ĐỀTHI CHỌN HSG LẦN 2 TOÁN 6

TRƯNG THCS HP THNH ĐỀ THI CHỌN HỌC SINH GIỎI MÔN: TOÁN 6 (Không kể thời gian giao đề) Câu 1. a. Chøng minh sè say ®©y lµ sè chÝnh ph¬ng. A = 44…4 x 88…8 ≥  n ch÷ sè 4 (n-1) ch÷ sè 8  !"#$%"& Câu 2. (2 điểm): So sánh &  $%! ! ' #( $% ) # #* $%  Câu 3. (1 điểm): +,-.***  "' #) +/0-1,21,' Câu 4. 34-5678#921:8!;$<=>71, &21:8*;$<=>71,!21:8;$<=> 1,*?04-56%,@ Câu 5: +,#-232+1-3.!A-+.#A3+.#3-232+8B %CD@E,@ FG&HIC#-232+,6=:?08GJ,,4B K18GJ&&,4BJLG,HIC#-232+ ,6=: Câu 6:M+FKN&"#$%!OL%CP%,8  @6,C,JQ)1*CD  …………………………………………………………………………………….………………………………………………………………………………………. ………………………………………………………………………………………. ………………………………………………………………………………………………………………………………………………………………………………………………………………… 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 ' ) ! ) * * ##  !   ) ## # B −   = × − × ×  ÷   −   = × − ×  ÷   = × × = 2' 2' 2'      # ) )      )' '( (& '(          ) ' ' ( ( & ' (   # #   ) ( ( ! C = + + +×××+   = + + +×××+  ÷     = − + − + − +×××+ −  ÷     = − = =  ÷   2' 2' Câu 2 (2điểm) &  .# #   .# ## ! ! .# )  ! .# # E# ## b# # &  b! !  2' 2' 2' ' #( .' #   .'   ) .    .  E'  b  ' #( b ) 2' 2' 2' # #* c# ) .# )   .!  $%  b  .    .  E  b!    b# #* 2' 2' Câu 3 (1điểm) ***  .* ' #) . ***  "' #) .*". E-8d L%-$%-' 2' 2' 2' 2' Câu 4 (1,5điểm) Ve4-56L%- E-a!&⇒-aa&&⇒-a& E-a*!⇒-aa!!⇒-a! E-a*⇒-aa**⇒-a* 2' 2' 2' R,8-aL%7N&2!2*$%-L%8#9**c-c  Q8J$%=>-a.') f6 '' 2' 2' 2' Câu 5 (3,5điểm) 8!"#.#≠#-3"-+≠3+ ⇒-CDg93$%+ a3g=;hi6=>3CDg9-$%+A +CDg9-$%3 6,#-A3A+CD8%,g9jL4 ⇒-232+CDB% 2' 2' 2' 2' 2' FG&HIC#-232+,6=:8G J&"#.HI a+e6,28$:*jL4 =>*,4BL%=1$:GJ2=>* ,4B K=1k,4B=>lLmn,8,4B$o=> L% * *  = ,4B 1?C1Ld,4BL%*,2' 2' 2' 2' 2' aVe$o=>&&,4BL% 8a.&&2=>.(f$%,L%'& 2' . 5 (3,5điểm) 8!"#.#≠#-3"-+≠3+ ⇒-CDg93$%+ a3g=;hi 6 =>3CDg9-$%+A +CDg9-$%3 6, #-A3A+CD8%,g9jL4 ⇒ -2 32+ CDB% 2& apos; 2& apos; 2& apos; 2 ' 2 ' FG&HIC# -23 2+, 6= :8G J&"#.HI a+e 6,  2 8$:*jL4 =>*,4BL%=1$:GJ 2 =>* ,4B K=1k,4B=>lLmn,8,4B$o=> L% * *  = ,4B 1?C1Ld,4BL%*, 2& apos; 2 ' 2 ' 2 ' 2 ' aVe$o=>&&,4BL% 8a.&& 2 =>.(f$%,L%'&. 4 (1,5điểm) Ve4-5 6 L%- E-a!&⇒-aa&&⇒-a& E-a*!⇒-aa!!⇒-a! E-a*⇒-aa**⇒-a* 2 ' 2 ' 2 ' R,8-aL%7N& ;2! 2*$%-L%8#9**c-c  Q8J$%=>-a.') f 6  '' 2 ' 2 ' 2 ' Câu. 34-5 6 78#9 2 1:8!;$<=>71, & ;2 1:8*;$<=>71, !2 1:8;$<=> 1,*?04-5 6 %,@ Câu 5: +,# -23 2+1-3.!A-+.#A3+.#3 -23 2+8B %CD@E,@ FG&HIC# -23 2+, 6= :?08GJ,,4B K18GJ&&,4BJLG,HIC# -23 2+ , 6= : Câu