TRNG THPT THCH THNH I S 1 THI MN TON, KHI 12 (2009-2010)Thi gian lm bi 180 pht, khng k thi gian pht PHN CHUNG CHO TT C TH! "INH (7 im)C#$ I (2 im!h" hm #$ % 22 1 y x mx m + (1 , &'i m l tham #$ th()*1 +h," #t #( bi-n thi.n & &/ 0 th1 hm #$ (1 khi1 m *2 2) 1nh m hm #$ (1 )3 ba im )() t41, 0ng thi )) im )() t41 )5a 0 th1 t6" thnh m7t tam gi) )3 8i9n t:)h b;ng % 2*C#$ II (2 im1 ng t4?nh22 @ 2 @ x x x x x + + 2 ng t4?nh 2#in 2 %)"# 1 0@x x _+ + + ,C#$ III (1 im T:nh t:)h phAn @B1B2xI dxx++C#$ I% (1 im!h" h?nh )h3p C S*DE!, F DE! )3 )6nh b;ng a, mGt b.n t6" &'i F m7t g3)B0o* T:nh th t:)h kh$i)h3p S*DE! & kh",ng ))h tH Inh D -n mGt phJng (SE! thK" a*C#$ % (1 imT?m gi t41 l'n nhLt & gi t41 nhM nhLt )5a hm #$ % 2 22 22 1 1 11 1 2x x xyx x + + + +PHN RI&NG (3 im):Th sinh ch c lm mt trong hai phn (phn ' hoc ()')T*+, -*./01 2340* C*$50C#$ %I)6 (2 im1* T4"ng mGt phJng &'i h9 t"6 7 NOy, )h" =ng thJng 8P 2 0 x y & =ng t4Qn (!P2 2R x y + * T?m t"6 7 im S thC7) =ng thJng 8 m TCa 3 kU =V) hai ti-p tCF-n SD, SE t'i (! (D, E l )) ti-p im #a" )h" tam gi) SDE C*2* T4"ng khng gian &'i h9 t"6 7 NOyz, )h" hai im D(1W0W0, E(1W1W1 & mGt )XC (SP2 2 22 % 2 B 0 x y z x y z + + + + * Yi-t ph=>ng t4?nh mGt phJng (Z i TCa hai im D,E & )[t mGt )XC (S thK" thi-t 8i9n l m7t h?nh t4Qn )3 8i9n t:)hB *C#$ %II)6 (1 imng t4?nh 2% 20 0 z z + + * T:nh gi t41 )5a biC th]) 2 21 22 21 2z zAz z++()T*+, -*./01 2340* N#01 -6,C#$ %I)7 (2 im1* T4"ng mGt phJng &'i h9 t"6 7 NOy,)h" tam gi) DE! n7i ti-p =ng t4Qn (! )3 ph=>ng t4?nhP( ) ( )2 21 2 R x y + + , g3) DE! b;ng^0o, D(2W0 & 8i9n t:)h tam gi) DE! b;ng %* T?m t"6 7 )) Inh D, E, !*2* T4"ng khng gian &'i h9 t"6 7 NOyz, )h" h?nh )h3p t] gi) C S*DE!_, bi-t S(BW2W%, E(1W2WB, _(BW0WB* ng t4?nh #aC )3 nghi9mP 221Bm x x x x + + *PHN RI&NG (3 im):Th sinh ch c lm mt trong hai phn (phn ' hoc ()')T*+, -*./01 2340* C*$50C#$ %I)6 (2 im1* T4"ng mGt phJng &'i h9 t"6 7 NOy, &i-t ph=>ng t4?nh =ng thJng i TCa im Z(8W@ & t6" &'i hai t4i) t"6 7 m7t tam gi) )3 8i9n t:)h b;ng 12*2* T4"ng khng gian &'i h9 t"6 7 NOyz, )h" D(RW8We11, E(BWRWe%, !(2W1We@ & =ng thJng thJng 8P1 2 12 1 1x y z * 2) 1n t"6 7 im S thC7) 8 #a" )h" MA MB MC uuur uuur uuuur 6t gi t41 nhM nhLt*C#$ %II)6 (1 im!h" #$ ph]) z th", mjnP 2@ 1B 0 z z + * T:nh @zz i++()T*+, -*./01 2340* N#01 -6,C#$ %I)7 (2 im%* T4"ng mGt phJng &'i h9 t"6 7 NOy, &i-t ph=>ng t4?nh =ng thJng i TCa g$) t"6 7 & )[t hai =ng thJng 2OeFkRf0, 2OeFk10f0 thK" m7t "6n thJng )3 7 8i l10 *R* T4"ng khng gian &'i h9 t"6 7 NOyz, )h" h?nh )h3p t] gi) C S*DE!_, bi-t S(BW2W%, E(1W2WB, _(BW0WB* ng t4?nh =ng thJngdi TCa imA & )hia tam gi)ABCthnh hai phXn )3 tI #$ 8i9n t:)h b;ng 2*2* T4"ng khng gian &'i h9 t"6 7 NOyz, )h" h?nh lbp ph=>ng m m m m* ABCD ABC D)3( ) ( ) ( ) ( )m0W 0W 0 , 1W 0W 0 , 0W1W 0 , 0W 0W1 C B D C* ng t4?nh mGt phJng )h]a hai =ng thJngMN& PQ*C#$ %II)6 (1 imng t4?nhP ( )( )22 %1 1l"g B 1 l"g B x x x< +()T*+, -*./01 2340* N#01 -6,C#$ %I)7 (2 im@* T4"ng mGt phJng &'i h9 t"6 7 NOy, )h" im( ) 2W 0 C & Kl:p( ) E )3 ph=>ng t4?nh 2 21% 1x y+ * T?m t"6 7 )) im , A B thC7)( ) E, bi-t 4;ng hai im , A B $i O]ng &'i nhaC TCa t4i) h"nh &^0 ACB o*d* T4"ng khng gian &'i h9 t"6 7 NOyz, t?m t"6 7 t4() tAmH)5a tam gi)ABCbi-t( ) ( ) ( ) BW 0W 0 , 0W 2W 0 , 0W 0W1 A B CC#$ %II)6 (1 imng t4?nhP 222 21l"g B 22 % Bx xx xx x+ + + ++ +---------------------------------H82---------------------------------T*9-* T*:0*; 01:< J1 2*>01 12 0?@ 2009) N1.AB 36 CDE (FB T3G T$H0TRNG THPT THCH THNH I S R THI MN TON, KHI 12 (2009-2010)Thi gian lm bi 180 pht, khng k thi gian pht PHN CHUNG CHO TT C TH! "INH (7 im)C#$ I (2 im !h" hm #$ B 2B % y x x + (1B +h," #t #( bi-n thi.n & &/ 0 th1 (! )5a hm #$ (12 o*2* T4"ng khng gian &'i h9 t"6 7 NOyz, )h" t] 8i9nABCD )3 )) Inh ( ) ( ) 1W 1W 2 , 1W BW 0 , A B ( ) ( ) BW %W1 , 1W 2W1 C D * Yi-t ph=>ng t4?nh mGt phJng( ) P i TCa , A B #a" )h" kh",ng ))h tHC-n( ) P b;ng kh",ng ))h tHD -n( ) P*C#$ %II)6 (1 imng t4?nhP ( ) ( )2 BB 2l"g 1 l"g 1 x x>+ +()T*+, -*./01 2340* N#01 -6,C#$ %I)7 (2 im8* T4"ng mGt phJng &'i h9 t"6 7 NOy, )h" h?nh th"i MNPQ )3( ) 1W 2 M, ph=>ng t4?nh =ng thJngNQ l 1 0 x y * T?m t"6 7 )) Inh )Qn l6i )5a h?nh th"i, bi-t 4;ng 2 NQ MP &N)3 tCng 7Am*^* T4"ng khng gian &'i h9 t"6 7 NOyz, )h" mGt phJng( ) P B B 2 Bd 0 x y z + + & )) im( ) ( ) ( ) %W1WR , BW 0W1 , 1W 2W 0 A B C* T?m t"6 7 imMthC7)( ) biC th]) #aC 6t gi t41 nhM nhLtP * * * MAMB MB MC MC MA + +uuur uuur uuur uuuur uuuur uuur C#$ %II)6 (1 imT?m #$ ph]) z th", mjn( ) 1 2 2@ z i + & * 2R z z *---------------------------------H82---------------------------------T*9-* T*:0*; 01:< J1 2*>01 12 0?@ 2009) N1.AB 36 CDE (FB T3G T$H0TRNG THPT THCH THNH I S @ THI MN TON, KHI 12 (2009-2010)Thi gian lm bi 180 pht, khng k thi gian pht PHN CHUNG CHO TT C TH! "INH (7 im)C#$ I (2 im !h" hm #$ % 22 y x mx (1, &'i m l tham #$ th()*% +h," #t #( bi-n thi.n & &/ 0 th1 )5a hm #$ (1 khi1 m *R T?m m 0 th1 hm #$ (1 )3 hai im )() tiC & h?nh phJng gi'i h6n bci 0 th1 hm #$ & =ng thJng i TCa hai im )() tiC LF )3 8i9n t:)h b;ng 1*C#$ II (2 im10 ng t4?nhBtan 2 #in 2 )"t2x x x + 11 ng t4?nh( ) ( )1 1 B1 1 Rx yx y x y + '+ C#$ III (1 im T:nh t:)h phAn B1BB 1 BxI dxx x+ + +C#$ I% (1 im!h" h?nh lpng t4i m m m* ABC ABC)3 F l tam gi) C )6nh a* q?nh )hi-C &Cng g3) )5a mA l.nmGt phJng( ) ABC t4lng &'i tAmO )5a tam gi)ABC * SGt phJng (Z )h]aBC& &Cng g3) &'i mAA )[t lpng t4i thK" m7t thi-t 8i9n )3 8i9n t:)h b;ng 2B8a* T:nh th t:)h kh$i lpng t4i m m m* ABC ABCthK" a*C#$ % (1 im!h" hai #$ th() , x y thaF ri & th", mjn iC ki9n 2 211 x y + * qjF t?m gi t41 l'n nhLt & gi t41 nhM nhLt )5a biC th]) 2P x xy + *PHN RI&NG (3 im):Th sinh ch c lm mt trong hai phn (phn ' hoc ()')T*+, -*./01 2340* C*$50C#$ %I)6 (2 im1* T4"ng mGt phJng &'i h9 t"6 7 NOy, t?m ph=>ng t4?nh =ng t4Qn ti-p O) &'i hai =ng thJng #"ng #"ng 2 R 0, 2 1R 0 x y x y + + + , n-C( ) 1W 2 A l ti-p im )5a =ng t4Qn &'i m7t t4"ng )) =ng thJng 3*2* T4"ng khng gian &'i h9 t"6 7 NOyz, )h"( ) ( ) 0W1W 2 , 1W1W 0 A B & mGt phJng (ZP 0 x y z + * T?m t"6 7 imMthC7) (Z #a" )h" tam gi)MAB&Cng )An t6iB *C#$ %II)6 (1 im2) 1nh tbp hVp )) im t4"ng mGt phJng ph]) biC 8isn )) #$ ph]) z th", mjn iC ki9nP 1Bz iz i+()T*+, -*./01 2340* N#01 -6,C#$ %I)7 (2 im10* T4"ng mGt phJng &'i h9 t"6 7 NOy, t?m t"6 7 )) Inh )5a m7t h?nh th"i, bi-t ph=>ng t4?nh hai )6nh 2 % x y + & 2 10 x y + , & ph=>ng t4?nh m7t =ng )ho" l 2 y x +*2*T4"ng khng gian &'i h9 t"6 7 NOyz, )h"( ) 2W1W 2 M & =ng thJng (8P 2 11 1 1x y z + * T?m t4.n(8 hai im , A B #a" )h" tam gi)MABC* C#$ %II)6 (1 imT4"ng tLt ), )) #$ ph]) z th", mjn 2 2 1 z i + , hjF t?m #$ ph]) )3 z nhM nhLt*---------------------------------H82---------------------------------T*9-* T*:0*; 01:< 1 2*>01 1 0?@ 2010) N1.AB 36 CDE (FB T3G T$H0TRNG THPT THCH THNH I THI MN TON, KHI 12 (2009-2010) S dThi gian lm bi 180 pht, khng k thi gian pht PHN CHUNG CHO TT C TH! "INH (7 im)C#$ I (2 im !h" hm #$ B 212 BBy x x x +(1@ +h," #t #( bi-n thi.n & &/ 0 th1 )5a hm #$ (1 *d ng t4?nh =ng t4Qn )3 bn k:nhR R & ti-p O) &'i =ng thJng 2 1 0 x y t6i im( ) BW1 M*2* T4"ng khng gian &'i h9 t"6 7 NOyz, )h" =ng thJng( )1 1 1P1 2 2x y z + & mGt phJng (ZP2 2 2 0 x y z + + * Yi-t ph=>ng t4?nh mGt )XC )3 tAm n;m t4.n =ng thJng( ) & ti-p O) &'i hai mGt phJngP mGt phJng( ) Oxy & mGt phJng (Z*C#$ %II)6 (1 im2) 1nh tbp hVp )) im t4"ng mGt phJng ph]) biC 8isn )) #$ ph]) z th", mjn iC ki9nP 1Bz iz i+()T*+, -*./01 2340* N#01 -6,C#$ %I)7 (2 im11* T4"ng mGt phJng &'i h9 t"6 7 NOy, t?m ph=>ng t4?nh =ng t4Qn i TCa im( ) 1W 0 A & ti-p O) &'i hai =ng thJng #"ng #"ng 2 2 0, 2 18 0 x y x y + + + *2* T4"ng khng gian &'i h9 t"6 7 NOyz, )h" =ng thJng (8P 21 2x ty tz t ' & mGt phJng (ZP1 0 x y z + + * 01 1 0?@ 2010) N1.AB 36 CDE (FB T3G T$H0TRNG THPT THCH THNH I THI MN TON, KHI 12 (2009-2010) S 8Thi gian lm bi 180 pht, khng k thi gian pht PHN CHUNG CHO TT C TH! "INH (7 im)C#$ I (2 im !h" hm #$ 2 12xyx+ (18 +h," #t #( bi-n thi.n & &/ 0 th1( ) H)5a hm #$ (1 *^ !h]ng minh 4;ng 0 th1( ) H )3 & #$ )Gp ti-p tCF-n #"ng #"ng, 0ng thi )) =ng thJng n$i ti-p im )5a )) )Gp ti-p tCF-n nF lCn i TCa m7t im )$ 1nh*C#$ II (2 im1% ng t4?nh#inB )"#BR )"# B )"# 21 2#in 2x xx xx+ _ + ,1R ng t4?nhB 2 10x y x yx y x y+ + '+ + C#$ III (1 im T:nh t:)h phAn % 2B)"t)"# 2xI dxxC#$ I% (1 im!h" h?nh )h3p* S ABC)3( ) , SA ABC tam gi)ABC&Cng )An t6iC&SC a * T:nh g3) giha hai mGt phJng( ) SCB &( ) ABC th t:)h kh$i )h3p* S ABCl'n nhLt*C#$ % (1 im2) 1nh m ph=>ng t4?nh #aC )3 ng hai nghi9m th()P( )( )2 2 % 2 21 1 2 2 1 1 1 m x x x x x m + + + + PHN RI&NG (3 im):Th sinh ch c lm mt trong hai phn (phn ' hoc ()')T*+, -*./01 2340* C*$50C#$ %I)6 (2 im1* T4"ng mGt phJng &'i h9 t"6 7 NOy, )h" hai Inh( ) ( ) 2W 1 , 1WB A B l hai Inh li.n ti-p )5a m7t h?nh&Cng* T?m )) Inh )Qn l6i )5a h?nh &Cng*2* T4"ng khng gian &'i h9 t"6 7 NOyz, )h" h?nh &Cng MNPQ )3( ) ( ) RWBW 1 , 2WBW % M P * T?m t"6 7Inh Q, bi-t 4;ng InhNn;m t4"ng mGt phJng @ 0 x y z + *C#$ %II)6 (1 imT?m h9 #$ )5a #$ h6ng )h]a 8xt4"ng khai t4in )5a biC th]) 12%11 xx _ ,()T*+, -*./01 2340* N#01 -6,C#$ %I)7 (2 im12* T4"ng mGt phJng &'i h9 t"6 7 NOy, )h" hai Inh( ) ( ) BW 0 , %W1 A C l hai Inh $i 8i9n )5a m7t h?nh &Cng* T?m )) Inh )Qn l6i )5a h?nh &Cng*1B* T4"ng khng gian &'i h9 t"6 7 NOyz, )h" )) im( ) ( ) ( ) 1W 0W 0 , 0W1W 0 , 0WBW 2 A B C & mGt phJng( ) P 2 2 0 x y + + * T?m t"6 7 imM , bi-t 4;ngM))h C )) im , , A B C & mGt phJng( ) *C#$ %II)7 (1 imng t4?nh #aC t4.n tbp #$ ph])P 2 281z w zwz w '+ ---------------------------------H82---------------------------------T*9-* T*:0*; 01:< 2 2*>01 1 0?@ 2010) N1.AB 36 CDE (FB T3G T$H0TRNG THPT THCH THNH I THI MN TON, KHI 12 (2009-2010) " 9 Thi gian lm bi 180 pht, khng k thi gian pht PHN CHUNG CHO TT C TH! "INH (7 im)C#$ I (2 im !h" hm #$( )B 2 2 2B B 1 B 1 y x x m x m + + (1, &'i m l tham #$ th()*10 +h," #t #( bi-n thi.n & &/ 0 th1 )5a hm #$ (1 khi1 m *2 T?m m hm #$ (1 )3 )() 6i & )() tiC, 0ng thi )) im )() t41 )5a 0 th1 )lng &'i g$) t"6 7O t6" thnh m7t tam gi) &Cng t6iO*C#$ II (2 im1@ ng t4?nh22#in 2 )"# d 1 )"# x x x 1d ng t4?nh22 8 2 2 10 1@ 2 x x x x x + + + +C#$ III (1 im T:nh t:)h phAn 2B11dxIx x+C#$ I% (1 im!h" h?nh )h3p tam gi) C* S ABC)3 )6nhABb;ng a( ) 0 a >* !) )6nh b.n , , SA SB SCt6" &'i F m7t g3)@0o* 01 1 0?@ 2010) N1.AB 36 CDE (FB T3G T$H0TRNG THPT THCH THNH I " 10 THI MN TON, KHI 12 (2009-2010)Thi gian lm bi 180 pht, khng k thi gian pht PHN CHUNG CHO TT C TH! "INH (7 im)C#$ I (2 im !h" hm #$( ) ( )22 2 1 y x x (111 +h," #t #( bi-n thi.n & &/ 0 th1 (! )5a hm #$ (1*12 T?m m 0 th1 (! )3 hai ti-p tCF-n #"ng #"ng &'i =ng thJng y mx * , )6nh b.n t6" &'i F m7t g3)@0o* ng t4?nh tham #$ )5a =ng k:nh )5a mGt )XC2 2 22 @ 11 0 x y z x y z + + + + m n3 &Cng g3) &3i mGt phJng R 2 1d 0 x y z + *C#$ %II)6 (1 imng t4?nh #aC t4.n tbp #$ ph]) 2 1 B1 2i izi i+ + +()T*+, -*./01 2340* N#01 -6,C#$ %I)7 (2 im1@* T4"ng mGt phJng &'i h9 t"6 7 NOy, )h" h?nh b?nh hnhABCD )3 8i9n t:)h b;ng 12, hai Inh l( ) 1WB A &( ) 2W % B* T?m t"6 7 hai Inh )Qn l6i, bi-t 4;ng gia" im )5a hai =ng )ho" n;m t4.n t4i) h"nh*1d* T4"ng khng gian &'i h9 t"6 7 NOyz, )h" mGt )XC (SP 2 2 22 @ 2 8 0 x y z x y z + + + + & =ng thJng (8P % %1 B1x ty tz t + +' +* !h]ng minh 4;ng )hI )3 m7t mGt phJng ti-p O) &'i mGt )XC (S & TCa =ngthJng (8* Yi-t ph=>ng t4?nh mGt phJng nF*C#$ %II)7 (1 imng t4?nh ( ) ( )2 2R B^ % Rl"g B 2 l"g B 2 1x yx y x y '+ ---------------------------------H82---------------------------------T*9-* T*:0*; 3901 L>01 01:< J 2*>01 1 0?@ 2010) N1.AB 36 CDE (FB T3G T$H0