7/26/2019 DADeThiThuTHPTQG2016 04.Hiast.edu.Vn

1/5

C!KINH T"- CNG NGH#TPHCM !A !$THI TRUNG H%C PH&THNG QU'C GIA N(M 2016

http://hiast.edu.vn Mn thi: TON.

!$THI TH)S'4 Th!i gian lm bi: 180 pht, khng k"th!i gian pht #$.

----------------------------

Cu 1.2. Ta c !y = "1

x "1( )2.%i"m M! C( )"M m;

m

m#1$%&

'()"IM

! "!!

= m#1;1

m#1$%&

'().

Ph&'ng trnh ti(p tuy(n ! c)a C( ) t*i Mc d*ng

y = !1

m!1( )2x !m( )+

m

m!1"x + m!1( )

2

y !m2= 0.

! !

u" = m#1( )

2

;#1( ).

! " IM! "!!

# "

u!$IM

! "!!

= 0# m%1( )3

%1

m%1= 0# m%1( )

3

=

1

m%1# m%1( )

4

=1#m = 0

m = 2

&

'( .

V+i m = 0 ta #&,cM

10;0( ) ; v+i m = 2 ta #&,c M2 2;2( ).

Cu 2.[1 #i"m] 1. Gi-i b.t ph&'ng trnh log!

log2

x2+x +8

1" 3x

#

$%

&

'( < 0. 1( )

%i$u ki/n

x2+x +8

1! 3x> 0

log2

x2+x +8

1! 3x> 0

"

#$$

%$$

&x 1

"

#$$

%$$

&x ng x-y ra khi t =1!C 3;5;4( ).

Cu 6.T?gi-thi(t ta c SCA! = 600.Ta c

SA= AC! tan60o= a 3; S

"ABC =

a2

3

2.

VS.ABC =1

3SA!S"ABC =

1

3!a 3 !

a2

3

2=

a3

4.

Ta c SE= SA2 +AE2 = 3a2 +3a

2

4=a 15

2

K@HK! SE. Ta c !SAE! !HKE" SA

KH=

SE

HE"KH =

SA#HE

SE=

a 3 #a 3

6

a 15

2

=

a

15

.

V BC! SAE( ) nn BC!HK, k(t h,p v+i HK! SE"HK! SBC( ).

Suy ra d H, SBC( )( ) =HK =a

15.

7/26/2019 DADeThiThuTHPTQG2016 04.Hiast.edu.Vn

4/5

Cu 7. %i"m I!" :y = 3# 2x$I m;3# 2m( ).

CI=2BI! CI2 =4BI2 ! m" 5( )2

+ 6" 2m( )2

=4 m" 3( )2

+ "2m( )2#

$% &

'(

!15m2 +10m" 25= 0!

m = 1 n( )

m ="

5

3 l( )

#

$

%%%

)I1;1( ).

Ta c IC! "!

= 4;!4( ) = 4 1;!1( )""

nAC

= 1;1( ). %&!ng thAng ACqua I 1;1( ) c ph&'ng trnh l x +y ! 2 = 0.

%i"m A!AC:y = 2"x#A a;2" a( ).

Ta c BC! "!!

= 2;!6( ) = 2 1;!3( )""

nBC

= 3;1( ).

Ph&'ng trnh #&!ng thAng BC:3x +y !12 = 0. Suy ra d A,BC( ) =2a !10

10. T?gi-thi(t ta c

S!ABC

= 12"1

2#d A,BC( ) #BC =12"

1

2#2a $10

10. 40 =12"2a $10 = 12"

a = 11 l( )a =$1 n( )

%

&

''

(A $1;3( ).

Ta cBI

! "!

= 2;2

( )= 2 1;1

( )! n

BI

= 1;"1

( ).%&!ng thAng

BD

quaI 1;1

( ) c ph&'ng trnh l x!

y = 0.

Ta c AB! "!!

= 4;0( ) = 4 1;0( ). V BD !AB!"nBD

=

"nAB

= 0;1( ).

%&!ng thAng BD qua C 5;!3( ) v c vector php tuy(n l!

nBD

= 0;1( ) nn c ph&'ng trnh l y + 3= 0.

V D =BD!CD nn to*#8#i"m D l nghi/m c)a h/x !y = 0

y + 3= 0

"#$

%x =!3

y =!3

"#$

&D !3;!3( ).

Cu 8.Gi-i h/ph&'ng trnh3x

2+ 2xy + 2y

2 ! 3x ! 2y = 0 1

( )5x

2+ 2xy +5y

2 ! 3x ! 3y = 2 2( )

"

#$%$

.

Ta c 3!1( )" 2( )#4x2 + 4xy +y2 " 6x " 3y + 2 = 0 # y2 + 4x " 3( )y + 4x2 " 6x + 2 = 0. $( )

Ta xem #y l ph&'ng trnh b3c hai theo Bn y,

lc ny ta c

!x= 4x " 3( )

2

" 4 4x2

" 6x + 2( ) = 1# !x=1.

7/26/2019 DADeThiThuTHPTQG2016 04.Hiast.edu.Vn

5/5

Ph&'ng trnh !( ) c hai nghi/my =

! 4x! 3( )+12

=!2x + 2.

y =! 4x! 3( )!1

2=!2x +1.

"

#

$$$$

Thay y =!2x + 2 vo 1( ) ta #&,c 7x

2

!11x + 4 = 0"

x =1#y = 0

x =4

7#y =

6

7

$

%

&&

.

Thay y =!2x +1vo 1( ) ta #&,c 7x2 !5x = 0"x = 0#y =1

x =5

7# y =!

3

7

$

%

&&

.

V3y h/ph&'ng trnh c b5n nghi/m l 1;0( ), 4

7;6

7

!"#

$%&

, 0;1( ), 5

7;'

3

7

!"#

$%&

.

TR*+NG CAO !,NG KINH T"- CNG NGH#TPHCM