THI T

UY

N S

INH

V

O L

P

10

M

N T

O

N

Tp. H

C

h M

inh

- 201

5

Cu

1.

(2

im

) Gi

i cc

ph

ng

trnh

v h

ph

ng

trnh

sau:

2

.

8

150

ax

x

2

.2

2

20

b

x

x

4

2

.

5

60

cx

x

2

5

3

. 3

4x

y

dxy

Cu

2.

(1,5

i

m) T

rong

mt

ph

ng t

a

cho

para

bol

2

:P

yx

v

ng

ng

thn

g :

2.

D

yx

.a V

P v

D tr

n c

ng m

t h

tr

c ta

.

.b T

m t

a

giao

i

m c

a P v

D b

ng

php

tnh

.

Cu

3.

(1,5

i

m) T

hu g

n c

c bi

u th

c sa

u:

1

10

0,

4

4

2

2

134

37

43

820

243

243

x

x

x

A

x

x

x

x

x

B

Cu

4.

(1,5

i

m) C

ho p

hn

g tr

nh

2

20

1,

xmxm

x

l n

s.

.a C

hng

min

h ph

ng

trn

h 1

lun

c 2

ngh

im

ph

n bi

t v

i m

i

.m

.b

nh m

h

ai n

ghi

m 1

2,xx

tha

mn

:

2

2

1

2

1

22

24.

1

1

x

x

x

x

Cu

5.

(3,5

i

m) C

ho ta

m g

ic

ABCAB

AC

c b

a gc

nh

n.

ng

trn

tm

O

ng

kn

h BC

ct

cc c

nh

,AB

AC l

n l

t t

i ,

.EF

Gi

H l

gia

o i

m c

a BE

v

;CF

D l

gia

o i

m c

a AH

v

.BC

.a C

hng

min

h AD

BC

v

.

..

AHAD

AEAC

.b C

hng

min

h EFDO

l t

gi

c ni

tip

.

.c T

rn

tia

i c

a tia

DE

ly

im

L sa

o ch

o

.

DLDF

Tn

h s

o

gc

.

BLC

.d G

i

,RS

ln

lt

l h

nh

chi

u c

a ,BC

ln

.EF

Ch

ng m

inh

.

DEDF

RS

P

N

TH

I TU

YN

SIN

H V

O

L

P 10

M

N

TO

N

Tp. H

C

h M

inh

- 201

5

Cu

1. G

ii c

c p

hn

g tr

nh v

h p

hn

g tr

nh.

.a

2

5

8

150

.3x

x

x

x

Vy

ph

ng

trnh

c h

ai n

ghi

m l

3x

v

5.

x

.b

2

2

2

20

x

x

2

2

1

2

4

2

42

2

18

32

23

22

2

4

23

2

2 .

2

4

2

b

ac

b

x

a

b

x

a

Vy

ph

ng

trnh

c h

ai n

ghi

m l

2

x

v

2 .

2

x

.c

4

2

5

60

x

x

t

2 ,0.

txt

K

hi

2

6

56

0

1

(nha

n)

(lo

ai)

t

t

t

t

Vi

2

6

6

6

.6

x

t

x

x

Vy

ph

ng

trnh

c h

ai n

ghi

m l

6

x

v

6.

x

.d

2

5

3

2

5

3

2

5

3

1 .

3

4

15

5

20

17

17

1

x

y

x

y

x

y

x

xy

x

y

x

y

Vy

ngh

im

ca h

ph

ng

trnh

l

1;

1.

C

u 2

. Ta c

2

:

,

:

2.

Pyx

D

yx

.a V

th c

a

P v

D tr

n c

ng h

tr

c ta

.

.b P

hn

g tr

nh h

onh

giao

i

m c

a P v

:

D

2

2

1

1

2

20

2

4.

x

y

x

x

x

x

x

y

Vy

P v

D g

iao

nhau

ti h

ai

im

1;1,

2;4

.

A

B

Cu

3.

Rt g

n c

c bi

u th

c

1

10

4

2

2

2

1

2

10

4

4

2

2

102

8

4

4

4

2.

x

x

x

A

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

134

37

43

820

243

243

134

37

43

820

24

33

134

37

43

83

31

35

B

Cu

4. P

hn

g tr

nh

2

20

1

x

mxm

.a

Ta c

2

2

2

4

2

4

8

2

40,

.

m

m

m

m

m

m

Vy

ph

ng

trnh

1 lu

n c

hai

ngh

im

ph

n bi

t.

.b

Theo

n

h l

Vi-

t ta c

1

2

12

2

xx

m

xx

m

Ta c

2

2

2

2

2

2

12

1

2

1

2

1

2

12

1

22

22

12

1

2

12

12

1

2

2

2

2

2

4

2

2

1

1

1

2

2

4

1

2

2

2

2

4

2

1

.

xx

x

x

x

x

x

x

xx

xx

xx

xx

xx

xx

xx

m

m

m

m

m

m

Suy

ra

2

2

2

2

1

2

1

2

2

2

24

4

8

2

1

1

m

x

x

m

m

m

x

x

Cu

5.

.a

V BEC

v BFC

l c

c gc

ni

tip

chn

na

ng tr

n

ng

kn

h BC

nn

90o

BE

AC

BEC

BFC

H

BF

AB

l tr

c t

m c

a tam

gi

c

.

ABC

AD

BC

Hai

tam

vu

ng ADC

v AEH

c g

c DAC

chun

g n

n

.

..

AD

AE

ADC

AEH

ADAH

ACAE

AC

AH

.b

Ta c

1

EOB

BE

Mt

kh

c ta d

dn

g ch

ng

min

h

c t

gi

c BDHF

ni

tip

nn

1

2

2

HFD

HBD

EC

Ta c

ng c

1

3

2

EFC

EC

T 2 v

3 su

y ra

4

HFD

DFE

EFC

EC

T 1 v

4 su

y ra

180o

EOBDFEBE

ECBC

Suy

ra t

gi

c EFDO

ni

tip

.

.c

V

5

FDH

FBH

ECH

EDH

FDB

EDC

BDL

Hai

tam

gi

c BED

v BLD

c

ED ch

ung.

FBD

LBD

(d

o 5)

FD

DL

(gi

thi

t)

BED

BLD

(c-g

-c)

;

90.

: chu

ng

o

FBC

LBCBF

BL

BLC

BFC

BLC

BFC

BC

.d

V t

heo

cu c

ta

c

0

90

BLC

nn

.

L

O

Gi

,

,

.

M

CS

ON

BM

LEM

C

Khi

ta d

dn

g th

y NBE

cn

ti

,N

NLM

cn

ti

.N

.

NENB

ELBM

NM

NL

M

.

RSBM

MNNM

LNNE

ELED

DLED

EF

TRU

NG

T

M C

N

G H

C

TO

N