Đề và đáp án kỳ thi chọn học sinh giỏi lớp 8 cấp thị xã

rV rnr cHeN Hec srNH cror Lop a cAp rrU xA
NAnn Hoc: zots-zotl
DC thi m6n: Vat lli 8
Thdi gian: 150 phirt (kh6ng tC ttrOi gian ph6t

.

dO)

CAu 1: (5di6m)

a. MQt 6 t6 chuy6n dQng trdn nira dopn duong dAu v6i v6n t6c 60km/h. Phan con lai
,i
chuy6n dQng v6i vfln t6c lskmih nua thdi gian dAu vd 45km/h trong nua thdi gian sau.
Tim vfln t6c trung binh cira 6 t6 tr€n c6 do4n dudng.
b. Lirc 6h mQt ngudi di xe dap xu6t ph6t tu A di vC B v6i vfln t6c v1 12kmlh. Sau d6
2h, m6t ngudi di bO tu B vO A v6i v6n t6c v2: km/h. Bi6t AB : 4Skm.
- Hqi ngudi g{p nhau luc mdy gid? Ncri g{p nhau c6ch A bao nhi6u km?
- Ntiu ngudi di xe dpp sau khi di dugc 2h r6i nghi th thi hai ngudi gflp nhau hic mAy
gid? Noi gip cfrch A bao nhi6u km?
C6u 2: (adi6m) MQt xe dd khdi hanh tir thanh phO e di thenh ph6 n c6ch nhau l60km
vdo lirc 7 glir s6ng v6i vQn t6c 60km/h. Sau d6 1 gio 30 phirt, -9t *. 6 t6 khdi hdnh tir B
vC A vdi vpn t6c S0kmlh. Hoi:
a. D6n m6y gio hai xe gpp nhau? Vf tri g{p nhau c6ch thdnh ph.o A bao nhi6u km?
b. Xe ndo t6i noi tru6c? D6 hai xe tdi cirng m6t hic thi xe d6n sau ph6i khoi hdnh hic
r ..^
may glo'/
C6u 3: (3di6m) MQt qu6 cAu c6 trgng lugng ri6ng 8200 N/m3, the tich 100m3 n6i t.Crt
mdt m6t binh nu6c. Ngudi tar6tdAu vdo phu kfn hodn todn qui cAu.
a. Tinh th6 tich phAn qui cAu ngap trong dAu.
b. N6u ti5p.tuc r6t th6m dAu thi th6 tich phAn ngQp trong nu6c cria qu 6 cAu c6 thay d6i

kh6ng? (ni0t trgng lugng ri6ng: ctra dAu 7000 N/m3, cria nu6c 10000 N
Cdu 4: (adi6m) Cho m4ch diQn c6 so d6 nhu hinh v6:
a. Bi6t ampe tC e chi 5,A., culng clQ ddng di6n
chpy qua ddn I vd ddn 2bingnhau vd bing 1,5A.
X6c dinh cudng dQ ddng diQn chpy qua E3
vd cudng dQ ddng diQn chay qua Da.
b. Mpch di6n tr6n dugc m6c vdo ngr6n diQn c6
hiQu diQn th} l2Y. niet hiQu diQn th6 gifia hai
dAu b6ng ddn Dz bing 4,5Y. Tim hi6u dipn th6
gita hai d6u cdc b6ng ddn cdn 14i.
Cdu 5: (adi6m) Hai gucrng phing G, vd" G,
D,c
dugc bO tri hqp v6i nhau mQt
g6c a nhu hinh vE. Hai di6m s6ng A vd B dugc dpt vdo gifia hai gucrng.
a. Trinh bdy c6ch vC tia s6ng su6t phSt tu A ph6n xa lAn luort
l6n gucrng G, d€nguorrg
rOi cl6n B.
b. NCu 6nh cta A qua G, circhA ld l2cm vd anh cria A

:

q

qua G, cSch A ld 16cm. Kho6ng c6ch
anh lA 20cm. Tinh goc a ?

gita hai

&z

rY r'r

":n*ffi; iH5,;JiJi%

s

cAp rrq xA

DC thi m6n: Ngt Vin 8
Thdi gian: 150 phrit (kh6ng tC tnOi gianph6t d6)

CAu 1: (8di€m)
NgA., ngt Hi laO
"Hgc vdn c5 nhtng chirm rE ctang cay nhrmg f,roq W1 lpi ngqt
"9c6u:
ngho". Em hi6u y ki6n tr6n nhu th6 ndo? Hdy n5i 16 quan niQm ctra em v6 ,r6n cl6 ndy.

Cdu2: (l2di6m)
TrCn co s0 c6c truyQn nghndS hgc: TOi ali hgc, Lflo H?c, Chi6c
Thuytit minh dflc di6m chinh cua thti lopi truyQn ngin.

HET

H cuiii cirng, ...


rY rnr cHeN Hec srNH cr6r Lop s cAp rrq xA
xAtvt Hec: zors-20r6
OC tl,i M6N: GIAI TOAN BANG MAY Ti]\Ig CAU TAY

Thdi Bian: 150 phut (kh6ng t
A:

6227020800. Vi6t quy trinh 6n phim:
Cdu 1: (adi6m) Cho s6
t,
a. Tim sO c6c uoc ducrng c[ra s6 A.
b. Tinh t6ng c6c u6c ducvng cira

sO

Cdu2: (adi6m) Cho da thric f(x)
nhQn

gi|tri

a.

: l*' *lr'
5 3

*l*+2008.
15

Chimg minh ring

(x)

1u6n

nguy6n v6i mgi x nguy6n duong.

Cdu 3: (adi6m) 86 cira Bpn Minh grii cho b4n minh 20.000.000 d6ng vho ngdn hdng
v6i 15i sudt 1$Yolthdng.
a.

Hoi sau

1 ndm bpn

Minh c6 dugc

sO

ti6n o ng6n hdng ld bao nhi6u. Bi6t ring hirng

th6ng kh6ng rut ldi ra.
b. NCu hdng th6ng bpn Minh rut tt ngan hdng ra 900.000 d6ng vdo ngdy ngAn hang
tinh ldi dC sinh ho4t vd hgc t4p. H6i sau 1 ndm ban Minh cdn lai bao nhi6u ti6n o
ngAn hang?

4: (adi6m) Trong m{t phEng tqa d0 cho ba di6m A(-z; s), a(-+;z), c(t;-l). Tt
dinh A vE dudng cao AH, dudng nlran gi6c AD vd ducrng trung tuy5n AM (c6c di€m
H, D, M thuQc c?nh BC). Cho bi6t tinh ch6t cria dulng ph6n gi6c trong tam gi6c
C6.u

DB
DC

AB

AC

a. Tfnh diqn tich tam giSc ABC.

b. Tinh d0 ddi cria AH, AD, AM vd di6n tfch tam gi6c

ADM.

'

(Ktlt quA ldy v6i 2 chtr s6 o phAn thpp ph6n). Don vi do tr6n c6c tryc tga ilQ ld cm.
CAu 5: (adi6m) Cho hinh thang cdn c6 hai dubng ch6o vu6ng g6c v6i nhau, d6y nh6
ddi 13,54cm vd canh b6n ddi 18,45cm. Tinh d0 dai d5y 16n vd diQn tich hinh thang d6
(lay ket qu6 chinh x6c d6n ba cht sO tt pp phdn).

HET


xY rnr cHgN Hec srNH cror Lo? a cAp rrU xA
xAvr Hoc: 2ors-2016

.

DC thi m6n: Ho6 hoc 8
Thdi gian: 150 phrit (kh6ng tC tnOi gian phSt

11€)

l:

(adi6m) Khi hda tan 21g m6t kim loai h6a tri [I) trong dung dich HzSO+ lodng
du, neudi ta thu dugc 8,4 lit hidro (dktc) vd dung dich A. Khi cho l6t'tinfr *rrOi tron!
dung dich A thi thu dugc l04,25gtinh th6 hidrat h6a.
CAu

a. Cho bi6t t6n kim lopi.

b. X5c clinh c6ng thric h6a hgc cira tinh th6 mu6i hidrat h6a d6.

Cdu2: (3di6m) De khtl hodn todn 15,29 h5n hqp Oxit kim lopi gdm CuO vd FeO bing
khi Cacbon Oxit (CO). Thu dugc 4,48 lit khi Cacbon dioxit (COr) o diAu ki6n ti€u
chuAn. Tinh thenh phAn phAn trdm cdc Oxit kim loai c6 trong h5n hqp.
Cdu 3: (adi6m) Nrrg h6n hqp mu6i g6m CaCO3 vir MgCO3 thu dugc 7,6gh6nhqp hai
Oxit vd khi A. H6p thp khi A bing dung dich NaOH thu dugc 15,9g mu6i Na2CO3. Tinh
thdnh phAn phAn trdm cria c6c mu6i trong h6n hqp.

Cdu4: (3di6m) DAn tu ti 13,44lit khi H2(dktc) qua m-gam Oxit Sdt Fe*O, nung n6ng.
Sau phin img thu dugc 36,89 h5n hqp A g6m hai ch6t rin vd 10,8g nu6c.

a.LW phuong trinh h6a hgc xby ra vd tim m?
b. Tim c6ng thirc phdn tu Oxit Slt Fe*O, bi6t trong A chria gl,3yo tCdu 5: (adi6m)

a. Tinh s6 mol phdn tir CO2 .cdn ldy cl6 c6 1,5.1023 phAn ttr CO2.
CO2 0 di6u ki€n ti6u chu6n dO c5 s6 ph6n tu CO2 nhu tr6n.

Phii lAy bao nhi6u lit

b. C6 bao nhi6u nguy6n tir chria trong 6,39axrtnitric (HNO3)?

c. Cd cpn 1609 dung dich CuSO41006 d6n khi,t6ng s6 nguydn tri trong dung dich chi
cdn m6t nira so v6i ban dAu thi d.mg Ipi. Tim kh6i lucrng nu6c bay ra.
CAu 6: (2di6m) MOt h5n hqp khf A g6m hidro vd Cacbon Oxit c6
ll,4.Xitc dinh phAn trdm thti tich m6i khi trong h6n hqp.

ntr

ti kh6i

so

v6i hidro ld


Ho vir tOn thi sinh:.

Chfr ky gi6m th!

1:

Sii nao danh:.

PHONG GD&DT THI XA GIA

RAI

OT CTTINH THTIC
(Gdm

0l

KV THI CHON
HSG LOP 8 VONG THI
a.
NAM HgC 20ts - 2016

* MOn thi: TOAN
* Ngiry thit 241412016

trang)

* Thoi gian: 150 phrlt (Kh6ng k€ thdt gian giao di)
DE

Ciu 1: (5 tli6m)
a) Chtmg minh

rirg'

n3

+ 20n chia h6t cho 48, v6i mgi n ch8n.

b)Tinh,S = 1' -2'+3'-4' +...+

2015'? -20162 +20112

Cdu 2z (5 tli6m)

r' + 4y' + 22 = 2r +l2y + 4z -14
b) Chtmg minh: r' + y' 2 *oa + ry4 vli r + y;r +a >
a)

Tim

n,a,,Z thoa mdn:

O

Ciu 3: (5 tli6m)

!rt +r+l
:L -a +2r'-r+l
a) Rirt ggn bi6u thric l.
b) Chung t6 ring I kh6ng 6m vdi moi gi6 tri c[ra x..
chobiSuthirc:

.

x=

-

ro

c) Tim gi6tnnho nh6t cua A.

Cffu 4: (5 tli6m)

Cho tam giSc ABC c6 ba goc nhgn; ba ducrng cao BD, CE vit
nhau tqi H. Chirng minh ring:
a) HD.HB = HE.HC

b) BH.BD + CH.CE = BC2
.AE BE- DF I
n\

,CFDEBF
-

-

-

--- HBT ---

AF clt


ri

rnr cHeN Hec srNrr cror Lop s cAp rru xA
NAtu Hoc: 2ors-20r6

.

Hu6ng dAn chAm m6n: Vat ry
Thdi gian: 150 phrit (kh6ng t

t16)

CAu 1: (5di0m)
a. Ggi ci qudng dudng la S, S > 0.

Nira qudng duong

clAu

ld S,

:

Thoi gian di nua dopn ducrng

rl s.SS
,l 2vr l2o"

:

i, qudng ducrng sau ld S, i

(0,25di6m)

clAu ld:

(0,25di6m)

Goi thoi gian di h6t qudng duong cdn lpi ld: t2
Qudng dulng di duoc trong nira thdi gian dAu vir nira thdi gian sau cita t2ld:.

15tr
-S'' t :-Yt.t"t
-:J!::2 :- :::-:=' : J rJl,
(0,25cli6m)

'22

.

.'S'r :-vr.tr
-::2:11 :'1-"
-45tt-:
'22

(0,25di6m)

22r5t2

s
Mes"*S":i.

O

(0,25di6m)

7,5t2+ 22,5t2:1

2

S rr:fth

S<)3.0t2:io
VQn t6c trung binh tr6n

,:{-t

ci

(0,25di6m)
dopn ctulng ld:

s = ., s ., =4okmrh
tt+t2 s_*{
r20

(0,5ili6m)

60

b.

- Gqi khoing c6ch gifra hai ngudi la AB. Thdi gian tir lirc xe di tir A Uat AAu xuAt phat
d6n lirc gdp nhau ld t.
Qudng ducrng m5i ngudi di dugc d6n ch5 g{p nhau:

Sr:Vr.t vdSz:vz.(-Z)

(0,5cti6m)

Vi hai ngudi chuy6n dQng nguoc chi6u g{p nhau n6n:
51 + 52: AB

flvr.t*yz$-2):AB
€ v-r .t * v2.t - 2v2: AB
<)t(v1 +vz):AB*2vz

a t(12+4):48+2.4:56
e t: 3,5h
Thay t: 3,5h vlro Sr : vlt : 12.3,5 : 42 (kJrL)

(0,5di6m)
(0,5di6m)


VAy hai ngudi g{p nhau lirc 9 gio 30 phft.
Noi g[p nhau c5ch A: 42k{\
(0,25di6m)
- Qudng dudng ngudi di xq dap di dugc trong 2hld: 72x2:24km
:4
(0,25di6m)
km
Qudng dudng ngudi di b0 di dugc trong th ld: 4 x I
Ggi t' li thoi gian tir hic ngudi di b0 di dugc 4 km dOn khi 2 ngudi gdp nhau.
Qudng Aucrng mdi ngudi di duqc d6n khi g{p nhau lAn luqt ld:
S'l : 24 + v1.t' :24 + lzt'
(0,5di6m)
S'2:4*vz.t':4+4t'
Theo bdi ra ta c6: S'1

* S'2 :

AB

l2t'+ 4t',+28:48
l6t' :20

t' : lr25h
Thay t' :1,25 vlro S'r:24 *vr.t'

:24+

l2t' :12.1,25:39km

Vfly hai ngudi g{p nhau hic 10h 15 phut vd noi gpp cSch A: 39 km.
Cdu2: (adi6m)
a. Qudng ducrng xe dd di dugc trong 1,5 gid ddu ld:
s1 : v1t1 : 60.1,5 : 90 (km).
Thdi gian OC trai xe g+p nhau te tu lirc xe 6 t6 kh0i hdnh

(0,5di6m)

.J

(0,25di0m)
(0,25di6m)

s:Sr+(vr+v2)t2
s-st 160-90 :0,5h
;,t2=
vt+v2- 60+80

(0,25di6m)

Thoi di6m OC trai xe gip nhau ld:
t:to +t1 + tz:7 + 1,5 + 0,5 : 9 (h).
Vf tri g[p nhau c6ch A ld:
S : vt (t, + tr) : 60(1,5 + 0,5) :,120 (km).
b. Thdi gian d0 xe dd di tt A d6n B ld

(0,25di6m)
(0,5di6m)

td:
'=ry:2h41(phirt)
"r,60

(0,5cli6m)

Thoi diOm xe dd t6i B ld
ta :to1to:7 +2h40:9h40
Thdi gian d6 xe 6 tO di tu B d6n A ld:

(0,5di6m)

t6r6:;:s

160

*

(0,5diOm)

=2(gid).

Thdi di€m xe 6 t6 t6i A ld:
t6to :t6*t1 *toto :7 * 1,5 + 2 : 10h30
(
xe dd t6i tru6c.
= to tot6 n6n
ioi noi cing mQt lirc thi xe 6 t6 ph6i khdi hanh d thdi di6m:
DO hai
".
t : ta - t6t6 : th4} -2 - 7h40

(0,5di6m)

(0,5di0m)

CAu 3: (3diCm)
a. Goi V ld th6 tich cria qui c6u.
Ggi Vr ld th0 tich cira qui cAu ngap trong dAu.
Gqi Vz ld th0 tich ctra qui cAu ngap trong nu6c.

Tac6:V=V1 *V2 ->Yz:V-Vr
Vi qui cA, tt6i tr6n mflt nu6c n6n:

(*)

(0,5diOm)

(0,5di6m)

P:F nnlF o,
O d.V : dr.Vr + d2.V2
a1 g200.100 :7000.vr *

(0,5di6m)

10000.v2

Thay V2 vlro:

,a

A

r

/\

:31tt33: ffiYtii3333;$l',;,'i1,,
3 'f:};d ;iT#ihc

60
tich cua qui ciu ngpp trong ddu ld

m3'

ro,-'i;;;'

dAu cfing rr,o
CAu 4: (adi6m).
Ma.h diQn g6m (PJ I

a"6lr'c-

"a"'

D/lD:) nt D+
;
SO.ticuaAmpet6eld5A'
r,\r-(A
mach chmn Ia r - Jr\
VQy cuong dQ ddng diQn trong
Ta-co: l:loz: I+: 54
i6t -uth di6n g6m (Dtll DzllD)
Ta c6: lrzt= 11+ 12 + 13

) I:: Irzt -\
-5-1,5-1,5
:2 (A)

-Iz

N;" ff;-

{J

-: urzz :

: U1

:4,5Y
12 - 4,5 :.7
'5Y

IJ: 1 4,5 (V)
ili!" art th6 giira hai dAu ddn 4:
CAu 5: (adi6m)

Uz:

rJa:7

(0,25di6m)

iO.iSOiCri

io,zsaic-)
iO.ZSOiOm)

io.iSaiA-l
iO,ZSAiCt")

(0,5di6m)
(0,25di6m)
(0,25diOm)
(0,5di6m)
(0,5di6m)
(0,5di6m)

b. Ta c6: U: g,r, + lJa
:
Md U1z: : IJ1 : IJz IJ:
Urz:

(0'5di6m)

php thuQc vdo dQ sdu ctra qui cauirong
kh6ng
trong.nu6c
ng.pp
c6y
qu6
cfia
(0'5di6m)

$rffif",

Mi

(o,5di6m)

'5Y

'

(0,5di6m)
a. VE hinh dirng:

(0,25di6m)

-A'lAinhctraAquaguongGrbingckchlsyA'd6ixlmgv6iAquaG.z
-VcB,leanhctraBquaguongG,bingc6ch|SyB,d6ixirngv6iBquaG,

(0,25diOm)

: -NOiA'v6iB'catGryl,chtq0J
cdn v6'
sang
ctratia
di
ducrng
dugc
ta
- NOi A v6i I, I v6i l, I uOi B

(0,5di6m)

(0,5diOm)


b. VC hinh dirng:
Gqi Ar le anh ctra A qua

guong Gl

ld enh cira A qua gucrnE Gz
Theo gi6 thitit: AA1: l2cm ,
AA2 : 16cm, Ar Az:20cm

Ggi

,A.2

+ 162 : 4oO
Vpy: tam giSc A Ar Az ld tam gi6c vu6ng t4i A.

ra ihay:
Suy

202

=

722

ra a -900

(0,5di6m)
(0,25di6m)
(0,25di6m)

(0,5di6m)
(0,25di6m)
(0,25di6m)


ri. rnr cHeN HQC srNH cror LoP s cAp rru xA

.

NAvt HQC: 2ots-20r6
OC tt i m6n: Ngt Vdn B

Thdi gian: 150 phut (khOng kC thdi gian ph6t

dC)

A. YGu cAu chung
kitim tra ki6n thirc co bin, gi6m khag cAn ph6t hiQn vd trAn
trgng lhirg bdi ldm tnffrign tO cfrat cria mQt hgc sinh gioi: Ki6n thric vdn hoc vtng
;iA;, ra" .d"g; ndng lyc cim thp van chuong tinh t6, -sdu sfc; ki ndng ldm vdn tOU diSn
d4t tiong s6ng c6 cin xirc, c6 gigng diQu ri6ng (khuyt5n khich nhimg bdi ldm c6 sy s5ng
1. Ngodi viQc d6nh gi6,

tao).

2. Hu6ng d6n ch6m chi n6u ra nhfing f chinh,vit citc thang di6m co b6n, tr6n co sd
chi ti6t vd nhtng thang cli€m cU th6.
d6 gi6m khaolO th6 thdng nnat Ainn ,u
"A"1i
3. Gi6m kh6o cAn d6nh gi5 bdi lirm cira thi sinh trong tinh tdng th6 d ttmg c6u vd cA
bdi, kh6ng d6m cho di6m mQt c6ch m6y m5c, nhim d6nh gi6 hqc sinh tr6n c6c phucrng
diQn: kitln thric, ki ndng, tu duY

j

4. TOng di6m todn dC ld 20di6m, chi ti5t d6n 0,25di6m.

B. Y6u cffu cg th6

Ciu 1: (8di0m)
I. YGu ci,r tii ki nlng
gi6t c6ch lirm bdi vdn nghi

luQn xd hQi: BO cqc vd hQ th6ng y s6ng r5. Bi6t trinh bdy
thdnh bdi v6n nghf lupn giailhi_ch k6t ho-p trinh bdy qugn di6m cua b6n thdn. Hdnh vin
tr6i ch6y. L1p 1u0n chpt che. DAn chring Lngr, tqc, itrrryet phpc, Khdng mic c6c tdi aiSn
dpt, dirng tu, ngfr Ph5P, chinh t6.

II.

YOu cAu

rii ki6n thftc

Hgc sinh c6 thQ trinh bdy theo nhi6u c5ch kh6c nhau nhung cAn d6m b6o nhfing f
co b6n sau:
1.

Y nghia ciu ng4n ngir

C6u ng?n ngt c6 phdp An dp: chirm rE ding cay, hoa
nghia hdm sirc, c6 dgng.

-

qui nggt ngiro - tpo n6n

- HQc v6n dugc hi6u ld trinh dQ hi6u bi6t ctra ngudi c6 hqc.
- Con duong di t6i hgc v6n dAy kh6 kh[n, gian kh6 (nhfrng chirm rE Oang cay).
- HQc 116, murrg l4i niOm vui vd hanh phfc cho con ngudi (hoa qui ngqt ngdo).
- phei nhin thSy cbhai m{t ctra v6n d0 vir cAn x6c dinh 16 chi co kh6ng ngpi kh6,
chirng ta m6i c6 thO thdnh c6ng trong hqc tQp.


Khing ilinh chin li trong c6u ngpn ng[r
- C6 hgc v6n thi con-ngudi m6i c6 dir khi ndng ldm chu thi6n nhi6n, ldm chri xd

2.

hQi, nhAt ld ldm chir v4n menh cria minh. TrOn co sd 6y, ddi s6ng vpt ch6t ve tinh thAn
m6i dugc nAng cao.

- Mu6n c6 hgc v6n cao phni n5 lgc kh6ng ngirng. Lao dQng tri 6c vdtve, ph6i lao
tAm kh6 tri.
- Cdn c6 th6i d9 kh6 khdn m6y cflng kh6ng lii bu6c. Thang khdng ki€u, bpi kh6ng

nin.
t

,

,

1

I

- TAm gucrng tiOu bi6u vugt kh6 trong hoc tAp: B6c H6

nghiOm tirc trong hgc tQp
n6n dd dpt t6i trinh d0 hqc vdn cao, gi6o su Ng6 B6o Chdu dpt gi6i to6n hgc limg danh
tr6n th6 gi6i, cbcthu khoa trong c6c dgt thi vdo clpi hgc hdng ndm... Ldy ddnchimg trong
hgc tpp lre re, luyQn cria bin thdn, ctra nhtng nguoi md minh UiCt AC ldm s6ng to th6m
ch6n li trong cAu ngpn ngfr tr6n.
'

^^

(biy t6 quan tli6m)
- Hgc v6n kh6ng chi ld tri thric md cdn bao g6m ci vi6c rdn luyQn tu tucrng, tinh
c6m, dpo dirc, nhdn c6ch cao quy. DC dpt dugc nhimg didu d6, chring ta cAn cO gingrdt
3. M& rQng vir nffng cao

nhi6u. Tir b6 mOt th6i x6u, ldm mQt viQc t6t cflng cAn phAi d6u tranh v6i bAn thdn, vugt
qua kh5 kh[n, thu th6ch.

- Kh6ng ph6i khi ndo trong qu5 trinh hoc t6p cay dhng cflng d6n tru6c, nget nglro
d6n sau. Trong hgc tpp nhi6u hic vira c6 n6i kh6 vira c6 niOm vui. Khi dd ham hoc, chdm
hgc thi sp say mC sE ldm ta qu6n c6 mQt nhoc. Nhfrng hic d6, k6t qui hgc t4p dqt dugc sE
rdt cao.

III. Bi6u cli6m
- Di6m 6 - 8: D5p ring dugc c6c y6u cAu n6u tr6n; Vdn vi6t c6 cim x[rc. DAn chimg
chgn 19c vd thuyt5t phUc. C6 th6 cdn mQt vdi sai s6t nho.

- Di6m 3 < 5: Co b6n d6p ring dugc c6c y6u cAu n6u trOn. Ddn chirng chua th4t
phong phir. C6 th6 cdn mQt

vii

sai s6t nho.

- Di6m 1 < 3: Chua hi6u chic y6u cAu cira dC bdi. Ki6n thric so sdi. Cdn mic nhi6u
l01.

- Di6m 0: Kh6ng hi6u t16, sai lpc phucrng ph6p.

Cdu2: (l2di0m)
a. Vij

ki nlng:

(2di6m)

- Hgc sinh nhpn thirc dugc y6u cAu vC t i6u bdi, nQi dung, gi6i hpn...

-

giet ldm bdi v[n nghi lufln chimg minh: b6

cr,rc 16 fdurg, lQp 1u4n

dpt trong s6ng, bi6u c6m; kh6ng mac 16i chinh tA, dirng tir, vi6t c6u...

b. VO nQi dung: (10di6m) Hgc sinh n6u dugc nhflng y sau:

ch6t che; diSn

bhi: (1,5di6m) Gioi thiQu chung v6 truyQn ngin'
o ' .- -!-1
ld m6t th6 lopi v6n hgc thuQc loai hinh tu su ft6 viQc hoflc dpg lai
do
q,u ao bevt6
dang di6n * -0,";;:'i
,,0,
'e;h
phong
nnfit AUI cira ngudi ,riet. SO lugng trang vr}t ithcrn truyQn vira vd truyOn ddi, vdn
1. MO

d.];;ffi

;TJ:l|ffi

ila;";ffi

nghngon nhtmg c6 sric chria l6n.
2.

Thin bni: (7di0m) D4c di6m chinh

cua truyQn ngan'

- DUng ldi ke vd ldi mi6u ta dC th6ng b6o thdi gian vlr gcri ra dpc di6m tich c6ch cua
nhAn vpt.
- phAn tich t6m ly cua nhan vAt, n€u sg kiQn tinh hu6ng nhim ldm hiQn l6n birc

tranh vd con ngudi vlr cuQc s6ng.

- TruyQn nggnphai c6 c6t truyQn, nghia ld c6c sp kiQn, bi6n cO niy sinh nOi ti6p

thi
nhau, dile6; Airf"t Aar" mau thu6n, U"O. pnai giai quyet m6u thu6n, gitri quyiSt xong
truyQn k6t thirc.
- Iruyen ngiin phii c6 nhdn.vpt. 56 luo,ng nhdn vQt cria truyQn nglnrAtit. Tinh c6ch
s6 phpn .iru nila" vQt dugc tho hign m6t phAn hoflc to]rn b6 cuQc doi th6ng qua hinh
diLng,iOi .rOi vd hdnh dong ctra nhdn vflt trong nhfing tinh hu6ng kh6c nhau.

^

- Nhdn v6t trong truyQn nggnthuolg AO hi nhimg 6n tugng sdu sic.

- Hinh thric ng6n ngt cira truy6n ng6n dadpng, phong phir, c6 ng6n ngt cira ngudi
k6 chuy6n, ng6n.rgt .t u nhdn vft, ng6n ngir d6i thoai, ng6n ngt dQc thopi nQi tAm'
Tinh ngdn ggn. CAu chuyQn trong truyQn.tgdtt dugc miOu ti o mQt thoi gian,

-

kh6+g gian nhAt dinh.

s. x6t biri: (1,5di6m)
Nhd nhimg dac di6m trQn, truyQn ngSn c6 khi ndng rat,lOlrtrong viQc phin 5nh hiQn
thu, ..rO.t;5;g: B6n canh tintr ctrAt hi6n thuc, truyQn nghn cdn g6 tinh ch6t try tinh.
*,r6t'sic c6 sirc s6ng vi gi6 trf 16u ddi, t6n vinh t6n tu6i ct:r.tdc gitt.
Nhid"*re"

"!6n

* Thang tli6m

vi

nQi dung. 86 cyc dAy
12: D6p fng t6t cdcy6u cAu vA hir,h thrlc
dtr c6c phan, nQi dung- .frpt .hC, thuytii phpc: Cht vi5t dgp, cAn thfln, 16 rdng, cAn d6i,
b6 d6u O,ing ch5 c6 th6 m6c mQt viri sai s6t vC 16i chinh t6.

- Di6m l0

-

- Diem 8 < l0: D6p,ring

cly v.:l^:Ay:P"_.o'^91, 91,,1:i'.* *".,'?i :11v,
\a
mpch lac, c6 suc thuy6t phr,rc. C6 mdc vdi loi diOn dat. Cht vi6t kh6 dgp, kh6 cdn,1r0-n,
ring. Khoang chch ciri cht chua deu. Vdi 16i b6 dAu chua dirng.
- Di6m 4 < 8: D6p img c6c y0u cAu nhrmg chug sAu. 86 cpc trinh bdy co th6 chua
ho,p li. Loi vdn chua that thuyet phqrc, nhi6u 15i b6 d6u chua dung
- Di6m 2 < 4:NQi dung so shi. C6c phAn khdng dAy dir. Vdn vi5t lung cung. M6c

16

nhi6u 15i di6n dpt.
- Di0m

| <2: Kh6ng dpt dugc c5c y6u cAu tr0n'
4

KY THI CHQN HQC SINH GIoI LOP 8 CAP THI xA
NAnn Hoc: zots-zorr
Hu6ng d6n ch6m m6n: GIAI IOAN BANG MAy riNu CAM TAy
Thdi BJan: 150 phrit (kh6ng tCAu 1: (adi6m)
u..Qry trinh b6m phim d0 ph6n tich s6 A ra thira s6 nguy6n t6:

BAm 6227020800 : Shift FACT
Ta dugc k6t qui A: 621,.7020800 :210 * 3s , 52 x 7
Ap dpng c6ng thric tim s6 u6c ducnrg cira n ld:

I(hi

n:d.U

.....C thi

st5

x

11

13

c6c u6c ducrng ctra n ld:

I)

(x+ 1)(y+1)...(z +

x

(0,25di6m)
(0,25cli6m)

(0,25di0m)

-1 bY*r -l
a-l b-I

-I
c-l

d*r

C'*1

(0,25di6m)

Vfly s6 cdc u6c ducrng cua s5 A ld: (10+1)(5+1X2+lX1+1)(l+l)(1+1) (0,25di6m)

:

11 x 6

x3 x2 x2 x2:

1584 (u6c)

(0,25di6m)

T6ng c6c u6c ducrng cira A ld:

3s*r-1 52+l-r
x-x-x-x-x

210+t-1

2-t
:

211

-l

36

-l 11r*r-l

3-1 5-1 7-t

-l

53

-1

72

12461012

2b47 7zB
: -X-X-X-X

J1*1

-l

t24 48 tzo

112

131*1-1

l1-1

(0,5di6m)

13-1

-1 X-132 -l

(0,5di6m)

168

t24610t2

:2047x364x31x8x12x14
-X-X-X-X-

(0,5cli6m)

:

2047 x 1 5 165 6 96 (ddy ld ph6p nhdn trdn mdn hinh)
Ta b6m 2047 x 151 65696: ta dugc ktit qui 3.104417971x10'o 1trd, mdn hinh)
BAm ti6p - 3.1044 FtOl tO
ta dusc ktit qu6 l7g7l2
(0,5ili6m)
Do cl6 2047 x 15165696: 31044179712
(0,5di6m)
Cdu 2: (adi6m)

:

' A:1x,
15
5 +!r,
3 *L*

D6t

Ta chimg minh

(0,25di6m)

A ld mQt s6 nguy6n v6i mgi x nguy6n

ducrng tir d6

f(x) ld mQt

SO

nguyOn.

1. +_x"
1, +-x
7 : _x"
l. +_x'+x_
1"
8x
53155315
1.1.. +x--x--x
I I
: -x'+-x5353
Ia co A:

_.tr-

xt -x x'-x
:___+I

53

Ta chimg minh: x'

(0,25di6m)
(0,25diOm)

- x chia htit cho 5, {' - * chia htit cho 3

x' - x = *60 -r)= r(,'

:r(r'-1Xr'-++5)

(0,25di6m)

-r[x'

+r)

(0,5cli6m)
2


:(r' - a*')-(r' - +r)* (sr' - sl)

(0,5di6m)
(0,25di6m)
: *Q' - +)- *6' -+)+ sr(r' - r)
(0,25di6m)
*6'* 1Xr' - +)* sr(r' - r)
(0,5di6m)
: (, - z\. -t)r(, + lX, * z) + s(x- t)x(x + t)
Ta th6y: (*-zk-1)rG+1Xr+2) le tich cira 5 s6 nguyOn li6n ti6p n6n chia h6t cho 5.

:

Do d6

l+

Vlr x'

-*=*(*'-r)=(r-l)rft+1)

)

(0,5
nguy6n.

chiahtit cho 3 n6n

nguy6n.

+

Vay f(x) 1u6n nhQn gi6tringuyOn v6i mqi x nguy6n duong.
CAu 3: (adi6m)
a. (1.5di6m)
Goi a la sd ti6n ban ddu; 15i su6t ld x.
:
Sau mQt th6ng 16ng 16 ti6n ci S9c lan tii ld: a + a x a (1+x)
Sau hai th6ng t6ng sd ti6n ca g6c 16n 16i ld:

a (1+x) + a (1+x) x: a (l*x)'

A.:

(0,5di6m)

(0,25di6m)
(0,25di6m)
(0,25di0m)
(0,25di6m)

a (1+x)"
Sau n thSng t6ng s6 tidn ci g6c l5n 15i ld:
Vfy sau mQt ndm (12 thdng) ban Minh c6 t6ng s6 ti6n ld:

(0,25c1i6m)

:

(0,25di6m)
000 000 (1+0,015)t' 23 912363,43 (d6ng)
b. (2,5di6m) .
Goi a ld s6 ti6n ban ddu, 15i su6t ld x, s6 ti6n rut hdng th6ng ld T, thdi gian ld n(0,25di6m)
1 * x)
- Sau 1 th6ng: sO ti6n c6 a* ax: a (1 +x) :ka(V6i
(0,25di6m)
56 tiAn cdn lai sau khi rit: a (1 + x) - T - ka - T
- Sau 2 thdng
'. I
^(

50 tlen co:
(0,25di6m)
ka - T + (ka - T)" (ka - TXl * x) (ka - T)k
SO tiOn cdn lpi sau khi rirt:

A:20

k:

:l*a-kT

:

:

kza-kT- T:k2a-T(1

+k): kza-T q+
k-l

(0,25di6m)

-:) )k:
k-l

- Sau 3 thangso ticn c6 ld: (k'u - T .G;'
SO

tiAn cdn lai sau khi rrit:

k3a-T.

(k'-k) - r-k3ak-1

- Sau n th6ng

sO

tie,

r

k3a -

T

(k'-k)
.

((f.i)+ 1): r,'o-rt-:!
kna-Tk'-l
k-l

cdn lPi ld:

k-1

(0,25di6m)

(0,25di6m)

(0,25di6m)

Vfly sau 1 n[m (12 thdng) cdn sO tiAn o ng6n hdng ld
(1+0,015)r2x 20 000 000

- 900 000

(1+ 0,015)12
(1+ 0,015)

(

di6m)

a.Tac6; AB'+AC2
BC2 =32

+ll2

= 130

=22 +32 +62

(0,25di€m)
(0,5di6m)

:12175273,1a (d6ng).
C?n 4:

-1
-1

+9'=1i0


(0,5di6m)

Suy ra tam gi6c ABC vu6ng tai A.
s.qnc

b. Tam gi6c ABC vu6ng tpi A n6n: s.^- Lnu*AC
AD\22
Suy ra: AH

Ta c6:

,q,o =

AM

(0,5di6m)

=lou" AC =l9,5ocm2

=4'#

=Lsc*eu

x3,42 cm

DB = ou * DB = 4!_" u'_= 2,g5 cm
DC AC= DB+DC AB+AC AB+AC
DB

--

AB

r[,qt{ * nd

x 3,82cm

-

s oao

=

1,
*
\ * G BC - B D)= 3. 42(5,7 o - 2,85) 4,87 cm2
z

(0,5di6m)

(0,5di6m)
(0,5di6m)

=!2 sc =5.7ocm

s tou = s ou,

(0,5di6m)

(1diom)

\!

Cdu 5: (adi6m)

- VC hinh dring:
a. Ggi giao di6m cua hai ducrng ch6o AC vd BD le H.
Vi hinh thang ABCD cdn n6n ta c6:

(0,25di6m)

AH: BH; CH: DH

(0,25di6m)
4


*

AH2

(0,25di6m)

=2DH2 =CD2

:
AH2 + DH2 = AD2
= AHz AD2 - DH2 =

(0,25di6m)

AH2 + BH2 = AB2
=2AH2 = AB2
DH2 +CH2 =CD2

) AB2 =2AD2 -zDH'
= CD2 =2AD2 - AB2

A82

(0,5cli6m)

2

(0,5di6m)
(0,5di6m)

=2AD2 -CD2

)

2.18,452 -13,542
cD =rl2AD' - AB2
=22,304 (cm)
b. K6 ducrng cao AK, ta c6:

cD _ AB _ 18, 45 - 13, 54
DK =
= 2,455 (cm)

(0,5 di6m)

(0,5di6m)

22

S urr,

=

(AB + CD)AK

(13,54+22,304).2,455

= 43,999 (cm')

nrr

(0,5di6m)


rY rnr cHeN Hgc sINH cr6r LoP s cAp rru xA
NAnn Hec: zors-zolr
.Hu6ng d6n ch6m m6n: Ho6 hgc 8
Thdi giurr, 15b phirt (kh6ng tC tnOi gian ph5t

Cdu 1: (adi0m)
a. Gqi kim lopi h6a tri GD le R.
rtHz
8,4 : 22,4 : 0,37 5 (mol)

:

R +

:

HzSO+

0,375

0,375 mol
MR

)1

:

RSO4

+

H,

mol

(0,5di6m)
(0,5di6m)

t

0,375 mol

(0,5di6m)

S6(g)

,*:

clO)

(0,5di6m)
(0,5cli6m)

NTK ctra kim lopi R la 56 dvC d6 ld Fe.

Fe + HzSO+ : FeSO+ + Hz t
0,375 mol
mol
:
FeSO+.x'HzO(tinhthC)
+
x.H2O
FeSO+
0,375 mol
0,375 mol

b.
0,375

(0,5di6m)

._ 104,25 _=278(S)
\tr
Mtinhrhd:

ffi

FeSO+ . xH2O :278
(56+96) + x.18:218
\,-

278- (56 +96\
\ee

-rv

(0,5cti6m)

'-'

-'7

18

C6ng thric tinh th6 mu6i hidrat h6a FeSO q.7HzO

Cdu2: (3di6m)

(0,5di6m)

- 56 mol cria CScbon dioxit ld:

(0,5di6m)

+ CO -J-+
lmol

CuO

lmol
xmol

CO -!--+

FeO +
lmol

l mol

n:

#:0,2(mo1)

Cu

(l)

(0,25di6m)

lmol

Coz
1mol
xmol

Fe+

Coz

(2)

(0,25di6m)

lmol

1mol

+

ymol

ymol

Tt (1) vd(2)tac6 hQ phuong trinh:
80x+ 72y : l5,2virx *Y : 0,2
)x:0,1 vdy:0,1

) rlcuo : 0,1 (mol); rllcro : 0,1 x 80 : 8(g)
) fIF"o :0,1 (mol); lrlFeo : 0,1 x 72 :7,2(g)
> %CuO: -!- x rc}% * 52,63Yo

-

(0,5cli6m)
(0,25diOm)
(0,25di6m)
(0,5cli6m)

15,2

)%

Feo

:

7,2
15,2

x 1oo% =

47,36%o

(0,5di6m)


CAu 3: (adi6m)

- 56 mol cira NazCO3r nNazcor:

:

#

0,15(mol)

(0,5cli6m)

- Gqi x, y lAn luot ld s6 mol cria CaCO3 vd MgCO3

CaCO3 --t--+ CaO
x mol

+

x mol

ymol

+

COz

MgO +

-r\

MgCO3

ymol

->

NaOH

0,15mol
- Tt ( 1), (2), (3) ta co
56x + 40y 7,6

:

COz

(1)

(0,5diOm)

x mol
COz
ymol

(2)

(0,5di6m)

(3)

(0,5cli6m)

Na2CO3
0,l5mol

hQ phucrng

+ HzO

trinh:

x + y :0,15
) x:0,1 vlr y : 0,05
) mcaco: : 0,1 x 100 : 10(gam)
mMsco3 : 0,05 x 84 : 4,2(gam)
-

: l0 + 4,2 :

frlh6nhqpmu6i

YoCaCO3:
o%MsCO.

e

"

Jq ,19g :
14,'-

(0,5di6m)
(0,5di6m)
(0,5di6m)

14,2(gam)
7O,42Yo

(0,25cIi6m)

: 4'2 x 100 :29-58o/o
14.2

(0,25di6m)

Cdu 4: (3di6m)
a. Fe*O, + yHz -J--->xFe

*

yHzO.
(mol)
13,44:22,4:0,6
1lH2o: l0,B: 18 :0,6 (mol)
Theo PTHH: rrH2: n1126 n6n H2 ph6n tmg h6t;
Ch?trhnA g6m: Fe vd Fe*Oyao.
Theo dinh luAt b6o tohn nguy6n t6 vd b6o todn kh6i lugng:
1tH2 :

I11

:

ffIA

*

mO

fl6 ltrorg nu6c): flH2O 016 (mOl)
mo 0,6 . 16 :9,6 (g)
VQy m: 36,8 + 9,6:46,4 (g)
b. Ta c6:
91.3X36.8

:

rrIF.:

ff

=33,6 (g)

mo

:

46,4

Ta c6

ti

lQ

)

x

,

- 33,6 :

VQy c6ng tric ph6n tu oxit
CAu 5: (adiem)

:

(0,25di6m)

12,8 (g)

y: T{,
t6
56 Y:3

(0,25di6m)

:4

(0,25cli6m)

sit ld: Fe3Oa.

:0,25 (mol)
the tich CO2 d dktc : Y :0,25 x22,4:
a) SO mol CO2

(0,25di6m)
(0,25cIi6m)
(0,25cli6m)
(0,25cti6m)
(0,25
(trong nu6c)

:

)

(0,25di6m)
(0,25di6m)
(0,25di6m)

(0,25cIi€m)

(0,5di6m)

''j1t^',i'
6x70"

5,6

(lit)

(0,5di6m)


b. 56 nguyen tu c6 trong 6,3 gamHNo3-63
- 6'3x5x6xlo23
c-

:3 x 1023

(ldiCm)

rnoi lugng cuSoa : 16 gam) ncuSo+ :0,1 mol. Kh6i lugng Hzo :

144 gam
n nu6c 8 mol .Vi 1 phAn tri CuSO+ chria 6 nguyCn tu
0,1 mol CuSO a chua 0,6 mol nguy6n
( 1 di€m)
vi 1 phgn tt H2o chria 3 nguydn tu 8 mol H2o chria 24 molnguy€n tri.
T9rg s6 mol nguy6n tir tru6c khi c6 cqn : 0, 6 + 24:24,6 mol
T9rg s6 mol sau khi c6 cpn 24,6:2: 12,3
56 molnguy6n tu gi6m tli do H2O bay hoi:
Ggi kh6i lugng Hzo bay hoi ld x gam. c6 3x / l8 mol nguydn tu bi bay hoi
12,3:3xl18
73,8
(ldi6m)

Cdu 6: (2di6m)
Goi x, y lAn luo,t s6 mol cua H2 vd CO cd trong h6n hqp A
tIl4
2x+ 28y

)
)

:

tir.

=

) x:

(g)

li

:
d/^lll2:.'Hr.nA 2.(x+y)
) 2x + 28y : 22,8 (x+y)
) 5,2.y : 20,8. x
-:
-xl
_\,
, y4

ll,4

Vi

ti 16 s6 mol chinh

Tac6:

(0,5di6m)

c6c chAt khi do trong ctrng di6u ki6n n6n

:;
> %V (CO) :

%V (hidro)

I

. 100:20oh
100Yo

- 20%

(0,5diOm)

la

ti lO th6 tich
(0,5cli6m)

:

80%o

(0,5cti6m)

HET


pHoNG GD-ET GrA

RAr

HrloNG oAN cnAu ri rnr cHeN HSG Lop
cAp rHI - NAnn Hec 2ots-2016

s

M6n: TIENG ANH

Part 1: LISTENING (2 tli6m)

Udi cilu ilfing ttrqc

1.A

2.8

0,25 di6m.

4.C

3.D

5.C

6.4'

7.D

8.B

Part 2: LANGUAGE FOCUS

I.

(3 ifiAm) Ptdi cilu dfing tlwqc 0,25 itihrn

1.B 2.8 3.C 4.8 5.B 6.B 7.8 8.C 9.C 10.C 11.D
II.

(3 itiOm)

Mdi cAu dfing tlwqc 0,5 iti6m.

It took the students two hours cleaning the school
Z.lhave lived in this city for 2 years.
1.

yard.

t am often given books as birthday presents.
4. It was so hot that we had to wear sun hats.
3.

5. The ticket was not so/as expensive as I had expected.
6. The,cake was so hard that

III.

(2 ifiA@

I couldn't eatitl too hard for me to eat.

Mdi cilu ttfing tlwqc 0,25 iti6m.

l. harmful
2. interested
3. polluted

4. advertisements
5. scientist
6. collector
7. encourages/ed
8. competitors

Part 3: READING

I. (2 tli6m) Mdi cfru itfing tlwqc 0,25 itiirru
1.

activities

5.

read

2.time
6. daily

than 4. on
7. adults 8. risen

3.

r2.B


ll.

(2 tli6m) tVtdi cfiu ititng itwqc 0,25 di6nt

1.B
III.

3.C' 4.8

2.C

(2 tli6m)

*tdi

s.B

6.8

7.A

8.B

cAu dfing ituqc 0,5 di6m.

1. He used fire to keep himself warm at night, to cook food, to frighten away enemies
and wild animals, to signal messages.

2. They used fire for making smoke signals.
3. Yes, it can.

lt took 12 hours to burn.
Part 4: WRITING ( ili6m)

4.

(Cho dihm thng ti1u chi theo thang iti6m 0; 0,25; 0,5; 0,75; 1,0)

enough words

0.5

qood spelline

1.0

exact grammar

1.0

coherence

0.5

good ideas

1.0

Total

4.0


PHONG GD&DT THI XA GIA
r frra
ON rrfrri.rrr
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THUC I

r---=

RAI Ti'TUI

CHQN HSG LOP 8 VONG THI
NAM HQC 2015 - 2016

:ii;;;-rn'.-,

* M6n thi: TOAN

(GOm 04 trang)

HTIONG oAN CHAM
A

C6u

So

NQi dung

tIi6m

I

.- -.7
(5
drem)

Ta c6: n

Khi d6:

eZ,

n3

nchdn

= n-

2k,k

eZ

0,,25d

+20n = 8k3 +40k
=

sr(r'+

=

sr[(r'-r)+o]

0,5d

-,)(*

0,25d

= 8k(k

a)

0,25d

s)

0,,25d

+ r) + a8k

Md: k(*

=
-

-,)(r + r)i6,yk e z
+ r)i48
vr, .z
IT(f -,)(r
)

l.

0,25d,

0,5d

+ttt, +t

Vay: n3 +20ni48;Vn eZ vd n chin
Tac6: S =l'-2'+3'-4' +...+ 2015'z -20162 +20172
=

l'+ (l' - ,')*(s'

=

t*(: *z)(t-z)*(s++)(r-o)+...+

- a')*...n(zot72 -20t6,)
(zon+zoio) (zon -zoro)

b)

0,5d
0,5d
0,5d

=l+2+3+ 4+5+..'+2017
= (, * zon).20t7 :2 = 2035t53
,S

)

0,25d

0,25d
0,5d

= 2035153

0,25d

(5 tli6m)

r' + 4y' + 22 = 2r +t2y +42-14
e r'-2r+l+4y2 -l2y +9+ z'-42+4=0
o (*-,)' * (r, -r)' * (, -r)' -0

Ta c6:

a)

[e-r=o

1d

0,75d

l'=t.

olrr-3-o=ja:)
lz_2=o l,=;

0,5d

I

=,

f*

),, = 1
VAv:
'J
l"
')
t4
l- -'t

0,25d

l'- '

r
s
s4
zx:y+ry
r'+alaco:

4

ert-roy+yt-ryo>0
e ra ("-r)-ao ("-y)
b)

>

0,5d

o

o(*-r)(,^-y')=o
o (, - r)' (" * y)(r' * y') > o (1u6n dring)
Vi: r +y=(*-r)' ro,(, *r).0,(r' *s')=o
VQy:

3

0,25d

* yt > roy * *yo vbi r,a * 0;r +Y > 0

"t

0,5d

0,75d
0,25d
0,25d

(5 tli6m)

Ta c6: roo - tr'

+2r' - r +l = (, +f)(r' - z +1)

l,
Md: l'" -r+r=[r-!l
z

r2

[

2)

t, +l>O;Vr
Lr

a)

*1ro;vr
4

> (r' +l,)(r'-n+t) >o;vr

0,25d

YQy A luu6n x6c dinh v6i mgi gi6 tri cua x

0,25d

r' + r*t

(,',* + t)' (*' - r

=

(r+t)' (r, -r+1)

+t)_ (r + r)'

=,4=f(,'r' + 1) (r' -r + 1)
,

YQy A =

ra co:l('

4

12

+r

0,5d

0,25d

12 +1

. t)' > o;v'

0,5d

[.r'*l>0;Vz

_' (, * l)' .,tw.vI.,..
r'+l
Vfly: A2liYr

0,25d

r
V0y: Mi,nA- 0 e r+1 = 0 e r = -l
Ta c6: A

0,75d

\2

(r+t)

=+

c)

0,25d,

'j

Ta lpi co:): ro +

b)

0,75d

>-

0;Y

Hinh vE dring

0,25d
0,25d
0,75d

0,25d

(5 tli6m)
2


x6t
a)

r(*,

eoo) vn

=
\/
^HEB(frE
^HD
frE = 6D (2 g6caoi ainn;
) LHEB a LHDC (1 goc nhgn)

*

= ro') co:

ld

HE
HD

HB
HC
HD.HB = HE.HC

Xet

^BHF(BFH

= eoo) vir

0,25d
0,25d

rcCo(BDC

= e00) .o,

DBC chung
+ LBHF cn LBCD (1 e6c nhqn)
BH BF
<

BC BD
> BH.BD = BF.BC (r)
b)

0,5d

Chimg minh tuong tU:
) ACHF a ACBE (1 g6c nhqn)
CH CF
CB CE

=

CH.CE =

cr.ca(z)

0,25d

Tri (1) vd (2) ta duoc:
BH,BD + CH ,CE = BF,BC + CF.CB
= BC (ar + cF) =

sg'

0,5d

VOy: BH.BD + CH.CE = BC'

xdt

^ADr(^*
6ic chung

c)

=

AADB

AD
AB

= eoo)vit

n+nr(u,

0,25d

- eo )

"0,

a A,AEC (1 e6c nhon)

AE
AC
x6t LADE vit LABC co:

0,,25d

BAC chuns
AD
"" (chimg
'-:1- AE

minh tr6n)

AB AC. .
cn
= AADE LABC (c-e_c)
(r\
-AE
DE=AC
BC\ /

0,5d

Chime minh tucrng tg:
LBEF ' LBCA (c-g-c)

(o\
-uE
BF=nc
BA\ /
Vir:

A

0,25d

CDF cn LCBA (c-g-c)

DF

BAr-t

0,25d

= cp: cA\t)

Tir (3), (4), (5) suy ra:

AE .BE .DF AC .BC .BA
=

=l
DE BF CF BC BA CA
DF
t
Hav:AE BE._

'CFDEBF

-

--- HET---

4

0,25d
0,25d