (tr30) GV tim eie vi dy cd thfle te cupc sdng de eho HS thay rd tinh chat hinh hpe eua mit trdn xoay Chang hgn nhfl: Ip hoa, bit, cdc, ndn, w Vdi hf tpa dp khdng gian, bing hinh inh trii dat vi trgm vfl try khdng gian, xie dinh vj tri ciia diem theo vectd mi O li gdc tpa dp, hf trye xbx, yby, zbz vudng gdc vdi tflng ddi mpt gpi li hf trye tpa dp Deeie khdng gian Oxyz Ky hifu tpa dp eua diem M = (x;y;z) hoge M (x;y;z) vi dpe li diem M cd tpa dp x; y; z Cic bfle tfldng eua tda nhi eao tang hifn dgi eho ta hinh inh cua mat phlng khdng gian (tr.69) Phfldng trinh mat phlng: Ax + By + Cz + D = O dd A,B,C khdng ddng thdi bang O Neu ei hf so A, B, C, D deu khic ta cd phfldng trinh cua mat phlng theo dogn chin: £ £ £ _ a b a Tfl djnh nghia, qua bii toan chflng minh mgt phlng r«^ nV,5n ^Ar t^ " i^n, ,Ar frt (a) nhgn vee td n Iam vee td \hL h ^,^n AA rhir^h \>> v^r khc^^r;dPii^^^^^^^^ khac o v a CO gia vuong goe vdl ^/etdnh!ltvt^^e^^^^^^^ vee td phap myen la eae hg sd A,B,C cua phfldng ^nnh mgt phlng, dflpc Viet li « = (A; B; C) Cdng thflc tinh tpa dp cua vee td vdi diem ngpn vi diem gdc: de chgy dpng ca chi^u Neu x7T/ ^^^S Pi"'