Toan khoi A-A1

5/23/2018 Toan khoi A-A1

1/6

S GD&T VNH PHC KTCL N THI I HC LN 2 NM HC 2013-2014M!" T#$N% K'( )* )1

Thi gian lm bi: 180 pht, khng k thi gian pht

I+ PHN CH,NG CH# TT C. TH/ SINH *0 im

C 1 2*0 im+ Cho hm s ( )2 1

2

xy C

x

=

.

5Kho st s bin thin v v th (C) ca hm s cho.

6!"m t#n (C) t$t c cc i%mM sao cho ti& t'n ca (C) tiMc*t hai ti+m c,n ca (C) ti hai i%mA,sao cho 2 1-A= .

C 2 1*0 im+ ii &h/0n t#"nh1 cos 3

sin 2 sin 2tan 4

xx x

x

+ = +

.

C 3 1*0 im+ii h+ &h/0n t#"nh( ) 2 2

4 2 2

4 1 1 2 2 1

1

y x x y

x x y y

+ = + +

+ + =.

C 4 1*0 im+!5nh t5ch &h6n

-

2

4

1 2sin 2 2cos

!x"

x x

= + .

C 7 1*0 im+ Cho h"nh ch7& #$AC% c7 AC%8 h"nh than c6n91:

4

aA% C= = 9 2A a= 9

:

2

aC%= 9 m;t &hi m;t &hi h+ tHa @ )xy9 cho ba i%m (1N 1N 1)9 ( 1N -N 2)9 (-N 1N -)A C .!"m tHa @ i%m%t#n tia )xsao cho th% t5ch Bhi tG Di+nAC%bn 19 Bhi 7 h vit &h/0n t#"nh m;tcR' noi ti& tG Di+nAC%.

C 6 1*0 im+ ii b$t &h/0n t#"nh: :8o 8o (: )

W.1O O -x x

x + .\\\\\\\\\\\\\HB\\\\\\\\\\\Th sinh khng c s dng ti li!"# $%n & coi thi khng gi'i thch g thm*

]H v tn th5 sinh^^^.^^^..^^.^^.^.^.N _ bo Danh^^^^^^.S GD&T VNH PHC $P $N KTCL N THI I HC LN 2 NM HC 2013-2014

M!" T#$N% K'( )* )1


2/6

I+ L, J CH,NG"\ ]/>n DXn ch$m chQ t#"nh b m@t cch ii v>i nhn ` c0 bn &hi c7. Khi ch$m bi hHc sinh 8m thAocch Bhc n' n v ` th" vXn cho i%m ti a.\ S>i C 7n' th5 sinh Bh=n v h"nh &hRn no th" Bh=n cho i%m t/0n Gn v>i &hRn 7.\ Li%m ton bi t5nh n -92O v Bh=n 8m t#Tn.II+ $P $N"

C, J NI D,NG IM

1 2*0 (O5 !PL 2d% .=

Cc i>i hn2 2

8im 2N 8im 2N 8im N 8imx x x x

y y y y+ +

= = = + =

_' #a 2x= 8 ti+m c,n Gn9 2y= 8 ti+m c,n nan ca th.-92O

_ bin thin 2:

e -9( 2)

y x %x

= <

]m s nhch bin t#n cc Bhon ( N2) v (2N )+-92O

fn bin thinx 2 +yg

y2 +

2

-92O

L th iao v>i t#c )xti1

N-2

9 iao v>i t#c )yti1

-N2

9 th c7 t6m i YGn

8 i%m (2N2)"

-92O

6i s ( )

2 1N 9 22

aM a aa

th'@c th (C). !i& t'n ca th (C) tiMc7 Dn

2

: 2 1( ) ( )

( 2) 2

ay x a

a a

= +

-92O

Hi A8 iao ca ti+m c,n Gn v>i ( ) 9 s' #aW

(2N 2)2

Aa

+

8 iao ca ti+m c,n nan v>i ( ) 9 s' #a (2 2N2) a -92O

Khi 7 22

:W(2 4)

( 2)A a

a= +

9 thAo bi #a ta c7 &h/0n t#"nh

22:W4( 2) 4-( 2)a a + =

4 2( 2) 1-( 2) M -a a + =

-92O


3/6

2

2

1

( 2) 1 :

1( 2) MO

a

a a

aaa

= = = = = =

S, c7 4 i%mMthEa mn 8 (1N 1)9 (:NO)9 ( 1N1)9 (ON:) .

-92O

2 1*0 (O1 cos 3

sin 2 sin 2 (1)tan 4

xx xx

+ = + .

LB { ( )sin - sin 2 -cos - 2kx

x x kx

-92O

( ) ( )2(1) 1 cos cos sin sin sin 2 cos 2x x x x x x + =

( )cos 2 cos sin 1 -x x x + =cos 2 -

1sin

4 2

x

x

= + =

-92O

j) ( )cos 2 -

4 2

kx x k

= = + -92O

j)( )

( )

21sin

24 22

x k lx

x k l

= + = = +

. S, (1) c7 nhi+m ( )

4 2

kx k

= + . -92O

3 1*0 (O

( ) 2 2

4 2 2

4 1 1 2 2 1 (1) ( )1 (2)

y x x y "x x y y

+ = + +

+ + =.

L;t 2 1 1x t+ = &h/0n t#"nh (1) c7 Dn ( )22 4 1 2 1 -t y t y + =

-92O

( ) ( ) ( )2 2

4 1 F 2 1 4 :y y y = = 2 11

( )2

t y

t l= =

-92O

j) S>i 2 2 21

2 1 1 1 2 14 4

yt y x y

x y y= + = =

tha vo (2) ta /Uc -92O

( ) ( )22 2 21W 1 4 1 1 - 1y y y y y y + + = = (Do 1y ) -x =

S,9 h+ (") c7 nhi+m (-N1) .-92O

4 1*0 (O!a c7

- -

2 2 2

4 4

1 2sin 2 2cos sin 4sin cos :cos!x !x"x x x x x x

= = + +

-2

2

4

1costan 4 tan :

!xxx x

= +

-92O

L;t2

1tan

cost x !t !x

x= = LZi c,n

x4

-

t 1 -

-92O

S,

- - -

21 1 1

1 1 1

4 : ( 1)( :) 2 : 1

!t !t " !t

t t t t t t

= = = + -92O

( )

-

1

1 : 1 1 :8n 8n : 8n 2 8n

2 1 2 2 2

t

t

= = = -92O


4/6

7 1*0 (O

HiM9*8Rn 8/Ut 8 t#'n i%m caA"v C%.

?o ( ) ( )#C% AC% v #A #" = t#on m;t &hiAc*t C%ti/th"/8 h"nh chi' ca #t#n m&(AC%)

-92O

'a*B[ /In thiCc*tAti+

1: : :9 :

4 4 2 2

a a a a*+ "+ *" /M / a = = = = =

( )( ) ( ) 9 ? 9 :- AC # / #/ = = = #/ a =

-92O

:

: :2

1 1 3 :2 2.

: : 2 24AC% AC%

a aa

a0 #/ # a

+ = = =

(vtt) -92O

( ) C% #A v ( ) ( ) ( )( ) ( )( )9 9 9#" #A ! C% #" ! C% #A ! / #A = =

( ) ( )/M A #/M #A . Hi/8 /In cao ca tam ic #/M s' #a

( ) ( )21

93

a/ #A ! C% #" / = = .

-92O

8 1*0 (O

( ) ( ) ( )F F 1a b b ' ' a ab' ab'= + + +

( ) ( ) ( ) ( ) ( )F a b b ' ' a a b ' ab b' 'a ab'= + + + = + + + +

( ) ( ):a b ' ab' a b ' ab' + + + +

-92O

s' #a ( ):

:

F M :

: :

ab'a b ' a b '

ab' ab' ab'

++ + + + -92O

:

: :

1 : 12( ab'

a b 'ab' ab' + +

+ +-92O

?$' pq Y #a Bhi v chQ Bhi 1a b '= = = . S,9 min 2 1( a b '= = = = . -92O

+5 1*0 (O


5/6

Hi*28 i%m i YGn v>i*k'aAC9 DoAC8 &h6n ic ca 7c A% nn*2th'@c

A%.**2v'=n 7c v>iACv k'a i%m ( )MN4* nn c7 &h/0n t#"nh O -x y = .

Hi"8 iao caACv**29 tHa @"8 nhi+m h+ ( )O - :

:N 21 - 2

x y x"

x y y

= = + = =

S""8 t#'n i%m ca**g nn e( :N F)*

-92O

L/In thiCv cch x'Cs' #aCi k'a t#'n i%m"caA%.

-92O


6/6

Hi ( )N4 a b 8 iao i%m ca%-vM"s' #a 48 t#Hn t6m ca tam icA%M

( )

11 : ::F : 1 O

:

aa-% -4

bb

= = = = =

uuur uuur 1 ON

: :4

-92O

rh/0n t#"nh /In th . S" (_) k'aA, , C, %nn ta c7 h+

2 2 2 :

2 4 O

2 1

W M

a b ' !

a ' !

b !

a !

+ + + = + + = + = + =

-92O

ii h+ t#n ta /Uc 29 29 :9 :a b ' ! = = = = S, &h/0n t#"nh m;t cR' 2 2 2( ) 4 4 W : -# x y x y + + + + =]a 2 2 2( 2) ( 2) ( :) 14x y + + + = .

-92O

+6 1*0 (O

LK -x> . !a c7 : :8o 8o (: )W.1O O -x xx + :: :1

8o8o 8o2: W.1O O.O -

xx x + -92O

( ) :

: :

8o8o 8o: W :. O O.O -

xx x +

::

8o8o: :

W O -O O

xx +

-92O

L;t:8o

:9 -

O

x

t t

= >

. !a /Uc 21

W O -O

tt t

t

+

S>i:8o

:

:1 1 8o - 1

O

x

t x x

-92O

S>i:

:

O

8o8o O

: :

O

:O O 8o 8o O - M

O

x

t x x

<

S,9 t,& nhi+m ca fr! 8:

O

8o O

-NM y1N )# = +

+

-92O

\\\\\\\\\\\\\]t\\\\\\\\\\\

Toan khoi A-A1

Documents

Transcript of Toan khoi A-A1