PHoNG GrAo DUC va oAo rno olEN csAuoE xrBivr rRA rrEN rHUc rRudc rY rHr vAo r0p t0 THpr NAnn Hec zots-20r6 MOn thi: TOAN Thdi gian ldm bdi 120 phrit CAu 13,0 didm.
Trang 1PHoNG GrAo DUC va oAo rno olEN csAu
oE xrBivr rRA rrEN rHUc rRudc rY rHr vAo r0p t0 THpr
NAnn Hec zots-20r6 MOn thi: TOAN
Thdi gian ldm bdi 120 phrit
CAu 1(3,0 didm) Cho bidu thftc .q
a) Tim didu kiOn cl&ra xdd, ,qc6
b) Tinh giStrt cria bidu thtc,q khi x = 9
c) Tim tdt cit cdc gt6 tri cfia x dd, ,q <0
Cau 2 (I ,5 didm)
Cho phuong trinh bAc hai dn *: x' - x * m = 0
a) Gi6i phuong trinh v6i m = -6
b) Tim m dd phuong trinh c6 hai nghiOm phAn biOt th6a m5n: lx,-xrl=2
CAu 3 (1,5 didm)
Hoc sinh lcrp 9B cfia mot trudng THCS quy0n g6p trng h6 hoc sinh nghbo huyOn Tuong Duong Ndu m6i em quyOn g6p duoc 3 quydn v& thi tdng
sd v6 quyOn g6p duoc wgt qu6 mrlc du dinh ld 12 quydn Ndu m6i em quyOn
g6p du-o c 2 quydn v& thi tdng sd vO quy0n g6p duoc it hon mrlc du dinh1d,22 quydn H6i lorp 9B c6 bao nhiOu hoc sinh vd sd quydn v& du dinh quyOn g6p ld
bao nhiOu?
Qi^ !!3,5 didm)
cho tam gi6c vudng cAB nQi tidp duong trdn tdm o(a= 900;cB<cA).Tia phAn gi6c c:iua g6c C c6t dudng trdn tai didm rhrl hai le D, CD c6t AB rai E .
a) Chirng minh: frD=frD;
b) Chrrng minh DB2 = DC.DE ;
c) Tron tia cB la'y didm M sao cho CM = CA Tt M k6 tia Mx//cA cit tia
cD tai N, AN c6t duong trdn (o) r4i F chfng mi4h 3 didm o,c, F thing hdng;
d) Goi I td giao didm cria BD vI MN Ctrung minh AI h tidp tuydn cira
duong trbn tAm O
Qu 5(0,5 didm)
Cho a,b,c le dO dAi 3 c4nh ctta mdt tam gi6c vd, a.b.c =t .
o+b-c b+c-a c-fa-b
Hdt
Trang 2PHoNG GIAo DUC vA DAo rAo otEN cHAu
HUoNG tAN cnAu oi rrdrvr rnn xrfN THUc rRuoc xi rHl vAo lop l0 THPT
MOn thi: TOAN
1,0
0,5
0,5
0,5
/l-n- J*,;J; _) d;;;j
2 (J; - 4.di +2)
L = 7 ,' ,1 = 7- =
"le -2
)
1
1.c
t:1
v, - r
fl=- - 1U
^lx -2
fJi-r'o [Ji-r'o
lJx-2<0 lJr'-2>0 timduoc: 7<x<4
2.a rm=-6, phuong trinh tr&thdnh : x2 -x-6=0; 0,25
0,25
+ Tinh duoc L=25
0,25
0,25
2.b
Dd phuong trinh c6 hai nghiO
khi d6 PT c6 hai nshiOm
m phAn bi0t thi A =1- 4m> 0 o rr.!
A
phAn biot th6a mdn: {x'
lxt.X2 = m
= (" -*r)' =(x, * xr)t'4x,xr:l-4nt =lt, - ,.1=,ltJm=2, tim duoc m:-0,75
3.
+ tr9i;-18 so hoc sinh cria l6p 98,
y ld so quydn v& du dinh quy0n g6p( x;y ld' c6c sd nguy€n duong) + Ndu m6i em g6p 3 quydn v6 thi sd vd g6p duoc cua ldp ld 3x
g_6p- dugg
"qqe lOp Ii, ?r
0,5
0,5
; so hoc sinh l6p 98 le 34 em, sd luong v& du dinh quyOn g6p ld 90 quydn.
l;:i4
€<
lv=90
0,5
,': " -" " '- ''-"j'1 "'-'-"'
DB DD
- 'L e DBz = DC.DE
DQ DB
) -^9W +cj!("c:s,c) vd M-N/C-A
= e vw = eAN = lv = CF la dudng k(nh
d) LCAD = LCMD (c.g.c) = DA = DM,
6)=58 =DA = DB,=DB = DM = L,DBM cdn
- 6rfu * rEfu = eoo = BMD * 6it = 6it * i6it
= 6tfu = 6it = LMDI can(dinh D) = DI = DM
=4 didm A,B,M,I ndm trOn dudng trdn dudng kinh BI
=6h -6fu =p=- ll lol =_AI l+-tisp_lsyen g_9r d_{gps ggt,t?$ o,
Hinh v6 dfns
I
DI=DM=DA=DB
0_f 0-,5 . 0,5
0,5 0,5
0,5
0.5
Trang 3_- r | 4
Ta c6 x;y ld,hai sd duong thi :-.- ' > L t
t\;+b-c-i*c-ac+a-b' 'Qbcabc
1 1 - 1 r- 1 >-ab+bc+ca; dA'u "=" xdYrakhi a=b c'
* Chrt y: - Hoc sinlt gidi cdch khdc dfing cho didm t,i da
-
- HQc shhLhAng vd hinh kh1rtg chd'm didm cdu 4'