Đề tuyển sinh THPT môn Toán năm 2020 2021 sở GD ĐT Hà Nội

so crAo D TAO xi rm rUYEN sINH LoP to rHPT NAU Hec zozo - zozt

Kh6a ngiry 171712020

oAp Ax-THANG DIEM

M6n thi: TOAN

0'5

1)

T{nh gid tr! cfto bi6u thrbc A khi r - 4.

Thay r - 4 (thoa mdn DKXD) vdo bitiu thric A, tinhdugc: .4 3

4

GI 0t

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2)

r- Vr+1

1

1

2

- (c-r)(.6+r)

(c (l; B- 3 J" -t

3 + )-(

Ch*ngminh B - +Jr +t

.6+r)

J-" +s

,(l; - r)

0'5

BNi I 2,0 didm

3)

Tim ttit crt gid tr! crta r it| bi\u thtbc P - 2A.B + J " dqt gid tr! nhd nhdt. P-2A.B+J;:#r+J;

Tac6: P -2 -++J; -2- +> 0 voimoi r > 0. Jr +z Jr +2-

Suy ra P > 2. Dingthric xtty rakhi vd chi khi r - 0

KL: r - 0 thi bi6u thric P dqt gi6 tri nhO nh6t.

l15

VAn t6c di xe dpp cira An la r * I (km/h).

Thdi gian An di b9 ttr nhe An dtin nhd Binh l' 3 a - (gio).

... + r' +9r - 36: o <+ (r - 3)(" +12) - o <+

, Tinh vQn tbc iti b? crta An.

LAp lupn d6n d6n phucrng trinh 3

Thcri gian An di xe d4p tir nha Binh v0

Gqi v0n di b0 cua An lir r (dcrn vi: km/h, u > 0).

r-3 r--t2

3 nhaAnh r+g Gio). 33 r r*9 4

Bii II 2,0 diam

I

1)

Di6m v Dfp 6n Bni

kiQn lopi r 12 , thu 14i r - 3 thoa mdn y6u u bii to6n.

KL

hqrp di

t6c di ctra An la 3 km/h. 0,5

2) Tinh diQn tich bi mfit cfia qud bdng bdn.

S - 4trR2 x 4x 3,14 x22 - 50,24(.-').

bc mdt cira qui b6ng ban do li: DiQn tfch

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r)

Vdi b - 1 + + - 1 + u : 2(thoam6nDKXD). y -l

v

KL: hQ phucrng trinh co nghiQm duy nh6t le (r; y): (r'r).

Gidi hQ phwong trinh

<+ .... e

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

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

DKXD: U =L.

1 DAt - -b, tac6hq y-I

Giai he b:l f:l 2r * 3b :5 4r-b:3

0,75

2a)

Ggi tgadO diem ,4 la (rr;Ao). Do cli6m ,4 thu6c tryc Oy n€n ro - 0.

Do di6m ,4 thuQc dudrng thing (d),A : n'Lr * 4 n6n

ut: ffine * 4 - m.0 * 4 - 4.

KL: tsa d0 di6m A la (0;a).

fim cua m A.

0,75 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.

(*utrr). oo di6m B thuQc tryc or ndn vo - 0.

Vi di6m B thuQc ducmg theng (d),y -- rrln + 4 dan d6n 0 - mna * 4

Yt m*O + nB:a * OB -prl - l#l Vi A OB - 900 n€nclOtam giitc OAB ldtam gitrccdnthi OA - OB. Md OA:4 n€n OB - 4.

KL:m-l

Ggi tga <t0 cli6m B le

m-l m--l m--L

Giai phuong trinh: l=l - 4 e.. * [ - l*l t

BNi III ^ . -.; ./,) drcm

2b)

BNi IV

a

00( rl(

1r0 l) Chirng minh trb gitic BHEK ld ttb gitic nQi tiiip.

2

Di6rr D6p 6n Bei Y

)

,

Chtmg minh dugc BHE - 900 vir

Suy ra BHE + BKE - 1800.

Lap luan d6n Aen fr giAc BHEK la ffi

^, ,.i grac nQl trep.

BKE : 900.

A

H

E

F

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2)

Ap dgng he thftc lugng cho L,AEB vu6ng tqi E, dulng cao EH c6:

BH,BA _ BE2.

Chtmg minh tuong tg c6: BK.BC : BE2.

Y$Y BH,BA : BK,BC,

Chftng minh BH.BA: BK.BC.

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3)

-

-^ chtmg minh dusc BHK - BEK (l). ( BHBK le tf gitrc nQi ti6p)

Chimg minh dugc BEK : BCE (2). (Cung phU voi EBC )

Chimg minh dusc frE - ffi (3). ( BCEF la tri gitcnQi ti6p) ^ ^ chimg minh dusc HFE - FHI (4). (tam giitc FHI c6n tai /. )

Ttr ( l),(2),(3), (4) suy ra ffiK -frt. Do A.ABCnhqn, hai di6m I vd K

nim ctrng phia AOi vOi duong thing HF n6n I/, I, K li ba ili6m thing hing.

hdng. Ch*ng minh ba th 'm H ,I,K ld ba

3,0 diam

0r5

Bni v 0,5 diam

Gidiphwongtrinh J" +,h. 1- 12 *!

Lap luan dan Aen r - | (thoa mfrn DKXD).

KL: phuong trinh co nghiQm duy ntr6t lir r - 1.

-0. 3r -2 -l

, + zJr +z 3r -2 -2r2 *2

3r -2 - 12 +L

. . <+,(* -r)' * (.6- r)' * (

2 DKXD: r ) -. -3 Ji+

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

ddn ch6m. uong H

J

Di6m Ddp 6n Bii f

K

2 3 a

,(

,/ov