TRIIONG r.Tnpr I,t xoAY
Ndm hgc 20ll-20X2
nn cuimr rrruc
Cfiu I: i Giei phucrng trinh :
2.Cha p,Q>I,p,qeN
Bn rnr KrrAo sAr cnAr r,uot-rtG,LAN rrl:,.
nn0x : ToAN rr- rcror b
Thli gian: 180 phrfrt (kh6ng te tnUi gian ph{t tlii)
sin 2x -.6sin x - 2 cosx + 6
sin{x +
f)
CMR I pq+C|+C] =C'o*n
-0
CAu TI:
1 .Tim m d6 phugng trinh: xo - 2mx' + 2m -1 = 0 c6 bOn nghiQm phAn biQt 10p
thanh mQt c6p sO cQng.
Z.Cho t?p hqg M g6m 5 do4n th6ng c6 d0 dei len lugt lp 1cm,3cm,5cm,7cm ,9cm.Lhy ngSu nhi6n ba dopn tt @p M.Tinh x5c su6t AC Ua doqn 15y ra co th6 tao thanh mQt tam giitc
.l AAN
Qiu III: Cho tam gi6c ABC c6 ba g6c 2,,it,e theo thri tg l$p thhh mQt cAp s6 nhdn c6 c6ng bOi q:2.
i.Tinh c6c goc ctra tam giac ABC
2.Ki hiQu BC = a,AC =b,AB = c Tinh gi6 tr! cira bi6u thric
".1 r 2
M=a2(-*,+i)
b'c'bc!
Ciu IV: Cho hinh chop S.ABCD c6 d6y le hinh vu6ng cAnh a TrOn canh
aeldy Ai6m M voi AM:x (0<x<a) ,@; lir mat ptring"q.ru Vf ui rong song vdi mp(SAD) cit SB,SC,CD ldn lucrt tai N,P,Q
2.cMR giao di6m I ctra MN vi PQ iuon thuQc mQt duong thing Co ainn mi
M ch4y tr6n AB
3.Bi;5t SA:a , MN L Me TtnhdiQn tfch tir gi6c MNPQ theo a vd x.Tim x d6 diQn tich tir gi6c MI{PQ U** T
CSu V:Cho da gi5c d€u A.A2 A, (n> 3,ne N) nQi ti6p trong duong
trdn(O).Bi6t sd duong ch6o cria da gi6c bing 2O.Tfnh sO trintr chfi nhpt c6 c6c dinh ld 4 trong n di6m 41,A2, A,,
Het (CAn np coi thi khing girti thich gi thhm)
Trang 2oAp AN THANG DrEM vr0x roAn xu6l-n ,:, .: i
Lop 11 r,.A.x nr ' :: '": '':'
Cflu I
(2d) l.(lilGiAi pt
n
EK: x*- -+kn(keZ)
6
pt<+ sin2x J3 sinx - 2'cos.tr + .fr = 0
l
F -'
<+ (sinx - 1)(2cosx - Vl; = g
F
lSlnI=l
I
.Jl
"13
L2
r-lr=" +k2tr
t2
c>l
td
lx=t-1 +k2n
L6
TL
, :
t+ k21r IIoQC x =
POi ctii6u OI{ ta duqc nghigm cua pt ld
0,25
0,25
0,25
0,25
z.(rd) cM
BDVT pq + Ctr.i;
-::.^#^.d\
: pq + p(p -r) * q(q -l)
22
YP:C|.n _-._& ;- q)t* *
_- G- ; il b ; A :,
Vi
Zt(p + q -z)l
+y pq + C2, i*c]:c\*n 1Cj
0,25
0,25
0,25
0,25
CiUII
(2d) 1.(1d) Tirym
l_2
-2m+l)=0*L;, -1-l
=2m-I
Trang 3D€ptco4nghigmpbtaph6ic6 l, e:<m+I
+, N5u m>l pt c6 4 nghi€m pb ld: .
x., = -^l2m-l,xz = -1,rs = 1,xa ,=.12m-l c6c nghiQm ndy lap thanh
osc khi trr +.tr3 - Zxr e -J2*-I +l= -2 e Jrm1= 3 <+ m =5
1
*, '2 l m <l ptco 4 nghi€m pb ld x, - -l,xz = -Jrm1,*r = J2i:l,xo =l
C
C6cnghiQmndyldcsckhi ,yi +x3 =2*? '9 e3^tZm-1=1 e m=:
\
KL m = 5,m: j- t/mycbt
'9
[,25
0,25
0,25
CAU
rlr(a
2(1al) Tfnh XS,r
S6'crlctrt61, 3 dogn &nng tu 5 do4n thAhg criart{p Nd la C; = 10 -+ JOI = tO 0,25 GAi A ta di6n i6 "3 dogn thdirg l6y ra tao thanh tarar gi6c "
Ta c6 I = f1l;5;7), (3;7;9), (5 ;V ;9)\-+]O, | = f 015
lei,l 3
1.(1d) Tfnh 3 g6c cfra tam giic
,AAn
Theo gid thi6t ta c6 B = 2 A,C = 4 A 005
Vi l+ B+c = tr +J A= n + A='o ^B =o'o ^C -1/L
7' 7' 7
015
(trong d6 R 1&b6n kinh ducmg trdn
7777
Ta co y =l a(b +
") l' *.o dinh h? sin Ta co
L bc l'
a = ZRsinlL.b :2Rsin'" .c =
ngo?r ti6p MBC)
, a(b+c)
laco
4pz 6io?L ,-rinl1x*[ 2sinlsin ?o
"oro
w-m:'
0r5
015
Trang 4YI
'(3d)
r\lur r$ grac $rl\rv Ia ninh gi?
l{4rr1smy
Ta c6
J Cs,<ry a(ABCD) = AD + Me l AD L(a)n(ABCD)=MQ
l{")rrtsdn)
16A8) n (SAD) = SA
= MN lt SA
f(o)n(,SlB) =Ivfr,{
MQrAii ffi-ADi/itc
-Do d6 (q) n(^SBC) = NF,/t Me// BC :
a/a t\
-:- - +.^ T
0'5
I
I 0,5
i
:\ru, \nau ursur r sua tyll\ va rU nam trOn dt c0 dinh
Do ABCD ld hinh vuOn
ft;i;jrJi1"1l#f,?i;ffif*) va (sDC) n€n giao tuvtin crra chring rd
0'5
iaco:lwN
^f9= I -+ I e MN c(SAB),] e Pe c (SCD) i suy ra I ld di6m chung cira 2mp (sAB) va (scDfDo ao I a co il* 0r5
Trang 53(1d) Tfnh diQn tich ttfr gi6c-
T6 trufing: Nguy6nthi HPnh
viMN//SAtheo tarets
"a W =
# =T + MN = a - x
NP/lBc -#=# =#-+NP :AM =x
MQ:a
Do MN IMQ suy ra tir gi6c MNPQ la hinh thang vudng
- (NP + MQ)MN (x + a)(a - x)
c - 3o' r-,(x+ a)(a - x.)
-3o' o o' - " =3o' o * =!
Th* gt t" .6 tO O,"ttttg ch6o cia da gi6c ililu ln tC: - n 70
o'l " )r.(n-Z)t -n=20.: ry.@:l) 2 -n=2o<:'nt
ttuimg trirn li ttulng ch6o lfn Thi tla gi6c tI6 cho cd 4 iludng ch6o lfn
.nndi ninn chir nhflt
"O "e dinh li 4 trong 8 tli6m 4,Ar,'.''4, c6 cfc tlulng ch6o li hai ilulng ch6o lfn.Ngug'c l4i, m6i c{p itulng.ch6o lfn cho
ta mQi hinh chfr nhflt, Vly s6 hinh ch* nhgt phii tim bing s6 c[p iludng
ch6o lt6'n lh Cl :6.
-3n-40=0el
L n = -5(L)
Vinh tulng ; l2ll2l20Lt
GV ra tI6 NguySn Vlinh 'l'ri
' Tr''
lV- i'u'