DAPANMONTOANTHITHPTQGIAHAY0615

<span class='text_page_counter'>(1)</span>men: loan (thi thu Ian 3 ngay 13/6/2015) -Tnvcmg ChUYE!n TNH. DAp AN vA BI~U DI~M Ciiu. i Y. Bai giai. Diem. 1. 0.25. y. 0.25. --. ---. b. Viet ohuono trinh tiep tuven cua do th] (C) t<;lidiem c6 hoanh do x thoa man y"=O. o y'=6XL-6x " 0 O Y = ~x=2. 1. o. o Ma: y'( '-"-'-. - _.. - -. - - ._. ... -. - - -. 2)= -~y( 2 2'. 2)= 2 2 -"'-'._."_ 2. -"-"-"-'"-"-"-"'-"-"-"-'. 3. Oketqua(t). y=-2(X- )+2 2. i la. (t): y=y'(. - '- - _ .. _ .. -. ,-,,_. i i i) )(x-. )+y(. .. _".- ._."-. --._. .. _.--. '-"-"-"-"-"-. - --"-"-"-"-'--"-"-. 1. 1. ~(t):y=-2x+4. (1-2i)Z=X+2y+(y-2X)i ._ => (1-2i)z+3(1+i) { 3(1 + I)Z = 3(x + y) + 3(x - y)1. 3. _.. -"-"'-"-"-'. _ .. _-.- .. -. '-"-'._".-. ._ .. _ .. _ .. _ .. _ .. _ .. -. '-"-"-. 5. _.. I. i. f----T--+. b,. Giai bat phU'O'n9 trinh. 0.25 ._ .. _ .. _ .. _ .. - ._. ._. _ .. _ .. _. __ .. _.. 0_25 =2+7i_ Tinh. O.5d. Ii±. z =2+7i <=> 4x+5y-2+(x-2y-l)i=O. c. 0_25. {x. 4X + 5y = 2 = 3 . ~ => z=3-21 { X - 2y = 7 Y =-2 · - - - ._- - - -- - -- --- -_. - -. - - - - -. -- -- - - - -- - .. _. - _. - - - - - - - - .. .. - .. -- -- - - ---- -- _. - - - -- - - _. - - - - -. ---- - ._--- - - • z=3-2i => i+ =3+3i => [i+ 1=312 <:=:>. z. '-'"-"-"-"-"-'. 0.25 ._ .. _."_. _ .. _ .. _.. .. _ .. _.'-'._ .. _ .. -. Cho s6 phlic Z thoa (1-2i)z+3(1+i)z GOi z=x+yi voi X,YE!R va i2=_1 •. _ .. _ .. _ .. _ .. _ .. _ .. - _ .. _ .. -. --'-'"-"-"--'-"-"-"-"--'-"-"-"--. tiep tuyen voi (C) t<;lidiem co h.do x= ._ .. _ .. _ .. _ .. - .- ._ .. - ._ ..- _.- ._. - - - - - - - _.. Ph.trinh. .- .. --.- '-"-"-"-"-. Ciiu 2 ~ a,. 0.25. -"-"-"-"-"-'"-"-"-"-"-"-. ._.. 1diem. ~ y"=12x-6. _. z. 6.I09~ x +. _. 5.109,.12. x - 4 s 0 voi x la s6 thvc. .. - _.. _. - _ ... 0.25 0.5. 2 ..--------.--.--.-..-.----- ..--.-----.-..--.- ..- ..-.-----------..- ..- -----..--.--.- ..- ..----..- ..- ..- ..--- ---..- ..- ... • Dkxd: x>O • 6.109~ x + 5.109J2 x - 4 s 0 ~. 0.25. 3109~ x + 51092 X - 2 s 0 ~. 2. 1 3. 1 4. • -2 S 1092 x S - ~. «r:. 0.25. - s x s ~2. n. cso 3. Tinh: n. f. sin 2x o(sinx+2)2. 1diem. dx. -n. f. -. 1=. 1=. sin2x o(sinx+2)2. dx = f2sinxcosx 0 (sinx+2)2. dx 0.25. COS xdx = dt. • £)~t: t=sinx+2. '------'--'-_.------. ---_.-_ .._-------. ~. J. 2 sin x (sinx+2)2. ----.---._-----_. = 2 t - 2 dt. ..__ . __ ._._----.------. t2. - -_. __ .. _- - - - -- - -_.---- .. _-----. ----. ._-._--_.. -,------------.-_.,-_._-----_.--. -------. ._.--_._-. I..

<span class='text_page_counter'>(2)</span> • • x=O => t=Z: x= ~ =>t=3 ._ .. _ .. _ .. _ .. _ .. - .. _ .. ~.. _ .. -.~ .. - .. _ .. _ .. - .. _ .. _ .._ .. _ .. _ .. _ .. _ .. _ .. _ .. _ .. _ .. _ .. _ .. _ .. _ .. _ .. - ..- .. _ .. _ .. _ .. _ ..- .._.' _ ..- ..- .. _ ..- ..- .. _ .._ .. _. • 1. =. 2ft t~ 2 dt = 230il!_t 2. 2.~)dt t. '-"-"-"-"-"-"-"-"-"-"-"-"-"'-. 3. .-. 1. 1. + 2(!)\3) t 2 _.'- ._ .. - _.- - .. - .. - .. - .. - .. - .. - ..- .. -.-- .. - .. -.-- .. -.-- .. --.- .. - .. --.- .. -.-- .. - .. -.'- .. -. '-"-'--"-"-"-"-. 025 '-"-'--"-'._"--. 2. 0.25. Cau 4 : a,. Giai: sinx+sin2x=sin3x • sinx+sin2x=sin3x. <=>sin3x-sinx=sin2x. x = k.n [ 21t X = m.21t <=> x = n'T • <=> 21t. X. =. <=>2cos2xsinx=2sinxcosx. <=>. sinx [ cos2x. = 0. <=>. = cosx. voi k,n,m 113cac so nguyen. x=1t+k.21t. n.3. 0.5d 0.25. 0.25. -. Cho x=O. Tim so h,;mg khong chua x trong kh.trien. 'b I. _ .._ ..- ._ .._ .._ .._ .._ .. - .. = 2[(lnX)I~. 3. .1=2In2"+4(3"-2")=2In2"-3". 0.25. '-"-"-". cua: (x. -1J. '. biet: . A n2. =. Cnn-2. +. Cnn-1. 0.5d. + 4n + 6. • £)kxd: n E N va n~2 •A2 = n. n! cn-2 + cn-1 + 4n + 6 <=>A 2 = c-: + 4n + 6 <=>-n+1 (n-2)! n. n. =. n. n E N 1\ n ~ 2 {n E N 1\ n ~ 2 {n <=> <=> <=> { 2n(n -1) = n(n + 1) + Sn + 12 n2 -11n -12 = 0 n • Khi n=12 ta dU'Q'C: ( x -. (n+1)! 2!(n-1)1. + 4n + 6 <=>. E. N 1\ n ~ 2. E. {-1; 12}. <=>n = 12. JX2 )12 . k. So hanq thu (k+1) cua kh.trien. k. • T k+1khOng co chtza x ~. • W.y so. cau. E. 113:Tk,1. ~-D. = C~2(-2rx-2.x12-k. =. C~2(-2rx. 2. { 24 - 3k = 0 <=>k = S <=>k = S. hi;lng k6ng co crura x la: T 9= 28 C~2. .g..(?)_co_!. .Y.t.pt. ~a.~.:=J1;:.1~~),-I/~. dl~~) .0.e~..~ ~~.1_vt~pJa._~.~J~~.~ ~!...._.._.._.._.._ ._.._.._.. n_ I. b,. p £)th . O ang d co. {1vtc :n=(1;-1;2) M(1,-1,2)Ed. => Ph trlrln h d:.. IX=1+t ri t E ," m. y ---1-t VO'l 1 2 2t lZ = +. Viet phtrinh m.cau co tam narn tren true Ox va tiep xuc voi mp(P) tai M ME (P) nen Tam cua rn.cau (8) can tim 113giao diem cua d va true Ox .~~~_d~9~_~9.~I ..Q.~_?y'~.~<?:i_t.=:=.:1._.. _ .. _ .. _ .. _ .. _ .. _. __.. _ .. _ .. _ .. _ .. _ .. _. __.. _ .. _ .. _ .. _ .. _ .. _ .. _ .. Ban kinh cua (S) 113R=OM => R2=OM2=6 V$y: (8): x2+l+z2=6. cse. 6. 0.25. N,k ~ 12. Cho mat phanq (P): x-y+2z-6=0 va diem M(1 ;-1 ;2). Viet ohvono trlnh dlJ'anq di qua M va vuonq g6c voi mp(P). 5 : : a,. 0.25. Cho hinh lang tru ABC.A'B'C' co day 113£lABC vuong can tal C, AB=2a. Hinh chieu vuong g6c cua dinh A' tren mat ph~ng day 113H trung di§m cua earth AB, g6c giQ>aA'C va mp(ABC) la 45°. Tfnh th§ tlch cua khoi lang tru ABC.A'B'C' va khoang each giQ>adU'ang th~nq BB' va A'C A'. /. /. C'. :. ___ /:A. S'. 'H. ,. _ -. JL. ,. / /. c '----_~_...J....._.._.._.._.._.._...9.'2!.!J~.!~~qi.~~.g.~.~I~_~!].?~.q:..~~_~~jl. I::!.~~~.~'-'.._.._.._.._:._.._... .. 9.~.~.~~.~9' ... 1 diem 0.5d 0.25. 0.25 0.5d. 0.25 0.25.

<span class='text_page_counter'>(3)</span> -~ABc~'~6'~;-~-~~-t~iC-;&i"H'i~'tr~~g"di~~'~G;'AB',-AB~2~-;-C'A~C'B~~-J2";~'CH-~;"-"-" 0.25. • H=Hc(ASC)(A') =:> CH=Hc(ASC)(A'C) va 00<,.i\'CH <900 =:> ,.i\'CH =450. _·_H.I::!C!-i~!?~Jy.? ..~~~~g'y~.<?.']g_C?_~.t.§l.i..t1.? ~.'.Ij:=:~;.. _.._.._.._.._ .._ .. _.._.. _.. _.. _.._.. _.._.._ .._ .. , ·VASC.A·S·C·= 5MBC.A H =. ",a. 0.25. ."._B.!?:(IM'_? __~~'.!(~~.f:.~r;L~.~iB.!?:;g.AJ=:=.9.(!?f?.:;(~~~q)2=.q(~~(~'~)l=.~~_(t!;lP:~'_r:;J). • IHIIBC =:> BC.lIH va BC.lA'H =:>BC.l(A'HI) =:>(A'HI).l(AA'C) theo q.tuyen A'I Ma HKc(A'HI) va HK..LA'I, nen HK.l(AA'C) =:> HK=d(H;(AA'C)) , ". • 6.AHI vuong tal H .. co. • Do do: d(BB';A'C)=. _ aJ2 1 1 HI--=:>-=-+--=-+-=-=:>HK 2 HK2 Hf. 1. 2. 1. 3. HA'2. a2. a2. a2. =-. __.. .. 0.25. .. a.J3 3. 0.25. 2a.J3 3. cao. (Chu It: H.sinh co th~ qiai each dunq t.chat d.cao cua tLi' dien vuong H.AA'C tc;li H) Cho hlnh thang ABCO vuonq tai A(1;1) va B. Tren AB lay diem M sao cho BM=2AM, N(1;4) la hlnh chi~u cua M tren dU'ang thllng co. Tim tea do cac dinh B,C,O bi~t CM.lOM, BE d vai d: x+v-z=O. 7. A(1;1). 1 di~m. " D. ,. , ,.:r., : '". N(1~'I). c. B d:x"y.2=O. '-O'Cmr:'-BN~AN':-C~c'tc;'gi~c-Bc-N-M ';;~-MNDA~n¢iti~~'tr~ng-d-U;t;;n'gtrb-n~"-'-"-"-'-'-"..-.- ..-..- .-.-.-.- ..-..-. CNB = CMB , rna CMB = M6A do: MC.lOM va OA.lMB; MDA = ANM Do d6: 90 = CNM = CNB + BNM = 8NM + MNA = BNA =:> BN.lAN --"-"----"-"-"-"-"-"-'--"--'-"-"-"--'--'----"-"-"-"-"-"-"-"-"-"-"-'--"-"--'-'--"-''-"-"-"----"-"-"-"-"-"-"-"-"-"'-"nen:. 0.25. 0. o __... o. BEd~B(b;2-b);. f~~=(b-1;-2-b)=:>NB.lAN~b=_2=:>B(_2;4) lAN = (0;3). .._ .._.__.__.._ .._ .._ .._ .._ .._ .._ .._ .._ .._ .._ .._"_"_"_"_'._. GQi: M(X;Y)). o. 3. -. - - - - - - - - - -. C=COnBC. 0.25. .._ .._ ._.._ .._ .._ .._ .._ .._.,_.._ .._ .._ .._ .._ .._ .._ .._ .._ .._ ..- .._ .._ .._ .._ .._ .._.'_"-0.- ._.._ .._ .._ .._ .._.. rna AM = 2AB ~ {x -1 = -1. AB = (-3;3) lAM=(X-1;y-1). =:>MN = (1;2). - - ._ .. - ._-.-. -_.- -_ .. _ .. _ .. _ .. _ .. _". -. -. -. -. c::>. y-1=1. {x = 0 =:>M(0;2) y=2. Do d6 CO x+2y-9=0. _.. - - -. -.-. - - -. -,. - - - - - - - - - _.,-. - - -- _._-. 0.25 - .. -. - -. --. - - .-. _.-. va O=COnAO. Ma BA = (3; -3) =:> Be x-y+6=0. TOc;ldo C la {x + 2y = 9 ~ x - Y = -6. AD x-y=O TOc;ldo 0 18 {x + 2y = 9 ~ x - Y= 0. {x = -1 =:>C(-1 ;5); Y= 5. 0.25. {x = 3 =:> 0(3;3) Y=3. V$y: B(-2;4), C(-1 ;5),0(3;3). csu 8. '>'lXY2(~ Giai: (3x. I I. • 8kxd:. + 1) = 3JY2.:9. + 3y. .' VO'l. 2. 3. -1)Jx y. + xy - 5 - 4x. X,y E lR.. 1 di~m. 3. + 3x y - 7x = 0. x2y+xy?5. • 3JY2.:9 ma xy2 (~. + 3y = 3(~. + y) > 3(1Y I +y)? 0 'ily E lR.va ~. + 1) = 3JY2.:9. + 1>0 voi 'ilXE lR. 0.25. + 3y =:>x>O. Voi x>O va y(x2+x)?5. =:>y>O Do d6 dieu kien cua he la: x>O va y>O. Xet h.s6: f(t)= tJt2;"1. + t voi t>O =:>f '(t) =. ........... : :~;~~o·::y~~~·~'( J x,~ ~~;)·03J~:: . 9·:3 y=~;;x:~ 1:'):7[J(~F,:,r······ . 'oN + 1 +. ~ + 1> 0 ,'ilt>O =:>f tang tren (0;+00) '-,If + 1. 0.25. I I. v« x>O va. ~ >0 nen f(x) = f(~J. ~. x = ~ vai x>O. .._.._.._.._..~.._.._ ._.._.._.._.._.._.._..t._ .._.._.._.._.._.._ ._.._._y_. _.._.._.._.. Y._ .._. _ ._.._._._. ._.._. _.._.._.._ ._.._.._.._. _.._ ._.._ ._.._.._.._.._.._.._.._.._ ._.._.._.._.._.._.. '--_~! ----'._9_()_cJ~.:_.._.._.._.._.._.._.._.._.._.._.._.._.._.._.._. _.._.._.._. _.._.._.._.._.._.._.._.._.._.._.._.._.._.._.._.._.._.._.._.._.._.._.._.._.._.._.._.._.._ ._.._.._.._.._.._. ..:.

<span class='text_page_counter'>(4)</span> • 0.25. -J. X>O + 1) = 3~y2 +9 + 3y. xy2(~. 4x3. + xy - 5 -. 3x3y. +. 2. 3. - 2 - 4x. + 9x. 3. y=. <:::>. X ~ (3x -1)-v3x. 1 1. (3x _1)~x2y. l. 3. <:::> Y=-. 1. Y. - 7x = 0 <:::>. {X > 0 /\ 3x - 2 ;:: 0. :. 3. X=-. { (3x _1)~x2y. + xy - 5 - 4X3 + 3x3y - 7x = 0. 2 X;::3. -/\. X. (3x -1)·J3x. <:::>. =. - 2. - 7x = 0. 4X3. 9X2 + 7x. -. «-'-'-'-:-'--:-f~~'~-~-~-~-~-«-'-'--------~F~t~~'~I'-'--.--.----.-.-----.: l l. : l. -1).J3x -. (3x. 1. 9X2 + 7x. -. (3x -1)(. y = ~ /\ X ;:: ~ X 3. <:::>. 1. 2 = 4X3. l. .J3x -. (x-.J3x-2)[4x(x+.J3x-2)+3x-1)=0. 1. !. ==> 4x(x+ .J3x -. (Vl: x z ~. y. 2) + 3 x-1 > 0. ==> 4x(x+ J3x -. X j xE{1;2). Cho a, b,. C. Cau 9. dU'O'ng.. <:::> 0.25. x2-3x+2=0. vt:. 2) + 3 x-1 = 0. nqhiern). V$y: T={(x;y)/(1;. so thvc. 103cac T =. -1 )2]. y = ~ /\ X ;:: ~ X 3. J3x-2=x. X ;:: ~3<:::> {X = 1 v jX = 23. 3 yY ---2. = ~ /\. <:::>. l. (.J3x. 2 - x) = 4X[X2 -. y = ~ /\ X ;:: ~ X 3<:::>. <:::>. ..-«-.--.--.-.-.---.. 3),(2; ~ )}. Tim gia tr] Ian nhat cua bieu thvc: 1 diem. 4 _ 9 2 2 +b +c +4 (a + b)J(a + 2c)(b + 2c). Ja. 2. Vol: a,b,c>O ta duoc: • a2+b2+c2+4;:: (a + b + c + 2)2. .. f( • ( a+ b) -va+. 4. 2 )(b 2) (a + b)(a + b + 4c) (3a + 3b)(a + b + 4c) 1 (2 2b 2)2 c + c $ = $a+ + c. 2. 6. 0.25. =. 6. _ 2(a + b + C)2. 3 Nen: T. 4. =. _. 9. Ja2 +b2 +c2 +4. .. <. (a+b)J(a+2c)(b+2c). 8. _. - a+b+c+2. 27 2(a+b+c)2. Xet ham s6 f(t)= _8_ - 2~ vai t E (0;+0-:) t +2 2t - - _.- - - - - -" - - - - - _.- - -.- - - - - - - - - - - - - - ._. 8 27 {I>O f '( t) = - (t + 2 )2 + t3 ==> f' (t) = 0 <=> (t _ 6)( 8 + 21 t + 18) = 0 <=> t = 6. - - --. - - -. 0.25. -. -.-. - - _.-. ._ ... _ .. - -. - - _ .. -. ,-,. e. ! 0. t. '-"-'1-"-. .i'(tl. f(t). .- .._..-«_ .. _. _.. -. UJ. _.._.. _. _. «_. ••. _. .~. ••. ._ ..- ..- ..-. _. ••. _. ••. _. ••. _. •.. _. ••. 6. _..-. ._. -. _. .. .•. _. ~ ==>. DU'a . vao bbt ta duoc: . vt, t>O. Mo3'. .. _.. " __. •. _. ••. a b c>O , , _. ••. _. ••. _. 0.25. 8. 1. •. «_ .. _.. _.._.._«_.~_ .._.._.._.. _«_ .._.._.._. _0 _ . _. II. 1. +x. ._ .. _ .. _.. _ .._.. _.._ .._ .._ .. _ .. _. _ .._ .._ .._ ..-. ••. _. ••. _.. ==> __. ••. ==>. a+b+c>O _. ••. _. ••. _. ••. _. ••. _. ••. _. ••. _. ••. 5. f(t)$- 8. T< 8 _ 27 <~ - a + b + c + 2 2(a + b + C)2 - 8 -. ,.. -. ,"_""_. ••. _. ••. _. ••. _. ••. _. a,b, c > 0 /\ a. va.b.c= O, T$-. 5 8. l. ••. _. ••. _. ••. _. ••. -. ••. =b=c. . 5 a + 2c = b + 2c va T= - <:::> 8 3a + 3b = a + b + 4c. _. ••. =. _. ••. _. ••. _. ••. _. ••. _. ••. _. ••. _. ••. _. ••. _. ••. _. ••. _. ••. _. ••. _. ••. _. ••. _. ••. _. ••. _. ••. _. ••. _. ••. -. -0_". __. •. _. ••. _. ••. _. •. _. ••. _. ••. _. ••. _. ••. 2 <:::>a=b=c=2. 0.25. a+b+c=6. V$y: Gia trj Ion nhat cua T 103. %,. khi: a=b=c=2. GHI CHU: - Thi sinh lam dung b~ng each khac voi dap an, GK v~n cho du di~m phan twO'ng LPng. - Di~m 56 khong lam tron, ------ Het ------. -:. _. ••. __.

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