Đề thi HSG Toán 9 năm 2015 - 2016 phòng GDĐT thị xã Giá Rai - Bạc Liêu

Ho 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 ---

PHONG GD&ET THI XA GIA RAI KV THI CHQN HSG LOP 9 VONG THI # --NANi*nq.2ots-zor6 on cniNn rntlc , . ' *M6nthi:TOAN (G6m 05 trang)

TIUONG OAN CTTAVT

Cflu NQi dung S6 tIi6m

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'lm,*n=89

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

.= (G - r)(..1; -') = o

le-2=o el ' 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 - ln=2 lZr-r=2 lu=2l...l5 lm:2 fr' - 4u :2 lr = 2y -l 1 .Thi:lr u el fn=l l2r-r=l lu=2x'10 Hp phllcrng trinh c6 04 nghiQm z+2Ji l*=z-2Ji f,=t+zJ6 f*=t-2J6 r- i1 .;1 .;1 r 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

rl; _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 r- 'g =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