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rfr s il a a ltt#in'Lr,ror er er i

12. 7
ranEJ arfiororasr{ 2 300 airri'nirrnr:'ta rfisru
9f or,tfi 2
9'/ 9,/
?lo 1 aau na 4 28
6uA
a.rA9,/AdAjrttct/
Un tT U 1*A 0.: tT U UR'l 1*'l O Uil TA q q ltO U'.l.l 1*0 U 1 R'l l9'l
riu6o n(nua) = so
alnrilrirru% n(AUB) = x+30
.'. x+30 = 50
x= 20
6uA
6u%R'ue16uo dr{ rd urHtoR'ue'rfi :luo dru6 ur drur u 42 nua'q
orn3rJrir.:Uu x+y - 42(u
20+Y - 42
Y = 22
.'. drururin 6uufd 6u%n1r*16u
= x + 30-y
= 20+30-22
=28
ln rfi s ar a a u'l#intuntr eu i

13. 7
rons nrf,srnrasr{ z 301 dtlnirrnr:'tnrfisEr
tv
?ro 2 grou 3 n'+ n
13
?JA
i,'i-1 [ ;
('.
') ]
(
^')(
t')
ornTovrri
9v
aou ?to
n4qt 1
q
13 +23 +33+... ..+n3
[;
(n*')
]
n2 (n + 1)2
4
n' (n + 1)2
{ n2 (n+1)2
n(n+1)
n2+n
4
-
(AB) 2
4
-
(AB)2
4
= AB2
-AB
-AB
-AB
lv
?ro 3 2 #qr'5' 2 "u1u'r.rrfiqriju#sr{un
rna 2q
at cX <rt
fln? rnuf $nFt?uurJ
tllsr 1 LLnr 2
I
e.t 6'
fln?un
frr{ 2 rj
ffn{ 2 11
A
HTO
n:rJq
vd
5[n?un
vd
6[n?un
A
I
la rfi n ar a a r,rt#in'[nn m ar #
ffn{ 2 11

14. r$nEJ srrfisrFflan{ z 302 rir rin irr nr :'[ a ufr s, &r
ty 91,/
uo 4 aou ?ra 2
9/A
lJ 0 2 9.lO
rir
9'/ 9,/
nl a<bLtn?-a<-b
o
!1 {T1r nlilUql a < b
9,/
e't 9/
-1 u'l9ltil?l.] 2 lj'l.l .'. -a > -bq
9y lr,/ .2
?ro 5 aou ?ro 3 x
nn tllT'ly$
_3x+1 :
[._:)'
_+
n rfJuonrrnuv dlr,hu zn qi'oruflluoarrnuyoiru1.
2.
3.
nn Lil{r'rv (r*,t6 ) x (r-,t6 ) -
fie L?lrry ( *
.
=X
3 2 13
_t
z) 4
2 3x+
4. nn Ly,trlr I r" I
913
44
1
aou z?ag -I2
(x+z)'+("-r)'- o
^2
+ 4x + 4 + *2 2x + 1 _ o
2x2 + 2x + 5 _ 6
2x2 + 2x 1 _ 0
^2
3x
tv
sa6
-2tln
zunsil,l"l
'l'. Jo)
r-'- fr)
[ 4 ,[ 4 )
d'lgn (Conjagate) to{ff1fi'urravfi'u
e./ 3vr . ey aa o c'vl e,/
?tilt1EJ t?ta 101,[ Lila 0{ u6[9t.:rlytrfl Lc{
-
nlaau il Loaytilu6 q
2
4
A 6l e'/
[1 lT'lY Ltl S [U6[AT x -il
(t/t d 9'/ Vl 9'/
nilnunqo{ Lq 1 uY,
U
13
44
1
2
-b +
la rfi s il a a ?b'[#5ntr,rn r,r ar {

15. -
rans nrflErarasri 2
303 air r['n ? g'r n 1 :-[ n tfi s e.r
lv
sa7
ila 8 nail ila1
I
lx
-2
2+5
3
aau z?a 1 t-3 , sl
*2 2x
^2 2x - 1s
(*-s) (*+3)
Lsetrirqou6o [-3 , 5]
H
@-30s@
t.lt ( x <rI
5l
x-5
X
X
lv
so I aau ila+ 11
3
(,'0 );
3
( 24't;
)
23 (-
8+3 =
3)
11
-27
1 n rfr cr au a o r,u'[#in'[u er rr ar i

16. 7
rans nrf,srdran{ 2 304 airrinirrnr;'[n rfrsil
#a 10 aau ila 1 atbo
{a3b2:,
( a-t b-' 1z
t-v"3b2
a3 b2
a-3 b-6
rfiut'
"3
b4
9l'/ 9,/
?to 11 mou zta 4 1 , 3 , 5 , 11 ,21
2n+1 + (-1)n
3
A'ln a
22 1
3
23 + 1
3
24 1
3
25 + 1
3
26 + 1
11
21
1 n 16 s, er r a ut#in'lr,uor rr er i

17. 7
rilns nrfinorasr{ 2 30s eirrlnirrnr:'tn tfieril
z?a 12 aau
1
1-
2nlv
?to 1
1-
nu'ir 1+ I +
2
1
fl
1
+
4
[;)
m
[;.1
1
+
I
ldra
... + tulAol,[nTilLTIJ1nfUA
aq
n
f=
a1
1r
H'l
S n
Sn*t
a1 ( ,-rn*1
1r
1
11
^n*1z
9,/ ly
ga 13 aou zta 4 6
:-- -Y-. e..-^.r L' &
dr ur uL 6[lAyl'.t.1 Yl LLq n q1.] n u?l { 14 u ql
1 ,n*1
aulu't + t,tnrc[?::ri'q
1
2
(
'-'^ )
1 l.1)'*'
2)
1
1
2n
1 rn
[;)'
2
X
nr.,rtyn{ -+ ou5'u'lqq
cy
6 f flU?]'l.l
d
l,$FITfl?TTFI -+ rfru.:tHil
'[ n rfi s e.r a o ut#inlu o rr a.r i

18. radEJ Frrf,srcrran{ z 306 iirrfinirrnra-ta rfisil
9y 91,/
?ro 14 aou ?ra 2 !
6
n(S)=6X6=36
rirur.ro E 6 o rtsrr o.: rnsrnr:n[fi r.r nu?nr a{ usi'rurrnn'irnto ryir n-u 1 0
E = {(+,0) , (6,4) , (5,5) , (5,6) , (6,5) , (6,6) }
3 t-l- # -3,3)
*2g
lv 9y
?to 15 aou ?to
a1n y
"'
n(E) = 6
a./ y ,_ n(E) 6 1
o.tl,ll,t p(E) -' n(S) 36 6
.'.(*-s)(x+e)+o
x + 3 , -3
r4ilr'r EJ lil a qir cir uqiol'Lri ryir n-u 0
r?o to srou fio z r, : ftx,y;lx < 0 unry = o)
nrtru#rulnt-uf r firilufirrifu 6o qrrrru#rufiuffi4d'ue-rorirarir 1x; qlorhirnfioun-u
rior r,,= t(",v) lx = ouns y < o)
uu'jr nruT fintu 4 r?iu (0 , -1) uns (o , -2) d.:fiq'i6'ue-usTrnfirrnfioun-uCJ
fraz rr: {(",r)l* < ouns y=o}
nu'jr surfintu r, rdu 1-t, 0) unr G2, 0) d.ror'lilfiqio"uqi'utqrnu dria"'uEium-rnrir(llcJ
uHfioun-u
rios r-: t(*,v)1" < ouns v . o)3 '' /
n:-r'jr erur8nlu r, uiu (-1, -1) un: (-1, -zy d.:fiqjfuel-usTrnfi'rrnfiourYu,u
ila+ ro= t(",u)1" = outo y=o)
nu'jr nrurEnlu ro tau(0, 1) unt 1o,oy d.:firid-'ud-um-rnfirrnfiouriu
ln ufr u il 610 %t#inlunx1 il i

19. rans nrf,norao{'2 307 eia rinisr nr :'[a ufi s s,r
9r/
?to 17
9v
AOU TTA 4
ooA
n1alfr9tlj0.l f 9t0 (0)q
9,/
lJ0 1 fior LT{T'ry 6[run'lr f(x) - 0 6tlqroi'eLLfl% x olnnrlrnh^lu'ir
sYA,t
o
oiriu ri'r$ouuo.tfliln1T f(x) - 0 firfru.: 2 enqau
cr,/ A A o e-
1J0 2 llo rilT'tv Tqrilu 6o Lsala.:dru'lua3{ (R)
do 3 fisr Lvlltu t:ud'to.: t 6o [-r,*) (a1nnilill)
e,/Jaa_/&,JA
110 4 On Ly.lTlr Aqql'lflO 910 x=0 91.11{1,[ Fl'l9l'lqqnO f (0)
uqqq
rsafl o.:dru?%o3{fi fr eir rurnn'it 1
- l*l+t
I
D :R'
r
d'.rriu x # o
.ll
.. lxl
y1
a,/ &
9l.l1,[1,b y
R - (1,@)
r
tv
0f ou rra 2 410
oirloufl'rr uil.lrfju z eiru
eier,ufi t qirueirloun'r:riuoi'u +o u'ryr
'iAaAa'/;8g'/6il?%11 2 noQ1nffi urnl.lTn?{41nff?TTtuRilnnun.lu'lu 45
A'/
aqaoLtnuxfi'209tqq
9r/
sa 18
9v
?lo 19
_ l-l
ovrririlurAotd'
lv
gtou va 4
fior:n*r y
alY
o.rt,tl* y - 1
rflaooln T
0
0
1
aT9,'rrT
10 n LntS,JaTttTn a0.lo'lun1 [ou6['lT
aT9./rr
20 n Ln rilar#q'lil qi'0.:qir usirle u6r'tr
AaTiac,,rrT
on 15 fl Ln L8.JATil tUn 0 A o.lQ'l Ugt'l L9tU6['lT
r?ruoi'0.:qil ueirTq u6r'rr tuairufd 2lfluutu G0
alY49,/rrTdra
O.]ltU fltlT'lnqt0.l0'lUFl'l [qUfl'lTt]J1,{1.,:1.[ 40 + 370 - 410 U'lYl
af
n Ln rilar
10 X 6 = 60 U'l?l
20X8 = 160 U'l?]
15X 10 = 150 U'lYl
+ 160 + 150 = 370 U'lyl
la rfr s il a o ?bt#intuerere.r i

20. rilns arflsrgT asr{ 2 308 eirrinisrnr:-[a rfiser
lv
ra 20
lv
aau so 1 16
8 rtJsr:
Sior:rHr A eco
nr
ilu'j1 tJu EcD riluruilil1n tfiotorn rA ?Jn'ru Gqq
e.t &
er{uu ilil e6c = 30o (r{rlnrutu:il A :rruri'ulsi 180')q
fior:r*r A nso lryu'ir sin 3oo
n?lilu1?30.,1 AB
n?1ilU'l?110.,1 AD
g
X
.'.x=16ty
e,/ {J t e./
9t.,tu1+ Ft?'ltJU'l?110{ AD tyl'lnu 16 tilaT
195 $Jnr
1
2
D
ila zt nau ila z 16s",6
300 urn:
E
fior:r*r A nro
Itu'ir tan 600 -
x:
X:
9t?1il U'l?1J0.,1 AE
U1?1J0',1 EDn?'1il
300
X
300
Js
300
Js
,.6
Js
- 1ooA tiletT
lnrfisruaaut#intrrnerrui

21. 7
r6rnEJ Frrf,srgfran{ 2 309 aiT rinirr nr:-ta rfi s a,r
fior;rHr A BCD
Itu'ir tan 60o =
e'ilruurrto': BC
Fl?'luU'l?fl0.1 DC
.'. y- ryxf =
"/s '..6
d'.:riu:snsvirt:rn'irt:J:snren:tiunti'trt = x+y = roo"6 + 65rA = ros.6 lilel:
ilazz srou ria + vl
Ft y LrlAl*d.,: fi rin 13 u uil Tv u'r tr* 20o/o t o .:ld'er v u%1.[ c[r n'j r 6 o Pso
H..roi'rLL14il.r P -
r ( N+1)
r 100
-
80(16+1)
- 13.6
100
Pao od:vu'irrqi'luurirfd 13 LLns 14 riu6oa{:ru'jr.: 89 LLfls 93(u
. 93-89 x
14 -19 13.6 - 13
X
+
0.6
2.4:x_&
O.ll*U Pao = 89 + 2.4 = 91.4
99
ilo zg nou rTo 3 fi'uoruro.rrirurin#runr:nornrirufilosJff'r:rfi.:unsneiruei'loun-rmrsfirirrvirrYu4quuqg
y . - 9+15+17+18+20+20+25+24+ 37+35 ar u
1J0 1 nn x - = - 22ntnn:il. ?ltu.t 10
rio z nn fi#uto.rneirufiIornr:r1u = 35 -7 = 28ru .t qI
av '
qjl
fiffita.:ncirriloruar:nrfir = 37 - 9 = 28q.ua
rio g fio il-rud1tlta.ir'llounr:mu - 16 + 20
= ra ttn;ril'uo'ruro{riTousr:ufir = 20@ql
2oqlu
rio + nn fi'roruro.rfiTouar:vYrililo = 20qt4.u
aq,fv
o']uiluilTo.ltJ [qum:n{?luo = 204qt
t- 195
{3-
.J;
195
v_ ,.6
65.6 tilar
la rfi s il 6{ a ltt#inlun ?'l r,r i

22. [anEJ srrf,srqran{,2 310 drfin?mnr:'tnrfieril
9v,ty
zta 24 aou ua 2 40
9v
zta 25
drurueiTq unr:fi#runr:srfi u 20 fiInniru = 8 nu(u
acr8
Flglt:JU x100-40%
20
ty
aou ?lo1 2,4
ryr
ilarrafiofi 1 x _#
,i
6[? U tU U.1 tU lAtl'l 9l T0'l 1*
20 + 19 + 21 + 18 + 22 + 23 + 17
S-
(zvzo)'* (tvzo)'* (ta-zo)'* (zs-zo)'*
20
(n-zo)'(zz-zo)'*(zl-zo)'*
I
S - 4+ - 2
ilaernfioftz x-#
9t?'1il urj::Jr?u (,s',)
25+24+26+23+27+28+22
25
s- (zs-zs)'+ (24-2s) 1 (zr-lzs)'* (zz-zs)'* (za-zs)'* (zz-25)'(n-2s)'*
-4
1 a rd s sr a o u'[fin'[r+n er er i

23. rons nrfinrrran{ 2 311 atrrin?rrnr:'tn rfrsil
lv t,/
ra 26 aou ?to 2 B
oQ9'/Aa{-ra/
fl'll4l.tgt LHLnrq?T'l?l 4 t?l'lnu x
j
LnTqLilnU = 2.75
(g"z )t(z"g )+(rl.+ )+z* - 2.rs
Ig * 2+1+2 ]
6+6+ 4+2x : 2.75
I
16+ 2x = 22
x=3
-&vaA
fr.rl.rl.r [t1q a.]fl ou lr:rn 4 loirn:q g
9/ tYioa
?lA 27 AOU gA 3 nltilnutnlntun > ilr',Ud',tu > d']ltl*Uilp4
nt
ria U n fi rrivl't.tr?'t (Ri ght-skewed distri bution )ru.
nu'ir orufiuil < ris'soru < rirradutntntflqrop
r7o zB srou ila + fiqrouuuuiir:rosia.:finmrui uns:J:;nunr:nfrfiurn-unr:tdrin:rfl:6er.ll ,u
e l" - A y A oqrllls a d A u qyv o j
nn:*il3?1fl'tn6u11fln1a{Hqau?10sYt't[14 [qn?1ilnqtilu [nu?nun1TtTlJo:tn:o9tytoq(ll
v a e e 4 v t d A - q eu
nna 0{ n 0 ila 0u a 0{ iln?l ilTun;lJ:rflljn1Tiltn u? nunlT lxu gtrrnro aql ,u ,u
ln rfr s il 6[ a r+'[#in'[r,ta ?1 il i