ࡱ> gifZq` 6gbjbjqPqP ::```t44445tO2P69999AAANNNNNNN$PhFSN`TB @ATBTBN99fOFFFTB89`9NFTBNFF:?L,H`L9D6 Цv4TBDkL M|O0OuLR0TD0TL0T`L4AAFA BSAAANNXF(AAAOTBTBTBTBttt'x+D tttx+ttt  Trng THPT chuyn KIM TRA HC K I  NM HC 2009 - 2010 NGUYN BNH KHIM Mn : TON 10 (Dnh cho lp chuyn Ton) ---*--- Thi gian : 120 pht (Khng k thi gian giao ) Ngy kim tra : 23.12.2009 -------------------------------------------------------------------------------------------------------------------------------------- Bi 1 : (1.0 im) Tm tt c cc hm s f(x) tha mn : 2.f(x) +  EMBED Equation.DSMT4  =  EMBED Equation.DSMT4  ; ( x ( 0 . Bi 2 : (3.0 im) Cho hm s : y = f(x) = x2 + (m + 2).x  3 - m , (Pm) 1. Khi m thay i, tm cc im c nh ca h Parabol (Pm) . 2. Kho st s bin thin v v  th (P) ca hm s y = f(x) khi m = 0 . Tm cc gi tr ca tham s k  phng trnh : (x2 + 2x - 3 ( = k c 4 nghim phn bit . 3. Xc nh m  bt phng trnh : f(x) d" 0 c nghim ch l mt on c  di bng 2 . Bi 3 : (2.0 im) 1. Chng minh rng :  EMBED Equation.3  ; ( n ( N, n e" 6 . 2. Trong khai trin  EMBED Equation.3 , n ( N* ; hy tm s hng nguyn , bit rng :  EMBED Equation.3  Bi 4 : (2.0 im) Cho (ABC u c  di cnh bng 3a (a > 0) . 1. Tm tp hp cc im M trong mt phng sao cho :  EMBED Equation.3 . 2. Ly cc im P, Q, R ln lt nm trn cc cnh BC, CA v AB sao cho BP = a , CQ = 2a v AR =  EMBED Equation.DSMT4 . Chng minh rng : AP ( QR . Bi 5 : (2.0 im) Trong mt phng ta  Oxy ; cho tam gic ABC c : A(2; -1) , B(0; 1) , C(3; -4) 1. Tm ta  trc tm H ca tam gic ABC . 2. Tm ta  ca im M trn trc Ox sao cho  EMBED Equation.3  t gi tr nh nht . ===Ht=== -------------------------------------------------------------------------------------------------------------------------------------- H v tn : . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . SBD : . . . . . . .. . . . Lp : 10/1 TRNG THPT CHUYN KIM TRA HC K I  NM HC 2009 - 2010 NGUYN BNH KHIM P N V HNG DN CHM MN TON  CHUYN 10 -------- ( ( ( --------- Thi gian : 120 pht - Ngy kim tra : 23.12.2009 Ni dungimBi 1 : (1.0 im) ( Ta c : 2.f(x) + f EMBED Equation.DSMT4  =  EMBED Equation.DSMT4  , ( x ( 0 (1) ( t x =  EMBED Equation.DSMT4  , t ( 0 . Khi  t (1), ta c : 2.f EMBED Equation.DSMT4  + f(t) =  EMBED Equation.DSMT4  ( Xt h phng trnh bc nht 2 n f(x) v f EMBED Equation.DSMT4  :  EMBED Equation.DSMT4  Kh f EMBED Equation.DSMT4  ta gii c : f(x) =  EMBED Equation.DSMT4  (2) ( Th li ta thy (2) tha mn (1) . Vy : f(x) =  EMBED Equation.DSMT4  , x ( 0 l hm s duy nht cn tm .  Bi 2 : (3,0 im) y = x2 + (m + 2)x  3  m (Pm) 1.(0,5 im) ( Gi A(x0; y0) ( (Pm) ( y0 = x02 + (m + 2)x0  3  m ( (x0  1).m + x02 + 2x0  y0  3 = 0 (*) ( A l im c nh ca h Parabol (Pm) ( phng trnh (*) tha vi mi m  (  EMBED Equation.DSMT4  Vy, vi mi m, (Pm) lun i qua im c nh A(1; 0) . 2. (1,5 im) Khi m = 0 : y = x2 + 2x  3 (P) a. 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(  th :  th (P) l mt Parabol c nh I(-1; -4) v nhn ng thng x = -1 l trc i xng . b.(0,5 im) Ptrnh : (x2 + 2x - 3( = k (1) ( V  th (H) : y = (x2 + 2x - 3( ( Nhn xt : Pt (1) l pt honh  giao im ca  th (H) v ng thng (d) : y = k (l ng thng cng phng vi trc Ox) ( Vy pt(1) c 4 nghim phn bit ( thng (d) ct  th (H) ti 4 im phn bit Cn c vo  th , ta c gi tr tham s k tha YCBT l : 0 < k < 4 . 0,25  0,25  0,25  0,25  0,25  0,25   0,25  0,25  0,25  0,25   0,25  0,25 3. (1,0 im) f(x) = x2 + (m + 2)x  3  m d" 0 (2) ( f(x) = 0 c ( = m2 + 8m + 16 = (m + 4)2 e" 0 m = - 4 ( ( = 0 ( f(x) e" 0 , ( x ( R : khng tha YCBT m ( - 4 ( ( > 0 ( f(x) d" 0 , ( x ( [x1; x2] vi x1, x2 l hai nghim ca pt f(x) = 0 ( Vy : bpt (2) c nghim ch l mt on c  di bng 2 f(x) = 0 c hai nghim phn bit x1, x2 tha (x1  x2( = 2  EMBED Equation.DSMT4   EMBED Equation.DSMT4  Vy : m = -6 ( m = - 2 . 0,25  0,25  0,25  0,25 Bi 3 : (2,0 im) 1. (1,0 im) S dng kt qu :  EMBED Equation.DSMT4  ; ( x, y ( N v 1 d" y d" x . Ta c :  EMBED Equation.DSMT4  2. (1,0 im) ( Ta chng minh c :  EMBED Equation.DSMT4  ; ( x, y ( N v 1 d" y d" x . ( Ta c : EMBED Equation.3  (  EMBED Equation.3  (  EMBED Equation.3  (  EMBED Equation.3  ( 2n + 1 = 19 ( n = 9 ( Khi  khai trin  EMBED Equation.3 c s hng tng qut l :  EMBED Equation.DSMT4  ( Vy, Tk + 1 l s hng c gi tr nguyn  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Kl : c 2 s hng c gi tr nguyn, l : T4 =  EMBED Equation.DSMT4  v T10 =  EMBED Equation.DSMT4   Bi 4 : (2,0 im) 1. (1,0 im) ( Gi O l tm ng trn ngoi tip tam gic u ABC . ( Ta c :  EMBED Equation.3  0,25  0,5  0,25   0,25  0,25  0,25  0,25    EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4  ; v :  EMBED Equation.DSMT4  ( MO2 = 4a2 ( OM = 2a ( Vy tp hp cc im M l ng trn tm O, bn knh bng 2a . 2. (1,0 im) ( Ta c :  EMBED Equation.DSMT4  ( Ngoi ra :  EMBED Equation.DSMT4  ( Khi  :  EMBED Equation.DSMT4   EMBED Equation.DSMT4  . 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CHj: Z3ԜīOűġ]l팭o3YNO #z SzAer6}JE8}Θ7ƚDd +|4*b ! c $A? ?3"`? 2iYmIZЛ+wxEFtH `!=YmIZЛ+wx `M0 xڥS1oP)M)NKJJ0T"U4PJ8!KPDR1: DJLR?:u;3!=;UϾw߽{߽3! h؇ A#D<-kbM9l9Ld0G=&X8*?x=%)!R/vސRz ƭ`hv]1b? ]4BJ&i,w(b2Yc&hʱGED)"1<7c(n,G\C@ۏ+]iwvQ0 ^m;].={?>ߖn]vIٙjpz>0uꙛU~<㥌 /HRpͫcr ks<7Iג.5z6縗%.E#r2(2O 6b!mLQQNQ2O%]U"agu ?:pm2V=Nw( Dd |4*b " c $A? ?3"`?!2Zi%bԘ9 6ewH `!.i%bԘ9 t`x 0xڥRAkQm4i`79n z(4-Hr(tY,H$UW $$&FiTc$$If!vh58$5#v8$#v:VlF t'58$5a3Dd o!b $ c $A? ?3"`?#2} s 'Y~H `!Q s '5 RdxڭUMLA~3--n[`$:m)J( K#*Ru& Dbr5@b =h?@ABCDEFGHIJKLMNOPQRSTUVY\]^_`abcdefghijklmnopqrstuvwxyz{|}~2  + MB 2  + MC 2  -  12(BC 2  + CA 2  + AB 2 ) =  15a 2 2  FMathType 6.0 Equation MathTy_1323242644FЦvЦvOle CompObjiObjInfope EFEquation.DSMT49q<R DSMT6WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  ! (MO  + OA ) 2  + (MO  + Equation Native _1323242822FЦvЦvOle CompObjiOB ) 2  + (MO  + OC ) 2  -  12 3.(3a) 2  =  15a 2 2  FMathType 6.0 Equation MathType EFEquation.DSMT49qObjInfoEquation Native _1323243034FЦvЦvOle 4RTDSMT6WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  ! 3. MO 2  + (OA 2  + OB 2  + OC 2 ) + 2MO .(OA  + OB  + OC ) -  27a 2 2 =  15a 2 2  FMathType 6.0 Equation MathType EFEquation.DSMT49qCompObjiObjInfoEquation Native _1323243096FЦvЦv|R DSMT6WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  ! 3. MO 2  + 9a 2  -  27a 2 2 =  15a 2 2  FMathType 6.0 Equation MathType EFEquation.DSMT49q|R DSMT6WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_EOle CompObjiObjInfoEquation Native _A  OA = OB = OC = a 3  OA  + OB  + OC  = 0 { FMathType 6.0 Equation MathType EFEquation.DSMT49q_1323245932FЦvЦvOle CompObjiObjInfotR DSMT6WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  PB  = - 12PC  ! AP  =  AB  +  12AEquation Native _1323245961FЦvЦvOle CompObjiC  32    hay    AP =  23AB  +  13AC  FMathType 6.0 Equation MathType EFEquation.DSMT49qObjInfoEquation Native _1323246170FЦvЦvOle tR DSMT6WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  QR  = AR  - AQ   =  ARAB.AB   -   13AC     hay    QR =  415AB  -  13AC  FMathType 6.0 Equation MathType EFEquation.DSMT49qR DSMT6WinAllBasicCodePagesCompObjiObjInfoEquation Native _1323246448FЦvЦv      #$%&'()*+,-./014789:;<?BCDEFGHIJKLMNQTUVWXYZ[\]`cdefghiklmnopqrtuvwxy{Times New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  AP .QR  =  23AB  +  13AC (). 415AB  -  13AC () =  845AB 2  -  19AC 2  -  215AB .AC  FMathType 6.0 Equation MathType EFEquation.DSMT49qOle CompObjiObjInfoEquation Native \R DSMT6WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  =  8459a 2  -  199a 2  -  2153a.3a.cos60 0  = 0_1323253841wFЦvЦvOle CompObjiObjInfo FMathType 6.0 Equation MathType EFEquation.DSMT49q`DRTDSMT6WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  ! AH Equation Native |_1323250080FЦvЦvOle CompObji = (x - 2; y + 1) , BH  = (x ; y - 1) , BC  = (3; -5) ,  AC  = (1; -3) FMathType 6.0 Equation MathType EFEquation.DSMT49q|R DSMT6WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  !AH "^ BCBH "^ AC { ! 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