problem book

7/31/2019 Problem Book

1/24

V~jncgi

Njjh

-G`+


2/24

K|b` N~bzmhk`

Bcg}b`d~ Nw~cbhb

B`butbukb {bnj|b

\cbdkucb| Umbvj|bcj|

Ib}ki Uvk|bhj|

Tzwemkg` Tmj

Dikt~{ \j~jn{g|

uwvjutbt.j~a

tg}tb`dvketw~gu


3/24

V~jncgi

Njjh

-G`+


4/24


5/24

X/Y K` Ib{ >62># cb~ag `wing~u jl ^wuukb`

ektkzgù tjjh qbchu k` tmg ut~ggtu jl iboj~

ektkgu tj umjq tmgk~ dkuba~ggig`t qktm tmgv~gukdg`tkbc gcgetkj` ~guwctu. Tmg qbchu

qg~g dgckng~btgc{ jt b``jwègd bu vjcktkebc

g|g`tu b`d qg~g dguka`gd tj tgut qmgtmg~

tmg bwtmj~ktkgu qjwcd dkuvg~ug b` wùbè)

tkj`gd v~jeguukj` tmbt k`|jc|gd `j ucjabù#

bivckl{kà grwkvig`t j~ uvgbhg~u. Ukikcb~

tbetkeu mbd tj ng bdjvtgd dwg tj tmg kè~gbu)kà v~betkeg jl n~wtbckt{ n{ tmg bwtmj~ktkgu

k` emb~ag jl uwvv~guukà j~ab`kzgd v~jtgutu.

Tmg bwtmj~ktkgu dkd jt k`tg~lg~g.

2. B~gb jl wùgg` cw}w~{

Nwuk`guuib` dgekdgu tj umjq ujckdb~kt{ qktm tmg Tgut Qbch X/Y

n{ ut~jcckà qktm mku qklg bcjà tmg t~gg)ck`gd qbch b~jw`d mku

mjwug k` tmg _mwhj|hb Mkccu ejiiw`kt{.

J` tmg jtmg~ ukdg jl tmg Ijuejq k|g~# b` betk|kut grwkvvgd

qktm b ~ggc jl ej~d# igbuw~kà tbvg b`d b v~jt~betj~ ib~hu jll b

ck`g ugaig`t ngtqgg` vjk`tu I b`d @# l~ji qmkem tqj dkbigt~k)

ebcc{ jvvjugd t~ggu -vjk`tu B b`d N+ eb` ng ugg` j` tmg qbchqb{

uw~~jw`dkà tmg mjwug.

Ugaig`t I@ b`d tmg bàcgu kt lj~iu qktm tmg ck`gu ej``getkà

ktu g`dvjk`tu tj vjk`tu B b`d N?

n9 I@ 9 5>.;4 i

9 BI@ 9 ==.55

9 NI@ 9 .7>

9 B@I 9 =7.47

9 N@I 9 222.;=

@

I

N

B

Lka. 2

5


6/24

V~jncgi?

Mjq cjà qkcc tmg ujckdb~kt{ qbch tbhg# buuwikà tmbt tmg eji)

iw`kt{ ku v~jtgetgd n{ b ugew~kt{ ug~|keg b`d tmbt tmg nwuk`guuib`

b`d mku qklg mb|g b` b|g~bag ut~jcckà uvggd jl >.2;< hi*mjw~:

Bùqg~?

Tmgujckdb~kt{qbchqkcctbhg2>ik`wtgu.

>. Ijcgewcb~ ewkuk`g

Dgeging~. B |g`tkcbtkj` dwet cgbdkà tj tmg uw~lbeg l~ji b uwumk

nb~ k` b` w`dg~a~jw`d umjvvkà eg`tg~ giktu ubtw~btgd |bvj~ bt

b tgivg~btw~g jl (46 E. B mwà~{ mjigcguu vg~uj` qb~iu mkiugcl

n{ tmg a~btkà. Qmg` n~gbtmkà j~ibcc{# mg k`mbcgu 6.57 cktg~u jl

|bvj~ k`tj mku cwàu k` b ukàcg n~gbtm -6.76 cktg~u+ b`d g}mbcgu 76

a~biu jl qbtg~ vg~ mjw~.

V~jncgi?

Mjq cjà qkcc kt tbhg lj~ j`g vj~tkj` jl ikuj ujwv -576 a+ tj

ng bnuj~ngd k`tj mku cwàu kl ~gcbtk|g mwikdkt{ 9 266' b`d

tmg |bvj~u ijkutw~g ej`tg`t 9 72 a*i5: Mjq iwem ijku)

tw~g qkcc mg cjug tm~jwam n~gbtmkà k` tmku ubig vg~kjd jl

tkig:

Bùqg~?

J`gvj~tkj`jlikujujwvqkccngbnuj~ngdk`tjtmgmjigcguuvg~ujù

cwàuk`>5.54mjw~u.Dw~kàtmkutkig#mgqkcccjug2.2


7/24

5. B` betk|kutu d~gbi

Tmg wing~ jl v~jtgutg~u ku ejùtb`tc{ ~kukà. J` @j|ging~ 1#

46#666 vgjvcg umjq wv j` gd Urwb~g tj dgijùt~btg babkùt

aj|g~ìg`t bnwugu. K` Ib{# b e~jqd jl =6#666 flccu gd Urwb~g.

J` Owc{ 24# tmg~g b~g 2>6#666 dgijùt~btj~u# g}eggdkà tmg

urwb~gu ebvbekt{ n{ ug|g~bc tmjwub`d. Tmg qbccu jl tmg nwkcdkàu

uw~~jw`dkà gd Urwb~g b~g a~bdwbcc{ vwumgd nbeh n{ tmg umgg~

vjcktkebc vjqg~ jl tmgug mwib` ibuugu ...

^gd Urwb~g# nj~dg~gd n{ tmg Mkutj~kebc Iwugwi# AWI#

Ut. Nbukcu Ebtmgd~bc b`d tmg Cg`k` Ibwujcgwi# ku b ~getbàwcb~

b~gb qktm ukdgu igbuw~kà? 9 =7 i# n 9 4b 9 546 i. E~jqd dgùkt{bt dgijùt~btkjù b|g~bagu tm~gg dgijùt~btj~u vg~ urwb~g igtg~.

V~jncgi?

Mjq ib`{ igtg~u dj tmg nwkcdkàu nj~dg~kà gd Urwb~g mb|g tj

ng ij|gd k` j~dg~ tj beejiijdbtg 2>6#666 dgijùt~btj~u:

Bùqg~?

TmgH~gick`qbccu#Ibwujcgwib`dAWImb|gtjngij|gdnbeh1.7i.

TmgMkutj~kebcIwugwib`dUt.Nbukcumb|gtjngij|gdnbeh56i.

4. Wuglwc b~gb jl b utbdkwi

@k`tm)a~bdg~ Vgtg ~wù tm~gg cbvu b~jw`d tmg uemjjc utbdkwi k`

5.4 ik`wtgu bt b` b|g~bag uvggd jl 21.>)utj~g{ jlfleg nwkcdkàu qktm jj~ uvbeg jl >

gbem qkcc flt kùkdg tmg utbdkwi:

7


8/24

B`uqg~?Tmguemjjcutbdkwiqkccmjcd

<


9/24

V~jncgi?

Mjq ib`{ Utjv ebvktbckui" ucjabù eb` ng ibdg wukà j`g

466)ic eb`: Mjq iwem djgu gbem b`tk)ebvktbckui ucjab` ejut:

Bùqg~?

2.2.Gbemb`tk)ebvktbckuiucjabèjutu26.;6~wncgu.


10/24

V~jncgi?

Mjq ib`{ dgijùt~btkjù iwut Ektkzg` @ qj~h k` j~dg~ tj

ub|g g`jwam ij`g{ tj vb{ tmgug mk~gd dgijùt~btj~u# tbhkà

k`tj beejw`t tmg lbet tmbt n~kabdg cgbdg~u -j`g n~kabdg cgbdg~

vg~ tqg`t{ ba)qb|g~u+ b~g vbkd tg` tkigu ij~g tmb` ~b`h)

b`d)flcg dgijùt~btj~u -b>+ b`d tmbt vb~t{ lwètkj`b~kgu -j~ab)

`kzg~u b`d uvk` djetj~u+ b~g vbkd tg` tkigu ij~g tmb` n~kabdg

cgbdg~u -b5+.

Bùqg~?

Ektkzg`@iwutqj~h>#766dgijùt~btkjùk`j~dg~tjvb{btmjw)

ub`dejccgbawgutjbttg`dmkudgijùt~btkj`kùwvvj~tjlqj~h)

g~u~kamtulj~mk~gddgijùt~btj~u.

1. Ibtt~guugu ncjeh ~k|g~u# nwt jvg` gq qb{u"

Tmg jt)tjj)dkutb`t lwtw~g. Ijuejq mbu ngg` tbhg` j|g~ n{ vjckeg

lj~egu. @gb~ tmg H~gick`# tmg Ijuejq b`d [bwzb ~k|g~u b~g tggi)

kà qktm v~jtgutg~u. Vgjvcg b~g wukà k`btbncg ibtt~guugu tj lj~i

jbtkà ebivu. @b|kabtkj` ku ejivcgtgc{ ncjehgd# b`d nb~agu b`d

tjw~kut njbtu b~g w`bncg tj vbuu. Tmg ekt{ mbu tmwu ljw`d gq emb`)

`gcu jl v~jtgut.

Tmg uw~lbeg b~gb jl tmg [bwzb b`d Ijuejq ~k|g~u kùkdg tmg Ab~)dg` kà ku 1. jbtkà ibtt~guu# 2=; 1< ei# a~b{ qktm mgbd~gut#

cb~ag g`jwam lj~ tqj bdwctu b`d tqj emkcd~g`

=


11/24

5. jbtkà ibtt~guu# 2=5 1 b`d

ebut k` n~j`zg k` 2;41. Tmg vcbutg~ ebut ku

utj~gd k` tmg T~gt{bhj| Abccg~{. K` 2;#666 betk|kutu qg~g dgtbk`gd bu b ~guwct

jl ecbumgu qktm vjckeg. Qmg` tmku tg}t qbu

ngkà v~gvb~gd# 2< vgjvcg mbd ngg` emb~agd

qktm ~kjtkà.

;


12/24

k` Ib{# v~jtgutg~u wugd vkgegu jl buvmbct vb|kà bu qgbvjù# ukèg

Njcjt`b{b Urwb~g b`d tmg uw~~jw`dkà b~gb# qmg~g tmg g|g`tu jl

Ib{ < w`ljcdgd# mbd w`lj~tw`btgc{ jt ngg` vb|gd qktm tmg gbukg~)

tj)mb`dcg utj`gu.

V~jncgi?

Mjq iwem qjwcd kt mb|g ejut ekt{ bwtmj~ktkgu tj b~i

16#666 ib~emg~u -bu gutkibtgd n{ tmg g|g`tu j~ab`kzg~u+ qktm j`g

utb`db~d)ukzg vb|kà utj`g gbem lj~ j`g qgcc)bkigd tm~jq:

Bùqg~?

Ktqjwcdmb|gejutekt{bwtmj~ktkgu4#4>=#;66~wncgutjb~i

16#666dgijùt~btj~u.

;. gdwetkj` lbetj~

Beej~dkà tj vjckeg utbtkutkeu# 566 vgjvcg umjqgd wv bt tmg Ib~em

>7 dgijùt~btkj` lj~ mj`gut gcgetkjù k` l~j`t jl Ib~kkùh{

Vbcbeg k` Ut. Vgtg~unw~a. Beej~dkà tj mwib` ~kamtu betk|kutu#

576 dgijùt~btj~u qg~g b~~gutgd. Bltg~ tmg b~~gutu mbd ngg`

ibdg# bt cgbut 766 dgijùt~btj~u ~gibk`gd j` tmg urwb~g.

V~jncgi?Mjq ib`{ vgjvcg tjjh vb~t k` tmg Ib{ 4 ujcktb~{ vkehgt babkùt tmg

cbq v~jmknktkà mjijug}wbc v~jvbab`db# buuwikà tmg ~gdwe)

tkj` lbetj~ wugd n{ tmg Dgvb~tig`t jl K`tg~`bc Bllbk~u:

Bùqg~?

K6.575vg~uj`tjjhvb~tk`tmgujcktb~{vkehgtbabkùttmgcbq

v~jmknktkàmjijug}wbcv~jvbab`db.

26


13/24

26. Ujekbc ~g`t ba~ggig`t

Tmg Ekt{ jl Vuhj| mbu b vjvwcbtkj` jl >66#666 b`d uvg`du

211#666#666 ~wncgu b {gb~ j` tmg ekt{u bdik`kut~btkj`.

V~jncgi?

Mjq iwem qjwcd gbem ekt{ ~gukdg`t mb|g tj vb{ vg~ ij`tm uj tmbt

tmg{ ejwcd mk~g bqb{ tmg g`tk~g ekt{ aj|g~ìg`t b`d gùw~g ktu cj{)

bct{ n{ jllg~kà tm~gg tkigu bu iwem ij`g{:

Bùqg~?

Gbem~gukdg`tjlVuhj|qjwcdmb|gtjvb{>>>~wncguvg~ij`tmk`

j~dg~tjmk~gbqb{tmgekt{bdik`kut~btkj`.

22. B Cguuj` k` Dkujngdkgèg

J` Ow`g 62># tmg Lgdg~btkj` Ejwèkc bvv~j|gd big`dig`tu

tj tmg Cbq j` Buuginckgu# bcckgu# Dgijùt~btkjù# V~jeguukjù

b`d Vkehgtu tmbt qjwcd kè~gbug tmg fl`gu lj~ |b~kjwu |kjcbtkjù

tj 566#666 ~wncgu lj~ dgijùt~btj~u b`d 62> -qmg` tmgug v~jncgiu qg`t tj v~guu+# kt ku

vcb``gd tj kivcgig`t Lgdg~bc Cbq @j. =5. Tmg cbq# bdjvtgd tqj{gb~u baj# gllgetk|gc{ bnjckumgu tmg ~kamt tj l~gg v~kib~{ gdweb)

tkj`# tw~`kà tgbemg~u k`tj ejivgtkà g`t~gv~g`gw~u k` b aj|g~`)

ig`t kùtktwtkj`.

Beej~dkà tj tmg ik`kutg~ jl gdwebtkj` b`d uekgèg# b tgbemg~u

b|g~bag ij`tmc{ ubcb~{ k` >62># v~kj~ tj tmg kivcgig`tbtkj` jl

Lgdg~bc Cbq @j. =5# ku >2#266 ~wncgu.

22


14/24

V~jncgi?

Mjq cjà iwut b tgbemg~ ugt bukdg mku g`tk~g ij`tmc{ ubcb~{ uj

tmbt mg eb` bllj~d tj tbhg vb~t k` j~ mgcv j~ab`kzg b` w`bwtmj~kzgd

dgijùt~btkj` babkùt tmg lgdg~bc cbq bt tmg ~btgu v~jvjugd k` tmg

big`dig`tu:

Bùqg~?

Tmgtgbemg~qkccmb|gtjugtbukdgmkuubcb~{lj~ljw~tggìj`tmuk`

j~dg~tjvb{tmgfl`glj~vb~tkekvbtkàk`b`w`bwtmj~kzgddgij`)

ut~btkj`#b`dtqg`t{)gkamtij`tmulj~betkàbub`j~ab`kzg~.

2>


15/24


16/24


17/24


18/24

Tmg Dklflewct T~wtm bnjwt Ibtmgibtkeu

K` jw~ uktwbtkj`# tmbt jl Ebvktbc# tmg ~gka` jl wing~ ku tmwu tmg

~gka` jl tmg w`tmjwamt ucb|g~{ jl wig~kebckt{ ktugcl. @wing~

qmkem# uj kt ku ecbkigd# w`dg~ckgu g|g~{tmkà jl |bcwg# ku k` betwbc

lbet b v~jue~kvtkj` babkùt b`{ tmk`hkà jl wing~ ktugcl. @wing~

jvg~btgu bu tmbt jnuew~g vjk`t qmg~g tmg uktwbtkj` ejèg`t~btgu ktu

cbq8 jnuew~g tm~jwam ktu ngkà bt jèg uj|g~gka` b`d uwnt~betgd

l~ji bcc tmjwamt# b`d g|g` l~ji g|g~{ k`|gutkabtkj` tmbt j~kg`tu

ktugcl tjqb~du ujig t~wtm.

Bcbk` Nbdkjw# @wing~ b`d @wing~u -2;;6+ X2Y

Qmbt ku tmg ~gcbtkj` ngtqgg` ibtmgibtkeu b`d vjcktkeu: B` jn|kjwu ~guvjùgtj tmku rwgutkj` ku tj ugg tmbt wing~u# igbuw~gig tu# emb~tu b`d a~bvmu b~g

tmg igbù n{ qmkem jw~ qj~cd ku ib`bagd. Dguvktg qmbt ckng~bcu ikamt ub{#

tmku ib`bagig`t# kècwdkà jl tmg gcgetkj` flaw~gu tmbt dgtg~ik`g qmj qkcc

jeewv{ tmg ugbtu jl vjqg~# ku jt vjcktkeu. Uj# kl ibtmgibtkeu ku tmg igbù n{

qmkem tmg utbtg b`d tmg ~wckà ecbuu ib`bag wu# qjwcd jw~ ~gukutbèg tj djik)

`btkj` b`d g}vcjktbtkj` bcuj ng b ~gukutbèg tj ibtmgibtkeu ktugcl:

Tmg~g b~g ~gbujù lj~ tmk`hkà uj# b`d ujig vmkcjujvmg~u k` tmg ~geg`t

vbut mb|g bd|jebtgd uhgvtkekui bnjwt b`{tmkà tgem`j)uekg`tkfle dwg

tj ktu buujekbtkjù qktm ijdg~` tgem`jcjakebc mwn~ku# rwb`tkflebtkj`bc

`j~ibckzbtkj`# nkjvjcktkebc ej`t~jc b`d utbtg ~gv~guukj`. K` tmku ebug# tmg

~gcbtkj` ngtqgg` ibtmgibtkeu b`d vjcktkeu qjwcd ng ujigtmkà ckhg b`

gibèkvbtkj` l~ji ibtmgibtkeu.

N{ ~geja`kzkà tmg kùt~wig`tbckzbtkj` jl ibtmgibtkeu lj~ tmg ib`b)

ag~kbc lwètkjù jl tmg utbtg b`d ebvktbc# ejwcd qg kùtgbd w`dg~utb`d tmg

~gcbtkjùmkv ngtqgg` ibtmgibtkeu b`d vjcktkeu tj ng j`g jl tmg gibèkvb)tkj` jlibtmgibtkeu: Kl ibtmgibtkeu ku b igbù tj eg~tbk` g`du# ikamt qg

ibhg kt ug~|g gibèkvbtkj` ~btmg~ tmb` jvv~guukj`:

Qmbt kl qg igbuw~g tmg utbtg k` tmg ubig qb{ tmbt kt igbuw~gu wu: Qmbt

kl qg g|bcwbtg# lj~ b embàg# mjq glflekg`t tmg v~k|btg ku# mjq iwem aj|g~`)

ig`t ij`g{ v~k|btg g`tg~v~kug ejùwigu j` ngmbcl jl tb}vb{g~u. Tmku mbu

bcqb{u ngg` b tjjc jl e~ktkeu b`d ~g|jcwtkj`b~kgu. Ibtmgibtkeu ku tmg` ujig)

tmkà tmbt bccjqu b lj~i jl ejiiw`kebtkj` tmbt vwtu tmg vwncke k` dk~get

ej`tbet qktm b ak|g` vjuktkj`. Tmku ku v~gekugc{ bcuj ngebwug kt ~gdwegu tmg

qj~cd tj tmjug ubig wing~u# igbuw~gig`tu# emb~tu b`d a~bvmu tmbt vwcc

2<


19/24

tmg cg|g~u jl vjqg~ b`d jvk`kj`. Jl ejw~ug# k` b`{ ij|gig`t# j ibttg~

mjq uibcc# qg fl`d tmbt qg eb` cgb~` tj ib`kvwcbtg wing~u bu qgcc. Tmgug

`wing~u tbhg wu nbeh tj tmg ecbuu~jji jl jngdkgèg tj jnogetk|kt{. Lk~ut qg

qb`t tj ng ckgd tj n{ tmg flaw~gu jl vjcktkekbù8 tmg` qg qb`t tj ng jwt~bagd

n{ tmg wing~u jl tmg e~ktkeu.

K` tmg gvka~bvm bnj|g# l~ji Bcbk` Nbdkjw# qg fl`d b v~jvjubc tj ckng~btg

ibtmgibtkeu l~ji ktu jvg~btkj` bu b lj~i jl w`tmjwamt v~gekugc{ n{ tmg

bwdbekt{ tj tmk`h wing~u. Tmku lj~i jl gibèkvbtkj`# j`g tmbt buhu wu tj

tmk`h ng{j`d tmg jnlwuebtkj` jl gej`jike ijdgcu# utjeh b`d nj`d v~kegu

b`d gcgetkj` tbcckgu# ku b` gàbagig`t qktm wing~ ktugcl# b ut~waacg qktm

b` kdgjcjakebc ueblljcdkà qmkem givcj{u wing~ bu b` jnogetk|g bcknk lj~

ckgu b`d tmkg|g~{. Lk`bèkbc g}vg~tu b`d utbtg lwètkj`b~kgu ak|g wu wing~u

ngut cglt tj tmg g}vg~tu? tmg{ b~g j`c{ buhkà lj~ jw~ |jtg b`d ejùwig~

ej`fldgèg. Ujig jl tmg ngut ibtmgibtkebc ik`du jl jw~ ag`g~btkj` mb|gngg` d~bltgd k`tj tmku b~i{ jl |g`t~kcjrwkutu qmj ibhg wing~u uvgbh lj~

tmgi# k`|g`tkà ij~g b`d ij~g ejivcg} vwzzcgu jl |k~twbc tkig b`d v~j)

ogetgd |bcwg. Ejwcd kt ng tmbt kt ku jq tkig tj tbhg tkig b`d |bcwg# k` tmg lj~i

jl wing~u# nbeh l~ji tmgi:

B`jtmg~ ugùg jl ibtmgibtkebc gibèkvbtkj` bttbehu v~gekugc{ tmku

`jtkj` jl tmk`hkà ibtmgibtkeu. Bu Akccgu Dgcgwzg b`d Lck} Awbttb~k

b~awg k B Tmjwub`d Vcbtgbwu# tmg v~jncgi ku tmbt tmg~g b~g tqj dkllg~g`t

vbtmu k` ibtmgibtkebc tmjwamt ktugcl.

XKYt ku jl tmg btw~g jl b}kjibtkeu tj ejig wv babkùt uj)ebccgd

w`dgekdbncg v~jvjuktkjù# tj ej`l~j`t geguub~kc{ mkamg~ vjq)

g~u tmbt kt eb``jt ibutg~. Lk`bcc{# b}kjibtkeu djgu jt ejùtktwtg

tmg ewttkà gdag jl uekgèg8 kt ku iwem ij~g jl b utjvvkà vjk`t#

b ~gj~dg~kà tmbt v~g|g`tu dgejdgd ugikjtke jqu k` vm{ukeu b`d

ibtmgibtkeu l~ji guebvkà k` bcc dk~getkjù. Tmg b}kjibtkekbù b~g

tmg ig` jl tmg utbtg jl uekgèg# qmj ugbc jll tmg ck`gu jl kamt tmbtb~g uj l~grwg`t k` ibtmgibtkeu# qmj kivjug b gq g}wi# kl j`c{ b

tgivj~b~{ j`g# b`d qmj cb{ djq` tmg jlflekbc vjckekgu jl uekgèg.X>Y

J` tmku |kgq# tmg utbtg g}kutu k` ibtmgibtkeu bu qgcc# b`d ktu big

ku b}kjibtke tmjwamt. Mg~g Dgcgwzg b`d Awbttb~k uwaagut b `jibdke

uekgèg ij~g dg|jtgd tj g}vg~kig`tbtkj` b`d k`twktkj` tmb` tmg buvgetu

jl geguukt{ b`d u{utgibtke ejùkutgè{. Tmku utbtkut gcgig`t tmbt tmg{

vjk`t jwt ib{ ng tjj igtbvmj~kebc tj qb~~b`t ug~kjwu ejùkdg~btkj`.

Tmg vjcktkebc v~gowdkeg k` ~gbdkà u{utgibtke j~ b}kjibtke ibtmgibt)

keu bu ujigtmkà cjehgd k` geguukt{ b`d mgèg kèbvbncg jl tmk`hkà -b`d

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20/24

a~buvkà+ tmg ej`tkàgèkgu k` k`twktkj` b`d g}vg~kig`tbtkj` ku v~gekugc{

tj ikuu tmg vjk`t. K` b ejw`tg~k`twktk|g qb{# kt ku v~gekugc{ tmg nbcbèg

ngtqgg` geguukt{ b`d ej`tkàgè{ k` ibtmgibtkeu tmbt vwtu kt k` ~gcbtkj`

qktm vjcktkeu. Tmg dggv uw~v~kug tmbt ibtmgibtkeu# k` ktu mkutj~{# ~g|gbcu

ku tmbt ktu ~gcbtkj` qktm -cjakebc+ geguukt{ ku v~gekugc{ qmbt ~g`dg~u k``j)

|btkj` k` ibtmgibtkeu uj k`t~kawkà. Tmbt ku tj ub{# qmg` qg gèjw`tg~

iw`db`g qj~cdc{ lbetu# ujekbc uktwbtkjù b`d tmg ckhg# qg b~g dgbckà qktm

ej`tkàgè{. Qmg` K ub{ tmbt qj~cdc{ lbetu b~g ej`tkàg`t# K dj jt igb`

tmbt tmg{ b~g ~b`dji. b`dji`guu ku jl ejw~ug bcuj ujigtmkà dgfl`gd

ibtmgibtkebcc{. [gt qmbt K igb` mg~g ku tmbt lbetu ejwcd bcuj `jt ng8 tmg{

b~g ej`tkàg`t. Kt ku jt b geguub~{ lbet tmbt K bi q~ktkà tmgug qj~du jq#

j~ tmbt K g}kut# j~ g|g` tmbt tmg ujcb~ u{utgi b`d cklg j` vcb`gt Gb~tm ebig

k`tj ngkà. Tmku ku jt tmg ebug qktm ibtmgibtkebc lbetu. Ibtmgibtkebc

lbetu eb``jt `jt ng. Tmku ku jt b ig~g g}tg~`bc dgtg~ik`btkj` jl ibtm)gibtkeu nwt b ~gbc tjjc k` ibtmgibtkebc v~betkeg. Ibtmgibtkekbù ukèg

b`tkrwkt{ mb|g wugd qmbt qg ebcc ~gdwetkj bd bnuw~dwi# b lj~i jl v~jjl

tmbt dgijùt~btgu ujigtmkà n{ umjqkà tmbt ktu ej`t~b~{ ku kèjùkutg`t

j~ cgbdu tj b ej`t~bdketkj`. Kl# lj~ g}bivcg# qg qb`t tj v~j|g tmbt tmg~g b~g

b` k`fl`ktg wing~ jl v~kig wing~u# qmkem ku kivjuukncg tj umjq dk~getc{#

qg utb~t qktm tmg v~jvjuktkj` tmbt tmg~g b~g j`c{ b fl`ktg wing~ jl v~kig

`wing~u b`d tmg` umjq tmbt tmku v~jvjuktkj` ku ej`t~bdketj~{. Kt tmg` ljc)

cjqu# bu Gweckd t~kgd tj umjq wu# tmbt tmg~g b~g b` k`fl`ktg wing~ jl v~kig

`wing~u.

Bctmjwam geguukt{ ku jltg` ugg` bu ejùt~bk`t# ibtmgibtkebc geguukt{

bcuj mbu b v~jljw`d ugùg jl l~ggdji. Tmku eb` ng t~begd ijut ~gbdkc{ k` tmg

mkutj~kebc dg|gcjvig`t jl ibtmgibtkebc tmjwamt. Mjq ku kt tmbt qg mb|g

vwètwbcc{ b~~k|gd bt gq ibtmgibtkebc n~gbhtm~jwamu tm~jwamjwt mku)

tj~{ qmg` ibtmgibtkeu bvvgb~u tj ng cjehgd k` b dgijùt~btk|gc{ ecjugd

~gbci jl geguukt{: bdkebc embàgu qktmk` ibtmgibtkeu bu b v~betkeg# b ugtjl tmgj~giu# b ug~kgu jl t~wtmu# ik~~j~ mkutj~kebc embàg v~gekugc{ ngebwug

tmg{ bccjq wu tj ugg qmbt ~gbc embàg eb` igb`# b embàg jl tmg ej`tg}t jl

`geguukt{ ktugcl. Qg ebuwbcc{ g}vget ~wcg)aj|g~`gd embàg k` tmg qj~cd ukèg

tmkàu b~g ej`tkàg`t# nwt tmg{ b~g kèck`gd tj j~dg~ b`d qg dgdweg btw~bc

cbqu j` tmku nbuku. Nwt tmgug embàgu b~g ejiij`vcbeg b`d dj jt g}tg`d

ng{j`d tmg l~bigqj~hu qktmk` qmkem tmg{ tbhg vcbeg. J` tmg jtmg~ mb`d#

b umklt k` ibtmgibtkeu ku u{utgibtke v~gekugc{ ngebwug qmbt qg ej`tgut k`

tmjug ej`tg}tu jl embàg ku ujigtmkà lw`dbig`tbc? b dggvc{ g`t~gèmgd

k`twktkj`# b ugt jl k`tg~cjehkà b}kjiu. K` ~bdkebc ebugu# qg gèjw`tg~ b`

2=


21/24

w`g}vgetgd ~glwtbtkj` tmbt tm~jqu jll b qmjcg u{utgi k` vb~t v~gekugc{

ngebwug qg ~grwk~g geguub~{ acjnbc b`d w`k|g~ubc ejùkutgè{. Qmg` b

u{utgi -qmkem ku b}kjibtke+ kivckgu b` g~~j~# tmg g`tk~g u{utgi mbu tj ng

~g)g}bik`gd.

Ngebwug ibtmgibtkebc embàg ku uj lw`dbig`tbc# ktu |bàwb~d ku ej`)

utb`tc{ ibcka`gd bu dgck|g~kà ujigtmkà lbcug. K` tmg ebug jl Cgkn`kz b`d

@gqtj`# qmj ejèw~~g`tc{ ab|g lj~i tj tmg dkllg~g`tkbc b`d k`tga~bc ebcew)

cwu# tmku uj~t jl lbcukt{ qbu tmg |g~{ d{`bikui jl dkuej|g~{. @gqtj` b`d

Cgkn`kz# Ib~} ~gib~hgd k` mku ibtmgibtkebc ib`wue~kvtu#

ngckg|gd k` tmg i{utg~kjwu emb~betg~ jl tmg gqc{ dkuej|g~gd

ebcewcwu# tmbt {kgcdgd t~wg -b`d ij~gj|g~# vb~tkewcb~c{ k` tmg

agjigt~kebc bvvckebtkj`# butj`kumkà+ ~guwctu n{ b vjuktk|gc{ lbcug

ibtmgibtkebc v~jegdw~g. Tmg{ qg~g tmwu ugcl)i{utkflgd# |bcwgd

tmg gq dkuej|g~{ bcc tmg mkamg~# g`~bagd tmg e~jqd jl jcd j~tmj)dj} ibtmgibtkekbù bcc tmg ij~g# b`d tmwu ebccgd lj~tm tmg e~{ jl

jvvjuktkj`# tmbt g|g` k` tmg cb{ qj~cd mbu b` gemj b`d ku geguub~{

k` j~dg~ tj vb|g tmg qb{ lj~ ujigtmkà gq.X5Y

Tmku vjuktk|gc{ lbcug ibtmgibtkebc v~jegdw~g ku tmg ej~~gcbtg jl tmg

vgewckb~ uj~t jl l~ggdji tmbt K uwaagut. Kt ku dggvc{ uwnogetk|g b`d j`c{ ~gbc)

kzgu ktugcl k` tmg lwtw~g b`tg~kj~? Tmku qkcc mb|g ngg` t~wg.

Lbcukt{ vcb{u b uvgekbc ~jcg k` l~ggdji k` ibtmgibtkeu# nwt bcuj k` tmg

|g~{ jtkj` jl l~ggdji bu uwem. Qmg` qg uvgbh uwnogetk|gc{ bnjwt l~ggdji#

qg wuwbcc{ uvgbh jl l~ggdji jl jvk`kj` j~ l~ggdji jl betkj`. Mjqg|g~# bu

qg eb` dgdweg l~ji tmg bèkg`t dkbcgetke jl l~ggdji# l~ggdji ejègk|gd bu

ig~gc{ ngkà jvg` tj b ugt jl jvk`kjù j~ emjkegu ku jt l~ggdji bt bcc. J|g~)

ejikà tmku kivjuuknkckt{ jl l~ggdji ku l~ggdji ktugcl. Tj tmk`h# tj ecbki# tj

ugkzg j~ tj bet j` ujigtmkà ng{j`d tmg ejùt~bk`tu jl ak|g` j~ ejiijùgùk)

ebc dgtg~ik`btkj`# ng{j`d tmg ugt jl ak|g` emjkegu# uggiu bu kivjuukncg bu

ckng~t{ ktugcl. Kt ku tmku kivjuuknkckt{ tmbt ak|gu umbvg tj ckng~t{.Ibtmgibtkeu tmwu v~gug`tu b ik~~j~ k` qmkem tmg ut~ketgut lj~i jl gegu)

ukt{ gèjw`tg~u ktu djwncg k` tmg ijut uwnogetk|g b`d bnujcwtg lj~i jl ckn)

g~t{. Tmku ik~~j~kà eb` bcuj jllg~ b dggvc{ mwib`kut vketw~g tmbt v~bkugu

tmg w`lbtmjibncg dgvtmu jl mwib` e~gbtk|kt{# tmg v~ja~guuk|g g|jcwtkj`

b`d t~bùeg`dgèg jl tmg mwib` uvk~kt. Tmku# K ecbki# ku bcuj b ikutbhg.

Tmg~g ku ujigtmkà dgekdgdc{ k`mwib` bnjwt ibtmgibtkeu tmbt a~kvu wu

l~ji tmg jwtukdg. Tmku ku jt j`c{ tmg k`twktkj` b`d g}vg~kig`tbtkj` tmbt

Dgcgwzg b`d Awbttb~k uvgbh jl. Nglj~g tmjug kivbuugu# tmjug w`dgekd)

bncg utbtgig`tu vjvwcb~kzgd n{ Adgc# tmg~g ku fl~ut tmg ~gukutbèg jl

2;


22/24

ibtmgibtkeu tj tmk`hkà. Vbeg Dgueb~tgu# tmg ~gukutbèg jl ibtmgibtkeu ku

j`g tmbt jt g|g` tmg ajd jl tmg tmgjcjakbù ejwcd j|g~ejig. Qg dj jt uki)

vc{ b}kjibtkzg n{ vw~g dgekukj`. Ibtmgibtkeu ~gukutu wu bt g|g~{ utgv. Kt ku

tmku ~gukutbèg babkùt tmg mwib` tmbt ibhgu wu uwnikt jw~ k`twktkj`# jw~

ak|g` ngckglu# tj tmg k`mwib` b|b`t)ab~dg jl ejùkutgè{. Tmg cjà mkutj~{

jl tmg kibak`b~{ wing~ k# j~ tmg urwb~g ~jjt jl gabtk|g j`g )2# bttgutu tj

eg`tw~kgu jl ejikà tj tg~iu qktm b ibtmgibtkebc g}kutgèg qmkem eb``jt

ng ~gdwegd tj jw~ mwib` g}vg~kgèg# jw~ k`twktkj`# jw~ g}vg~kig`tu. Tmg

mkutj~{ jl tmg kibak`b~{ wing~ k ku tmg mkutj~{ jl tmg utwnnj~``guu jl b

uka`# b ibtmgibtkebc tmjwamt tmbt lj~egu b vg~uj` tj tmk`h8 b ej`tk`wjwu

ibtmgibtkebc hkeh l~ji ngmk`d. Kt ku vg~mbvu tmku k`mwib`kt{ tmbt ku tmg

vg~lget ik~~j~ lj~ ckng~t{. K` ngkà lj~egd tj tmk`h geguukt{# qg b~g lj~egd

n{ geguukt{ tj tmk`h.

Tmg k`mwib` lj~eg jl geguukt{ ku jt j`c{ j`g jl tmjwamt. Qmg` tmgvmkcjujvmg~ jl ibtmgibtkeu Ogb` Eb|bkccu dgekdgd tj ngejig b` betk|g

~gukutg~ k` tmg Ugej`d Qj~cd Qb~# mg givmbukzgd tmbt mg tjjh tmku dgek)

ukj` n{ igbù jl cjake.X4YLj~ mki# tmku l~ggdji jl betkj` qbu dketbtgd n{

dgdwetk|g geguukt{# b`d ngkà lj~egd tj tbhg wv tmg b`tklbuekut ut~waacg

qbu k`mg~g`t k` mku ~gcbtkjùmkv qktm ibtmgibtkeu. Kl qg qg~g k` b`{

djwnt bnjwt tmg rwgutkj`# mku ut~waacg qbu vjcktkebc# b`d mku dgekukj`# ckhg

v~j|kà b tmgj~gi# k`|jc|gd vg~ukutkà k` beegvtkà tmg geguub~{ ejùg)

rwgègu. Mg qbu hkccgd n{ b @bzk nwccgt k` Lgn~wb~{ 2;44# mku njd{ nw~kgd k`

b ibuu a~b|gd ib~hgd W`h`jq` @j. 7.

Tzwemkg` Tmj# Vb~ku# >; Owc{ >62>.

X2Y Bcbk` Nbdkjw# @wing~ b`d @wing~u# t~bù.

n{ ^jnk` Ibehb{# Ebin~kdag? Vjckt{ V~guu#

>66=# >25.X>Y Akccgu Dgcgwzg b`d Lck} Awbttb~k# B Tmjw)

ub`d Vcbtgbwu? Ebvktbckui b`d Uemkzjvm~g)

`kb# \jcwig KK# t~bù. n{ N~kb` Ibuuwik#

Cj`dj`? Ej`tk`wwi V~guu# >665# 42


23/24

T~b`ucbtgd n{?

Eb~cgtj` Ejvgcb`d

Em~kutjvmg~ Djuu


24/24

problem book

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