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2
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12. 7
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=
=
da-3,ffiLLnv-ffi
100
h (3)
fos (3)
r (g(3))
f (10)
102 =
aou 9
oln 82
LLflY B-1
82 + 3B-1 _
82 + 3B-1 -
oln g (3) = 32 +1
"'
g (3) = 10
L: :,1 [: :,]
1 [-t -s.l
oetalo 3l
[: ;]
+{
t[;'
[: :]
.[;
:]
rro e
]
L' -z)
["', 1 a,r]
l^r, 'rr)
I
ornloyrri
rs.]
lo1
1 [-t_t
-3*oLo
tl l
?tz =
ln rfi er ru aout#in'lr,lsrrT rui

13. r6rasJ nrf,ngrasr{ 1 22s eirrinisrnr:'[arfrsru
aou I
oQtv
n1nugt 114 Z
Yrul al
s$aartYi I
k-2
k=3
k=4
=64
1r/ ,i
-.1
I a &
eto.lrunuu z tu:rj ufrflr$
nu'ir r = l=l
frae
[rn3 e
a.t &
O',11t1{ Z
.'. Z
=0
: r(cosO * isin0)
= 64(cos0 + isin0)
tl r !
*r .l
?lrdna$n 2 gTa.,:n1Tnaor1nfr
6tsl:ts zk
k=1
6 ta.,: Z
V;(
"or2kr*o
+ isinSl"-fo)
n
"-)
1r2r"" n
W(cos
2(1)n+o
+ isin
2(1)ru+o)
6
+lsln
6 )
z(
"o"L
+isinr) = ,( I.{,.]
3 3) [2 2 )
z1
/
W(cos
2(2)n+o
+ isinz(z)n+o)
66)
z(
"o"?n
+ isin'"]
t 3 3)
/ .6.)
2l -! + = -1+ ,.6i
t-2 2)
W(cos
2(3)n+o
+ isin K"+o)
6
+lsrn
6 )
z(cosn + isinru)
-2
?l*(cos
2@)T*o
+ i sin
z(+)l + o)
66)
z(
"o"!n
+ i sin
o"')
3 3)
/
"6.) . t:2l -! - -1-"6i
t2 2)
z2=
zg=
zg=
z4=
:
zt = r*16
z2
la rfr s rr a a ul#intun er ru i

14. ranEJ Frrflsrrfran{ 1 226 ei'r ri'n i rr n r :'[ a rfi s e,r
W(cos
2(5)zu+o
+ isin K)n+o)
6
+rsln
6 )
,(
"o"-sn
+ i sin
u")
. 3 3)
,( r-s,l : r-",8
[2 2)
w(cos
2(6)rc + o + i sin
z(6)ru + o)
66)
z(coszn + isin2ru)
2
+ l-rl + l-,1 + l,l + lrl
+1+1+2 = I
z5
.'. Z6 :
:
:
lorl : l,l + l-,1
= 1+1+2
k:5
k:6
6
14'l Ik-1
Tra 7 nou 2
tx-l01n lim rc* ,- |
x-)0[ r/x +4 -2)
limc+ lim
-
r+0 x-)0r/x +4 -2
ffi+2lim
-
x
*50
^l
**+ -2 ffi +2
c+
c
a
oa
c+
lim
x-)0
-6X
+4 = 6
c=2
x+ 4-4
ln rfi s sr a a ut#intr,rn m ru i

15. rans ertflsrgfran{ 1
227 eir fini gr n'l :'t a tfi et eJ
etou I
x iA j
1^l UYI U T t? TUYI LLT.I t.] 1
2 (2
- 7r*2d* + I - J-
-2d^
I
o l.d )
: [+F]
+[L+F])
: T.[ L:])
16 B 24I-
T
333
r?a s
r?o g
=8
9tou 48
9
o
(x,y)
(x,y)
(3 , 18)
(12 , 9)
@
@
a"t
0 9t9t9rq
AJ
aoaoq
o
n1il}b91 27+
21+
30 -+
LLny @
LLflU @
rYirrTu +a
3x+y
x+y :
x+2y :
ttti:vuuflalnr: O
uuti':ruu6[un1T @
eir c ri'tidqer
I
T{U't1
qoqru (x,y) c
(0 ,27)
(3 , 18)
(12 , 9)
(30 , 0)
54
48
66
120
ln ufi s il a a ?t'[#in'[nner al f,

16. r6rnE a$srrrran{ 1 228 ei'r rin?gr nr :'ta 16 s ar
ly
?lo 10 aou 108
g d- A A
fl%ao}svr 1 rfionilTTgtn1Trila: 3 yr::n o1n 4 y,t:Tgt
.,iruruifi = C+,g
rYt rrt fi z o1n y{rrn g nttofd'lui'lurlrur*urn r6onfinl-n:v{r:nnr 1 nr{
'iruruifr = Ce,r XCs,r XGs,r
^aAilrv- a &
.'. 'irurui3m{1oi'iurdaner-roraqjoirryl::nfiu = cc,e X cs,r X cs,r X ce,r
= toe if
sraufiz
ila 1 oou ila z n. Bn rrn& s. fio
o1n A-{"eRl/x2 Tx+10
x2 7x + 10
(x-2) (x-5)
H
A = (2,5)
ria n gn o1n g = {x€t / x nr:2b uns st fire:*ru6orvirfiu}
-&er.lilu AnB = {x€tlz<x(5 unrnl:2sunrs1 firer:*rn6ormfru)=Q
A
tilo.:ornx€luflr 2(x(5
x*3 rlt:1r 3141:2s rnfiorerr* 1 unr 3 n1T s1 n{qr-r
x* 4 ry{:1s 4 141: Z5 rndorerr* 1 ttns 4 il1T St rilfiorqs g
fa s fio o1n g = {xct / qr-rnr:iailil1nra{ x rns o 6o z}
-&rt
otuu Anc = {x€ t I z <x (S uoyqr-lnr:jrrururnloit x rtnr 6 6o z]
= {+) +A
A
tflo.:otnx€luns2(x(5
x*3 [y{:'13 t4.T.rJ. Ta{ 3 un; O 6o g
x = 4 [?{T'li 14.T.il. ljoil 4 Unv O 6O Z
ln ufr sr N 6r o ilt#intr,ra ?1 il i

17. r6rner nrf,nerran{ 1
229 rtrrinirrnr:-[n rfrgn
l)'/
%a2
9L/
sa3
lv
%a4aou
2
detA A =
Q1n det A
.'. 5a-3
a
6
a+1 2 a+1
&
- gcu1jl.[
+ 4a* 3l -b'z
n.1
a2
3
'2
tu
+
fl
lo^
5a
7
7
2
.11J
11
+ a +2a* 6l
&
niln{ - nculuq, qr
Z= =
40 - (-2)
7
Z =6
aou #a g 7l
rirHt,ter t(4)= (4) LLnvf =(5) =5LLnrf -(6)=6
!- - -" ri'fuo'rn A+A lijufi.rri'd'urad.:qi oHdr0'11*?u1 l.tnTl,[Qln A+A LUl+l l.]nTuulti
= 7 x q x q x L x I x I x I x E
A-+o@@@@@@@
X Z X T
@@
7!
ilat aou #as y=
"6*-2"[39"/ &
H't o q a q fl a { ? { n n il n .t 6[8.: Tq u n'] T Llti;y u u 6ril nl Tq
^2+y2 - 4-O
(*-5)'+y2 = e-@
(*-s)'+^2 - 5
- 10x +25 - 5
5
@-o
'[ a rfi g er a a r+t#in'[r,r or er ar i

18. rcrner nrfisroT asr{ 1 230 eirrinirrnr:'tnrfrsru
ttYlil x
4+y'
v
L p.iru qooi'ollo.t?.tnnurionol6o e, 0) =q
Ft?'le.Juu (m) 10.1 L
= -2 tuO
=4
=0
(xr,Yr )
X=5
6[iln17 Y -Yt
y-0
v
= tan60o
=rG
m(x-xr)
"6t* -2)
"[g* -2-rli
ly
?lA5 aau ila Z 7x' + lily' = 112
6[iln']Tnr;rTun1 *2 + 12y = o
^2
_ -12y
.'. 4C = -12
C - -3
ArJ rruu dil nr: ?'tr: rlunr
do *2 = 4cy
C:3
?=4
u fi o .t a'l nIo vr riri r H uotri' c r fl u:y u y yr 1 .: :s u'i 1 .r
n
o u o q u n y o qlill n-fl
gY..:riu c)0 .'. c = 3
si'.,:riuoeTillrinto.,:r.:3 (t .,0) : (t s,o)
unsarurerro{r.ri (* G + r)o) - (r 4,0)
a2 - b2+c
16
b2
la ufi s ru a a ul#intuerer au i
a
aa
a
aa
= b2+9
7
01n

19. rerns errfiodran{ 1 231 iirrinirrnr:'tarfrsil
froe
-A
6tr,In1:?07
*2 u2
J-t : 0
16 7
7x2 +16y2 - 112
gtou ilal m = 2.5
nilnlrlarr{oflunr (x - z)2 -(y -1)2 = 1
4
olncrilnlTri'rrfu 6o y = + 2(x- 2) +1
^J
tl.to.,lotn L lilqlortaul r ofTu nl unsn?'r rufur#uri'rri'u uvirrYu
e.. &
ol.,rriu m>2 Hto m<-2
ln rfr e, il a a %'[#in'Lr,rn er eu i
A
9t0 2 LLny -2

20. r6las ntf,nerrasr{ 1 232 eiT #nirrnr:'[nrfisau
lv
nau so 1
Ton ri
vvel
9l',11{1,[
(-@, 2l
l)/
ra7
+3x -2
-2
z+
ttflnri'rrj:ynouro(l *3 - 3x2
{:)
','[9-lL*-J
'[:)
'[:)
IX
0
0
-3
2
3
-2
014il'lutfiaq
t3)r7o a nau ila z
Ton ri rn("' - r)- rn(x + 1)
,n[*' -
'IL x+1J
,n(x-1Xx+t )
x+1
ln(x - 1)
.'. x-1
^2-x-o
(x-3Xx +2)
x=3 , -2
x = -2 rfio.,ro'ln x 2 1
.'. x=3
Uns x+1 q
'[ n rfi s er a a u'[#in'[uor tr er i(u

21. rcrds afisrorasr{ 1 233 etr rin irr nr ;-[n rfi g a,r
Ntv
IN2
=l-1,t,1;;1,.1;_ll,l-r zl
= (-z-r-rl) T -d-r) J* (-z-r-rl) [
= -l-sJ-[
ornTonri 6+(u.v) = "lu'vl
fro e aou ilaz I
7
rirHuo A = arccos
cosA =
ila io nou fra g 'Jn
a1n u = 2l-j*[LLnv V = i-j-zk
U'V = 2+1+2-5
2
Jt
2
Jt
q,& Tt t 2lo.,tul* sin- sinf2arccos
T )
.77
sin- x sin2A
3
= sinl x 2sinA cosA
3
t- t-
r/g A r/g 2
^, G-/-,t:. j
2
"lt "lt
=97
6+5 = t
11 = .Jna
.'.a=L t-
4tt
= .Jn
uXV =
ijRl
2 -1 ,|l
1-1 2l
ln ufr sJ ar a a ul#in'[r,rn rr e.r i

22. r6ras arfisrnrasr{ 'l 234 itrrin?r'rnr:-tn rfrHil
9v
?to 11
tv
aou ?to
fd
a1n Lam u
A
9t0 nlTn'l
1-x
99x
117x
X
- o i8
a,/douA
O,}|nTil01*1,[A?l0.1n1quLTlJ'lFltUgl f -X , a1 =X
a,
AlnfTAT S -
|
', 1-r
x = 18
99
1B - 18x
18
2
13
ila tz aou ila + 6{iln1:?ro0r#u#arfraT6.rlr*nr 1o , t; 6o zy + sx+ 2= 0
o nn !T'lT'ly(u
dy
d-
d
dx
_h
"(1-5x)
2
: * --Z(1-5x)-1r :;(1-5x) -t
25
d-
rllouunt,l x=o tu
tr
1) = -',2
2+(1 -s*)
d25
d_
(1 - 5x) _ -;(1 - 5x)
X
j
d;
7d
(,- s*)t:;(,' -s*)-
d'y
;F
I
4(1- 5x) 2
nn LilT'ly(u
ar 9,/ f q.z
H't9t?'liltut6[1,[[9t.] rt[ 19t
(0,
.'. Ft?'lrufur#uki'.: il qgl (0,
Bn LvrTlr
f qiotfit.:fi x:o lfio.taln
O H1(o)_1
@ (o) =
*50
_E
2
@
@
dy
dx
@
la 16 s ar a a r,rt#intnn m er i
1-5x

23. rilau nrfisrcrran{ 1 23s airrinisrnr:'tn16sru
@ figr t?lTry
nr:nfr.t6[iln1T T0.,]l#u#lrin il nq (0, 1)
O oqhiru (xr,yr) = 1o#'u#n (0, 1)
@ n?1rud'ur#u#ruein (m) = qo#rurin (0, 1)q'
@ freJnlT y-yt-m(x-xr)
tr
y 1 _ -t(* 0)
2
2y+5x-2 - 0
9" - 4 t e./ v eA
?ro3 f e,ra16[oqo6[rJT{niiri x:1
,1,2
fio Lilrlry
r rfilufr.,rri-d'ueirufiru rfro tt(*)
4x3 -12x2 + Bx
*(*-zX*-1)
m
o0@'o2@r rilufi.rri'd'uni'rrfiiluurir.,r (0 , 1) v(2, *)
tv
?ro 13 aou
o t{o Ll^lT'ly
a'ln f(x) : x4 - 4x3 + 4x2 + 1
rt(*) -4x3 -12x2 +gx
rareir?nqorTou ufi'arun1: tt(") - o
4x3 -12x2 + 8x - o
"(+*' - 12x* 8) _ o
*("'-3x*2) _ o
x(*-zX"-1) - o
X-0
@
ln rfr s e,r a o r,r1#in'[r,ln rr er i

24. rans afisretrasr{ t 236 iiT rlnigr nr :'tn 16 s e,r
@ en Lwr'lv
f"(*) _
*4x3-12x2+8x
- 12x2 - 24x+ 8
rir?nqorturio O unu'lu f"(*)
lru,ir f" (1) - - 4
.'. rftoir6[.tflgr#run-yrffi x - 1(Uq
@ fior LilT'tv
sirinqorturio O unutuftt(*) nu'jr rtt(o) - 8
,,r
.'. rfioirqofi'ruU;nlfi x-0turir.rilq t0,1]qqJ
ila t+ aou ila+ 11
12
n(s)=Cro,g=#=Po
ririluq'hi E rnu uaqnT:nffi4nri"rld'n:Jorriunqilncir:?iln-uillnn'jrntorvirriu zoo
ad - ve , :
t- qr ru
n:rflfi t toi'orrJo.rtiunq:rilrYu 200 ulyr 1rafiu'loinnuonfiuo.r 1 nn uncerrr 2 nn)
.rj _ T:tTut^=
cs,zxcs,z = 5ifr
n:rfifi z "lsierrJottiuaq :rilriu 250 u'ryr 1ra0u'[oi'nnuonfiuq{ z nn ttn;f;sl? 1 nn)
'iruruii = Cs,zXCs,r =5ii
aA ue a ^ u.d e
n:rfifi a tein:Jorriunq:riln-u 3oo uryr 1rafiu1ffiuro.:vr'.: 3 4n1ql'
'iruruif = cs,3 = 1o ifr
n(E) = 50+50+10=110
Fri.lfiu p(E) =
n(E)
=
110
=
11
n(S) 120 12
1 a rfr sr il 6r a %:[#intr,rrr ?1 Er ;

25. raa EJ Grrfisrrlran{ 1 237 siriintrT nrr'lnrfrsil
.yu
sa 15 glou ra 4 86.41
fd-
0'ln[Anu x=50t1fl3S:12
nE': Z -
*-r
ts
a d utv 74-50
finufnou"ld'z+ :.2^ "-'-
"u-2
frnur 12
o:*rfi:grnould az .'. z ^ : 62-50
= 1
q ot*rut*..I 12
n:rilrrso.:'irururirrireoudaould'nyttuurioun'irourfl:*rniorurnn'irurufiiluf,.uq
cr vX
tu1,[o.11{
9,/ I
AA
1 l1,[71ttTt.l'l Y,l.Yl e<1) +Y{.Yt e>2)
(o.u+o.341 3) +(o.s- o.4rr2)
0.8641
i[s,/9/rAA.Adtet
vl fl 0 u L9t 9t v ttul{lAo u n ?'l o 19tut91 14 t 0 ul n n?1 u't u fln uf uytr n u 86.4 1
c)/ 9,/ 9,/
T0 U nf lJ0.l zu L1J'l flO
il
U
91,/ 9Y
?to 16 aou ?to 1 184.5
ALAi,vt
h fl zunan? Liln 0.1 tan un 0 LT
j
9t?1iln
6
10
18
14
2
ln rfr u E r 6{ o %61#in'[r,la ?1 il {
A
gt?'l iln 6[96[u
6
16
34
48 * Prro Ei
frr,lor:R'ln#nfi
50
120 - 139
140 - 159
160 - 179
180 - 199
200 - 219
oJaArurts-A
r{nilfiqnxrfi6olradueialdg.:n'jr o-.:nr"q6u I rJxrurruiauni zs 6a pru
druur.it Pzc : tn
=
75x50
:37.5
100 100
('"-s
) 100 LfL
-l
r |
-L.r|-
f
- 1re.5 + ,o(
st 's - "/
. 14-)
:184.5
6[A: Pcr 75

26. raall nrf,gtgrasrf 1 238 et'r ri'n irr nr :'[ a rfi s sr
lY t/
ila tt oou rTa g fla:rru?roiretnsi'lo:rra'irousiasrirsoofroslariucirrodE rnsnlfiorsaoU
9/ & ar ! s d
?l o il atro}[l.[ 3.t Ft1 [?11 n u G{$El t6tet o
O figr til:rs orufiuruaroovfinirtvirn-ueir#.rrnqfifoudqo ntoo'roorrvirriurir#{rnsrI
il
ilil1nflfl9r
@ fio tn:'tg ri'rriapnrotqfi€irfioilnG os'lrifirunn:rvrusion-r'us'nr unrolufiuil usios
. ,.1
t,
a c, iu ,
4
yt't lil n1 tiln il tnlj n ilq tu iln1 n n1 { 71 [u [14 tJ't r fl tJ
N/-
@ en !r{r1t I F' - *)= o rntJo
i=1
@ fio rn:r; eirilre:oru 1z; ro.:riorunfiritioun'jr niorvi'rriugurl'loi'
9'/ 9r'/
?lo 18 aou %a 2 3.0
ilarJn rfjualrnral r?n1qq
Tl T{.F1. X cir'l#Eirs (y) xy
2
x
2545 -2 1 -2 4
2546 -1 ,2 -2 1
2547 0 4 0 0
2s48 1 5 5 1
2549 2 7 14 4
ailnr:tffuq:.: y = ax+b
NNn
arunr::Jn6 It, = "I"i +Nb-O ilil.lrrp4st I*, =0
i=1 ' F1 i4'
19 = 5b
.:.b = 19 : .
5
.I",u, = "I*,' * o$*, -@i-,1 ' '
l-l l:l I:l
15 = 10a
3
,.4 =
2
o1 riu sru nr::J :y rur rudrtdd'r utunr :IsJ :*rur fi usir 6 o
319y--x+-
25
ln rfr s ilr 6r a r,t:[#intun ?rar i

27. rons arfisretrasr{ 1 239 eir rin ?rr nr :'[ a rfr s a,r
r tl vr al I u
n1t501Utun1:lnl]9rU',tflUFt't 1r{.fl.2553 tlytlr x = 6
.'. Yl =it l.f -e
r aN vr q f a e
nlttro'ru[1.[n1T[eNJ:*il'tflun1 v{.f1.2551 rryru x = 4
,. Yz=ltol.T -@
ri rtfd r utunr :I"ru unn duoirlufl n .?t .2ssg ufi ru duo r nfl il.q .2ss1 r vi r riu
Y'r -Y z= ]rut -|et
_.)_)
tt/ I
sa 19 nou ?to 1 55
or n #ru :J :s?yrf,nr : u:J : niur a.: rin 6 r um r ryir riu o. 2+
.. :ro = 0.24
x5'lU
12
-
= 0.24
XT'I U
NnXn +Nqfq
Nn Nq
x.. =
(zo t so)+ (so t oz)
-
3500 + 3100
= 5s nrrr.rilv 70+50 120
ila zo aou r7o r 0.3
orn A ras B rilurilqnr:nilr t fil*rfioderufiu
"'P(AAB)
= 0
plRtne'; = p(AUB)'
= l- P(AJB)
= t_ tp(A) + p(B) _ p(AnB)l
= l- [0.3 + 0.4 - 0]
= 0.3
ln rfi u il 6r a r,lt#intua ?1 il i
.'. xT'lu = 50
ets rLuuLilfi ur o.trin 6ur*fd rrir 610 urf;o" uor fr) :