Đề số 15 ĐỀ THI THỬ HỌC KÌ 2 – Năm học 2010 – 2011 Môn TOÁN Lớp 11  I. Phần chung: Câu 1:  x x x x 2 3 3 lim 2 3 →− + + −  x x x 2 2 5 3 lim 2 →− + − + Câu 2:!a"#$x% x x khi x f x x a khi x 2 7 10 2 ( ) 2 4 2  − +  ≠ =  −  − =  & Câu 3:!'()"  y x x 2 3 ( 1)( 2)= − +  x y x 4 2 2 2 1 3   + =  ÷  ÷ −   Câu 4:*+(,-$./0+&/′0′+′12/0+34++/%a +0%b5#//′0′034&6+78+9⊥/0′9:;;/′09∈/0′:∈//′& +.-< 0+⊥+:/0′⊥+9:& '1=5>//′0′03+9:& '7(?6/@5>+9:& II. Phần riêng:*Thí sinh chỉ được chọn một trong hai phần sau: 1. Theo chương trình Chuẩn Câu 5a:!'  n n 2 2 1 2 2 2 lim 1 3 3 3 + + + + + + + + & Câu 6a: +(" y xsin(sin )= &'  y ( ) π ′′ & +(+  y x x 3 2 3 2= − + &A@BC-@2@)+()+3-$ (& 2. Theo chương trình Nâng cao Câu 5b:!+.-<@"a, b, cDEF"E"x, y, zGD EF"E3  x a bc 2 = −  y b ca 2 = −  z c ab 2 = − & Câu 6b: +(" y x x.sin= &+.-<  xy y x xy2( sin ) 0 ′ ′′ − − + = & +(+  y x x 3 2 3 2= − + &A@BC-@2@)+@@2@3413 B>H y = x 1 1 3 − + & IIIIIIIIIIIIIIIIIIII9@IIIIIIIIIIIIIIIIIII Họ và tên thí sinh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SBD . . . . . . . . . . ! Đề số 15 ĐÁP ÁN ĐỀ THI THỬ HỌC KÌ 2 – Năm học 2010 – 2011 Môn TOÁN Lớp 11  Câu Ý Nội dung Điểm 1  2 3 3 3 3 lim lim ( 3)( 1) 2 3 x x x x x x x x →− →− + + = + − + − &J 3 1 1 lim 1 4 x x →− = − − &J  ( ) →− →− + − − + = + + + + x x x x x x x x 2 2 2 2 5 3 ( 2)( 2) lim lim 2 ( 2) 5 3 &J 2 2 2 4 2 lim 6 3 5 36 x x x →− − − = = = − + + &J 2 x x khi x f x x a khi x 2 7 10 2 ( ) 2 4 2  − +  ≠ =  −  − =  2 2 2 2 2 7 10 ( 2)( 5) lim ( ) lim lim lim( 5) 3 2 2 x x x x x x x x f x x x x → → → → − + − − = = = − = − − − J f%KLa  f x #$x%⇔ 2 lim ( ) (2) 4 3 7 x f x f a a → = ⇔ − = − ⇔ = :@D3a%"#$x%& J 3  2 3 5 3 2 ( 1)( 2) 2 2y x x y x x x= − + ⇒ = − + − J 4 2 ' 5 3 4y x x x⇒ = − + J  4 3 2 2 2 2 2 2 2 1 2 1 14 ' 4 3 3 ( 3) x x x y y x x x     + + − = ⇒ =  ÷  ÷  ÷  ÷ − − −     J − + ⇒ = − x x y x 2 3 2 5 56 (2 1) ' ( 3) J 4 J  +.-< 0+⊥+:/0′⊥+9:& ′ ′ ′ ⊥ ⊥ ⇒ ⊥ ⇒ ⊥BC AC BC AA BC C C BC CK, (AA ) J ′ ′ ⊥ ⇒ ⊥ ⊥ ⇒ ⊥AB A B KH A B KH AB CH AB AB CHK, ' ', ' ' ( )P J  '1=5>//′0′03+9:& +1 ' ( ), ' ( ' ' ) ( ' ' ) ( )AB CHK AB AA B B AA B B CHK⊥ ⊂ ⇒ ⊥ J 0 (( ' ' ),( )) 90AA B B CHK = J   '7(?6/@5>+9:& M1 ' ( )( )AB CHK cmt⊥ 9# ( ,( ))d A CHK AH= J ( ), ' ( : ) ( ' ' ) 'AC BC gt CC AC gt lt AC CC B B AC CB⊥ ⊥ ⇒ ⊥ ⇒ ⊥ J = + = + = = + 2 2 2 2 2 2 , ' 2 2 2AB AC BC a b AB AB a b J -(∆/+0N34+  ′ ′ ⊥ ⇒ = 2 .CH AB AC AH AB 2 2 2 2 2 ' 2 2( ) AC a a AH AB AB a b ⇒ = = = + J 5a 1 2 2 1 2 1 1. 1 2 2 2 2 1 lim lim 1 3 3 3 3 1 1. 3 1 n n n n + + − + + + + − = = + + + + − − J 1 1 1 1 1 2 2 2. 3 2.2 2 3 lim lim 0 1 3 1 1 3 n n n n n + + + + +   −  ÷ −   = = − − J 6a  +(" y xsin(sin )= &'  y ( ) π ′′ & = ⇒ = − −y x x y x x x x x' cos .cos(sin ) " sin .cos(sin ) cos .cos sin(sin ) J π ⇒ = − − ⇒ =y x x x x y 2 " sin .cos(sin ) cos .sin(sin ) "( ) 0 J  +(+  y x x 3 2 3 2= − + & ′ = −y x x 2 3 6 &O()+3-$Px/!Q ( ) ( ) − +B C1 3;0 , 1 3;0 J @2@/!Q1R"1k%L*#S  = − +y x3 3 J @2@ ( ) −B 1 3;0 1R"1k%T#S  6 6 6 3y x= − + J @2@ ( ) +C 1 3;0 1R"1k%T#S  = − −y x6 6 6 3 J 5b +UV@"a, b, cD+W+"x, y, zGD+W+ 3  x a bc 2 = −  y b ca 2 = −  z c ab 2 = − & a, b, c F"E# + =a c b2 12% 2 2 2 2 2 , ( )b ca x z a c b a c− + = + − + J ⇒ 2 2 2 2 2 ( ) 2 2 4 2 2 2 2 2x z a c ac b b ac b b ac y+ = + − − = − − = − =  J 6b  +(" y x x.sin= &+.-<  xy y x xy2( sin ) 0 ′ ′′ − − + = & 1 = + ⇒ = + − = −y x x x y x x x x x y' sin cos " cos cos sin 2cos J ′ ′′ ⇒ − − + = − + − + −xy y x xy xy x x x x x x y2( sin ) 2(sin cos sin ) (2cos ) J  = 0 J  +(+  y x x 3 2 3 2= − + H y = x 1 1 3 − + & A@2@3413H  y = x 1 1 3 − + #R"1)@2@k%* J OX x y 0 0 ( ; ) (E)@& ⇒ ′ = ⇔ − − = ⇔ = − = +y x x x x x 2 0 0 0 0 0 ( ) 3 3 6 3 0 1 2; 1 2 J A = − ⇒ = ⇒ = + −x y PTTT y x 0 0 1 2 2 : 3 4 2 3 J A = + ⇒ = − ⇒ = − −x y PTTT y x 0 0 1 2 2 : 3 4 2 3 J * . x x x x 2 2 2 2 5 3 ( 2) ( 2) lim lim 2 ( 2) 5 3 &J 2 2 2 4 2 lim 6 3 5 36 x x x →− − − = = = − + + &J 2 x x khi x f x x a khi x 2 7 10 2 ( ) 2 4 2  − +  ≠ =  −  − =  2 2 2 2 2 7. + 2 2 2 2 2 2 , ' 2 2 2AB AC BC a b AB AB a b J -(∆/+0N34+  ′ ′ ⊥ ⇒ = 2 .CH AB AC AH AB 2 2 2 2 2 ' 2 2( ) AC a a AH AB AB a b ⇒ = = = + J 5a 1 2 2 1 2 1 1. 1 2 2. a bc 2 = −  y b ca 2 = −  z c ab 2 = − & a, b, c F"E# + =a c b2 1 2 % 2 2 2 2 2 , ( )b ca x z a c b a c− + = + − + J ⇒ 2 2 2 2 2 ( ) 2 2 4 2 2 2 2 2x z