NQi dung 6n tQp HKI Ndm hgc 2018 - 2019 A LY THUYET NQI DUNC O^I TAP HgC rcY I -TU6ru TOAN I/ Dai s6: Ciu 1: Thd nio td s6 hfru ti duong? Sd hfru ti am? Gi6 trf tuyQt d6i cria s6 hiru ti x dugc x6c dfnh nhu th6 ndo? Ciu 2z Vi6t c6c c6ng thric: nhdn, chia hai lfly thua ctng co t6 tty thira cria: lf,y thria, mQt tich, mQt thuong Cf,u 3: Ti 10 thric ld gi? Tinh chAt co b6n cria ti lQ thirc Vitit c6ng thric tinh chAt cria ddy ti sO Uang Cffu 4: Dinh nghia cdn b{c hai ctra mQt s61,h6ng 6m? Cho vi dp Cflu 5: Khi ndo thi hai d4i luqng y vd x ti lQ thuan v6i nhau? Tinh ch6t cria hai dai luqng ti lp thuen? Cffu 6: Khi ndo thi hai d4i luqng y vi x ti l0 nghich vcyi nhau? Tinh chdt ctra hai dai luqng ti lQ nghich? Ciu 7: DO thi hdm s6 y : f(x) li gi? EO thi cria him s6 y u (a* 0) c6 dang nhu th6 nio? llinh hoc: Cffu 1: Ph6t bidu dinh nghia, dinh lf vd hai g6c ddi dinh Ph6t bidu dinh nghia hai duirng thing vu6ng g6c ? Dinh nghia duong trung truc cira doan thing Cia 2z Ph6t bidu dinh ly vd d0u hi€n nhQn bidt hai ducrng thing song song ? Dinh lf vd tinh chat hai duong thing song song : IV dctit Phdt bidu c6c dinh Dinh ly vd ba dudng thing song song Ciu 3: Ph6t bidu tiOn dd lf vd quan hQ gifia tinh vu6ng g6c vdi tinh song song Cffu 4: Phdt bidu dinh ty vd tdng ba g6c cria mQt tam gi6c ? Tinh chat g6c ngoii cria tam gi6c Cffu 5: Thd ndo ld hai tam gi6c bang Ph6t bidu ba truirng hqp bing cira hai tam gi6c vd c6c hQ qui (Ve hinh, ghi gii thidt, kdt luQn) B - BAI TAP V D4i sd Dane,l; Thuc hiAn phdp tinh(Tinh hgp ut zz!.2-' 4's I 4'7 ' rg1 l! ndu c6 thA): [o.r-1']' '(-( p?-.1) 4) 4)\' at (e)" -!,+ "'(5,, ") fl) , l\2r?: 4tr -ly-t J\a' 3J4s -Ilq h) rv'1"'"^'1 " 12t1, 63.102 6' ' a>(z',+-+l "'(." '1-rl 9-r, t-" 10.^6:0r rr.ir c\ rc!7 fl) (.s/ +zs?,1 7s 1'f-1-1)*1'[-'-,'fi) " s'[ts oJ' s'( r ' ) ,( n(zl*E!) ^'(" 6'- )' ' 3'- 2)'\ -qL*r!)+z! e) il o#.r'(L*,2),+ a * (-l ,1*sf, +,2) , (3.+-#)'(+-+.;) *r [rs - z;-Q^,t Y),1^;-J-ux*ue] Dang 2: Tim x, y,z: Bni 1.' Tim x bidt: l*1 :2x=-5 43 Jm( a) , Ji*.,ffi)=* at(*-l)fr*1)=o '\ 4)\ 2) ,l*"n*r ,S-I=* lr+!l-1= "l'l sl q 10 s)28 -223*-16=0 NQi dung 6n tQp HKl h) (x - Ndm hgc 2018 - 2019 L)'=25 ,l'\.[,r*l)'=1 2) \ !, z bidt : a) x: !:z=5:3:4vix k) l2x - 25 1l = lx - 2l Biri 2: Tim -z=-12 b) 3x =2y iJy=szvdx+ y *z=92 d) x: y: z=3:4:5vi 2x2+2y2-3*=-100 c) 2x- 3y=5zvix+y- z=95 )c+y x-y vdx.y=250 *r+l 1! t .-=: -: v+2 z-l vdx+y-z=50 e) il:: !340'73' l +y HgcsinhthOitOpTdEquy€ng6pdugcs5s6chnQpchothuviQn Lop7Ac637 hgcsinh, lopTBc6 37 hgc sinh, 16p 7C c6 40 hgc sinh, 16p 7D c6 36 hgc sinh H6i m6i to'p quy6n g6p du-o c bao nhiOu quy6n s6ch ct ni6t rang s6 s6ch quyOn g6p dugc ti lQ voi sO hgc sinh cria m5i top vd lop 7C g6p nhiAu hon lorp 7D ld8 quyOn s6ch Ba dQi m6y cly, cdy tr€n ba c6ch ddng nhu DQi thf nhdt hoin thenh cOng vi0c ngiy, dQi hai hoin thinh ngiy vd dQi thua ba hoan thenh ngey H6i m6i dQi c6 bao nhiOu mdy ciy, bidt dgi thf nha't c6 nhidu hcrn dqi thrl hai ld mdy ciy vi cOng sudt c:iua cdc mdy li nhu nhau? Cho bi6t 56 c6ng nh6n hoan mQt c6ng viQc 2l ngity H6i phii tdng thOm bao nhiOu c6ng A' \ a, , at / Y i: -l r ^ nh6n ld nhu nhau) hoan c6ng viQc d6 14 ngiy (ndng su6t m6i c6ng d0 nhdn nfra vi cfia n6 ld} : diQn t(ch bing 40m2 ti sd hai c4nh kd chfi nhat, bidt Tffi chu vi ctra mqt hinh Ba td hqc sinh trdng dux,I79 cAy xung quanh tnr&rg SO cay td ftdng so v6i td Z Uing : 11 So cay t6 tdng so v6i td bing : 1O.H6i m6i td trohg dugc bao ntrieu cAy 1) BakhoA,B, Cchrlag4o,ndunhflpviokhoAthCm isdg4octran5.Xuat&khoBdi "' sdgaocita n6 thi d6 sd gao kho bang Tinh xem hic ddu & m5i kho c6 bao nhi0u tAn gao Bidt rang kho B chrla nhidu hon kho A li 21 tan Dane 4.' Hd.m sd - Dd thi hdm sd: Bii '5=!* L: Cho him s6 y him sd b) Tim gi6 tri cria him a) VC dd thi sd tai x = -1 ; x =0 dd thi c6 tung dQ 11 X6c dinh tga dQ didm d6 didm trOn c) Tim Bii '5= 2* 2: Cho him s6 y a) VE dd thi him s6 b) Trong c6c didm sau dAy thi didm ndo thuoc d6 thi him sd d6: M (-5 3: Didm B (2;-1) thuQc dd thi him s6 Y = ax a)Xdc dinh a b) Ve dd thi him sd vDa tim duo.c Dans 5: Cdc bdi tud.n ndng cao: BiiI: Tim GTLN, GTNN.' 1) Tim gi6 tri nh6 nhat cta bidu thrlc: ;2); N (0 ; 3); P tl ; -f ll5' Bii A=312x- 1l -5 2) Tim gi6 tri l6n nhdt cria bidu thrlc: C= 10 -5lx-21 Bii B=x2+3ly- 2l+l D=5 -(2x-l)2 2: So sdnh: NQi dung 6n tQp Ndm hgc 2018 - 2019 HKl 32oo b)32r yd.Z3r c) 9920 vI 999910 d) S= l+2+22 +23 + + zt0oydztol a) Z,o, vd Bii 3; Cho tt lQ thitc: , 5a +3b a) CMR: +: bd+ 5c +3d -,, 7o' +3ab - "' salb= tr-, Bii 4: Cho b6n s5 a, b, c, d thoi mdn di0u kiQn b2 : rro2 -Bb'ac; c2 :bd 'lc2 +3cd rF -gP chrmgminh: "1^*4*cr=9 b'+c'+d' b IU llinh hoc Bii L: Cho AABC (3 g6c nhqn).TrOn tia Ax song song vdi BC ldy AD = BC (AD, BC cing thuQc nta mit phing bd li ducrng thing AB) Chung minh: a) AADC = ACBA Bii b) G6c BAD = g6c BCD c) AB llDC 2: Cho AABC vu6ng t4i A c6 g6c B :300 a) Tinh sd g6c C b) VC tia phdn gi6c cria g6c C cat cqnh AB tai D Trdn canh CB l6y di6m M cho CM CA Chrmg minh: AACD: AMCD c) Qua C vE dulng thdng xy vu6ng g6c CA Ttr A k6 duong th6ng song song vcvi CD c6t xy o K : Bii Chrmg minh:AK = CD d) Tinh sO g6c AKC 3: Cho g5c xOy TrCn tia Ox ldy hai didm A OA = OC; AB = CD Chung minh: vi B, trOn tia Oy tay didm C vi D cho a) BC=AD b) Gqi I ti giao cira BC vi AD Chrrng minh rang: AAIB = ACID phAn gi6c cira g6c xOy c) OI ti d) OI vu6ng g6c v6i BD Bii 4: Cho tam gi6cABC Gqi Eld trung didm AC , F ld trung didm AB TrOn tia ddi cira EB lay didm M cho EM = MB TrOn tia ddi ctra FC ldy didm N cho FN = FC Chung minh: a) AAME = ACBE b) AM = BC vi AM //BC c)AM=AN d)M,A,Nthinghdng 5: Cho tam gi6c ABC (AB < AC) kB phan gidc AD LifyEthuQc AC cho AB = AE; Ldy F thu6c tia ddi cira tia BA cho BF = EC Chung minh: a) AABD = AAED Bii b)DF=DC c)F,D,Ethfnghlng d)ADTFC 6: Cho tam gi6c ABC Ggi M li trung didm cira BC ; N NM cho NM ='NE Chung minh: a) AE = MC suy AE // MC b) AMEA = AABM c) MN ll AB Bii li trung didm cira AC Ldy E thuQc tia ddi cira ... Bii A= 312 x- 1l -5 2) Tim gi6 tri l6n nhdt cria bidu thrlc: C= 10 -5lx- 21 Bii B=x2+3ly- 2l+l D=5 -(2x-l)2 2: So sdnh: NQi dung 6n tQp Ndm hgc 2 018 - 2 019 HKl 32oo b)32r yd.Z3r c) 9920 vI 999 910 d)...NQi dung 6n tQp HKl h) (x - Ndm hgc 2 018 - 2 019 L)'=25 ,l'.[,r*l)' =1 2) !, z bidt : a) x: !:z=5:3:4vix k) l2x - 25 1l = lx - 2l Biri 2: Tim -z= -12 b) 3x =2y iJy=szvdx+... 2x2+2y2-3*= -10 0 c) 2x- 3y=5zvix+y- z=95 )c+y x-y vdx.y=250 *r+l 1! t .-=: -: v+2 z-l vdx+y-z=50 e) il:: !340 '73 ' l +y HgcsinhthOitOpTdEquy€ng6pdugcs5s6chnQpchothuviQn Lop7Ac6 37 hgcsinh, lopTBc6 37 hgc