Đề + Đ/a HSG Toán 9- hay

Ubnd huyÖn ®«ng hng ®Ò kh¶o s¸t chän nguån HSG M«n To¸n líp 9 Phßng gi¸o dôc  (Thêi gian lµm bµi: 90 phót) ®Ò bµi C©u 1(            + − − +         + − + + a1 a1 a-1 a1 : a1 a1 a-1 a1  6 1 12 5 3 1 23 1 3 1 −++ C©u 2   ! "#$%&'()*+,!,"   14 23 222 > ++ + ++ zyxzxyzxy C©u 3  /)0  1 2131, 1 ,12%4#$&'- .5*/)06 6 2 .   .0/)0-78 97&!:687 8/)0 0 4 112 2 2 2 4 2 22 = − −−+ + + − − y mmy y m y C©u 4(  ;<=>?<6@1A$BC (BD;<=7.EFB<=>GH/I< =>?JC$H/IJ@JK.L<=GMC C@ #N#OJ#$ P. . P&&@. .CK#$/>7C@$CK#QRB '6CJ!D;<=?. C©u 5  @: B<=>?MJ@ SG$PPTU@$G MJ@SV$WVTU$W  MJS5$X5TU$X.  Y&V.W$5.X.  51 5X-% X- VWZ.PG[  ®¸p ¸n,biÓu ®iÓm. C©u 1: (4 ®iÓm)          + − − +         + − + + a1 a1 a-1 a1 : a1 a1 a-1 a1  . 6 1 12 5 3 1 23 1 3 1 −++ 3 L:68#$    ≠ < 0 1 a a 4 \ 3 L] . 1 2 1 2 1 : − + =−+== − +                 x x x x  - 7 - - -   - - - - - 3- - 7 3- - ! = − − + + + = + = (4 \ 3 E . 6 1 12 5 3 1 23 1 3 1 −++  . 12 625 3 1 23 1 3 1 − ++ 4 \ ( ) 4 \  % 1 7$! L4 \^L+_  == = −++ = − ++=  − ++= − ++= . 2 3 2 3 6 23232 6 23 23 1 3 1 )5,0( 32 23 3 1 23 1 3 1 12 23 3 1 23 1 3 1 2 iem C©u2.(4®iÓm) C/*(:E`-1.%a-11a  1 " 1 ! 1  "!"! . "!"! 1 " 1 ! 1  %.1aE 7 1 " 1 ! 1  "!"! .$ "!"! 1 " 1 ! 1  %. (b&'1Q&@L(c/D(b"!  (  1 " 1 ! 1  "!"! . "!"! 1 " 1 ! 1  %.a 1 " 1 ! 1  "!"! .1d "!"! 1 " 1 ! 1  %. 1 " 1 ! 1  "!"1! 1 " 1 ! 1  1. "!"! "!"1! 1 " 1 ! 1  %. 1 " 1 ! 1  1 "! 1. "!"! 1 "! %. 1 " 1 ! 1  1 "!"! % E ==+>+= ++ ++ ++ ++ +≥ ++ ++ ++ ++ ++ ++ + ++ ++ += ++ ++ +++ ++ ++ = ++ +++++ + ++ +++++ = =++ ++ ++ + ++ ++ = ++ + ++ = o zyxvi )1( C©u 3: (4®iÓm)  (2®iÓm ) ! 6 2 $/)0-7  1 21 6 2 31, 3 2 , 6 4 2%4  ef 0293422)x2632(2x23 2 =−++−−  7 =∆ / Z3 2 )16(62 −= f4/)0718/>8  0 4 112 2 2 2 4 2 22 = − −−+ + + − − y mmy y m y        − = −− = 6 638 x 6 64 x 2 1  (2®iÓm) `)0  1 2131, 1 ,12%4#$&'- #$/)0g17 =∆ / 31 1 3 1 ,13%3d,Z. `)078ef ≥∆ / 4ef3d,Z ≥ 4ef 6 7 ≤ . `)0 0 4 112 2 2 2 4 2 22 = − −−+ + + − − y mmy y m y 1 (®iÒu kiÖn x¸c ®Þnh 1!$1! −≠≠  `)01ef! 1 3131!, 1 ,13%4h `)01786$i6/)0h78*+: 68 1!$1! −≠≠ . `)0h#$/)0g17j8&'  /)0-D/3 )  0  h7  8  6    6 7 ≤  %.  K8  !    h  *  +  L^ 1!$1! −≠≠ ef      ≠−+−−−− ≠−++−− 032m2)2).(2(m2)( 032mm2).22(m2 2 22 ef      ≠−+ ≠+− 076mm 092mm 2 2  ef    −≠ ≠ 7m 1m  ^HO/%$7/)0178ef        ≤ −≠ ≠ 6 7 m 7m 1m C©u 4: (4®iÓm) a)(2®iÓm P&&@ . P?$GH/IDG ? Ck$. C$CGP$C?@>SG$?  7CPG7C@? jT7?CP l!7CPG$7C@?#$17m 1<kP$@C@#$!H DP&&@.^  A N O B M D C E b) (2®iÓm) CK#$/>7C@.- P@H/IGJKDGKQ7@ f DE ˆ NNE ˆ C = n4 4 fKTKPf BMNNMC ˆˆ = fCK#$/> 7C@. h6C(BD;<=?0CK#QR-' .- 5oCKM<=?J1#$^6C 717CK$@CKTD$I#$7BH/ <=?D^$@^Tf^#$U ^@'<=?'D^#$'. Eg!6C(BD;<=?0CK#QR'#$ U@=#J?. C©u 5 (4 ®iÓm) ∆@@@p40F  a(2 ®iÓm  Y&V.W$5.X. qr ∆ 5V$ ∆ WX75VWXBH/ f 0 180 ˆ ˆ =+ FJHFGH $ 0 180 ˆˆ =+ AGHFGH 6:j D FJAAGH ˆ ˆ = - sJ77 D ∆ 5V$ ∆ WXm(J. 4 \ f AF AH AJ AG = f5.XV.W.4 \ b) TÝnh DE = ? (2®iÓm) 5oPG @P G7,,-d-.4 \ t>7 5.XV.WfVV,VW%4V 1 ,ZV3%44 efV%f@Wd. )u>7G.PX.5f,-ef 1 ,-.14 \ $ 1 ,Za%9- 1 %78`      =+ =+ =++ )3(78 )2(14 )1(16 2 2 axa bxb bax 4 \ 9H`1$%O`3,,3d. !-$O33f3  !3$-7-434 \  !-434 \$%7-434 \ 1 ,-434 \Za ef 1 aaef 222 .4 \ A B C DE H J G F . (  1 " 1 ! 1  "!"! . "!"! 1 " 1 ! 1  %.a 1 " 1 ! 1  "!"! .1d "!"! 1 " 1 ! 1  %. 1 " 1 ! 1  "!"1! 1 " 1 ! 1  1. "!"! "!"1! 1 " 1 ! 1  %. 1 " 1 ! 1  1 "! 1. "!"! 1 "! %. 1 " 1 ! 1  1 "!"! % E = =+& gt ;+= ++ ++ ++ ++ + ++ ++ ++ ++ ++ ++ + ++ ++ += ++ ++ ++ + ++ ++ = ++ ++ ++ + + ++ ++ + ++ = =++ ++ ++ + ++ ++ = ++ + ++ = o zyxvi )1( C©u 3: (4®iÓm) .  % 1 7$! L4 ^L + _  == = ++ = − ++ =  − ++ = − ++ = . 2 3 2 3 6 23232 6 23 23 1 3 1 )5,0( 32 23 3 1 23 1 3 1 12 23 3 1 23 1 3 1 2 iem C©u2.(4®iÓm) C/*(:E`-1.%a-11a  1 " 1 ! 1  "!"! . "!"! 1 " 1 ! 1  %.1aE 7 1 " 1 ! 1  "!"! .$ "!"! 1 " 1 ! 1  %. (b&'1Q&@L(c/D(b"!.           + − − +         + − + + a1 a1 a-1 a1 : a1 a1 a-1 a1  6 1 12 5 3 1 23 1 3 1 ++ C©u 2   ! "#$%&'()* + ,!,"   14 23 222 > ++ + ++ zyxzxyzxy C©u