Chimg minh: a Tri giSc AMOAI ld hinh thoi.
Trang 1Ho vh t6n thi s Chfr ky girlm thi 1:
Sii Ueo danh:.
pHoNG GD&DT THI XA GrA RAr rY rnr CHQN HSG Lop e VONG THJ
ON CTTINH THTIC
(GOm 01 trang)
NAM HQC 20ts - 2016
* Mdn thi: TOAN
* Ngiry thi: 27 1121201.5
* Thoi gian: 150 phrit (Kh6ng k€ thdt gian giao di)
EE
Cffu 1: (5 tli6m)
a) Tim sO tg nhi6n a, biSt o + 10 vd a - 79 liL c6c s6 chinh phucrng
b) Cho: B = a3 + 5a;Y a e Z Chung minh: Bi6
Cdu 2z (5 tli6m)
a) Gi6i phucrng trinh: (z* *r)G = r' + 2
b) Giei hQ phucrng trinh: {@,' - +')(zo -') = 2
lu' -2Y -r =3
Ciu 3: (5 tli6m)
r-Cho bieu thuc: A = "l';3
r-24r -3
,(J; -3) Ji +t -Gi-1-G
a) Rrit ggn bi6u thtc A
b) Tinh gia tri cua bieu thlc A voir - 4 - 2J; .
c) Tim giatrinho nh6t ciua A
C6u4: (5 tli6m)
Cho dulng trdn (O; R), dubng kinh AB = 2R Gqi C ld trung diiSm cira
OA, qua C kA ddy MN vu6ng.g6c v6i OA Ldy di6m K ld m6t diOm tuy y tr6n cung nhb BM, gAi H ld giao di6m crta AK vit MIt{ Chimg minh:
a) Tri giSc AMOAI ld hinh thoi
b) Tf fiac ACTN n6i ti6p dugc
c) Tinh AH AK theo R
d) X6c dinh vi tri oiua di6m K dc (*u + KI{ + Na) dg giStri lcrn nh6t vd-tinh gi6 tri l6n nh6t d6
- nnr
Trang 2-PHONG GD&ET THI XA GIA RAI KV THI CHQN HSG LOP 9 VONG THI
# on cniNn rntlc NANi*nq.2ots-zor6
, ' *M6nthi:TOAN (G6m 05 trang)
TIUONG OAN CTTAVT
1
(5 tli6m)
a)
Ta c6: o + 10 vd a - 79 lil c6c s6 chinh phucrng
[a+10 =m2
DAt: ' { , \Ym,n e N
[a -79 = n' avnz -n'=89
o(*-")(*+n) =3e
Md: rn-n<rn+n
lm-n=l
L
( -lrn,:4)
^)
- )n=44
t
=a+I0=452
<3a=2015
0,5d
0,25d
0,25d.
0,25d 0,25d
0,5d
0,25d 0,25d
b)
Md:(a - r)o(a + r):O $ich cria 3 so nguyOn li6n titip)
Yd,:6ai6
= (, - 1)r(, *,) + 6ai6;Y a e z
YAry Bi6;YaeZ
Ta c6:
B=a3+5a
=(o'-a)+6a
= (r-l),(0+1)+64
0,75d
0,5d
0,25d
0,25d, 0,5d
6,zsa
2
(5 rli6m)
a) DK: r>0
Ta c6: (z* *r)G = r' + 2
o *J-,(l; -r)-(J; - z)
= o
0,25d
0,5d
Trang 3.= (G - r)( 1; -') = o
le-2=o
lrlr-1=0
fr=l el
l*=4
VQy: S = {r;+}
0,5d
0,5d
0,5d
0,25d
b)
[t'-+r)(za-*)=z lu'-2v-r=3
qa)(za -,) = 2 or)*(rr-,)=3
'-4a=*
y-tr=n
lm,.n = 2
Ta c6 hQ phucrng trinh:] .
lrn+n = J
rn=l
n=2 m=2 n=l
f*:1 - fy'-4y=l lr=2y-l
1 Thi: {u u el
lm:2 fr' - 4u :2 lr = 2y -l
1 Thi:lr u el
Hp phllcrng trinh c6 04 nghiQm
z+2Ji l*=z-2Ji f,=t+zJ6 f*=t-2J6
2+tl5 lu =2-.lS lu =2+tl6 lu =2-tl6
Ta c6:
(
)v
12
I
t
It,,
L(,,
D6t:
<=
v6i
v6i
vOy:
!*=
[u=
0,25d
0,25d
0,25d
0,5d
0,5d
0,5d
0,25d
3
,- -.7
(5 dreml
a) DK:z>0;r+9
t Z(Jr-t' ' I f\f -J \
r ct u\J .n -
-* -zJ* -z J* *r) 5
0,25d
Trang 4rl; _3 2(G -,) Ji +t
:@;ry61 G; G=
_ "J " - t - z(J " - t)' -(Ji z)(Ji i
(.6.r)(C-:)
*Ji-h+sJ;-z+
=@
_ (".s)(G-:)
-(.'6.r)(c-:)
, r+8
Y?y:A= -r/r+1
0,25d
0,25d
0,5d
0,5d
0,25d
b)
Ta
<)
e
=
co
trl
=q-zJ'
6-,)'
.6 -r
r-zJt +s
co: lx
* =(\
J;=
I
A- -4
6-t*t
=+Ji- z
0,5d
0,25d 0,25C,
0,25d 0,25d
c)
r+8
laCO: )=7
.'.lr +t
o
= /,
-l+-J r,/r + I
=1.lr+l+ -2
tlr +l
Ap dpng bdt dhngthric C6si cho 2 sO duong rg
Vz + l: Ta duoc:
Vr+1
A> 2
Vay: Mi,nA- 4 o J* *l= +- e r - 4
tlr +l
0,25d
0,25d
0,25d,
0,25d
0,5d
Trang 5(s tli6m)
0,25d
a)
Ta c6: AB L MI'{ tai C (gt)
= CM = CN = U!
(ducrng kinh vd d6y cung)
2\e
Mir:CA=CO=94 7 let)
= AMOIV la hinh binh hdnh (tir gi6c c6 2 ducmg ch6o c6t nhau tpi
trung di6m m5i ducrng)
C6:OA L MI{ tpi C (gt)
= AMON li hinh thoi (hinh binh henh c6 2 dudns ch6o vu6ng g6c)
0,25d
0,5d
0,25d
b)
XetBCHK co:
BCH = 90' (MI'{ L AB t?i O
aiu = sr'Ji nQi ti6p chin nta (O))
= BCH + BKH = l80o
= BCHK nOi ti6p dudne trdn duln s,kinh BH
0,25d 0,25d 0,25d 0.25d
c)
Xdt2Avu6ng,4 CH vitAKB co :
BAK chung
= AvuOngACH cn Avu6ngAKB
AH AC
AB AK
= AH.AK = AB.AC
22
= AH.AK 2R.! = R'
2
0,25d 0,25d
0,25d
Trang 6Ta c6: LOAM; LOAI{ l}r c5c tam gi6c d6u
= MOI'{ = l20o
- fritt = ffElv = +ffoN = 600 (g6c nQi ti5p vd g6c d tAm cirng
Xet LMBI{ co:
I
BM = Blr (tinh ch6t ducrng trung tryc) |
d) | Ct rrre *inh tucrne yly**
= NME + EMB = BMK + EMB = 600
= NME = BMK
= LNME = LBMK(g-r-g)
= NE = BK (2 canhtucrng ug)
=KM+KB=KE+EI{=KN
Md: Kl[ < AB (ducrng kinh ld ddy cung lcrn nh6t)
= KM + KB + KI'{ < AB + AB = 2AB = 4R
Vay: ttar(Ntw + KN + Na) = 4R e l{K di qua O
0,25d
0,25d 0,25d
0,25d,
0,25d
e K ld di6m chinh sitlacta MB
-