TRIIONG r.Tnpr I,t xoAY Ndm hgc 20ll-20X2 nn cuimr rrruc Cfiu I: i Giei phucrng trinh : 2.Cha p,Q>I,p,qeN Bn rnr KrrAo sAr cnAr r,uot-rtG,LAN rrl:,. nn0x : ToAN rr- rcror b Thli gian: 180 phrfrt (kh6ng te tnUi gian ph{t tlii) sin 2x 6sin x - 2 cosx + 6 sin{x + f) CMR I pq+C|+C] =C'o*n -0 CAu TI: 1 .Tim m d6 phugng trinh: xo - 2mx' + 2m -1 = 0 c6 bOn nghiQm phAn biQt 10p thanh mQt c6p sO cQng. Z.Cho t?p hqg M g6m 5 do4n th6ng c6 d0 dei len lugt lp 1cm,3cm,5cm,7cm ,9cm.Lhy ngSu nhi6n ba dopn tt @p M.Tinh x5c su6t AC Ua doqn 15y ra co th6 tao thanh mQt tam giitc. .l .AAN Qiu III: Cho tam gi6c ABC c6 ba g6c 2,,it,e theo thri tg l$p thhh mQt cAp s6 nhdn c6 c6ng bOi q:2. i.Tinh c6c goc ctra tam giac ABC 2.Ki hiQu BC = a,AC =b,AB = c. Tinh gi6 tr! cira bi6u thric ".1 r 2 M=a2(-*,+i) b'c'bc! Ciu IV: Cho hinh chop S.ABCD c6 d6y le hinh vu6ng cAnh a .TrOn canh aeldy Ai6m M voi AM:x (0<x<a) ,@; lir mat ptring"q.ru Vf ui rong song vdi mp(SAD) cit SB,SC,CD ldn lucrt tai N,P,Q 2.cMR giao di6m I ctra MN vi PQ iuon thuQc mQt duong thing Co ainn mi M ch4y tr6n AB 3.Bi;5t SA:a , MN L Me .TtnhdiQn tfch tir gi6c MNPQ theo a vd x.Tim x d6 diQn tich tir gi6c MI{PQ U** T CSu V:Cho da gi5c d€u A.A2 A, (n> 3,ne N) nQi ti6p trong duong trdn(O).Bi6t sd duong ch6o cria da gi6c bing 2O.Tfnh sO trintr chfi nhpt c6 c6c dinh ld 4 trong n di6m 41,A2, A,, Het (CAn np coi thi khing girti thich gi thhm) 1, oAp AN THANG DrEM vr0x roAn xu6l-n ,:, .: i Lop 11 r,.A.x nr ' :: '": '':' Ciu N$i Dung Ei€m Cflu I (2d) l.(lilGiAi pt n EK: x*- -+kn(keZ) 6 pt<+ sin2x. J3 sinx - 2'cos.tr + .fr = 0 l F ' <+ (sinx - 1)(2cosx - Vl; = g F lSlnI=l I .Jl "13 I cosr L2 r- lr=" +k2tr t2 c>l td lx=t-1 +k2n L6 TL , : t+ k21r IIoQC x = POi ctii6u OI{ ta duqc nghigm cua pt ld L+k2r (keZ) 0,25 0,25 0,25 0,25 z.(rd) cM BDVT pq + Ctr .i; -::.^#^.d\ : pq + p(p -r) * q(q -l) 22 YP:C|.n _ _& ;- q)t* * _- G- ; il b ; A :, Vi Zt(p + q -z)l +y pq + C2, 1Cj i*c]:c\*n 0,25 0,25 0,25 0,25 CiUII (2d) 1.(1d) Tirym l_2 -2m+l)=0*L;, -1 -l =2m-I pt<+ (x2 -lX*', 0,25 -t D€ptco4nghigmpbtaph6ic6 l, e:<m+I 12m -1+I 2 +, N5u m>l pt c6 4 nghi€m pb ld: . t. l- , fr.A x., = -^l2m-l,xz = -1,rs = 1,xa ,=.12m-l c6c nghiQm ndy lap thanh osc khi trr +.tr3 - Zxr e -J2*-I +l= -2 e Jrm1= 3 <+ m =5 1 *, l . m <l ptco 4 nghi€m pb ld x, - -l,xz = -Jrm1,*r = J2i:l,xo =l '2 C C6cnghiQmndyldcsckhi ,yi +x3 =2*? e3^tZm-1=1 e m=: '9 \ KL m = 5,m: j- t/mycbt '9 [,25 0,25 0,25 CAU rlr(a 2(1al) Tfnh XS,r S6'crlctrt61, 3 dogn &nng tu 5 do4n thAhg criart{p Nd la C; = 10 -+ JOI = tO 0,25 GAi A ta di6n i6 "3 dogn thdirg l6y ra tao thanh tarar gi6c " Ta c6 I = f1l;5;7), (3;7;9), (5 ;V ;9)\-+]O, | = f 015 lei,l 3 KL : P({):r, 1r - - lol 10 0,25 1.(1d) Tfnh 3 g6c cfra tam giic ,AAn Theo gid thi6t ta c6 B = 2 A,C = 4 A 005 A A n n r n )r t Ar Vi l+ B+c = tr +J A= n + A='o ^B =o'o ^C -1/L 7' 7' 7 015 (trong d6 R 1&b6n kinh ducmg trdn 7777 Ta co y =l a(b + ") l' .*.o dinh h? sin Ta co L bc l' a = ZRsinlL.b :2Rsin'" .c = ZRsin- 7' 7' 7 ngo?r ti6p MBC) , a(b+c) laco 4pz 6io?L ,-rinl1x*[ 2sinlsin ?o "oro ' 7 7'r 7 J 7 _, w-m:' 0r5 015 Ciu YI '(3d) r\lur r$ grac $rl\rv Ia ninh gi? l{4rr1smy Ta c6 J Cs,<ry a(ABCD) = AD + Me l AD L(a)n(ABCD)=MQ l{")rrtsdn) 16A8) n (SAD) = SA = MN lt SA f(o)n(,SlB) =Ivfr,{ MQrAii ffi-ADi/itc "tA Mai/Be ; MA:it6nA\ ' Do d6 (q) n(^SBC) = NF,/t Me// BC : a/a t\ -:- - +.^ T 0'5 I I 0,5 i :\ru, \nau ursur r sua tyll\ va rU nam trOn dt c0 dinh Do ABCD ld hinh vuOn ft;i;jrJi1"1l#f,?i;ffif*) va (sDC) n€n giao tuvtin crra chring rd 0'5 iaco:lwN ^f9= I -+ I e MN c(SAB),] e Pe c (SCD) i suy ra I ld di6m chung cira 2mp (sAB) va (scDfDo ao I . a co il* 0r5 3(1d) Tfnh diQn tich ttfr gi6c T6 trufing: Nguy6nthi HPnh viMN//SAtheo tarets "a W = # =T + MN = a - x NP/lBc -#=# =#-+NP :AM =x MQ:a Do MN IMQ suy ra tir gi6c MNPQ la hinh thang vudng - (NP + MQ)MN (x + a)(a - x) "MNPQ- 2 2 c - 3o' r-,(x+ a)(a - x.) -3o' o o' - " =3o' o * =! DMNPQ- g - 2 g 2 8 2 Th* gt t" .6 tO O,"ttttg ch6o cia da gi6c ililu ln tC: - n 70 o'l -n=20.: ry.@:l) -n=2o<:'nt " )r.(n-Z)t 2 ttuimg trirn li ttulng ch6o lfn . Thi tla gi6c tI6 cho cd 4 iludng ch6o lfn .nndi ninn chir nhflt "O "e. dinh li 4 trong 8 tli6m 4,Ar,'.''4, c6 cfc tlulng ch6o li hai ilulng ch6o lfn.Ngug'c l4i, m6i c{p itulng.ch6o lfn cho ta mQi hinh chfr nhflt, Vly s6 hinh ch* nhgt phii tim bing s6 c[p iludng ch6o lt6'n lh Cl :6. f n:8 -3n-40=0el L n = -5(L) Vinh tulng ; l2ll2l20Lt GV ra tI6 NguySn Vlinh 'l'ri ' Tr'' lV- i'u' . I,t xoAY Ndm hgc 20ll-20X2 nn cuimr rrruc Cfiu I: i Giei phucrng trinh : 2.Cha p,Q>I,p,qeN Bn rnr KrrAo sAr cnAr r,uot-rtG ,LAN rrl:,. nn0x : ToAN rr- rcror b Thli gian: 180. nhpt c6 c6c dinh ld 4 trong n di6m 41,A2, A,, Het (CAn np coi thi khing girti thich gi thhm) 1, oAp AN THANG DrEM vr0x roAn xu6l-n ,:, .: i Lop 11 r,.A.x nr ' :: '":. 10p thanh mQt c6p sO cQng. Z.Cho t?p hqg M g6m 5 do4n th6ng c6 d0 dei len lugt lp 1cm,3cm,5cm,7cm ,9cm.Lhy ngSu nhi6n ba dopn tt @p M.Tinh x5c su6t AC Ua doqn 15y ra co th6 tao thanh