TRAC NGrrrsM s iriem Ghi vdo bdi l&m chi rn{t chir cdi A, B, c hofie D trwfc cau firt lN itfing, cfiu t.. a Trnh d0 dai dopn thing MN... cDI-pHoNc coc.or viNu yrN HuoNG nAN cuAnn os r
Trang 1PHoNG GD&ET viNH yrN oE xrsnn rRA Hgc rcy r NAnn Hec
z0t7 - 2018
nn0N: roAx o
Thdi gian: 9a ph*t fthhng k€ thdi gian giao di)
r TRAC NGrrrsM (s iriem)
Ghi vdo bdi l&m chi rn{t chir cdi A, B, c hofie D trwfc cau firt lN itfing,
cfiu t so tzo sau khi ph6n tich ra thira s6 nguyOn t6 c6 ki5t qui ld:
D 40
Cfiu 2" K6t qu6 tfnh 30 + 3r.( 30 + 3 r + 32) bdng:
cffu 3 c6 bao nhi6u s6 nguyOn t6 c6 hai chir s6 md chfr s6 hdng dcrn vi id i?
C0u 4' Sip x6p cac s6 nguydn a+2;a - 8; a+ 4;a- l0theoihu*iugiani dAntaduqc:
A a+ 2;a- B; a+ 4;a-1A C a+ 2;a+4;a_g; a_ 10
B a+ 4;a+ 2;a- 8; a- 10 D.a-L0; a-8;a+2;a+4
cflu 5 Trdn tia ox l6y hai diOm A, B sao cho oA : 3crn, oB : 7cm D6 ddi doan
tndng AB 1A:
Cffu 5" vE ilucvc bao nhi6u dtrdng rhing cli qua 5 di6m ph6n bigt trong d6 kh6ng c6
3 di6ni ndo thlng hdng tsi6t rang ,r, quu 2 di6m ta v€ dugc
mQt duong thing
I
IL T[r'LUAN (7 di6rn)
{'Aov (1,5 tliim) Thr,rc hi6n c6c phdp tinh sau &dng crich hop t{ n€u c6 the;
OT cgiNH THIIC
a) 12.79 + 79 172 * 79.84
C6u 8 {1,5 itiiim) Tirn s6 t., nhi6n x, bi6t:
a)x-I0:3.{62:4)
CSar 9 (t,5 diiws).
b) (ro.t' :z').zotzo
b) (3.x 20).7t :2.76
Sd hoc sinh kirdi 6 cria mQt truong khi x6p hdng 10, hAng 12, hdng 15 dAu thi6u J
em' Tinl-r so hgc sinh khdi 6 bi€t r6ng s0 hqc sinh trcng khoang t* 300 d6n 400.
faAr' ! t\ {) a ,t:4= t T ^
vdrrr rt-' IA'u utern)- rrcn ila ur v€ hat doan thang (JM: 2cm, oN:5cm Tr€n tia
ci6i cua tia ot 16y di€rn P sao cho oP :4cm" Gqi I la trung c1i6m
cua dopn thing oF.
a) Trnh d0 dai dopn thing MN.
b) Tinh dq dei dopn thing ot" Di6m o co ld trung tlidra cfla dopn tirang IIv{
khoilg? Vi sao?
C6u 11 {{t,5 ttiing"
Tim s0 tU nhidn n sao cho p : (n Z).(n, * n _ 5) ld s6 nguyCn t0.
".stlt
(Gido vi€n coi ki€nt tra kh6ng gidi thich gi th€m)
Trang 2cDI-pHoNc coc.or viNu yrN HuoNG nAN cuAnn os rrurrl rRA HQc ri r .i
NAna Hoc: zotT - 2ot8 rvr6N: roAN o
r prrAnv tnAc Ncrrr$na: T6ng 3 di6m, mdi cau dfng dugo 0,5 di6m.
1 a t 2 te + 't9 L7z - 79.84:79(12+172-94;:79oo
(zu.s':z').zono
W
x - 10 :36 :4.3
x - l0:27 x:27 * l0
x:37
YQy x:37
= ( 2t.5').zo I 70 = 200.1 - 200
\L J ).Lv
L l
0,75
b
0,75
2
a
0,25
0,5
b (3., - 2u).7t :2.76 3.x - 2a :2.76:7s 3.x-24:14
3.x: 14 + 16 3.x:30
x:30:3
VQyx:10
0,25
0,5
J
Gei s6 hgc sinh mOi O te
vi khi x6p hdng 10, hdng t2,himg l5 d6u thi6u 3 em n6n a + 3 chia h6t cho lO, 12 vd 15 Suy ra a + 3 e BC( 10,12,15)
l0 :2.5; 12:22,3; 15 : 3.5
BCNN( 10,12,15; : 22 3.5 : 60
a * 3e { 0O; 120;tB0;240;300;360; a2O; }
* a e {sl ;t t7 ;17 7 ;237 ;297 ;3 57 ; afi ; }
vi300(a{400n6n a:357
Vfy s6 hgc sinh t<trOi O cira trulng ld 357 em
0,25
0r5
0,5
0,25
Su,
d*
,!t
'
Trang 3a VE hinh dring, chinh x6c
TrOn tia Ot c6 OM < ON (2cm< 5cm) n6n di6m M nim gita hai
ili6m O vA N Ta c6:
OM + MN: ON
Me OM :2cm, ON: 5cm n6n 2 + MN: 5
MN:5-2:3cm
0,25
0,5 0,25
b
Vi di6m I ld trung di6m cta doqn th6ng OP n6n
or:oP 22 -!=2"*
LAp lu4n dusc di6m O nim gifia hai di6m M vd I (1)
Me OM :2cm, OI : 2cm n6n OM:OI (l)
Tt ( I ) vd (2) suy ra O li trung di6m cira doqn thing MI
,Ar?5
0,25
0r5
5
Ttr p : (n * 2).(r' * n - 5) suy ran -2vd n2 +
" -S ta uOc c.ia p.
Vi p ld s6 nguy6n t6 n6n n -2:1 hodc ,r' + ,, -5 :l
+ Niiu n -2:1 thi n : 3 Khi d6 p : l (3' + 3 -5) :7 lds6 nguy6n
t6( thOa mdn)
+N6urr'+n-5:l
n'+ n :6
n.(n+1):2.3
Suy ra n:2 Khi d6 p: (2 * 2).1: 0 kh6ng ld s6 nguy6n t6
v4yn:3
0,25
0,25
chfi i,:
- HQc sinh gi6i c6ch kh6c, n6u dirng v6n cho di6m t6i da.
- Hgc sinh kh6ng vE hinh hodc vE hinh sai thi kh6ng chdm bdi hinh .r, ,
.':
,