NAvr Hec zot6- 2ot7 vrON THr: ToAN Hec 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 s
Trang 1NAvr Hec zot6- 2ot7 vrON THr: ToAN Hec ( 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 <l-uOc thting nh6t trong todn hQi tl6ng ch6m thi
- 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
UBND TINH THAI NGUYEN
so GrAo pvc vA pAo r4.o
II Dip rin vi thang tli6m
HIIONG NAN CHAM THI TUYEN SINH VAO LOP 10 THPT
n
I
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:
Hdm s6 , =(J1 -Ji)*+S ddng bitin tren tR ,
Vi a: Jl-Jlro
Cho x : 0 ta c6 y :3 suy ra toa dQ giao diiSm cria (d) v6i tryc tung ld
A(0;3)
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Ciu 2 Kh6ng dung miry tinh cAm
thtrc: A - (z +rJr)'- f&8 .
Gidi:
Ta c6: e-(z+sJz)'-.,D88 -* +2.2.3,12+1l,li1z -,!1aat
=4+lzJr+18-i2J,
-11
0'5 0r25 0,25 Cffu 3
chobi6u ,no",r-( G-!.:L ).(J Gl')
,,-[;;5*G-/[m
-F)''-x)0,x*4 Hay rut ggn B vd tinh gi6 trf cta B khi x - 3 + .6.
Gi,rti:
ra ruvv'"-[cG5-Gi)t@] c6:' =( *Y.i-l [v;'tr-('tr- zXv;.2)l
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Trang 2vdi r-3+ 6= (Jr.,)'= J; -J-z*t:+.8 -J|+t-1 =J,
Ciu 4
Xric tlinh c6c hQ s6 a vd b, bilth6 phuong trinh
c6 nghiQm (*;y) -(z;-t).
Gidi:
th6 x=2, y:-l vdo he ta c6:
+ Vdi a:l, b: -2 ta c6 hQ
Vfly de h0 c6 nghiQm (x,'
Vi he c6 nghiQm (2,-l) n€n
lzo+b1-r1-4 lzo-b-4
I a-l
={
lb 2
l*-2y'
lr.-,
1: (2;-l)
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Ciu 5 Kh6ng dung mdy tfnh cAm tay, hay gi6i pnuong trintL
x2 +6x-2016:0
Gidi:
Ta c6 a:1, b:6 (b':3), c:-2016
L = 32 - 1.(-2016) = 2o2s> 0,l[ = 45
Phuong trinh c6 hai nghidm ld: x, = -3 + 45 = 42;xz = -J * 45 - -48
Ciu 6
Cho phucrng trinh x' -zmx *(*' - +):O 1t;, z ld tham 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 = m' = "'* -4
Ma xf +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
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2
Trang 3Khdng 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:
Ta c6 bi6n cl6i sau: sin 380 = cos52o ,sin 88' = cos 20
Vdi 0 <d <900,n6u acdnglonthi cosa cdngnh6vd cosa<l
ndn 0<cos55'< cos52o <cos2Oo <cos20 <1
N6u 450 < P <900 thi tanp 21 = tan480 > I
Do d6 ta sEp xiip theo thri tU ting dAn nhu sau:
cos 55', sin 38", cos 20', sin88o, tan 480
Cdu 7
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CAU 8
Chotam gi6c ABC vudng tqi A,c6 sin B -:.HEy tfnh citctisri luqng
3
giric cria goc C C
Gidi: (Kh6ng cho diiim hinh vd)
Ta c6:
llA
sin,B=1=)CosC=-^^
JJ
ACIAC2IACzlACl
- BC 3- BC2 g- AB'- 8 - AB 2J,
I
haycotg , =-|-,suy 2J2, ra: tanC =ZJi
AB
',=+
AC
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Ciu 9 Cho dudmg trdn tdm O vi mQt di€:m AnAm ngoii duong trdn Kd 2
tiiip tuytin AB, AC voi ducrng tdn (B,C ld 2 n}p di6m) Qua C kd mQt
duong tlrang song song vu OB, cfut O,l t1i H Chung minh rang th gec
ABOC nQi ti6p duo c trong mQt duong tdn vd f/li trfc t6m cua tam gic
ABC
Grrii.' Flinh vE :
Xdt tu gdc ABOC c6:
trEd =frd =eoo (Theo
tinh ch6t cta ti6p tuyiSn).
Suy ra tu gi6c ABOC nQi
ti6p du-o c tong mQt ducrng
tdn
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B
a
J
Trang 4lca tloB
loB L AB
Trong tarn gircABC c6: {':,: 11=H h tuc tam cua tam gi6c ABC
IAH L BC
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Ciu 10 Cho tt gi6cABCD nQi ti6p trong ducrng trdn(O;R),c6 hai dudmg
ch6o vu6n g g6c vdi nhau vd cit nhau t4i L
a) Chrmg minh ring: IA.DC - ID.AB;
b) 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 D
cung BQ
Suy ra: NAB diing d4ng voi NDC do
=fi +IADC=ID.AB
rc
b) Ke ducrng ktuh CE cta duong tdn (O)
Ta c6 ili =ide =90'(g6c nOi ti6p chan duong kfnh EC)
Suy ' ra {n:"!* IAC LAE AE t tBD+ ABDE le hinh thang cdn (hinh thang
nQi titip duong trdn)+ AB = DE
Do d6 AB2 +CDz = DE2 +CD2 = ECz =(zn)' =4R,(DoADEC
vu6ng tai D)
YQy AB2 + CDz = 4R2
.IA
oo ta co
-ID
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ttd+
4