TUYỂN SINH TOÁN 10 THPT THÁI NGUYÊN HƯỚNG DẪN CHẤM

UBND TINH THAI NGUYEN

HIIONG NAN CHAM
THI TUYEN SINH VAO LOP 10 THPT
NAvr Hec zot6- 2ot7
vrON THr: ToAN Hec

so GrAo pvc vA pAo r4.o

( Bdn hudng ddn chtim

gim cd 04 trang)

I.Iluring din chung
- Gi6m kh6o cdn ndm virng y6u cAu cria hudng d6n ch6m Oe Oantr gi6 rhing bdi
ldm cta thf sinh. Thi sinh ldm c6ch khric d6p dn n6u dring v6n cho di6m tOi rla.
- Khi vfln dUng dbp in vi thang di6m, girim kh6o cAn chri tlQng, Iinh hoat vdi tinh
thAn trdnlrgng bdi ldm Lta hgc sinh.
- NiSu c6 viQc chi ti6t h6a di6m cdc,y cAn ph6i ddm b6o kh6ng sai lQch vdi t6ng
di6m vi - Di6m todn bdi ld t6ng dii5m cria c6c c-6u h6i trong dC thi, chSm di6m 16 di:n 0,25
vd kh6ng ldm trdn.
II. Dip rinn vi thang tli6m
Ciu
NQi dung
Di6m

.
.

CAU

I

Cho hdm s6 y=

(J1-Jr).+3

c6 Ao

tni (d). Ham so da cho ld ddng

biiin hay nghich biiSn tr€n R ? Giai thich? Tim tga d6 giao cti6m
c:ioa

(d)voi truc tung

Gidi:

, =(J1 -Ji)*+S

Hdm s6

Vi

I

0,25

ddng bitin tren tR ,

a: Jl-Jlro

Cho x :

0 ta c6 y :3

0r25
suy ra toa dQ giao diiSm cria (d) v6i tryc tung ld 0r5

A(0;3)

Ciu

2

Kh6ng dung miry tinh
thtrc: A

-

+rJr)'-

(z

..f&8

cAm

.

Gidi:
Ta c6:

e-(z+sJz)'-.,D88

-* +2.2.3,12+1l,li1z -,!1aat

0'5

=4+lzJr+18-i2J,
-11
Cffu 3

chobi6u

,no",r-(

x)0,x*4.

G-!.:L ).(J--Gl') ,,-F)''-

0r25
0,25

[;;5*G-/[m

Hay rut ggn B vd tinh gi6

trf

cta B khi x

-

3

+

.6.

Gi,rti:

ruvv'"-[cG5-Gi)t@]
*Y.i-l [v;'tr-('tr- zXv;.2)l

ra c6:' =(

o(G-t) l;$r._z)

-Wq'
_

0r25

0r25

4
1

0r25

vdi r-3+..6=
Ciu

(Jr.,)'= J; -J-z*t:+.8 -J|+t-1 =J,

0,25

4

Xric tlinh c6c hQ s6 a vd b, bilth6 phuong trinh
c6 nghiQm

(*;y)

-(z;-t).

Gidi:

Vi he c6 nghiQm (2,-l) n€n th6 x=2, y:-l
lzo+b1-r1-4 lzo-b-4

{

-2.(-r)

lzb

I

={

Ciu

5

--z

lb

c6:
0,25

--z

a-l

lb

+ Vdi

<>{

vdo he ta

0,25

--2
a:l, b: -2 ta c6 hQ

l*-2y'

0r25

lr.-,
(2;-l)

0,25

Vfly de h0 c6 nghiQm (x,' 1:
Kh6ng dung mdy tfnh cAm tay, hay gi6i pnuong trintL

x2

+6x-2016:0

Gidi:

a:1, b:6 (b':3), c:-2016
L = 32 - 1.(-2016) = 2o2s> 0,l[

Ta c6

= 45

Phuong trinh c6 hai nghidm ld: x, = -3 + 45 = 42;xz = -J * 45

Ciu

6

Cho phucrng trinh

x' -zmx *(*' - +):O 1t;, z

ld tham

- -48

0r25
0r25
0r5

si5.

a)Chung minh phuong trinh (1) lu6n c6 2 nghiQm phdn biQt vdi mgi

gi|tri

c: ia m.

b)Ggi x11x2li 2 nghiQm cria phuong trinh (l). Tim m di: xr2 +t =N,
Gidi:

a) Ta c6: A =m'-(*'-4)=4>0,Ym

suy ra phuong trinh lu6n
c6 hai nghiQm phdn biQt voi mgi gid,tri m.

b)

Theo viet ta

.o' {

xt + x2 =

[','',

"'*
-4

= m'

+4 =(x.,+xr)' -Zx,.xr=12*)' -2(*'-4)=2m2 +g
TheobAi xf +4=26+2mz +8=26*m=*3
Thri lpi: Vdi m=3, ta c6 phuong trinh x'-6x+5:0 c6 hai
nghiQm: x, =1,x, = 5 =+ t * 4 - 26,thoa m6n dAu bdi
ygl_!! - -3 cfing th6a m6n itAu bdi. Ydy m = +3

0,25

0r25

Ma xf

2

0,25

Ar25


Cdu 7

Khdng tinh tirng gi6 tr! cg thil, hay sip x6p cric ti sti lugng giitc
cos20', sin38', cos55', tan480, sin88' theo thti tg ting ddn, giii
thich?

Gidi:
0r25

= cos52o ,sin 88' = cos 20
Vdi 0 Ta c6 bi6n cl6i sau: sin 380

0,25

ndn 0N6u 450 < P <900 thi tanp 21 = tan480 > I
Do d6 ta sEp xiip theo thri tU ting dAn nhu sau:
cos

CAU 8

55',

Chotam

sin 38", cos

0r25

20', sin88o, tan 480

ABC vudng

gi6c

0r25

tqi

A,c6 sin B -:.HEy tfnh citctisri luqng
3

Gidi: (Kh6ng
Ta c6:

C

C.

giric cria goc

cho diiim hinh vd)

llA

sin,B=1=)CosC=-

^^
JJ

B

ACIAC2IACzlACl
- BC 3- BC2 g- AB'- 8 - AB 2J,
I
haycotg
=-|-,suy ra: tanC =ZJi
,
2J2,

0r25
0r25
0r25

AB

AC

Ciu

9

Cho dudmg trdn tdm

duong tlrang song song

ABOC

O vi

mQt

di€:m

AnAm ngoii duong trdn. Kd 2

AC voi ducrng tdn (B,C ld 2 n}p di6m).

tiiip tuytin AB,

0,25

',=+
Qua C kd mQt

vu OB, cfut O,l t1i H. Chung minh rang th gec

nQi ti6p duo. c trong mQt duong

tdn vd f/li trfc t6m cua tam gic

ABC.
Grrii.' Flinh vE

Xdt

tu

trEd

:

gdc ABOC

=frd

=eoo (Theo

tinh ch6t cta ti6p

tuyiSn).

Suy ra

tu gi6c ABOC

ti6p

c tong mQt ducrng

du-o.

0,25

c6:

0,25

nQi

tdn.
a

J


. {lca tloB +CHIAB

Trlc6:

Trong tarn gircABC c6:

Ciu

10

Cho

0r25

loB L AB

{':,:
11=H h tuc tam cua tam gi6c ABC.
IAH L BC

tt gi6cABCD nQi ti6p trong ducrng trdn(O;R),c6

ch6o vu6n

a)
b)

g

g6c

0,25

hai dudmg

vdi nhau vd cit nhau t4i L

Chrmg minh ring: IA.DC

- ID.AB;

Tinh t6ng AB2 + CD2 theo R.

Gidi:

Hinh vE kh6ng cho tli6m

a) Xdt hai tam gi6c IAB vd IDC c6:

vd

fri =i6Z (g6c nOi tii5p cung chiin

cung

0r25
D

BQ

Suy ra: NAB diing d4ng

voi NDC

do

0r25

.IA
rc +IADC=ID.AB
-ID =fi

oo ta co.

b) Ke ducrng ktuh CE cta duong

tdn (O).

ili =ide =90'(g6c nOi ti6p chan duong kfnh EC)
AE t tBD+ ABDE le hinh thang cdn (hinh thang

Suy ra {n:"!*
'
LAE

0,25

=(zn)' =4R,(DoADEC

0r25

Ta c6

IAC
nQi titip duong trdn)+ AB = DE
Do d6 AB2 +CDz = DE2 +CD2 = ECz
vu6ng tai D).
YQy AB2 + CDz

= 4R2

-- ttd+

4