Đề thi vào lớp 10 môn toán năm 2020 có đáp án sở GDĐT hà nội

so crAo

xi rm

rUYEN sINH LoP to rHPT
NAU Hec zozo - zozt

TAO

D

Kh6a ngiry

171712020

oAp Ax-THANG DIEM
M6n thi: TOAN

Bni

v
T{nh gid tr! cfto bi6u thrbc
1)

Thay

r-

-

vdo bitiu

thric A, tinhdugc:

3

.4

4

-+
Jr +t

lr0
3

-t

J"

0'5

4.

3

B-

BNi I
2,0 didm

A khi r

4 (thoa mdn DKXD)

Ch*ngminh B

2)

Di6m

Dfp 6n

(c + )-( J-" +s
(l; .6+r)
1

1

,(l; - r)
- (c-r)(.6+r)

GI

0t
2

r-

Vr+1

Tim ttit crt gid tr! crta

r

it| bi\u thtbc P

-

+J

2A.B

"

dqt gid

0'5

tr! nhd nhdt.

P-2A.B+J;:#r+J;
3)

Tac6: P

-2

0 voimoi r > 0.
-2- +>
Jr +2-

-++J;
Jr +z

Suy

ra P > 2. Dingthric xtty rakhi vd chi khi

KL:

r-

0 thi bi6u thric

P

dqt gi6

tri

r-

0

nhO nh6t.

,

l15

Tinh vQn tbc iti b? crta An.
Gqi v0n

di b0 cua An lir

VAn t6c di xe dpp cira An

r

la

(dcrn

r*

I

vi: km/h, u > 0).
(km/h).

Thdi gian An di b9 ttr nhe An dtin nhd Binh l'a

Bii II
2,0 diam

1)

Thcri gian An di xe d4p tir nha Binh v0
LAp lupn d6n d6n phucrng trinh

...

3

-

nhaAnh

3

33

r r*9

+ r' +9r - 36:

o <+

(gio).
3

r+g

Gio).

4

(r

-

3)(" +12)

-

o <+

r-3
r--t2
I


Bei

hqrp

2)

di

kiQn

lopi

r

12 , thu

r-

14i

3 thoa mdn y6u

u

bii to6n.

ctra An la 3 km/h.
t6c di
KL
Tinh diQn tich bi mfit cfia qud bdng bdn.
DiQn tfch bc mdt cira qui b6ng ban do li:

S

-

Gidi

hQ

2r* y 3 :b
-l
4r- y 1 :3
-l

phwong trinh

U

=L.

Ir0

2r * 3b - 5
4r - b : 3

1

DAt

0,5

x 4x 3,14 x22 - 50,24(.-').

4trR2

DKXD:
r)

Di6rr

D6p 6n

Y

-b, tac6hq
y-I
-

Giai he

2r

* 3b :5

4r-b:3

<+ ....

b:l

e

f:l

1+ u:
- 1+ +
y -l -

Vdi

b

KL:

hQ phucrng

v

2(thoam6nDKXD).

trinh co nghiQm duy nh6t le (r;

y):

a

(r'r).

00(
BNi

fim

III

-.;
^ . drcm
./,)

0,75

m A.

cua

Ggi tgadO diem ,4 la (rr;Ao). Do cli6m ,4 thu6c tryc Oy
2a)

Do di6m ,4 thuQc dudrng thing (d),A

ut:

*

ffine

4

-

m.0

*

4

-

:

n'Lr

*

4

n€n

ro

-

0.
)

n6n

4.

KL: tsa d0 di6m A la (0;a).
b) Tim tiit cd gid tr! cfia m AO dwong thdng (d) cdt tryc Or tgi itilm B sao cho
tam gidc OAB ld tam gidc cfrn.
Ggi tga
Vi di6m B
2b)

Yt m*O

thuQc ducmg theng

-

900 n€nclOtam giitc

Chirng minh

-

0.

mna

*

4

-

OAB ldtam gitrccdnthi OA

-

OB. Md

0,75

OA:4

m-l

- l=l - 4 e.. * m--l
m--L

KL:m-l
l)

dan d6n 0

ndn vo

l#l

4.

Giai phuong trinh:

BNi IV

(d),y -- rrln + 4

+ nB:a * OB -prl -

Vi A OB n€n OB

B le (*utrr). oo di6m B thuQc tryc or

trb

l*l

,

[

t

1r0

gitic BHEK ld ttb gitic nQi tiiip.

2

rl(


f

Bii

Di6m

Ddp 6n
A

3,0 diam
H

Chtmg minh
E

:

BKE

dugc BHE

-

900 vir

900.

F

Suy

ra BHE + BKE

-

1800.

fr giAc BHEK la ffi

Lap luan d6n Aen
,.i
^, trep.
grac nQl
K

Chftng minh

BH.BA:

lr0

BK.BC.

Ap dgng he thftc lugng cho L,AEB vu6ng tqi E, dulng cao
2)

BH,BA _ BE2.
Chtmg minh tuong tg c6: BK.BC
Y$Y BH,BA

:

:

BE2.

BK,BC,
'm H

Ch*ng minh ba

,I,K
-^

-

BEK (l). ( BHBK

Chimg minh dugc BEK

:

BCE (2). (Cung

frE - ffi

Chimg minh dusc

le

phU

(3). ( BCEF la

^
chimg minh dusc HFE - FHI (4).
^

Ttr ( l),(2),(3), (4) suy ra ffiK
nim ctrng phia AOi vOi duong thing

lr0

hdng.

th

ld ba

chtmg minh dusc BHK

-

3)

EH c6:

tf

gitrc nQi ti6p)

voi EBC

)

tri gitcnQi ti6p)

,(

(tam giitc FHI c6n tai /. )

,

/

o

Do A.ABCnhqn, hai di6m I vd K
HF n6n I/, I, K li ba ili6m thing hing.

v

-frt.

Gidiphwongtrinh

Bni

v

0,5 diam

DKXD:

2
r ) -.
-3

Ji+

3r

-2 -

+ zJr +z

3r

J" +,h. 1-

12

12

*!

0r5

+L

-2 -2r2 *2
,

. . <+,(*

-r)' * (.6-

Lap luan dan Aen

r- |

r)'

*(

3r

-2 -l

-0.

(thoa mfrn DKXD).

KL: phuong trinh co nghiQm duy ntr6t lir

r-

1.

Luu f:.c6c c6ch ldm kh6c n6u dring hqc sinh v6n tluqc di6m tuong img vdi bitiu ditim cria
H uong ddn ch6m.

J

2

3
a