50 ĐỀ +ĐÁP ÁN HSG TOÁN 9

TRUNG VĂN ĐỨC- THCS LAI THÀNH – KIM SƠN - NINH BÌNH- SƯU TẦM     (THỜI GIAN LÀM BÀI: 150 PHÚT KHÔNG KỂ GIAO ĐỀ ) !"          x x x x x P x x x x + − − + = − + − − + −   P   !"# P $ %   & ' (  ' ( x = + + − )*"#+,-. ( ) &   /  &x x− − − = !"( Ý 4 của bài 2 thí sinh bảng B không phải làm ) 01""+,-23.  01+,-.        (x x x x− + − = − +  01+,- .4  5456 ( +x 7&87&5 ≤ 099"#:3$";6    ba ba +++ 2<=>?:5@A)2<"B+,- (""*3C>"#+,-.     x xy y x y+ + = !"# ?,DEF.C6G45G)2<  $%?,DEF)3H?I3J?:"<?K"#  "#?:L1""M<"N?JO?P?,DEF"Q% !"$ ?,DRO8S?,DLB;TU3?:3J"?,DRLVP+3CPF"# ?,DR0W8)X),Y)"Z?,D3HQ"LVM;T?P?,DEF 0[)"Z?,D3HQ"LVM?P;T$.  W6  [  6;WT " ;T)P+3CP"#?,DR?,DLBW !"% (Bài 5 thí sinh bảng B không phải làm ) O8S?:;8T"<?%?,DR2"O;6S   ?:\>?,DR2"]\;5  \T?N099^ [_ Họ và tên thí sinh: …………………………. Số báo danh: ………………………. HỌC- HỌC NỮA - HỌC MÃI 1 `[a9[[b TRUNG VĂN ĐỨC- THCS LAI THÀNH – KIM SƠN - NINH BÌNH- SƯU TẦM & '()*+ ,-./0 1*23 445 6 [,KFc:3?:"!d05 78)*+ GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG 9: ;"<:8= !" G . &8 'x x≥ ≠  eK &8 'x x≥ ≠ "Q. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )                       A                     x x x x x P x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x − + − + = − − + − + − + − − − − + + = + − + − − + − − − − = + − − + − = + − − + − = + − − + = + − + = + T eK &8 'x x≥ ≠ "Q.      (    x P x x x x x + = = − + = + + − + + + +Ff!FE$"2C"2<LHZ x +   x +  "Q. ( )      A   x x x x + + ≥ + = + + g!3?E$"41C x + 6 ( )     ( (  x x x ⇔ + = ⇔ = + \ ehC0 !"# ( (P x= ⇔ =  "Q. HỌC- HỌC NỮA - HỌC MÃI 2 TRUNG VĂN ĐỨC- THCS LAI THÀNH – KIM SƠN - NINH BÌNH- SƯU TẦM ( )      & &  & &  & & ' (  ' (  A  ' ( ' (   A &  /  x x x x x x = + + − = + + − ⇔ − − = ⇔ − − = i3C. ( ) &  & & &  /    &x x− − − = − = g?Q46 & x )J*"#+,- !"  G        (x x x x− + − = − +  .     x≤ ≤ +Ff!?E$"T3"+4L8"Q. e6          x x x x− + − ≤ − + − = g!3j6k41CL  x − 6  x− 46 )N"Q.el6     (    x x x− + = − + ≥ g!3j6k41CL46 g?Qe6el46\ hC { } =S  . (  −≥x ".4  5456 ( +x  ⇔ 4  G455(45G '( ++x 6&  ⇔ 4G  5 ( ) &(  =−+x ( ) ( )      =−+ =− &( &   x x ⇔ 46\ ehC+,-m"*)46 > "Q;6       ++       ++       +            bab b a a n+FfTHG2"Q.       ≥+ a a 8       ≥+ b b 8 abab ba  (  =≥+ \oL""Q.  ( baba + ≥+ M?Q23C. ( )    ( (   (   = + = ++ ≥       + + ≥       + ba abba ab baba 23C. A   ≥+ ba ehC.;  /       =++≥  g!3j6k41CL.    ==⇔    =+ = ba ba ba  g?Q\l6    / ==⇔ ba HỌC- HỌC NỮA - HỌC MÃI 3 TRUNG VĂN ĐỨC- THCS LAI THÀNH – KIM SƠN - NINH BÌNH- SƯU TẦM #> :5@A)2<"B+,-  n p⇔ + =   A  8 n q p q N− = ∈      A '    'p q n n p q p q− = + − − = ⇔ − + = e'6'6+@Ip+5Iq+5I7&>  ' p q p q − =   + =  [o"   p q p q − =   + =  & ' p q =  ⇔  =  [o" A  p q =   =  eK & ' p q =   =   ⇒ 6/'\qeK A  p q =   =   ⇒ 6(\ ehCK6/'o"6(5@A)2<"B+,- ( "Q.  ( ) ( ) ( )           ( ( ( ( &               & &                         x xy y x y x xy y x y x y xy x y xy x y xy x y x y xy x y xy x y x y xy x y xy x y + + = ⇔ + + − = ⇔ + − + = − ⇔ + − − + + + = −  =    =  + − − = −       + + + = =     ⇔ ⇔   = − + − − =       + + + = − = −        =   hC+,-"Q*)48C6&q&qqGqGq ?"#  012r?,DEF?I3?:"<?\4 &q C & K L?Q. ( ) & &   y m x m m= − + − ∀   & & & & & & & & & & &    &     &  &    &  x m x m y m x m x y m x x x y y ⇔ − + − − = ∀ ⇔ + − + + = ∀ + = = −   ⇔ ⇔   + + = =   ehC?,DEF?I3?:"<?\Gq T HỌC- HỌC NỮA - HỌC MÃI 4 4 T ; O [ C F TRUNG VĂN ĐỨC- THCS LAI THÀNH – KIM SƠN - NINH BÌNH- SƯU TẦM s9P36F.C6L?QL1""M<"?J O&8&?PF% s9P3 ≠ . 0;T$=)?:"#?,DEFKf" f"3B?,Y"   q    m OA OB m m − = = − − 0O[)L1""MO?P;T8"Q. ( ) ( ) ( ) ( ) ( )                                 (  (      '  m m OH OA OB m m m m OH m m do OH m m − − + = + = + = − − − − ⇒ = ⇔ − = − + = − + ⇔ = ehCO[6p676 '  !"$ et?"B4"&8? uu   9<OeF)P+3CP"#ON>O3HQ"KF "Q.;WvvT"w3HQ"KF67;TW) gO;6OT6S8Ovv;WvvT"w3HQ"KF 67W6v"?,D3"#   · · CAI ACO= i)x8;WvvO8 · · ACO CAO OAC= V "Z · · CAI CAO IAC HAC⇒ = ⇒ =V V N3CyGQ" 67;W6;[,-=.T6T[ g ABCV JP+?,DR?,DLB;T> ABCV 3HN 67[  6[;[T6;WT*$"),Y"3H "Q. IAC HAC CI CH CK = ⇒ = = V V  8   IK H C⇒ ∈ \ CH AB⊥ N[ HỌC- HỌC NỮA - HỌC MÃI 5 TRUNG VĂN ĐỨC- THCS LAI THÀNH – KIM SƠN - NINH BÌNH- SƯU TẦM 67;T)P+3CP"#  8   IK C !"% B C A N M O 0)?:"#?NEO;KO8S>?NO)!C?:9 2"  OC ON = i3C === OM OA ON OM ON OC 23C MOA ∆ z NOM ∆ "" MNMA MN MA  =⇒=⇒ ( ) NBMBMNMBMNMBMA  ≥+=+=+⇒ LH?] g!3j6k41CL\3J"?N9T ehC\)?:"#?N9TK?,DRO8S Lu ý : - Tổng điểm tối đa là 20 điểm - Nếu học sinh giải cách khác đúng vẫn cho điểm tối đa - Câu hình không vẽ hình hoặc vẽ sai hình thì không chấm điểm. HỌC- HỌC NỮA - HỌC MÃI 6 TRUNG VĂN ĐỨC- THCS LAI THÀNH – KIM SƠN - NINH BÌNH- SƯU TẦM lR0g@{> `[W[i0[|{}9~•l'e€90WW9•\[‚&&G& 78@A8BC.D"="E8%F.GC> Z3.8?":3$" ( ( (   x x x A x x + − − − = − −  S;  4 Z∈ ?:; Z∈  Z3.8?  ";"Q"N)88"+r"3"#""$%. p p a p b p c p< − + − + − ≤  47&8C7&1ƒ45C ≥ [ƒC !"#l6  A  x y x y + + + " „464  54G/ & B„P6    /  /+ + − Z3.?  01+,-   ( ( y x y x x+ = − − +  *3C>F,-"#+,-.4  GC  5C6A@C  Z3(.?";T3HN;8?,D";[V[…8[†)X),Y3HQ" K;T8;  $  FB AB FC AC   =  ÷    $.TT…†6;[  Z3.?";T"Q[)="Z>[T8[")!C)X),Y\892" · · & '&AMC ANB= = $.;\6;9 ‡‡‡‡‡‡‡‡‡‡[P‡‡‡‡‡‡‡‡‡ Người coi thi không giải thích gì thêm HỌC- HỌC NỮA - HỌC MÃI 7 TRUNG VĂN ĐỨC- THCS LAI THÀNH – KIM SƠN - NINH BÌNH- SƯU TẦM &)H  ,-./0 \H@A8IJF+ Thời gian làm bài: 150 phút !"K#LM"N-O $%*32<' & G/ & "P"&q $%P3J2<"B+,-"Q"ˆ2<h"w% "ˆ2<"f")"ˆ2<)V !"K$LM"N-O :3$"       x x x x x P x x x x − + − = − + + + − Slq  !"#l !"#K$L%M"N-O 01*+,-      xy x y xy y + = +   = +  01+,-.4  545645  4 + !"$KLM"N-O $%. ( ) ( )  4 C 4C  4 C + − + ≥ + K 48C S∈ !"%KPL%M"N-O ?,DRZO8?,DLB;T6SMJ?:\>P+ 3CP"#?,DRN;8tP+3CP$\K?,DR)P+?:0 [)"P3"#>;T $.\OvvTq $[T;\6OT[q "O\6FB[xSF GGGGGGGGGGG[PGGGGGGGGGGG HỌC- HỌC NỮA - HỌC MÃI 8 QR TRUNG VĂN ĐỨC- THCS LAI THÀNH – KIM SƠN - NINH BÌNH- SƯU TẦM & S 3  )*+ (Thời gian làm bài 150 phút) 9:KM"N-O> B"#"":3$". ;6       − − − + T64  5&&4  CG&C  5&8P 4 C C 4 C 4 4 C =  9:K#M"N-O> 01+,-.  4  4  4+ = +  )K!"#:3$";6 4   4+ + −    G  5G6&$%.  (             + − + + < − +  9:KM"N-O> o+E?JO4C8"?:;Gq8Tq("?   ?J ?:>f"2"?JF;5T ! 9:3K#M"N-O> ";T3HN;8?,D";[[Tp[TP;[6 "8 T6"B?JF"N;T(không làm tròn kết quả) ?,DROqS"QFZC;T6S  P+3CPN;T"# O  q  S "‰3N\ B · ;\T  0)J?:"3C:?J>OqS8…)3?:"#;8 [  ) "P3"#…>T$%[3J"J?,D"< ? 9:3KM"N-O>   (    (   4 4 C C 4 C + + + = K47&8C7&87& B     4 C+ x GGGGGG[PGGGGGG HỌC- HỌC NỮA - HỌC MÃI 9 TRUNG VĂN ĐỨC- THCS LAI THÀNH – KIM SƠN - NINH BÌNH- SƯU TẦM &1T )UV3 '(>  D.&+(Không kể thời gian giao đề) 9: ;"ƒC"P=FNC"?)Š"  ehFf=?Q*"FNC?)Šj]Q""#J"k 9: $%. && (  − M i2+Z2<. (A (A A =  (' (A( B = """2<3C>F,-?:+Z2<.    n n + − )+Z2<<1 9:# 8 8x y z P.    q (x y x z= =    x y z− + = q   '   & &x x x− − + = "       x x x − − − − = 9:$ !"#  S x x = + K x ≥ \J"2?ƒ1,23.e x ≥ >+FfT!?E$"3"C"2<. x   x "Q.      S x x x x = + ≥ C  S ≥ g!3%4‹CL"ŒL     x x x = ⇔ =  ehC !"# S )   8?N?,Y"L   x = [ƒC"Œ2)X)D1> 1)N"? 9:%3H;Tg8)!C?:\3J"?,D"•;M?:\LV?,DE 22K;T"‰;g8T)X),YNUl)"P3"#\>g  $. ∆ U\l6 ∆ T\M?Q23CT\3HQ"KlUN[     MC MA = BŽ2<. MH QH  9:P?:;8T8"<?2";T5T6;et?,DRO!L•?I3T TLH+1)?,DLB"#OM;t""P+3CP;\8;9K?,DRO \89)P+?:~!CW)3?:"#?NET0?:\9K;)[ $.  9•?:;8\8O8W89"w3J"J?,DR  OC?]?JF;[LH?] WC HỌC- HỌC NỮA - HỌC MÃI 10 QR KX=Y-CZE8=O [...]... min = 2, khi x = 4 1 Ta cú : = P Bi 2 9 y 10 a/ x + xy + y = 9 => x(1 + y) = 9 y => x = 1 + y = 1 + 1 + y x nguyờn khi 1 + y (10) = {-10 ; -5 ; -2 ; -1 ; 1 ; 2 ; 5; 10} Suy ra : y{-11 ; -6 ; -3 ; -2 ; 0 ; 1 ; 4; 9} Khi ú x {-2 ; -3 ; -6 ; -11 ; 9 ; 4 ; 1; 0} Vy ta cú 8 cp s l : (y; x) = (-11; -2), (-6 ; -3) , (-3 ; -6) , (-2 ; -11), (0 ; 9) , (1 ; 4) , (4; 1), (9 ; 0) a b c + + =0 bc c a a b a b c +... TRUNG VN C- THCS LAI THNH KIM SN - NINH BèNH- SU TM S GD&T TNH HI DNG PHềNG GD&T HUYN NINH GIANG K THI CHN HC SINH GII LP 9 VềNG 2 CHNH THC MễN TON Nm hc 2011 - 2012 Thi gian lm bi : 150 phỳt Ninh Giang, ngy 15 thỏng 12 nm 2011 Cõu 1: (3.0 im) Rỳt gn cỏc biu thc sau: 4 4 A= 94 5 9+ 4 5 B= x+24 x2 + x+2+4 x2 (vi x >2) 4 4 +1 x2 x Cõu 2 (2.0im) 1) Tỡm cỏc nghim nguyờn dng ca phng trỡnh: 2x + 5y + 3xy... ỳng theo yờu cu chung ca bi C 1 K 1 E 0,25 2 A 1 H O D I B 4 ã a) Ta cú ã ACB = DEB =90 0 nờn AC// DE 0,75 b) Gi K l trung im ca CE, I l trung im ca BD Cú HK l ng trung bỡnh ca hỡnh thang ACED => HK vuụng gúc vi CE => CHE cõn ti H à à ả à à à => E1 =C1 Cú E 2 =B1 v B1 + C1 = 90 0 à ả ã => E1 +E 2 = 90 0 => HEI = 90 0 Vy HE l tip tuyn ca ng trũn ng kớnh BD 5 0,5 0,25 0.25 A D M K B H ã ã ã Ta cú MA =... 2 b) Xỏc nh v trớ ca im M trờn na ng trũn din tớch t giỏc ABCD nh nht Tớnh din t giỏc ú UBND HUYN TAM DNG PHềNG GD&T CHNH THC Kè THI CHN HSG TON LP 9 VềNG 1 Nm hc: 2011-2012 Mụn: Toỏn Thi gian lm bi: 150 phỳt thi ny gm 01 trang HC- HC NA - HC MI 29 TRUNG VN C- THCS LAI THNH KIM SN - NINH BèNH- SU TM Lu ý: Hc sinh khụng c s dng mỏy tớnh cm tay Cõu 1: (2,5 im) a) Tớnh giỏ tr ca biu thc: A =... ã ã ã ã ABH > BAH => BAH < 450 => HAC > 600 HC- HC NA - HC MI 28 TRUNG VN C- THCS LAI THNH KIM SN - NINH BèNH- SU TM 0.5 => ã AMH < 600 => AH < HM => AH < HB (Mõu thun vi (1)) 0.25 K THI HC SINH GII HUYN Nm hc 2010-2011 Mụn Toỏn -Lp 9 Thi gian lm bi 120 phỳt PHềNG GIO DC V O TO QUNH LU THI Cõu 1 : (2 im) a) Tỡm cp s t nhiờn x, y tha món phng trỡnh: 100 x + y 2 + 3 y = 1 09 b) Hóy vit cỏc a thc x 3... Cõu 5: (1 im) Cho a, b, c l cỏc s thc khụng õm v abc = 1 Chng minh rng: 1 1 1 1 + 2 + 2 2 2 2 a + 2b + 3 b + 2c + 3 c + 2a + 3 2 2 UBND HUYN TAM DNG PHềNG GD&T CHNH THC HNG DN CHM MễN TON 9 Kè THI CHN HSG LP 9 VềNG 1 Nm hc: 2011-2012 HC- HC NA - HC MI 30 TRUNG VN C- THCS LAI THNH KIM SN - NINH BèNH- SU TM Cõu 1: (2,5 im) Cõu a) Ta cú (1,5) 3 3 x = ( Ni dung trỡnh by 3+ 2 2 + 3 3 2 2 ) im 3 = 3 +... phn, cỏc cõu khụng lm trũn im ton bi lm trũn n 0,25 - Bi hỡnh khụng v hỡnh hoc v hỡnh sai thỡ khụng chm HC- HC NA - HC MI 33 TRUNG VN C- THCS LAI THNH KIM SN - NINH BèNH- SU TM thi hsg huyờn thanh miờn nm 2011-2012 toỏn 9- 150 phỳt (vong 1) Cõu 1 (2 im).Cho biu thc: A= x x 4x x + 4 2x x 14x + 28 x 16 a)Tỡm x A cú ngha , t ú rỳt gn biu thc A b)Tỡm cỏc giỏ tr nguyờn ca x biu thc A nhn giỏ tr nguyờn... cho din tớch tam giỏc MNO t giỏ tr ln nht v tớnh giỏ tr ln nht ú theo R Cõu5( 1 im) Cho cỏc s thc dng a,b,c Chng minh bt ng thc: 2 3 ab + bc + ac 3 (a + b)(b + c)(a + c) 3 thi hsg huyờn thanh miờn nm 2011-2012 toỏn 9- 150 phỳt (vong 2) Cõu1(2 im) a) Rỳt gn biu thc: 1 1 2 1 + + + ữ A= yữ x+ y x x 1 x3 + y x + x y + y3 : y x 3 y + xy 3 (vi x,y>0) 64 3a l s nguyờn b) t a= 3 2 3 + 3 2 + 3 ... 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