ĐỀ THI THỬ CAO ĐẲNG - ĐAI HỌC 2011 :TRƯỜNG THPT CHUYÊN QUỐC HỌC HUẾ MÔN TOÁN KHỐI A pps

.,raANQDlI!G :(70N.) gu: (2 o4fl.) V6i m& .A Ihyc _ ,. (c.) • .,& .6 I) KII60 MlI\I bih.1hi&I vi ve d6 dIIlnJIII tn~ II • ! 1) TIm ck !Iii lit cUa /II ~ da ck diI:m """ lit • (e.) 0,11: (l,O dJm) I) TIm ga trj 1611 nIJt v' ,ii lit nh6 nbAt cUa ftx) - sinx +cou+t8DX+OCIIls { 2" + 2'''' ~ 16 IJGWhtphllODgtrinh' 2''''.2''-16 (x,yeR). (i. I!I; (},Ot1lim) . " , I) Tlnh . 1= J,!I-Sin xdr o , 2) Cho a,b,c Ii clc sA !bile ruy y 1611 han I . Chimg minh rang: Jog. be + log. co + loge ab 2 4(J08dt C + 10 a + loS", h) . nll IV; (1,0 t1iem) . COO hiM ch6~ tir gi~ S.ABCD c6 day Ii', hinh ,bin!J1" AB.CD v6i !fun 0 , G9i p, q, u, v Ian hr\7! I. cae khoang cach tu ° den .m~1 ph3ng (SAB). (SBC). (SCD). (SDA). ChUng minh rAng n~u mp(SAC) vuOng g6e v6i m~1 pt!l1g (SaD) \hi: _I +_1 =_1 +_1 ,- p~ uJ ql v2 n. PHAN R1ENG (3,0 t1 ii m) Th i s inh chi dwc chon :::91 Irong bai pb'n: A botc B. PhA" A. nll Va: (2,0 lliim) 1) Irong m~t piling loa dO;; Ox.Y.cho duemg tron (T): x' ~ -8x +12 =0 va diSm K(4;1).Tim lOa dO;; diSm M iJ treD lr\Ie ~ sao eho tir M ke dUQe hai ti~p luyt1n ME, MF viJi (T) va duemg Ihing qua cae liSp diSm E, F chira dit\m K. 2) Trong khang gian tQ' dl) Oxyz, cho cae dit1m A(2;O;O) .D(O;-3;6).Vit11 phuong trInh m~t phAng (P) ehim dUOng thAng AD va cat cae !r\Ie y'y va z'z IAn IU\7! t~ B vii C sao eho !btl lieh I" di~n OABC bing 3. Ci. VI.; (I,D iMm) ChimgminhrAngnt1ueacsAphire z ,,', th6a Iz,+z,I=lz,lF2 thIlz,-z,I=lz,IF2. Phd" B. Cill Vb: (2,0 diim) I) Trong mat piling lQa dii OXY. I~p phl10ng lnnh eila conic (H) e6 tam sai birngF2 , tieu di.im 101 F(I ; I) va duiJng cbuAn l!. c6 phl1<Jng trinh x + y·1 = 0 ,Tim tam d3i xling eila (H). 2) Trongkhong gian lQadQ Oxyz. cho hai dUOng <hAng (a): x - I = y-3 = ! (b): x-s ~ y ~~ va 2 - 3 2 6 4 -s mal phAng (P): x ·2y+2z ·1=0. Xet diem M thuQe (a), di€m N thuQc (b) sao cho MN song song viJi (P) vA kboAng cach giQa MN Va (P) bang 2. Tim toa de> cae diem M va N. Call Vlb; (1.0 diim) ChUng minh ring v6i mQi sa phfrc Z •• Z2 luan c6 Iz I' +Iz I' +1:1 ~ +/;12 -/z + /' /- ' I J ." "':1 - J %2 + ". - Z1 • L-___ U'~. _____ . qua cae liSp diSm E, F chira ditm K. 2) Trong khang gian tQ' dl) Oxyz, cho cae dit1m A( 2;O;O) .D(O ;-3 ;6).Vit11 phuong trInh m~t phAng (P) ehim dUOng thAng AD va cat cae. 4 -s mal phAng (P): x ·2y+2z ·1=0. Xet diem M thuQe (a) , di€m N thuQc (b) sao cho MN song song viJi (P) vA kboAng cach giQa MN Va (P) bang 2. Tim toa de> cae diem M va. cbuAn l!. c6 phl1<Jng trinh x + y·1 = 0 ,Tim tam d3i xling eila (H). 2) Trongkhong gian lQadQ Oxyz. cho hai dUOng <hAng (a) : x - I = y-3 = ! (b): x-s ~ y ~~ va 2 -