Chuyen de Luong Giac 10

7/26/2019 Chuyen de Luong Giac 10

1/7

Chuyn lng gic lp 10 Nm hc 2015 - 2016

LNG GICPhn 1: Gi tr lng gic ca cc cung c lin quan !c "i#tA. Kin thc cn nh1. Cc hng ng h!c c" #$n

%& 1c'((in 22 =+ xx #&x

xx

c'(

(in%n = c&

x

xx

(in

c'(c' =

)& xx 22

c'(1%n1 =+ *& xx 2

2

(in1c'1 =+ +& 1c'.%n =xx

2. ,i c/% cc hm lng gic cung lin u%n c #i3%& 4%i cung i nh%u #& 4%i cung # nh%u c& 4%i cung 7hc nh%u

xx

xx

xx

xx

c'&c'8

%n&%n8

(in&(in8

c'(&c'(8

=

=

=

=

xx

xx

xx

xx

c'&c'8

%n&%n8

c'(&c'(8

(in&(in8

===

=

xx

xx

xx

xx

c'&2c'8

%n&2%n8

c'(&2c'(8

(in&2(in8

=+=+=+=+

)& 4%i cung 7hc nh%u *& 4%i cung ph9 nh%u

xx

xx

xxxx

c'&c'8

%n&%n8

c'(&c'(8(in&(in8

=+=+

=+ =+

xxxx

xxxx

%n2

c':c'2

%n

(in2

c'(:c'(2

(in

=

=

= =

B. Bi tp1. ; gi nh? nh@. ;


2/7


7& ( )22

Jc'F

1Ec'

2

J%n

F

1J%n

++

+ bb

l&

+

+

+

+

x

x

x

x

x

x

x

x

c'(1

c'(1

c'(1

c'(1

(in1

(in1

(in1

(in1

m& &%n18c'(&c'18(in EE aaaa +++

n&bb

b

c'%n

%n

+

'&a

aaF

FF

c'(

(inc'(1

p&

+

xxx

xxx

2

Ec'&.c'8.

2(in

&2(in8&.2c'(8&.(in8

&22

&2c'(82

Ec'(&(in8

2(in

+

+

+

xxxx

&

++

+

+

aaaaa

2

E%n&.%n8

E

5c'(.

E

2%n.

E(in

(& &5SE%n8&6c'8&F%n8&5S5c'8

+ baba

& oooooo J00%n.F00%n.260%n.250%n.1I0%n.50%nF. Ch' RS TS C l #% gAc c/% %m gic RTC. Ch!ng minhD%& -c'(RC&c'(8T:(in&(in8 =+=+ CBA c& -c'CT&c'8R:%n&%n8 =+=+ BCA

#&2

(in2

CTc'(:

2c'(

2

TR(in

AC =+=+ )&2

%n2

TRc':

2c'

2%n

CBCA =+=+

5. ;


3/7


%&

++

+

aa

aa

F(in2(in2

Fc'(2c'(2

#& ooooo JIc'(.6Ic'(21c'(.11c'(10c'( ++c& bababa %n.%n&c'8&.%n8%n E. Ch!ng minh 'ng mi %m gic RTC % u cAD

%& %nC%nR.%nT.%nC%nTR%n =++ #& 12%n.

2%n

2%n.

2%n

2%n.

2%n =++ ACCBBA

c& 1c'.c'c'.c'c'.c' =++ ACCBBA )&2

c'.2

c'.2

c'2

c'2

c'2

c' CBACBA =++

F. %& Ch'F

= ba S ch!ng minhD ab

b%n

%n1

%n1 =+

U ba

a%n

%n1

%n1 =+

.

#& Ch'F

=+ba S ch!ng minhD 2&%n1&8%n18 =++ ba U 2&c'1&8c'18 = ba

c& Ch'nya

max

==+

&%n8

&%n8. Ch!ngminhD

ab

bayx

+

=+1

&%n8 .

)& Ch' 52

%n =a S JE

%n =b &108 va, b


4/7

Chuyn lng gic lp 10 Nm hc 2015 - 2016B. Bi tp1. GH gn cc #i=u h!c (%uD

%&aaaa

aa

(inEc'(c'(E(in

F(in.

F(in

+

#&]%n

1]

%n 2

c& ooo ]0c'(.F0c'(.20c'( )& &(in8c'(c'((in2 22 aaaa

*& aaaa F22F (inc'((in6c'( + +&2

c'(

2

(inFc'( 222 aa

a

g& aa 22 c'((in]1 h& ooo F0c'(20c'(10c'(]i& aaaa E(inc'(FEc'((inF EE + K& aa 2(inF(inF 2F +

7&5

2c'(

5c'(

l& oooo ]0c'(60c'(F0c'(20c'(

m& aaaaaa E2%nE216%n16]%n]F%nF2%n2%n +++++

n&aa

aa

Ec'(c'(

E(in(inE

E

+

'&aa

aa

E(in(in

Ec'(c'(

+

2. Ch!ng minhD

%& aaaa E(inF

1

E

(in

E

(in(in =

+

. ^p )9ng UiI

=a .

#& 11](in]1](in] 2E =+

c&E2

c'E2

%n16

%n2]

%nF] =+++

)& 5J2%nE6%n 22 =oo

*& aaaa Ec'(F

1

Ec'(

Ec'(c'( =

+

. ;_nhD

1]

Jc'(

1]

5c'(

1]c'(

+&a

aaa

2

E

%nE1

%n%nEE%n

=

g& aaaa E%nE

%n

E

%n%n =

+

. Ch!ng minhD5210

1566%n5F%n6%n

+

=ooo .

E. %& Ch' &0S82(in >+

= baba

ab . ;


5/7


c&2

c'(F&c'(8c'(&(in8(in 222 ba

baba +=+++ )& a

aac'2

2c'

2%n =

*&

=

+

2Fc'

(in1

(in1 2 a

a

a +& ( ( 122E`E0J%n =o

g&2

c'(2&c'(8c'(c'(&(in8(in(in 2 ba

baabaa =+++

h&2

(inF&c'(8c'(&(in8(in 222 ba

baba =+

i&a

a

a

a

(in1

2F(in

(in1

2F(in

+

+

&08


6/7


2(in.

2(in2c'(c'(

2c'(.

2c'(2c'(c'(

2(in.

2c'(2(in(in

2c'(.

2(in2(in(in

bababa

bababa

bababa

bababa

+=

+=+

+=

+=+

ba

baba

ba

baba

ba

baba

ba

baba

(in(in

&(in8c'c'

(in(in

&(in8c'c'

c'(c'(

&(in8%n%n

c'(c'(

&(in8%n%n

=

+=+

=

+=+

B. Bi tp1. GH gn #iZu h!c%& N&8n&c'(8...&2c'(8&c'(8c'( +++++++ nbababaa

#&aaaa

aaaa

J(in5(inE(in(in

Jc'(5c'(Ec'(c'(

++++

c&aaa

aaa

E(in2(in(in

Ec'(2c'(2c'(

++++

)&a

aa

ac'(2

62c'(

62c'(

c'(

+

*&

2c'c'

Ec'(

Ec'(

aa

aa

+

+

+& aaaa 2c'(2

1Fc'(

F

1c'(2c'( 2 g& 2c'(Fc'(1c'(Ec'( 22 +

h& &15](in1128(in20E(in2I1(in1(in ooooo +++i& &1F0(in1E08(in1]5(in2125c'(E5c'( ooooo +++K& oooo ]0(in60(inF0(in20(in 7& oooo ]0%n60%nF0%n20%n2. Ch!ng minhD

%&16

E]0(in60(inF0(in20(in =oooo

#& naanaaa

anaaa%n

&12c'(8...5c'(Ec'(c'(

&12(in8...5(inE(in(in =++++

++++

c&

2(in

2

&18(in

2(in

(in...E(in2(in(ina

anna

naaaa

+

=++++

)&

2(in

2

&18c'(

2(in

c'(...Ec'(2c'(c'(a

anna

naaaa

+

=++++

E. Ch!ng minh 'ng mi %m gic RTC % u cAD

%& 2c'(2c'(2c'(F(in(in(in CBA

CBA =++#&

2(in

2(in

2(inF1c'(c'(c'(

CBACBA +=++

c& &c'(c'(c'(182(in(in(in 222 CBACBA +=++)& CBACBA c'(c'(c'(21c'(c'(c'( 222 =++

*&2

c'(2

(in2

(inF(in(in(in CBA

CBA =+

+& 12

(in2

c'(2

c'(Fc'(c'(c'( =+ CBACBA

g& CBACBA (in(in(inF2(in2(in2(in =++

;Lng ;4M; Mh%n ng Ou P Qn ;hnh P Ngh3 Rn ;%ng 6


7/7

Chuyn lng gic lp 10 Nm hc 2015 - 2016h& CBACBA c'(c'(c'(F12c'(2c'(2c'( =++i& CBACBA c'((in(in2(in(in(in 222 =+

F. Ch!ng minh #@ ng h!cD &(in8(in2

1

2(in yx

yx ++ Ui

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Chuyen de Luong Giac 10