HDC TOAN 8 HKI 2022 2023

PHONG GIAO DUC VA DAO TAOTHANH prrOrrAl DTIOI\G or xrnvr rRA cuol Hoc rY I NAvr Hec zoz2 - zozt M6n: Toin 8 Thoi gian ldm bdi: 90 phrit.. a Chtmg minh ttr giSc ANBH H hinh binh hdnh.. b

PHONG GIAO DUC VA DAO TAO

THANH prrOrrAl DTIOI\G or xrnvr rRA cuol Hoc rY I

NAvr Hec zoz2 - zozt M6n: Toin 8

Thoi gian ldm bdi: 90 phrit

EC bei gdm:05 c6u,01 trang Cflu 1 (2,0 di6m):

1) Thlrc hiQn c6c phdp tinh:

a) x.(2x + 3) - 2*

2) Phdn tich c6c da thirc sau thdnh nhdn tri:

a) Zxz - 6x

Cffu 2 (2,0 tli6m): Tim x biiSt:

b) (r'-t 2x* 1) : (x + 1)

b) ,'-y'-4x+4

a) 3(x + 1) - 2x=0

Ciu 3 (2,0 ili6m):

b) *'- 3x:0 c) x(x - 8) - 2x+ 16:0

I I 3x-6 a) Thlrc hiQn ph6p tjnh: 3x1- 3x{z- 4:g7

b) Tim a dC da thric : 3x3 + 2* - 7x* a+ 3 chia h6t cho da thric 3x - 1

Ciu 4 (3,0 tli6m):

Cho tam giSc ABC nhqn (AB < AC), dudng cao AH Gqi M ld trung diOm

cta AB, N ld di6m dOi xrmg cria H qua M.

a) Chtmg minh ttr giSc ANBH H hinh binh hdnh

b) TrCn tia d6i ciatiaHB 6y di6m E sao cho H ld trung di6m cria BE Chrmg minh: AE : NH.

c) Ggi I li giao di6m cria AH vd NE Duhng thing VII cit AC tai K

K6 NQrKH t4i Q Chung minh AQ r BQ

Ciu 5 (1,0 tli6m):

Cho si5 thpc x > 0 th6a mdn: xz - 4x* 1 = 0

Tinh giStyibirSu thric: B : (*' - 4xo +x' + x' l4r)'0" * / (x,'r+ l6x' l)' + 2020

uot

SBD: Ho vd t6n thi sinh:

PHoNG GIAo DUC va oAo r4o

TH4IyH PHo nAr PtIoNc

HrJcrNG UAN cnAvt

oB runiu rRA cuol HQC rV r

xAwt Hec zo2z - zo23

M6n: ToSn - 16,'p 8

Hu6ng d6n chAm g6m: 02trmg

I

ax,

v

1iliff\

*of, I

'i;v / /-4

ffi

Ciu 1

(2 tli6m)

la x.(Zx+ 3) - 2x2 :2x2 + 3x_ 2x2

:3x

0,25

0,25

1b (x2+ 2x+ 1) : (x+ 1) : (x * 1)2 : (x + 1)

:1*1

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2b x' - y' -4x + 4 : (x2- 4x * 4) - Y'

: (x - 2)' -y2 : (x - 2 -yXx - 2 + y)

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Ciu 2

(2 tli6m)

a 3(x+1)-2x=0

+ 3x+3-2x:0

V6yx=-3

0,25

0,25

b

Vay x e {o;:}

x'-3x=o=x(x-3):0 [x=0 [x=0

>l =l [x-3=0 [x=3

0,25

0,25

0,25

c *(r-8)-2x+16=0

+ x(x- 8) - 2(x-8) : 0+(x - 8)(x - 2) : 0

[x-8=0 [x=8

.t- t

- | lx-2=0 )tlx=2

Vpy xe {2;s}

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0,25

0,25

Ciu 3

(2 tli6m)

+-3x-2 3x+2 4-* 3x - 2 3x + 2 (3x + 2)(3x - 2)

+ (3x - 2)(3x+2) (3x + 2)(3x-2) (3x + 2)(3x-2)

3x+2-3x+2+3x-6 (3x + 2)(3x-2)

(3x+ 2)(3x-2) 3x+2

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0,25

02s

0,25

b Thlrc hiQn ph6p chia da thric 3x3 * 2x2 - 7x* a * 3 cho

da thric 3x * 1 dugc da thirc du ld a +1

E6 3x3 + 2x2 - 7x*a+3 chiah6t cho 3x- 1 thi a +1 : 0 + a:-1

VSy v6i a: -l thi da thirc 3x3 + 2xz - 7x* a +3 chia h6t cho da thirc 3x - 1

0,5

0,25

0,25

Cdu 4

(3 tli6m)

a Tir gi6c ANFIB c6 :

M le trung di6m ctra AB (gt)

M le trung tli0m cria NH (vi N eOi xtmg v6i H qua M)

-> Tri gi6c ANBH le hinh binh henh

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0,25

0,25

b - Chrmg minh dugo NA: tIE (: BH)

viNA llIJE,

:> Tir giSc NAEH h hinh binh henh

- Suy ra dugc AE : NH

0,25

0,25

0,25

0,25

c X6t INQH vu6ng t?i Q, c6 QM ld dutxtg trung tuy Suy ra eM = l*, mi NH - AR

Suy ra eM =;AB

=+ AAQB vu6ng tai Q=+ AQ I BQ

en

0,50

0,25

0,25

Cffu 5

(1tli6m) Tac6:x5- 4x4+x3+x2-4x

: x3(x2-4x + 1) + (x2 - 4x* 1) - I : -1

x2 - 4x* I : 0 :> x2 * 1 : 4x:) (x2 + l)2 : l6x2

(r,'+ 1)'

- ,

-.? l

l6x'

Do d6 : B : (-1)2022 1 1 + 2020 : 2022

0,50

0,25

0,25

Lins vAn cho di6m

Chri f: N6u thi sinh ldm theo c5ch kh5c, c6 lcvi gi6i dung

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