sat/ act/ accuplacer math review

7/30/2019 SAT/ ACT/ Accuplacer Math Review

1/40

Ory Hd`cmd

WM[ NM[A SJROJX

[aj g`lgju{w g`rjsjk l {aj WM[ nm{a wjg{o`lw olgdzkj mso{anj{og mlk lzncjs {aj`sy$ mdhjcsm mlk

bzlg{o`lw$ hj`nj{sy$ mlk km{m mlmdywow, _`z xodd l`{ ljjk {` il`x nm{sogjw$ d`hmso{anw$ b`snmd

{soh`l`nj{sy$ smkomlw$ w{mlkmsk kjrom{o`l$ s gmdgzdzw,

O, Lzncjsw mlk Mso{anj{og Us`ujs{ojw b ol{jhjsw Bmg{`sw mlk nzd{oudjw Bsmg{o`lw$ sm{o`w mlk us`u`s{o`lw Ujsgjl{w

Jqu`ljl{w Mcw`dz{j rmdzj Wj{w mlk wj}zjlgjw

Ol{jhjsw msj xa`dj lzncjsw$ ljhm{orj mlk u`wo{orj, Vjs` ow ml ol{jhjs$ cz{ ow ljo{ajs u`wo{orj l`s

ljhm{orj, Sm{o`lmd lzncjsw msj lzncjsw {am{ gml cj jqusjwwjk mw bsmg{o`lw, Sjmd lzncjsw olgdzkj

ol{jhjsw$ sm{o`lmd lzncjsw$ mlk ossm{o`lmd lzncjsw wzga mw $ j$ mlk 3,

G`lwjgz{orj ol{jhjsw msj ol{jhjsw ol m wj}zjlgj$ jmga cjolh = n`sj {aml {aj usjro`zw ol{jhjs6

$ ) =$ ) 3

Ob {aj wzn b {asjj g`lwjgz{orj ol{jhjsw ow hsjm{js {aml 1;$ xam{ ow {aj wnmddjw{ u`wwocdjrmdzj `b {aj bosw{ ol{jhjs0

) ! ) =/ ) ! ) 3/ < 1;7 ) 7 < 1;

< 38[aj wnmddjw{ u`wwocdj rmdzj bl ow 31,

[aj wzn `b{aj g`lwjgz{orj ol{jhjsw bs`n = {` ml ol{jhjs l ow j}zmd {`

!l ) =/ 3

[mij {aj wj{ `b g`lwjgz{orj ol{jhjsw bs`n = {` 75, [aj wzn `b {aj bosw{ mlk dmw{ ol{jhjsw ow= ) 75 > 7=$ {aj wzn `b {aj wjg`lk mlk wjg`lk bs`n dmw{ ol{jhjsw ow 3 ) 3? > 7=$ mlk {aj wzn

`b {aj {aosk mlk {aosk bs`n dmw{ ol{jhjsw ow 7 ) 31 > 7=, [ajsj xodd cj 753 umosw `b ol{jhjsw

{am{ jmga mkk {` 7=$ w` {aj {`{md wzn xodd cj 7= 753 > ;2:,

a{{u6//xxx,wgsock,g`n/mjawh`3g`ddjhj


2/40

Ory Hd`cmd

Mkkolh s nzd{oudyolh jrjl s kk ol{jhjsw xodd sjwzd{ ol m wzn `s us`kzg{ {am{ ow usjkog{mcdy jrjl

`s `kk6

jrjl ) jrjl > jrjl `kk ) `kk > jrjl `kk ) jrjl > `kk

jrjl jrjl > jrjl `kk `kk > `kk `kk jrjl > jrjl

Ml ol{jhjs gml cj korokjk ol{` m dono{jk wj{ `bbmg{`sw9 {ajsj msj ml olbolo{j lzncjs `bnzd{oudjw

{am{ gml cj korokjk cy m wujgobog ol{jhjs, Ml ol{jhjs xo{a `ldy 3 bmg{`sw !o{wjdb mlk =/ ow m usonj

lzncjs, = ow l`{ m usonj lzncjs$ cz{ 3 ow,

[aj djmw{ g`nn`l nzd{oudj `b {x` ol{jhjsw ow {aj wnmddjw{ u`wo{orj ol{jhjs {am{ ow m nzd{oudj b

c`{a ol{jhjsw, [aj hsjm{jw{ g`nn`l bmg{`s `b {x` ol{jhjsw ow {aj dmshjw{ ol{jhjs {am{ ow m bmg{`s `b

c`{a ol{jhjsw, _`z gml kj{jsnolj c`{a b {ajwj cy bolkolh {aj usonj bmg{`sw `b jmga ol{jhjs,

Xam{ ow {aj kobbjsjlgj cj{xjjl {aj djmw{ g`nn`l nzd{oudjmlk {aj hsjm{jw{ g`nn`l bmg{`s b =55 mlk 150

Usonj bmg{`sw `b =556 3 3 : :

Usonj bmg{`sw `b 156 3 3 3 3 :

=55 mlk 15 wamsj {x` 3w mlk `lj :, Nzd{oudyolh {ajwj usonj bmg{`sw {`hj{ajs horjw zw {ajos

hsjm{jw{ g nn`l bmg{`s6 3 3 : > 35,

Ol {`{md$ b`zs 3w mlk {x` :w muujms ol {ajwj usonj bmg{`sovm{o`lw$ jqgdzkolh sjujm{w,

Nzd{oudyolh {ajwj usonj bmg{`sw {`hj{ajs horjw zw {ajos djmw{ g`nn`l nzd{oudj6 3 3 3 3

: : > ;55,

[aj kobbjsjlgj cj{xjjl {aj DGN mlk {aj HGB ow ;55 35 > 715,

M bsmg{o`l hjljsmddy jqusjwwjw m ums{xa`dj sjdm{o`lwaou cj{xjjl {x` }zml{o{ojw, M sm{o` hjljsmddy

jqusjwwjw m ums{ums{ sjdm{o`lwaou mn`lh {x` `s n`sj }zml{o{ojw,

Ob {aj sm{o` `b c`yw {` hosdw ol {aj gdmww ow =3 {` =8 > =36=8 > =3=8

$ {ajl {aj bsmg{o`l `b c`yw ol

{aj jl{osj gdmww ow=3

=3)=8>

=3

3?,

Ob {aj sm{o` `b hsjjl {` cdzj {` sjk nmscdjw ol {aj fms ow :6;67$ {ajl {aj bsmg{o`l `b hsjjlnmscdjw ol {aj fms ow

:

:);)7>

:

=3,

=55 15

: 3 3

3 3

:



3/40

Ory Hd`cmd

M usù`s{o`l ow ml j}zm{o`l xajsj {x` sm{o`w msj wj{ j}zmd {` jmga `{ajs, W`drj usù`s{o`lw cy

gs`ww.nzd{oudyolh,

Ob >

$ {ajl > ,

M {smol amw {smrjddjk ;5 nodjw ol {aj umw{ ;: nolz{jw, Ob {aj {smol ow n`rolh m{ m g`lw{ml{wujjk$ xam{ kow{mlgj xodd o{ amrj {smrjddjk mb{js ; a`zsw0

G`lrjs{ {` {aj wmnj zlo{w6 ;: nolz{jw > 5,8: a`zsw,

Wj{ zu m usù`s{o`l6

;5 nodjw

5,8: a`zsw>

nodjw; a`zsw

Gs`ww.nzd{oudy mlk w`drj6 ;5 ; > 5,8:5,8: > =25

> 3=7=

7 nodjw

M ujsgjl{gml cj sjusjwjl{jk mw m bsmg{o`l xa`wj kjl`nolm{`s ow =55 `s mw m kjgonmd6 8:* >

8:=55 > 5,8:, W`drj m ujsgjl{ us`cdjn cy g`lrjs{olh {aj ujsgjl{ ol{` m bsmg{o`l mlk gs`ww.

nzd{oudyolh6

75 ow 25* `b xam{ lzncjs075

>25

=55

7555 > 25$ w` > :5Md{jslm{orjdy$ y`z gml wj{ zu ml j}zm{o`l mlk g`lrjs{ {aj ujsgjl{ ol{` m kjgonmd, [aj x`sk `b

njmlw nzd{oudogm{o`l6

75 ow xam{ ujsgjl{ `b =:50 75 > =:5$w` > 5,3 > 35* 75 ow 25* `b xam{ lzncjs0 75 > 5,2$ w` > :5

Ujsgjl{ olgsjmwj `s ujsgjl{ kjgsjmwj ow j}zmd {`

=55*

[aj usogj b muudjw amw kjgsjmwjk bs`n +5,??dc {` +5,8?dc, Xam{ ow {aj ujsgjl{ kjgsjmwjol usogj0

=55* >

+5,?? +5,8?+5,??

=55* > 35,3*



4/40

Ory Hd`cmd

M c``i amw cjjl kowg`zl{jk =:* mlk o{w gzssjl{ usogj ow +=3, Xam{ xmw o{w `soholmd usogj0 +=3

=55* > =:* +=3 > 5,=:

5,1: > +=3 > +=;,=3

Jqu`ljl{l`{m{o`l olkogm{jw {am{ m lzncjs ow cjolh nzd{oudojk cy o{wjdb, [aj lzncjs ow {aj cmwj

mlk {aj lzncjs `b {onjw o{ ow cjolh nzd{oudojk ow {aj jqu`ljl{, Jqu`ljl{w b`dd`x w{mlkmsk szdjw6

= > 5 > =

>=

> ) >

! / > > !/ > !

/

>

;= > ;

;5 > =

;3

>

=

;3

;3 ;7 > ;:

;:

;3> ;7

!;3/7 > ;2

;3 73 > !; 7/3

;3

73> !

;

7/3

;;: > ;;:

Ob :3 > : : $ {ajl xam{ owqol {jsnw `bm mlk c0:

3 > :

: : > :): > :)

q> m ) c

[aj mcw`dz{j rmdzj `b m lzncjs ow o{w kow{mlgj mxmy bs`n 5 `l m lzncjs dolj, [aj mcw`dz{j rmdzj

xodd mdxmyw cj u`wo{orj,

Ob > ;$ {ajl > ; > ;Ob 4 ;$ {ajl ; 4 4 ;

Ob < ;$ {ajl 4 ; < ;



5/40

Ory Hd`cmd

W`drj6 : > ; : > ; : > ;

> ? > =[aow njmlwqow ; zlo{w mxmy bs`n : ol jo{ajs {aj u`wo{orj s ljhm{orj kosjg{o`l,

M nmlzbmg{zsjs `b gjsjmd xodd kowgmsk mdd c`qjw xjohaolh djww {aml 31,: `v mlk n`sj {aml7=,: `v, Xam{ mcw`dz{j rmdzj j}zm{o`l sjusjwjl{w mdd xjoha{wq{am{ xodd cj kowgmskjk0

31,: `v mlk 7=,: `v msj c`{a =,: `v mxmy bs`n 75 `v, Ob {ajwj xjsj {aj xjoha{w {am{ xjsj

kowgmskjk$ xj x`zdk xso{j

75 > =,:[jw{6 75 > =,: 75 > =,:

> 7=,: > 31,:

A`xjrjs$ {aj nmlzbmg{zsjs xodd kowgmsk mdd c`qjw {am{ xjoha djww {aml 31,: `v mlk n`sj {aml7=,: `v{am{ ow$ {a`wj {am{ kobbjs n`sj {aml =,: `v bs`n {aj w{mlkmsk xjoha{ `b 75 `v, @zsj}zm{o`l wa`zdk sjmk

75 < =,:[jw{6 75 < =,: 75 4 =,:

< 7=,: 4 31,:

M wj{ow ml zl`skjsjk g`ddjg{o`l `b o{jnw, [ajwj gml cj lzncjsw$ g`d`sw$ dj{{jsw$ kmyw `b {aj xjji$

`{ajs wj{w$ j{g, [aj zlo`l `b {x` wj{w ow m wj{ g`lwow{olh `b mdd `b {aj jdjnjl{w `b c`{a wj{w, [aj

ol{jswjg{o`l `b {x` wj{w ow m wj{ g`lwow{olh `b `ldy {aj wamsjk jdjnjl{w,

ObM ow {aj wj{ `b {aj bosw{ {asjj u`wo{orj jrjl ol{jhjsw mlk wj{C > =$ 3$ 7$ ;~$ xam{ ow {ajzlo`l `b {aj {x` wj{w0 Xam{ ow {aj ol{jswjg{o`l `b {aj {x` wj{w0

M > 3$ ;$ 2~ mlk C > =$ 3$ 7$ ;~$ w` {ajos zlo`l ow =$ 3$ 7$ ;$ 2~, [ajos ol{jswjg{o`l ow 3$ ;~,

M wj}zjlgj ow ml `skjsjk dow{ b lzncjsw$ b{jl b`dd`xolh m wujgobog um{{jsl, M wj}zjlgj gml cj

kjbolo{j s olkjbolo{j, Ol ml mso{anj{og wj}zjlgj$ {aj ljq{ {jsn ow gsjm{jk cy mkkolh m g`lw{ml{ {`

{aj usjro`zw {jsn, Ol m hj`nj{sog wj}zjlgj$ {aj ljq{ {jsn ow gsjm{jk cy nzd{oudyolh m g`lw{ml{ {`

{aj usjro`zw {jsn,

Mso{anj{og wj}zjlgj6 3$ 2$ =5$ =;$ =1$ 33 ,,, Hj`nj{sog wj}zjlgj6 7$ =3$ ;1$ =?3$ 821 ,,,

_`z nmy ljjk {` bolk {aj wzn `s mrjsmhj `b gjs{mol {jsnw ol m wj}zjlgj$ `s {aj rmdzj `b m wujgobog

{jsn ol m wj}zjlgj, [` mlwxjs mly wj}zjlgj }zjw{o`l$ mdxmyw xso{j z{ m{ djmw{ : {jsnw{` jw{mcdowa



6/40

Ory Hd`cmd

{aj um{{jsl, _`z xodd ljrjs cj mwijk {` kjsorj {aj b`snzdm b`s m wj}zjlgj$ cz{ y`z nmy ljjk {` k`

w`nj{aolh `b {aj w`s{ ol `skjs {` mlwxjs {aj }zjw{o`lw, Ijju ol nolk6

Obm= ow {aj bosw{ {jsn b ml mso{anj{og wj}zjlgj$ kow {aj g`nn`l kobbjsjlgj cj{xjjl {jsnw$mlk l ow {aj lzncjs `b {jsnw$ {ajl

> = ) ! =/ Obm=ow {aj bosw{ {jsn `b m hj`nj{sog wj}zjlgj$ sow {aj g`nn`l sm{o` cj{xjjl {jsnw$ mlk l ow

{aj lzncjs `b {jsnw$ {ajl

> =!/=

Jmga {jsn ol m wj}zjlgj ow 7 {onjw {aj usjgjkolh {jsn, Ob {aj bosw{ {jsn ow 3$ xam{ ow {ajmrjsmhj `b {aj :{a mlk 8{a {jsnw0

8 > 3 72 > =;:1: > 3 7; > =23

[aj mrjsmhj `b {aj {x` {jsnw ow=;:1 ) =23

3> 1=5

W`nj wj}zjlgjw msj ljo{ajs mso{anj{og l`s hj`nj{sog, Jw{mcdowa m um{{jsl$ cz{ k`l{ xmw{j y`zs{onj {syolh {` bolk ml mdhjcsmog b`snzdm b`s {ajwj-

=$ ;$ :$ ?$ =;$ 37$ 786 jmga {jsn ow {aj wzn `b {aj usjro`zw {x` {jsnw, ;$ 2$ ?$ 7$ ;$ 2$ ?$ 76 {aj {jsnw sjujm{ gygdogmddy, M dmlj korokjs ol m wxonnolh u``d amw 88 bdmhw w{szlh ol m s`x, [aj g`d`zsw sjujm{ ol m

um{{jsl6 sjk$ cdzj$ hsjjl$ sjk$ cdzj$ hsjjl$ sjk$ cdzj$ hsjjl ,,, Ob {aj bosw{ bdmh ow sjk$ xam{

g`d`zs ow {aj dmw{ bdmh0

[aj {asjj g`d`zsw xodd sjujm{ {ajnwjdrjw 887 > 3:,22228 {onjw$ `s 3: {onjw xo{a {x`

sjnmolkjsw, B`dd`xolh {aj um{{jsl$ {ajwj dmw{ {x` bdmhw xodd cj sjk mlk cdzj$ sjwujg{orjdy,

[azw$ {aj dmw{ !88{a/ bdmh ow cdzj,

OO, Mdhjcsm mlk Bzlg{o`lw @ujsm{o`lw olr`drolh u`dyl`nomdw J}zm{o`lw mlk wyw{jnw b j}zm{o`lw Us`ujs{ojw b olj}zmdo{ojw X`sk us`cdjnw

Bzlg{o`lw mlk {ajos k`nmolw$ smlhjw W{smlhj wync`dw Doljms mlk }zmksm{og hsmuaw Hsmua cjamro`zs mlk {smlwdm{o`lw



7/40

Ory Hd`cmd

U`dyl`nomdw msj mdhjcsmog jqusjwwo`lw olr`drolh lzncjsw mlk rmsomcdjw, _`z wa`zdk mdsjmky il`x

a`x {` bmg{`s mlk nzd{oudy u`dyl`nomdw, Ijju ol nolk {aj kobbjsjlgj b w}zmsjw b`snzdm6

3 3 > ! ) /! /

Ob3 3 > 3:,2 mlk ) > 1$ xam{ ow {aj rmdzj `b 3 303 3 > ) ! / > 3:,2

1! / > 3:,2 > 7,3

3 3 > 3 > 3 7,3 > 2,;

Sjnjncjs xam{ {aj }zjw{o`l ow mwiolhb`s {aow us`cdjn$ o{ x`zdk amrj cjjl m xmw{j `b{onj {` w`drj b`sqmlkyolkorokzmddy-

_`z nmy ljjk {` w`drj wolhdj j}zm{o`lw mlk wyw{jnw b j}zm{o`lw, [` w`drj m wyw{jn `b j}zm{o`lw$

y`z gml ow`dm{j m rmsomcdj ol lj j}zm{o`l mlk wzcw{o{z{j {aj sjwzd{olh jqusjwwo`l ol{` {aj {ajs

j}zm{o`l, W`nj{onjw y`z gml mdw` wmrj {onj cy mkkolh s wzc{smg{olh {x` s n`sj j}zm{o`lw,

Ob ; {onjw m lzncjs nolzw m wjg`lk lzncjs ow j}zmd {` =$ mlk {aj wzn `b {aj {x` lzncjsw ow?$ xam{ ow {ajos us`kzg{0

Gsjm{j m wyw{jn b j}zm{o`lw6

; > =

) > ?

Mkk6 : > =5

W`drj6 > 3 > ? 3 > 8

> 3 8 > =;

X`si xo{a olj}zmdo{ojw mlk wyw{jnw b olj}zmdo{ojw {aj wmnj xmy y`z x`zdk x`si xo{a

j}zm{o`lw mlk wyw{jnw b j}zm{o`lw$ cz{ ijju ol nolk wjrjsmd ijy us`ujs{ojw, Mly ujsm{o`l

olr`drolh u`wo{orj lzncjsw amw l` jbbjg{ l {aj olj}zmdo{y$ cz{ nzd{oudyolh s korokolh cy m ljhm{orj

lzncjs sjrjswjw {aj olj}zmdo{y, Ob c`{a wokjw `b ml olj}zmdo{y msj u`wo{orj s ljhm{orj$ {miolh {ajos

sjgous`gmd mdw` sjrjswjw {aj olj}zmdo{y,

Ob 4 $ {ajl < Ob 4 mlk ow ljhm{orj$ {ajl < mlk

n`sj$ {`{md$ olgsjmwjk cy$ jqgjjkw$ hmoljk$

`dkjs$ bms{ajs$ hsjm{js$ wzn

mkko{o`l )

djww$ kjgsjmwjk$ d`w{$ y`zlhjs$ bjxjs$

kobbjsjlgj

wzc{smg{o`l .

`b$ us`kzg{$ jmga nzd{oudogm{o`l

b`s$ ujs$ `z{ `b$ }z`{ojl{ korowo`l

m{ djmw{ olj}zmdo{y

m{ n`w{ olj}zmdo{y

[aj {`{md `b Fmijw mlk Mnyw mhjw ow =8, Dmw{ yjms$ Mny xmw {xogj Fmijw mhj, A`x `dk ow Fmijl`x0

Ijy x`skw6 {`{md$ dmw{ yjms$ mlk {xogj

Dj{fsjusjwjl{ Fmijw gzssjl{ mhj mlk msjusjwjl{ Mnyw gzssjl{ mhj6 ) > =8



9/40

Ory Hd`cmd

[` sjusjwjl{ {aj sjdm{o`lwaou cj{xjjl {ajos mhjw dmw{ yjms$ wzc{smg{ = bs`n jmga `b {ajos

gzssjl{ mhjw6

= > 3! =/W`drj b`sf6

> =8 =8 = > 3! =/=2 > 3 3

=1 > 7 > 2

Fmij ow gzssjl{dy 2 yjmsw `dk,

Ml jrjl{ amw {x` mknowwo`l usogjw6 mkzd{ {ogij{w msj +=5 jmga mlk w{zkjl{wjlo`s {ogij{wmsj +1 jmga, [aj {ogij{ `bbogj amw w`dk 88 {ogij{w {`{mddolh +212, A`x nmly mkzd{ {ogij{w xjsj

w`dk0

Ijy x`skw6 jmga$ {`{mddolh

Dj{m sjusjwjl{ {aj lzncjs b mkzd{ {ogij{w mlk w sjusjwjl{ {aj lzncjs `b w{zkjl{wjlo`s

{ogij{w6

) > 88

[` sjusjwjl{ {`{md sjrjlzj$ nzd{oudy jmga {yuj b {ogij{ cy o{w usogj6

=5 ) 1 > 212W`drj b`s m6

> 88 =5

) 1!88

/ > 212

=5 ) 2=2 1 > 2123 > 85 > 7:

[ajsj xjsj 7: mkzd{ {ogij{w w`dk,

_`z gml `b{jl w`drj m x`sk us`cdjn olr`drolh sm{jw xo{a {aj b`dd`xolh j}zm{o`l6

>

Ml mosudmlj bdjx bs`n Nowwowwouuo {` Gmdob`slom, @l {aj sj{zsl {sou bs`n Gmdob`slom {`Nowwowwouuo$ o{w mrjsmhj wujjk xmw sjkzgjk cy :5 nodjw ujs a`zs mlk {aj sjwzd{olh bdoha{ xmw=

=5d`lhjs {aml {aj `soholmd, Xam{ ow {aj mosudmljw `soholmd mrjsmhj wujjk bs`n Nowwowwouuo {`

Gmdob`slom0

Dj{kcj {aj kow{mlgj$ scj {aj mosudmljw `soholmd wujjk mlk {cj {aj {onj$ ol a`zsw$ `b o{wbdoha{ bs`n Nowwowwouuo {` Gmdob`slom,



10/40

Ory Hd`cmd

>

B`s o{w sj{zsl {sou$ `rjs {aj wmnj kow{mlgj$ o{w wujjk ow :5nua djww mlk o{w {onj ow=

=5hsjm{js6

> :5 ===5

W`drj b`s s6

> :5 ===5

> ! :5/ ==

=5

> ===5

::=

=5 > ::

> ::5[aj udmlj(w `soholmd wujjk xmw ::5 nua,

Mkmn gml umol{ m a`zwj ol 2 a`zsw, Xajl Imsjl g`njw {` x`si$ {aj {x` {`hj{ajs gml umol{m a`zwj ol ; a`zsw, Mwwznolh {am{ c`{a x`si m{ m g`lw{ml{ sm{j md`lj mlk {`hj{ajs$ a`x d`lh

k`jw o{ {mij Imsjl {` umol{ m a`zwj md`lj0

Xj xodd zwj {aj wmnj j}zm{o`l$ cz{ {aj kow{mlgj kxodd sjusjwjl{ {aj lzncjs `b a`zwjw

umol{jk,

>

Dj{ Mkmnw sm{j cj , Aj umol{w = a`zwj ol 2 a`zsw6= > 2 > =2

Dj{ Imsjlw sm{j cj , [ajos sm{j {`hj{ajs ow ! ) /, [`hj{ajs$ {ajy umol{ {aj wmnj a`zwjol ; a`zsw6

= > ) ;

Mw Mkmnw sm{j ow =2$ xj gml w`drj b`s 6

= > !=2

) / ;=

2) > =;

> ==3

Imsjlw sm{j ow ==3

a`zwjw ujs a`zs$ w` waj gml umol{ = a`zwj ol =3 a`zsw,



11/40

Ory Hd`cmd

M bzlg{o`l ow m szdj {am{ mww`gom{jw lj wj{ b lzncjsw xo{a ml`{ajs kjujlkjl{ wj{ b lzncjsw, [aj

bzlg{o`l > ) = {jddw zw {am{ jrjsy sjmd lzncjs ow mwwohljk {` {aj g`ssjwu`lkolh lzncjs ) =, Ob y`z msj mwijk {` bolk7$ wonudy b`dd`x {aj szdj g`lljg{olh 7 {` o{w mwwohljk lzncjs6

7 > 7 ) = > ;,

Ob > 73 3 $ xam{ ow =3 )=0

=3

> 7 =3

3

3 =3

> 7;

= > =;

= > 7=3 3= > 7 3 > = =

3 )= > =

;) = >

7

;

Ob > 73 3$ xam{ ow!3 /03 > 7!3/3 3!3/ > 7; 33

Ob > 73 3$ xam{ ow!!3//03 > 733 33 > =3 ; > 11 > 713 31 > =?3 =2 > =823 > =82

[aj k`nmol `b m bzlg{o`l ow {aj wj{ `b mdd {aj lzncjsw b`s xaoga {aj bzlg{o`l ow kjboljk{am{ ow$ mdd{aj oluz{ lzncjsw b`s xaoga {aj bzlg{o`l w{odd x`siw, [aj smlhj `b m bzlg{o`l ow {aj wj{ `b mdd {aj`z{uz{ lzncjsw,

Xam{ ow {aj k`nmol `b {aj bzlg{o`l > ! ) 3/=3 0 > ! ) 3/=3 > ) 3

Cjgmzwj xj gml{ {mij {aj w}zmsj s``{ `b m ljhm{orj lzncjs$ xj il`x {am{ ) 3gml{ cjljhm{orj6

) 3 5 3

Xam{ lzncjs ow l`{ ol {aj k`nmol `b {aj bzlg{o`l > = 30Xj gml {mij {aj w}zmsj `b mly sjmd lzncjs q$ cz{ xj gml{ korokj cy vjs`, [ajsjb`sj6



12/40

Ory Hd`cmd

3 5 5

Vjs` ow {aj `ldy lzncjs l`{ ol {aj k`nmol `b `zs bzlg{o`l,

Olw{jmk b zwolh bzlg{o`l l`{m{o`l {` sjusjwjl{ {aj sjdm{o`lwaouw cj{xjjl wj{w b lzncjsw$ {aj WM[

xodd `b{jl zwj w{smlhj wync`dw6 wnodjy bmgjw$ w{msw$ czccdjw$ j{g, [sjm{ {ajwj {aj wmnj xmy y`z

x`zdk {sjm{ bzlg{o`l }zjw{o`lwd``i b`s {aj szdj$ mlk bohzsj `z{ a`x y`z wa`zdk muudy o{,

B`s mdd ljhm{orj rmdzjwq$ dj{ > ; ) 8, B`s vjs` mlk mdd u`wo{orj rmdzjwq$ dj{ > 73 ,Xam{ ow {aj rmdzj `b!.=/0

= > ;= ) 8 > 77 > 773 > 38

=

> 38

B`s mdd l`l.vjs` lzncjsw m mlk c$dj{ cj kjboljk mw > 3

Ob7 ; > 3$ xam{ ow {aj rmdzj `bq0

7 ; >3 7

;>

2

;

3 >3

3 > 2

;>

> 73

Dj{ sjusjwjl{ {aj lzncjs b bmg{`sw b mly sjmd lzncjs q, B`s jqmnudj$2 > ; cjgmzwj2 amw b`zs bmg{`sw6 =$ 3$ 7 mlk 2, Xam{ ow ?0

? amw {asjj bmg{`sw6 =$ 7$ mlk ?, [ajsjb`sj$ ? > 7,

[aj hsmua `b m bzlg{o`l ow {aj g`ddjg{o`l `b mdd `skjsjk umosw !$ /xajsj >, [azw$ {aj hsmua`b > ) = ow {aj dolj > ) =, _`z xodd ljrjs cj mwijk {` ksmx m hsmua `l {aj WM[$ cz{ y`znmy ljjk {` kjsorj ml j}zm{o`l `s bzlg{o`l cmwjk `l m hsmua,



13/40

Ory Hd`cmd

Doljms bzlg{o`lw gml cj sjusjwjl{jk ol {aj b`sn > ) $ xajsj n ow {aj wdùj mlk c ow {ajy.ol{jsgju{, Sjnjncjs {aj b`snzdm b`s gmdgzdm{olh wdùj6

> sowjszl

>3 =3 =

Bmg{w mc`z{ wdùj6

A`sov`l{md doljw amrj wdùjw `b vjs`, Rjs{ogmd doljw amrj zlkjboljk wdùjw, L`l.rjs{ogmd umsmddjd doljw amrj j}zmd wdùjw, L`l.rjs{ogmd ujsujlkogzdms doljw amrj wdùjw xa`wj us`kzg{ ow .=,

M dolj xo{a m wdùj `b : umwwjw {as`zha {aj uòl{w !i$ 8/ mlk !.=$ .7/, Xam{ ow {aj rmdzj `bi0: > 3 =3 = > 7 8=

:= > =5= > 3

> =

Ol {ajqy.g``skolm{j udmlj$ dolj a amw m wdùj `b 3 mlk ow ujsujlkogzdms {` doljh, Ob doljhumwwjw {as`zha {aj sohol mlk ol{jswjg{w dolj a m{ {aj uòl{ !m$ 7 ) m/$ xam{ ow {aj rmdzj `bm0

Dj{n sjusjwjl{ {aj wdùj `b doljh, Doljh mlk dolj a msj ujsujlkogzdms$ w`6

3 > = > =

3

Xj il`x {am{ doljh umwwjw {as`zha {aj `sohol$ w` o{wy.ol{jsgju{ ow 5, O{w j}zm{o`l nzw{ cj6

> =3

Udzh {aj uòl{ !m$ 7 ) m/ ol{` {aow j}zm{o`l {` w`drj b`s m67 )

>

=

3

7

3 > 7

> 3

]zmksm{og bzlg{o`lw gml cj sjusjwjl{jk ol {aj b`sn > 3 ) ) $ xajsj g ow {ajy.ol{jsgju{,[aj wohl `bm kj{jsnoljw xaj{ajs {aj umsmc`dm ujlw zuxmskw !m ow u`wo{orj/ `s k`xlxmskw !m ow



14/40

Ory Hd`cmd

M C

b!q/ > q3 . =

h!q/ > .q3 ) g

y

q

ljhm{orj/, _`z gml `b{jl bolk {ajq.ol{jsgju{w `b m umsmc`dm cy bmg{`solh9 {aj WM[ xodd ljrjs sj}zosj

y`z {` zwj {aj }zmksm{og b`snzdm,

[aj rjs{jq `b m umsmc`dm ow o{w d`xjw{ `s aohajw{ uòl{, Ob xj gmdd {aj g``skolm{jw `b {aj rjs{jq !a$ i/$

{ajl6

> 3

Xajl mwijk {` w`drj b`s `{ajs uòl{w l m umsmc`dm$ sjnjncjs {am{ m umsmc`dm ow wynnj{sogmd

mc`z{ {aj rjs{ogmd dolj {as`zha o{w rjs{jq,

Ol {aj bohzsj cjd`x$ > 3 = mlk > 3 ) $ xajsj g ow m g`lw{ml{, [aj {x`bzlg{o`lw ol{jswjg{ m{ uòl{wM mlk C, Ob > ;$ xam{ ow {aj rmdzj bg0

Cjgmzwj m umsmc`dm ow wynnj{sogmd mlk > ;$jmga uòl{ b ol{jswjg{o`l nzw{ cj 3 zlo{w mxmybs`n {ajy.mqow, [azw$ xj gml gmdd {ajos

g``skolm{jw !.3$y/ mlk !3$y/, W`drj b`sycy

udzhholh lj b {ajwj uòl{w ol{` {aj bosw{

j}zm{o`l6

> 3 = > 33 =

> 7

[aj {x` j}zm{o`lw ol{jswjg{ m{ !.3$ 7/ mlk !3$ 7/,

Udzh lj b {ajwj uòl{w ol{` {aj wjg`lk j}zm{o`l

{` w`drj b`s g6

> 3 ) 7 > 33 )

> 8

_`z nmy cj mwijk {` mlmdyvj {aj cjamro`zs `b

hsmuaw xo{a`z{ il`xolh s zwolh {ajos j}zm{o`lw,

[aj hsmua `b >!/ ow wa`xl cjd`x, Ob3 > $ xam{ ow03 > ;$ w` > ; >; > 5

5

3

;

2

1

=5

5 3 ; 2 1 =5

y

q



15/40

Ory Hd`cmd

M {smlwdm{o`l `b m hsmua ow m sohok waob{ rjs{ogmddy `s a`sov`l{mddy {am{ k`jw l`{ gamlhj {aj wovj `s

wamuj `b {aj hsmua, B`s {aj hsmua `b >!/$ m rjs{ogmd {smlwdm{o`l bm zlo{w mlk m a`sov`l{md{smlwdm{o`l bc zlo{w sjwzd{w ol {aj j}zm{o`l

>! /

Dj{w cjhol xo{a {aj hsmua b > 3, Ob xj waob{ rjs{ogmddy 7 zlo{w mlk a`sov`l{mddy 3 zlo{w$ xj hj{ 7 > ! 3/3, Ob xj waob{ rjs{ogmddy .7 zlo{w mlk a`sov`l{mddy .3 zlo{w$ xj hj{ ) 7 > ! ) 3/3,

Cjd`x msj {aj hsmuaw b {aj bzlg{o`lw > 7 3 mlk > ) $ xajsj g mlkkmsj c`{a g`lw{ml{w, Xam{ ow {aj rmdzj `b ) 0

y > q3

y

q

y . 7> !q . 3/3

y

q

y ) 7 > !q ) 3/3

y

q

!.=$ =/

!=$ .=/

y > b!q/

y

q

!=$ :/

!7$ 7/

y > h!q/

y

q



16/40

Ory Hd`cmd

Ol {aj j}zm{o`l >! /$ m sjusjwjl{w {aj rjs{ogmd waob{ mlk c sjusjwjl{w {aja`sov`l{md waob{, Sj.xso{j {aj j}zm{o`l bh!q/ {` d`ì wonodms6

>

Ajsj$ ksjusjwjl{w {aj rjs{ogmd waob{ mlk g sjusjwjl{w {aj a`sov`l{md waob{, Cy g`numsolh {aj{x` uòl{w horjl l {aj hsmua$ xj gml wjj {am{ {aj hsmua amw cjjl {smlwdm{jk 3 zlo{w

a`sov`l{mddy mlk ; zlo{w rjs{ogmddy, [azw6

> 3 > ;

) > 2

OOO,Hj`nj{sy Uòl{w$ doljw$ mlk mlhdjw [somlhdjw mlk wujgomd {somlhdjw U`dyh`lw mlk }zmksodm{jsmdw

Gosgdjw W`dok hj`nj{sy G``skolm{j hj`nj{sy

Mly {x` kow{olg{ uòl{w gml cj g`lljg{jk cy `lj mlk `ldy `lj dolj, M nokuòl{ow {aj uòl{ {am{

korokjw m dolj wjhnjl{ ol{` {x` j}zmd ums{w, _`z nmy cj mwijk {` bolk {aj djlh{a `b m dolj wjhnjl{ `s

{aj sm{o` `b `lj dolj wjhnjl{ {` ml`{ajs, _`z nmy mdw` ljjk {` bolk {aj `skjs `b uòl{w md`lh m

g`nn`l dolj,

Uòl{wM$ C$ G$ K$ mlk Jdoj `l m dolj$ l`{ ljgjwwmsody ol {am{ `skjs, C ow {aj nokuòl{ `bMK $ Gow{aj nokuòl{ bMC $ mlk K ow {aj nokuòl{ bCJ , Ob > ;$ xam{ ow {aj rmdzj `bGJ0

Cjhol cy ksmxolh m komhsmn {` uz{ {aj uòl{w ol {aj g`ssjg{ skjs, C ow {aj nokuòl{ `bMK 6

Gow {aj nokuòl{ bMC 6

K ow {aj nokuòl{ bCJ 6



17/40

Ory Hd`cmd

Xj il`x {am{ > ;$ w` xj gml xso{j ol {aj djlh{a `b jmga dolj wjhnjl{6

Mkkolh {`hj{ajs {aj g`nu`ljl{ dolj wjhnjl{w$ xj bolk {am{ > 35,

Ml mlhdj ow b`snjk xajl {x` doljw `s dolj wjhnjl{w ol{jswjg{, Il`x {aj b`dd`xolh kjbolo{o`lw6

Ml mlhdj njmwzsolh djww {aml ?5 ow ml mgz{j mlhdj, Ml mlhdj njmwzsolh ?5 ow m soha{mlhdj, Ml mlhdj njmwzsolh cj{xjjl ?5 mlk =15 ow ml `c{zwj mlhdj, Ml mlhdj njmwzsolh =15 ow m w{smoha{mlhdj,

Il`x mdw` {aj b`dd`xolh mlhdj wznw6

[aj wzn `b mly lzncjs `b mlhdjw {am{ b`sn m w{smoha{ dolj ow =15, [aj wzn `b mly lzncjs `b mlhdjw ms`zlk m u`ol{ ow 725, [x` mlhdjw {am{ mkk {` ?5 msj gmddjk g`nudjnjl{msy mlhdjw, [x` mlhdjw {am{ mkk {` =15 msj gmddjk wzuudjnjl{msy mlhdjw,

M dolj {am{cowjg{w ml mlhdj korokjw o{ ol{` {x` j}zmd ums{w, Ol {aj b`dd`xolh komhsmn$ ob > $ {ajldolj dcowjg{w MCG6

G`nudjnjl{msy Mlhdjw Wzuudjnjl{msy Mlhdjw



18/40

Ory Hd`cmd

Rjs{ogmd mlhdjw msj {aj uu`wo{j mlhdjw b`snjk cy {x` ol{jswjg{olh doljw, [ajwj msj g`lhszjl{6

> mlk > ,

Ob {x` doljw msj umsmddjd$ {ajy xodd ljrjs ol{jswjg{, Xj gml kj{jsnolj {am{ {x` doljw msj umsmddjd ob

{ajsj ow m {aosk dolj {am{ ow ujsujlkogzdms {` c`{a `b {ajn6

Ob m {aosk dolj !{smlwrjswmd/ ol{jswjg{w m umos `b umsmddjd doljw$ o{ b`snw joha{ mlhdjw, Il`x {aj

b`dd`xolh sjdm{o`lwaouw6

[aj umosw `bg`ssjwu`lkolh mlhdjw msj g`lhszjl{6 > $ >$ > $ mlk > , [aj umosw `bmd{jslm{j ol{jso`s mlhdjw msj g`lhszjl{6 > mlk > , [aj umosw `bmd{jslm{j jq{jso`s mlhdjw msj g`lhszjl{6 > mlk > , [aj umosw `bg`lwjgz{orj ol{jso`s mlhdjw msj wzuudjnjl{msy6 ) > =15 mlk

) > =15,



19/40

Ory Hd`cmd

Ol {aj komhsmn cjd`x$ borj doljw ol{jswjg{ ol m u`ol{ {` b`sn borj mlhdjw, Ob > 3$ xam{ ow {ajrmdzj `b0

[aj wzn `b mlhdjw ms`zlk m u`ol{ ow 7256

) 7 ) ) 3 ) ; > 725; ) 8 > 725

> 3$ w` xj gml wzcw{o{z{j mlk w`drj b`s 6

; ) =; > 725=1 > 725

> 35

Ol {aj komhsmn cjd`x$ dolj l ow ujsujlkogzdms {` c`{a dolj dmlk dolj n$ mlk dolju cowjg{wSW[, Xam{ ow {aj rmdzj `b0Cjgmzwj dolj l ow ujsujlkogzdms {` c`{a d

mlk n$ xj gml g`lgdzkj {am{dmlk n msj

umsmddjd doljw,

Dolju cowjg{w SW[$ m soha{ mlhdj$ mlkkorokjw o{ ol{` {x` mlhdjw `b ;: jmga, Xj

gml dmcjd {ajwj l {aj komhsmn,

Cjgmzwj dolju ol{jswjg{w {x` umsmddjd

doljw$ xj il`x {am{ umosw `b g`lwjgz{orj

ol{jso`s mlhdjw msj wzuudjnjl{msy,

[ajsjb`sj6

) ;: > =15 > =7:



20/40

Ory Hd`cmd

[somlhdj hj`nj{sy ow {aj n`w{ g`nn`ldy {jw{jk hj`nj{sy {`uog l {aj WM[,

[aj wzn `b {aj ol{jso`s mlhdjw `b m {somlhdj ow =15, Ml jq{jso`s mlhdj ow ml mlhdj {am{ ow b`snjk cy

jq{jlkolh `lj wokj `b {aj {somlhdj, Ml jq{jso`s mlhdj `b m {somlhdj ow j}zmd {` {aj wzn `b {aj {x`

`uu`wo{j ol{jso`s mlhdjw, Ol {aj b`dd`xolh komhsmn$ ) ) > =15 mlk > ) ,

[somlhdjw gml cj gdmwwobojk cy ol{jso`s mlhdjw mlk wokj djlh{aw6 Ml mgz{j {somlhdj amw {asjj mgz{j mlhdjw, Ml `c{zwj {somlhdj amw lj c{zwj mlk {x` mgz{j mlhdjw, M soha{{somlhdj amw lj mlhdj njmwzsolh ?5, Ml j}zodm{jsmd {somlhdj amw {asjj g`lhszjl{ wokjw mlk {asjj g`lhszjl{ mlhdjw, Mdd {asjj b

{ajwj mlhdjw njmwzsj 25,

Ml ow`wgjdjw {somlhdj amw {x` g`lhszjl{ wokjw mlk {x` g`ssjwu`lkolh g`lhszjl{ mlhdjw, M wgmdjlj {somlhdj amw {asjj wokjw b kobbjsjl{ djlh{aw mlk {asjj mlhdjw b kobbjsjl{

njmwzsjw,

Ol {aj bohzsj {` {aj soha{$ MCGow ml j}zodm{jsmd{somlhdj$ JBGow m soha{ {somlhdj$ mlk

>

, Ob {aj

njmwzsj `bKBJow 35$ xam{ ow {aj rmdzj `bq0

Bodd ol mw nmly `b {aj mlhdj njmwzsjw mw u`wwocdj xo{a

{aj horjl olb`snm{o`l, MCGow ml j}zodm{jsmd {somlhdj$w` jmga b o{w ol{jso`s mlhdjw njmwzsjw 25,



21/40

Ory Hd`cmd

> $ w` KBJow ow`wgjdjw mlk ,Cjgmzwj KBJnjmwzsjw 35 mlk {aj ol{jso`s mlhdjw`b m {somlhdj nzw{ mkk {` =15$ xj gml g`lgdzkj {am{

BKJmlk BJK jmga njmwzsj 15,

Bolmddy$ JBGnjmwzsjw ?5 mlk JGBnjmwzsjw25$ w` GJBnzw{ njmwzsj 75,

Xj l`x amrj mdd {aj olb`snm{o`l ljgjwwmsy {` w`drj

b`sq$ xaoga dojw `l m w{smoha{ dolj xo{a {x` `{ajs

mlhdjw6

) 15 ) 75 > =15 > 85

[aj ayu`{jlzwj `b m soha{ {somlhdj ow {aj wokj `uu`wo{j {aj soha{ mlhdj, Ob {aj {x` djhw `b m soha{{somlhdj amrj djlh{aw m mlk c mlk {aj ayu`{jlzwj amw m djlh{a g$ {ajl {aj Uy{amh`sjml [aj`sjn

w{m{jw {am{

3 ) 3 > 3

Wujgomd soha{ {somlhdjw amrj m wj{ sm{o` mn`lh {aj djlh{aw `b {ajos wokjw$ kjsorjk bs`n {aj

Uy{amh`sjml [aj`sjn,

M {somlhdj xo{a mlhdjw b75.25.?5 amw m wa`s{ djh njmwzsolh $ m d`lh djh njmwzsolh 7$mlk m ayu`{jlzwj njmwzsolh 3,

M {somlhdj xo{a mlhdjw b;:.;:.?5 amw {x` djhw {am{ jmga njmwzsj

mlk m ayu`{jlzwj

njmwzsolh 3, M 7.;.: soha{ {somlhdj ow m soha{ {somlhdj xa`wj wokjw msj ol {aj sm{o` 76;6:,



22/40

Ory Hd`cmd

Ol {aj komhsmn {` {aj soha{$ MCGow m soha{{somlhdj$ CKGow m soha{ mlhdj$ KGCnjmwzsjw 75$ mlk > =, Xam{ ow {ajujsonj{js `bMCG0

MCG$ MKC$ mlk CKGmsj mdd 75.25.?5{somlhdjw, Cjgmzwj {aj djlh{a `bMK ow

horjl$ xj gml bolk {aj djlh{aw `bMC6

> = > 3

Bs`n {aj djlh{a bMC$ xj gml bolk {aj

djlh{aw bCGmlkMG6 > 3

> 37 > ;

[aj ujsonj{js `b MCGow 3 ) 37 ) ; >2 ) 37,

[aj {somlhdj olj}zmdo{y w{m{jw {am{ {aj wzn `b {aj djlh{aw `b {x` wokjw `b m {somlhdj ow mdxmyw

hsjm{js {aml {aj djlh{a `b {aj {aosk wokj,

Ob {x` wokjw `b m {somlhdj njmwzsj ; mlk 2 zlo{w$ xam{ g`zdk cj {aj djlh{a `b {aj {aosk wokj0Zwolh {aj {somlhdj olj}zmdo{y$ xj il`x {am{ {aj djlh{a `b {aosk wokj nzw{ cj djww {aml =5

zlo{w6

; ) 2 < $ w` =5 <

Xj mdw` il`x {am{ {aj djlh{aw `b {aj {aosk wokj udzw jo{ajs `lj `b {aj `{ajs wokjw nzw{ cj

hsjm{js {aml {aj djlh{a b {aj sjnmololh wokj6

) ; < 2$ w` < 3

) 2 < ;$ w` < 3[aj djlh{a `b {aj {aosk wokj nzw{ cj hsjm{js {aml 3 cz{ djww {aml =5 zlo{w,

Obcsjusjwjl{w m {somlhdjw cmwj mlk a sjusjwjl{w o{w ajoha{$ {aj msjm `b m {somlhdj ow

> =3



23/40

Ory Hd`cmd

G`lhszjl{{somlhdjw msj {aj wmnj wamuj mlk wovj6 {ajy amrj g`ssjwu`lkolh g`lhszjl{ mlhdjw mlk

g`lhszjl{ wokjw, Xj gml us`rj {am{ {x` {somlhdjw msj g`lhszjl{ cy mly b {aj b`dd`xolh njmlw6

Wokj.wokj.wokj6 {aj g`ssjwu`lkolh wokjw msj g`lhszjl{

Wokj.mlhdj.wokj6 {x` g`ssjwu`lkolh wokjw mlk {aj mlhdjw {ajy b`sn msj g`lhszjl{

Mlhdj.wokj.mlhdj6 {x` g`ssjwu`lkolh mlhdjw mlk {aj wokjw cj{xjjl {ajn msj g`lhszjl{

Wonodms {somlhdjw amrj {aj wmnj wamuj cz{ kobbjsjl{ wovjw, [ajos g`ssjwu`lkolh mlhdjw msj

g`lhszjl{$ mlk {ajos g`ssjwu`lkolh wokjw msj us`u`s{o`lmd, Xj gml us`rj {x` {somlhdjw msj wonodms

ob {x` g`ssjwu`lkolh mlhdj umosw msj g`lhszjl{$ s ob `lj g`ssjwu`lkolh mlhdj umos ow g`lhszjl{ mlk

{aj mkfmgjl{ wokjw msj us`u`s{o`lmd,

Wonodms [somlhdjw



24/40

Ory Hd`cmd

Ol {aj komhsmn {` {aj soha{$ MCGow m soha{ {somlhdj$Gnjmwzsjw ;:$ mlk > ;, ObK ow {aj nokuòl{ `bMC mlk Jow {aj nokuòl{ bCG $ xam{ ow {aj djlh{a `bKJ0Mdd ol{jso`s mlhdjw `b m {somlhdj mkk {` =15$ w` M mdw`njmwzsjw ;:, MCGm ;:.;:.?5 {somlhdj mlk mlow`wgjdjw {somlhdj$ w` > ; mw xjdd,

K ow {aj nokuòl{ bMC mlk Jow {aj nokuòl{ bCG $w` CJmlk CK jmga njmwzsj 3 zlo{w, Cjgmzwj CJmlk

CK msj jmga amdb `bMC mlk CG$ mlk c`{a umosw b`sn

{aj wmnj soha{ mlhdj$ xj gml g`lgdzkj {am{ MCGmlk KCJmsj wonodms {somlhdjw, [azw$ KCJowmdw` m ;:.;:.?5 {somlhdj,

Ob jmga `b {aj djhw `b KCJnjmwzsj 3 zlo{w$ {ajl{aj ayu`{jlzwj nzw{ njmwzsj 33 zlo{w,

> 33

M u`dyh`l ow ml jlgd`wjk wamuj xo{a w{smoha{ wokjw, M sjhzdms u`dyh`l amw g`lhszjl{ wokjw mlk

g`lhszjl{ ol{jso`s mlhdjw, B`s m u`dyh`l xo{a l wokjw$ {aj wzn b {aj ol{jso`s mlhdjw ow

=15! 3/

M }zmksodm{jsmd ow m b`zs.wokjk u`dyh`l, [aj wzn `b {aj ol{jso`s mlhdjw `b m }zmksodm{jsmd ow 725,

M umsmddjd`hsmn ow m }zmksodm{jsmd xo{a {x` umosw b umsmddjd wokjw, Sa`nczwjw$ sjg{mlhdjw$ mlkw}zmsjw bmdd ol{` {aow gm{jh`sy, [aj uu`wo{j wokjw b m umsmddjd`hsmn msj g`lhszjl{ ol djlh{a mlk {aj

ùu`wo{j mlhdjw msj g`lhszjl{ ol njmwzsj, Mkfmgjl{ mlhdjw msj wzuudjnjl{msy, Jmga komh`lmd

korokjw {aj umsmddjd`hsmn ol{` {x` g`lhszjl{ {somlhdjw, [aj {x` komh`lmdw msj l`{ljgjwwmsody {aj

wmnj djlh{a$ cz{ {ajy cowjg{ jmga `{ajs,



25/40

Ory Hd`cmd

Obc sjusjwjl{w {aj cmwj b {aj umsmddjd`hsmn mlk a sjusjwjl{w o{w ajoha{ !ujsujlkogzdms {` {aj cmwj/$

{ajl {aj b`snzdm b`s {aj msjm b mly umsmddjd`hsmn ow

>

M sa`nczw ow m }zmksodm{jsmd xa`wj b`zs wokjw msj mdd {aj wmnj djlh{a, Mdd sa`nczwjw msj mdw`

umsmddjd`hsmnw mlk amrj {aj wmnj us`ujs{ojw, Mkko{o`lmddy$ {aj komh`lmdw b m sa`nczw msj mdxmyw

ujsujlkogzdms mlk cowjg{ {ajos ol{jso`s mlhdjw,

M sjg{mlhdj ow m }zmksodm{jsmd xo{a b`zs soha{ mlhdjw, Mdd sjg{mlhdjw msj mdw` umsmddjd`hsmnw mlk

amrj {aj wmnj us`ujs{ojw$ cz{ {aj komh`lmdw b m sjg{mlhdj msj {aj wmnj djlh{a,



26/40

Ory Hd`cmd

[aj msjm `b m sjg{mlhdj ow wonudy o{w cmwj nzd{oudojk cy o{w ajoha{, Ob o{w djlh{a ow dmlk o{w xok{a ow x$

{ajl {aj ujsonj{js `b m sjg{mlhdj ow

> 3! ) /

M w}zmsj ow m sjhzdms }zmksodm{jsmd{am{ ow$ mdd b`zs wokjw mlk mdd b`zs mlhdjw msj {aj wmnj njmwzsj,W}zmsjw msj c`{a sjg{mlhdjw mlk sa`nczwjw, [aj komh`lmdw b m w}zmsj msj `b j}zmd djlh{a mlk

ujsujlkogzdms$ mlk {ajy cowjg{ o{w ol{jso`s mlhdjw, [aj komh`lmdw korokj {aj w}zmsj ol{` g`lhszjl{

;:.;:.?5 {somlhdjw,

Ob {aj djlh{a `b m wokj ow w$ {ajl {aj msjm `b m w}zmsj ow 3 mlk {aj ujsonj{js ow ;,

M {smujvòk ow m }zmksodm{jsmd xo{a `ldy `lj umos `b umsmddjd wokjw, Ml ow`wgjdjw {smujvòk amw {x`

umosw b g`lhszjl{ mlhdjw$ mlk o{w {x` l`l.umsmddjd wokjw msj g`lhszjl{,

Obm mlk c msj {aj djlh{aw `b {aj umsmddjd wokjw mlk a ow {aj ajoha{ ujsujlkogzdms {` {ajwj wokjw$ {ajl

{aj msjm `b m {smujvòk ow

> =3

! ) /



27/40

Ory Hd`cmd

Xam{ ow {aj msjm `b {aj w}zmsj wa`xl {` {aj soha{0Xj il`x {am{ m komh`lmd `b m w}zmsj korokjw o{ ol{` ;:.;:.?5

{somlhdjw$ xo{a wokjw `b djlh{aqmlk m ayu`{jlzwj `b djlh{a 3,Ajsj$ {aj ayu`{jlzwj ow =2 zlo{w d`lh$ w` xj gml bolk {aj djlh{a `b

jmga wokj6

3 > =2 > =23 >

=233

> 13

Ob jmga wokj ow 13 zlo{w d`lh$ {ajl {aj msjm `b {aj w}zmsj ow

!13/3 > =31

Ol {aj }zmksodm{jsmdMCGK {` {aj soha{$ MC ow umsmddjd {`GK $ CK ow ujsujlkogzdms {` GK $ mlk Gnjmwzsjw 25, Ob > ;7 mlk > 3$ xam{ ow {aj msjm `b}zmksodm{jsmdMCGK0Ob xj ksù ml`{ajs dolj bs`n uòl{M ujsujlkogzdms {`

GK $ xj gml csjmi zu {aj {smujvòk ol{` m sjg{mlhdj mlkm {somlhdj, [aj sjg{mlhdj amw wokj djlh{aw 3 mlk ;7$mlk {aj {somlhdj ow m 75.25.?5 {somlhdj xo{a m d`lh

wokj `b djlh{a ;7, Cjgmzwj xj il`x {am{ m 75.25.?5{somlhdj amw m wa`s{ wokj `b djlh{aqmlk m d`lh wokj `b

djlh{a 7$ xj gml w`drj b`s {aj wa`s{ wokj67 > ;7

> ;

Xj l`x il`x {am{ {aj {smujvòkMCGK amw m wa`s{

cmwj `b djlh{a 3$ m d`lh cmwj `b djlh{a 2$ mlk m ajoha{

`b;7, [aj msjm `b {aj {smujvòk ow > =

3 )

> =3

;73 ) 2 > =27

Bohzsj l`{ ljgjwwmsody ksmxl {` wgmdj



28/40

Ory Hd`cmd

M gosgdjow m wj{ `b mdd uòl{w ol m udmlj {am{ msj {aj wmnj kow{mlgj bs`n m horjl uòl{, [aow kow{mlgj$

bs`n {aj gjl{sj `b {aj gosgdj {` mly uòl{ `l {aj gosgdj$ ow gmddjk {aj smkozw, Mdd smkoo `b `lj gosgdj msj

{aj wmnj djlh{a, M dolj g`lljg{olh {x` uòl{w l {aj gosgdj mlk umwwolh {as`zha {aj gjl{sj ow gmddjk

m komnj{js, [aj komnj{js `b m gosgdj ow j}zmd {` {xogj {aj djlh{a `b {aj gosgdjw smkozw,

Obkow {aj djlh{a `b {aj komnj{js mlk sow {aj djlh{a `b {aj smkozw$ {aj gosgznbjsjlgj `b m gosgdj ow

> > 3

Obsow {aj djlh{a `b {aj smkozw$ {aj msjm `b m gosgdj ow

> 3

Ml msg ow m wjhnjl{ `b {aj gosgznbjsjlgj `b m gosgdj, Msgw msj

njmwzsjk jo{ajs ol kjhsjjw s ol zlo{w b djlh{a, Ksmxolh {x` smkoobs`n {aj jlkuòl{w `b {aj msg {` {aj gjl{sj `b {aj gosgdj gsjm{jw {aj

msgw gjl{smd mlhdj$ xa`wj kjhsjj njmwzsj ow j}zmd {` {aj kjhsjjnjmwzsj `b {aj msg, [aj sm{o` cj{xjjl {aj djlh{a `b {aj msg mlk {aj

gosgznbjsjlgj b {aj gosgdj ow j}zmd {` {aj sm{o` cj{xjjl {aj kjhsjjw

ol {aj gjl{smd mlhdj mlk {aj kjhsjjw ol {aj jl{osj gosgdj, Ob {aj msgwgjl{smd mlhdj njmwzsjwqmlk {aj msgw djlh{a ow D$ {ajl6

3 >

725

M wjg{`s ow m sjho`l `b m gosgdj c`zlkjk cy {x` smkoo mlk ml msg, [aj sm{o` cj{xjjl {aj msjm `b m

wjg{`s mlk {aj msjm `b {aj jl{osj gosgdj ow mdw` j}zmd {` {aj sm{o` cj{xjjl {aj kjhsjjw ol {aj gjl{smd

mlhdj mlk {aj kjhsjjw ol {aj jl{osj gosgdj, Ob {aj wjg{`sw gjl{smd mlhdj njmwzsjw q mlk {aj wjg{`swmsjm owM$ {ajl6

3 >

725

M dolj {am{ ol{jswjg{w m gosgdj m{ jqmg{dy `lj uòl{ ow gmddjk m

{mlhjl{, [aj smkozw ksmxl bs`n {aj uòl{ b ol{jswjg{o`l{` {aj gjl{sj b {aj gosgdj ow mdxmyw ujsujlkogzdms {` {aj

{mlhjl{,



29/40

Ory Hd`cmd

Ob jrjsy rjs{jq `b m u`dyh`l dojw `l m gosgdj$ {ajl {aj u`dyh`l ow wmok {` cj olwgsocjk ol {aj gosgdj, Ob

jmga wokj `b m u`dyh`l ow {mlhjl{ {` m gosgdj$ {ajl {aj gosgdj ow olwgsocjk ol {aj u`dyh`l,

Ol {aj bohzsj {` {aj soha{$ CGow ml msg `b m gosgdj xa`wj gjl{sj owM, Ob {aj djlh{a `b msg CGow 3zlo{w$ xam{ ow {aj msjm `b wjg{`s

MCG0

[aj gjl{smd mlhdj `b msg CGow 25$ xaoga ow25

725>

=

2`b {aj {`{md

kjhsjjw `b {aj gosgdj, [aj djlh{a `b {aj msg ow 3zlo{w$ xaoga

nzw{ cj=

2{aj {`{md gosgznbjsjlgj b {aj gosgdj, [azw$ {aj

gosgznbjsjlgj nzw{ cj =3zlo{w, Xj gml zwj {aj

gosgznbjsjlgj {` w`drj b`s {aj smkozw6

> 3=3 > 3

> 2Ob {aj smkozw ow 2 zlo{w$ {aj msjm `b {aj jl{osj gosgdj ow 72 zlo{w w}zmsjk, [aj msjm b wjg{`s

MCGow=

2{aj {`{md msjm `b {aj gosgdj$ w` {aj msjm `bMCGnzw{ cj 2zlo{w w}zmsjk,

Ol {aj bohzsj {` {aj soha{$ w}zmsj HAOFow olwgsocjk ol m gosgdjxa`wj gjl{sj ow I, Ob {aj msjm `b w}zmsj HAOFow =2$ xam{ ow

{aj msjm `b gosgdj I0

[aj msjm `b {aj w}zmsj ow =2$ w` {aj djlh{a `b jmga wokjnzw{ cj =2 > ;,

Ksmxolh m komh`lmd `b {aj w}zmsj korokjw o{ ol{` {x` ;:.

;:.?5 {somlhdjw, Ob jmga wokj `b {ajwj {somlhdjw amw m

djlh{a `b ;$ {ajl {aj djlh{a `b {aj ayu`{jlzwj nzw{ cj ;3,



30/40

Ory Hd`cmd

[aow ayu`{jlzwj ow mdw` m komnj{js b gosgdj I, Ob o{w

djlh{a ow ;3$ {ajl {aj smkozw `b gosgdj Iamw m djlh{a `b

33, [aj msjm `b gosgdj Iow !33/3 > 1,

W`dok hj`nj{sy ow g`lgjsljk xo{a bohzsjw ol {asjj konjlwo`lw6 sjg{mlhzdms w`dokw$ usownw$

gydolkjsw$ uysmnokw$ g`ljw mlk wuajsjw, [a`zha mdd `b {ajwj w`dokw nmy muujms `l {aj WM[$ y`z xodd

usonmsody cj x`siolh xo{a sjg{mlhzdms w`dokw$ usownw$ mlk soha{ gydolkjsw,

M sjg{mlhzdms w`dok amw woq sjg{mlhzdms bmgjw {am{ ol{jswjg{ m{ soha{ mlhdjw, [aj wzsbmgj msjm b m

sjg{mlhzdms w`dok ow {aj wzn `b {aj msjmw `b mdd woq `b o{w

sjg{mlhzdms bmgjw, [aj r`dznj `b m sjg{mlhzdms w`dok ow o{w

djlh{a nzd{oudojk cy o{w xok{a nzd{oudojk cy o{w ajoha{, >

> 3 ) 3 ) 3

M gzcj ow m sjg{mlhzdms w`dok b`snjk cy woq g`lhszjl{ w}zmsjw{ajdjlh{a$ xok{a$ mlk ajoha{ msj j}zmd, Obwow {aj djlh{a b {aj gzcjw wokj${ajl

> 7 > 23

[aj komh`lmd `b m sjg{mlhzdms w`dok f`olw `uu`wo{j rjs{ogjwo{ ow {aj d`lhjw{ dolj {am{ gml cj ksmxl

{as`zha {aj w`dok, B`s m sjg{mlhzdms w`dok xo{a djlh{a d$ xok{a x$ ajoha{a$ mlk komh`lmd k6

3 > 3 ) 3 ) 3



31/40


32/40

Ory Hd`cmd

[aj bohzsj {` {aj soha{ wa`xw m gzcog c`q xo{a m wokj djlh{a`b 3, M sjg{mlhzdms uojgj b nj{md amw cjjl olwjs{jk ol{` {aj

c`q m{ m wdml{$ w` {aj c`{{`n jkhj GK ol{jswjg{w {aj olwokj

bs`l{ jkhj `b {aj gzcj, Ob uòl{wM mlk C msj nokuòl{w `b

{aj {ù jkhjw `b {aj gzcj$ xam{ ow {aj msjm `b {aj sjg{mlhdj

MCGK0

Xj il`x {aj djlh{a `bMC mlk GK msj jmga 3$ cz{ xj ljjk

{` bolk {aj djlh{aw `bMGmlk CK, Xj gml wjj {am{CK b`snw m

soha{ {somlhdj xo{a {x` `b {aj jkhjw `b {aj gzcj, Xjdd gmdd{aj {aosk uòl{ l {aow {somlhdj uòl{J,[aj wokj djlh{a `b {aj gzcj ow 3$ w` > 3, Xj il`x {am{C ow {aj nokuòl{ `b `lj `b {aj zuujs wokjw$ w` > =, Xjgml w`drj b`s CK zwolh {aj Uy{amh`sjml [aj`sjn6

!/3 > 33 ) =3 > :

[aj msjm b sjg{mlhdj MCGKow 3 : > 3:,

M wuajsogmd cmdd ow g`nudj{jdy olwgsocjk xo{aol m gzcj xa`wj r`dznj ow 2; gzcjk olgajw,Xam{ ow {aj smkozw `b {aj cmdd0

Dj{w ksmx m bohzsj, Ob {aj wuajsj ow olwgsocjk xo{aol {aj gzcj${aj komnj{js `b {aj wuajsj ow j}zmd {` {aj xok{a `b {aj gzcj,Xj il`x {aj gzcjw r`dznj ow 2; gzcjk olgajw$ w` {aj djlh{a`b jmga wokj `b {aj gzcj ow 2;7 > ; olgajw, [aj komnj{js `b{aj wuajsj ow ; olgajw$ w` o{w smkozw nzw{ cj 3 olgajw,

M a`dd`x gydolkjs : gjl{onj{jsw d`lh ow b`snjk w` {am{ {aj gosgzdms ùjlolh `l jmga wokj amwm komnj{js `b 7 gjl{onj{jsw, [aj `z{wokj `b {aj gydolkjs ow {` cj umol{jk sjk, Xam{ ow {aj{`{md wzsbmgj msjm b umol{ ljjkjk0

[aj z{wokj b {aj gydolkjs ow wonudy m sjg{mlhdj xa`wj konjlwo`lw

msj j}zmd {` {aj ajoha{ `b {aj gydolkjs mlk {aj gosgznbjsjlgj `b {aj

gosgzdms cmwj, [aj ajoha{ ow : gjl{onj{jsw d`lh$ mlk {aj



33/40

Ory Hd`cmd

gosgznbjsjlgj `b {aj cmwj ow > 7 gjl{onj{jsw, [aj msjm b {aj wzsbmgj {` cj umol{jk ow: 7 > =: gjl{onj{jsw w}zmsjk,

G``skolm{j hj`nj{sy kjmdw xo{a bohzsjw ol {aj g``skolm{j udmlj, _`z nmy ljjk {` gmdgzdm{j {aj

wdùj s djlh{a b doljw$ s {aj msjm s ujsonj{js b u`dyh`lw horjl {ajos g``skolm{j uòl{w,

Ijju ol nolk !bs`n {aj Mdhjcsm mlk Bzlg{o`lw wjg{o`l/6

A`sov`l{md doljw amrj wdùjw `b vjs`, Rjs{ogmd doljw amrj zlkjboljk wdùjw, L`l.rjs{ogmd umsmddjd doljw amrj j}zmd wdùjw, L`l.rjs{ogmd ujsujlkogzdms doljw amrj wdùjw xa`wj us`kzg{ ow .=,

Xj gml muudy {aj Uy{amh`sjml [aj`sjn {` bolk {aj kow{mlgj cj{xjjl {x` uòl{w ol {aj g``skolm{j

udmlj, Ob {x` uòl{w amrj g``skolm{jw !=$ =/ mlk !3$ 3/$ {ajl {aj kow{mlgj kcj{xjjl {ajn ow6

> !3 =/3 ) !3 =/3

Ob {x` uòl{w amrj g``skolm{jw !=$ =/ mlk !3$ 3/$ {ajl {aj g``skolm{jw bnokuòl{`b {ajwjhnjl{ g`lljg{olh {ajn ow wonudy {aj mrjsmhj b {ajos g``skolm{jw6

!= ) 3

3$

=)

3

3/

M w}zmsj dojw ol {ajqy.g``skolm{j udmlj xo{a rjs{ogjw !5$7/$ !7$5/$ !7$2/ mlk !2$7/, Xam{ ow {ajmsjm `b {aj w}zmsj0

Zwj {aj kow{mlgj b`snzdm {` bolk {aj djlh{a `b `lj

`b {aj wokjw6

> !3 =/3 ) !3 =/3 > !7 5/3 ) !5 7/3

>

=1

[aj msjm `b {aj w}zmsj ow !=1/3 > =1 zlo{ww}zmsjk,

!7$ 5/

!5$ 7/

!7$ 2/

!2$ 7/

y

q



34/40

Ory Hd`cmd

M {smlwb`snm{o`l n`rjw ml cfjg{ a`sov`l{mddy mlk`s rjs{ogmddy md`lh {aj g``skolm{j udmlj

xo{a`z{ gamlholh o{w wovj s wamuj, Ob m u`dyh`l ow {smlwb`snjk 3 u`wo{orj zlo{w a`sov`l{mddy mlk 7

u`wo{orj zlo{w rjs{ogmddy$ {ajl b`s jmga b o{w rjs{ogjw {ajq.g``skolm{j xodd olgsjmwj cy 3 zlo{w mlk

{ajy.g``skolm{j xodd olgsjmwj cy 7 zlo{w,M s`{m{o`l {zslw ml `cfjg{ ms`zlk m uòl{$ gmddjk {aj gjl{sj `b s`{m{o`l, Ob m uòl{ xo{a g``skolm{jw!$ / ow s`{m{jk =15 ms`zlk {aj `sohol$ o{w sjwzd{olh g``skolm{jw xodd cj !$ /,

M sjbdjg{o`l gsjm{jw m noss`s onmhj `b ml `cfjg{ `rjs m dolj$ gmddjk {aj dolj `b sjbdjg{o`l, M uòl{

mlk o{w sjbdjg{o`l xodd cj {aj wmnj kow{mlgj mxmy bs`n {aj dolj `b sjbdjg{o`l, Ob m uòl{ !$ / owsjbdjg{jk mc`z{ {ajq.mqow$ o{w sjwzd{olh g``skolm{jw xodd cj !$ /, Ob m uòl{$ ow sjbdjg{jk mc`z{{ajy.mqow$ o{w sjwzd{olh g``skolm{jw xodd cj !

$

/,

!3$ 3/

!7$ :/

!:$ 3/

!;$ :/

!:$ 1/

!8$ :/

y

q[smlwb`snm{o`l

!3$ 3/

!7$ :/

!:$ 3/!.3$ 3/

!.7$ :/

!.:$ 3/

y

q

Sjbdjg{o`l `rjsy.mqow

!3$ 3/

!7$ :/

!:$ 3/

!.3$ .3/

!.7$ .:/

!.:$ .3/

y

q

S`{m{o`l

=15

!3$ 3/

!7$ :/

!:$ 3/

!3$ .3/

!7$ .:/

!:$ .3/

y

q

Sjbdjg{o`l `rjsq.mqow



35/40

Ory Hd`cmd

M bohzsj amw sjbdjg{o`lmd wynnj{sy ob {ajsj ow m dolj {am{ korokjw o{ ol{` {x` amdrjw$ wzga {am{ jmga

amdb ow {aj `{ajs amdbw ujsbjg{ sjbdjg{o`l mc`z{ {aj dolj, Ol `{ajs x`skw$ ob {aj bohzsj xjsj sjbdjg{jkmc`z{ {aj dolj `b wynnj{sy$ {aj sjwzd{ x`zdk cj jqmg{dy {aj wmnj bohzsj, M bohzsj nmy amrj

nzd{oudj doljw b wynnj{sy,

M bohzsj amw s`{m{o`lmd wynnj{sy ob {ajsj ow m uòl{ ms`zlk xaoga m bohzsj gml cj s`{m{jk m gjs{mollzncjs b kjhsjjw$ gsjm{olh m sjwzd{olh bohzsj jqmg{dy {aj wmnj mw {aj soholmd, [aow uòl{ ow gmddjk

{aj uòl{ b wynnj{sy,

[aj bohzsj {` {aj soha{ wa`xw {aj hsmua `b dolj dol {ajqy.g``skolm{j udmlj, Ob dolj n ow {aj sjbdjg{o`l b dolj d

ol {ajq.mqow$ xam{ ow {aj j}zm{o`l b dolj n0Ob dolj n ow {aj sjbdjg{o`l b dolj dol {ajq.mqow$ {ajl

jrjsy uòl{ l dolj dxodd amrj m g`ssjwu`lkolh uòl{

`l dolj n, [ajwj uòl{w xodd amrj {aj wmnjq.

g``skolm{j cz{ {aj ljhm{orjy.g``skolm{j6

!5$ 3/!3$ 2/

Zwj {ajwj uòl{w {` xso{j ml j}zm{o`l b`s dolj n, [aj

y.ol{jsgju{ ow .3 mlk {aj wdùj ow mdw` .3$ w` {aj

j}zm{o`l b`s dolj n ow

> 3 3

Sjbdjg{o`lmd wynnj{sy S`{m{o`lmd wynnj{sy

!5$ 3/

!3$ 2/

y

q

d

!5$ 3/

!3$ 2/

!5$ .3/

!3$ .2/

y

q

dn



36/40

Ory Hd`cmd

OR, Km{m Mlmdywow mlk Us`cmcodo{y G`zl{olh G`ncolm{o`lw mlk ujsnz{m{o`lw

Us`cmcodo{y Njmlw$ njkomlw$ mlk n`kjw

Xajl g`zl{olh a`x nmly ol{jhjsw msj usjwjl{ cj{xjjl {x` jlkuòl{w$ o{ ow onu`s{ml{ {` l`{j

xaj{ajs {aj jlkuòl{w msj cjolh olgdzkjk,

[aj lzncjs `b ol{jhjsw cj{xjjl {aj jlkuòl{w l mlk n$ olgdzworj$ ow ) =, [aj lzncjs `b ol{jhjsw cj{xjjl {aj jlkuòl{w l mlk n$ jqgdzworj$ ow =, Ob ldy lj b {aj jluòl{w ow cjolh olgdzkjk$ {ajl {aj lzncjs b ol{jhjsw bs`n l {` n ow

,

Bs`n 16=:un {` ?635un$ {aj =w{{as`zha {aj :{a ujùdj ol {aj xmo{olh s``n xjsj wjjl cy mk`g{`s, Xam{ xmw {aj mrjsmhj sm{j b um{ojl{w wjjl ujs nolz{j0

Cjgmzwj {aj =w{{as`zha {aj :{a ujùdj xjsj wjjl$ `zs jlkuòl{w `b = mlk 8 msj cjolh

olgdzkjk, [aj lzncjs `b ujùdj wjjl ow : = ) = > :,

[ajsj msj 2: nolz{jwbs`n 16=:un {` ?635un9 `ldy `lj `b {ajwj jlkuòl{w ow cjolh

olgdzkjk, [azw$ {aj sm{j `b um{ojl{w wjjl ujs nolz{j ow:

2:>

=

=7,

[aj g`zl{olh usolgoudj {jddw zw {am{$ b`s {x` {mwiw$ ob {ajsj msj n xmyw {` g`nudj{j {aj bosw{ mlk l

xmyw {` g`nudj{j {aj wjg`lk$ {ajl {ajsj msj xmyw {` g`nudj{j {aj {x` `b {ajn, N`w{ `b {ajwj}zjw{o`lw olr`drj ujsnz{m{o`lw$ xajsj {aj `skjs `b {aj {x` {mwiw ow onu`s{ml{,

[` kj{jsnolj {aj =w{$ 3lk$ mlk 7sk usovj `b m d`{{jsy ksmxolh$ {asjj {ogij{w msj wjdjg{jk `lj m{m {onj bs`n m u``d `b :5 {`{md {ogij{w$ xo{a l` sjujm{w mdd`xjk, A`x nmly kobbjsjl{

g`ncolm{o`lw b =w{$ 3lk$ mlk 7sk.usovj {ogij{w msj u`wwocdj0

[ajsj msj :5 u`wwocdj {ogij{w b`s {aj bosw{ ksmxolh, B`s {aj wjg`lk$ `ldy ;? msj djb{$ mlk b`s

{aj {aosk$ {ajsj msj ldy ;1 u`wwocodo{ojw, [azw$ {aj lzncjs b kobbjsjl{ g`ncolm{o`lw!mg{zmddy$ ujsnz{m{o`lw/ ow :5 ;? ;1 > ==8255,

Fàl xml{w {` umol{ aow cjks``n$ cm{as``n$ mlk io{gajl jo{ajs uoli$ yjdd`x$ cdzj$ s hsjjl,Ob mly s``nw gml cj {aj wmnj g`d`zs$ a`x nmly g`ncolm{o`lw `b g`d`zsw msj u`wwocdj0



37/40

Ory Hd`cmd

B`s {aj bosw{ s``n$ Fàl amw ; u`wwocdj g`d`zsw, Cjgmzwj mly s``nw gml cj {aj wmnj g`d`zs$

aj w{odd amw ; u`wwocodo{ojw b`s {aj wjg`lk s``n mlk ; u`wwocodo{ojw b`s {aj {aosk, [ajsj msj

{azw ; ; ; > 2; ujsnz{m{o`lw b g`d`zsw u`wwocdj,

Ol w`nj }zjw{o`lw$ {aj skjs b {mwiw ow l`{ onu`s{ml{, B`s olw{mlgj$ ob Hmsy$ Nmsi$ mlk Komlm msj

cjolh korokjk ol{` umosw$ {aj umos Hmsy.Nmsi ow {aj wmnj mw {aj umos Nmsi.Hmsyo{ k`jwl{ nm{{jsxaoga lj ow ga`wjl bosw{, [ajwj msj gmddjk g`ncolm{o`lw mw uu`wjk {` ujsnz{m{o`lw$ {a`zha {aj

WM[ k`jw l`{ zwj {aow {jsnol`d`hy,

Wmsma xml{w {` xjms {x` csmgjdj{w {` wga``d {`n`ss`x, Ob waj amw borj csmgjdj{w {` ga``wjbs`n mlk o{ k`jw l`{ nm{{js ol xam{ `skjs waj xjmsw {ajn$ a`x nmly g`ncolm{o`lw `b

csmgjdj{w msj u`wwocdj0

Wmsma amw borj ù{o`lw b`s ajs bosw{ csmgjdj{ mlk b`zs ù{o`lw b`s ajs wjg`lk, [aow x`zdk horj

: ; > 35ujsnz{m{o`lw u`wwocdj, A`xjrjs$ o{ k`jwl{ nm{{js xam{ `skjs waj ga``wjw {aj

csmgjdj{w6 m uoli.yjdd`x csmgjdj{ g`ncolm{o`l x`zdk cj {aj wmnj mw m yjdd`x.uoli csmgjdj{g`ncolm{o`l, [azw$ jmga b `zs g`ncolm{o`lw ow jss`lj`zwdy cjolh g`zl{jk {x` {onjw, [aj

mg{zmd lzncjs b g`ncolm{o`lw u`wwocdj ow35

3> =5,

[aj us`cmcodo{y {am{ ml jrjl{ xodd {mij udmgj ow jqusjwwjk nm{ajnm{ogmddy mw m lzncjs bs`n 5 {` =,

M us`cmcodo{y `b 5 njmlw {am{ {aj jrjl{ ow onu`wwocdj$ mlk m us`cmcodo{y `b = njmlw {am{ ml jrjl{ ow

g`nudj{jdy gjs{mol, B`s jrjsy{aolh ol cj{xjjl$ us`cmcodo{y ow sjusjwjl{jk mw m sm{o`6

Ml ol{jhjs cj{xjjl 5 mlk ??$ olgdzworj$ ow ga`wjl m{ smlk`n, Xam{ ow {aj us`cmcodo{y {am{ {ajol{jhjs xodd jlk ol 50

[ajsj msj =5 ol{jhjsw cj{xjjl 5 mlk ?? {am{ jlk ol 56 5$ =5$ 35$ 75$ ;5$ :5$ 25$ 85$ 15$ mlk

?5, [aj lzncjs b bmr`smcdj z{g`njw ow =5, [aj lzncjs b u`wwocdj z{g`njw ow

?5 5 ) = > =55$ mw {ajsj msj =55 ol{jhjsw {`{md {` ga``wj bs`n, [azw$ {aj us`cmcodo{y{am{ {aj ol{jhjs ga`wjl xodd jlk ol 5 ow

>=5

=55 >=

=5

Hj`nj{sog us`cmcodo{y }zjw{o`lw mwi y`z {` bolk {aj us`cmcodo{y {am{ ml jrjl{ xodd `ggzs xo{aol m

wujgobog sjho`l `b m hj`nj{sog bohzsj, Ol {ajwj gmwjw$ {aj lzncjs `b bmr`smcdj `z{g`njw ow {aj msjm`b {aj sjho`l ol }zjw{o`l$ mlk {aj lzncjs `b u`wwocdj `z{g`njw ow {aj msjm `b {aj xa`dj bohzsj,



38/40

Ory Hd`cmd

[aj bohzsj {` {aj soha{ wa`xw m {mshj{ nmkj `b g`lgjl{soggosgdjw, Ob {aj komnj{js b {aj olljs gosgdj ow ; olgajw mlk jmga`b {aj gosgdjw msj wumgjk 3 olgajw mums{$ xam{ ow {aj us`cmcodo{y

{am{ m kms{ {as`xl m{ smlk`n xodd dmlk ol {aj wamkjk sjho`l0

Xj ljjk {` gmdgzdm{j {aj msjm `b {aj wamkjk sjho`l mlk {aj

msjm b {aj jl{osj bohzsj, [aj smkozw `b {aj olljs gosgdj ow;

3> 3

olgajw$ w` o{w msjm ow 33 > ; olgajw w}zmsjk, [aj smkozw b{aj ljq{ gosgdj ow 3 olgajw n`sj$ w` o{w msjm ow ;3 > =2olgajw w}zmsjk, Bolmddy$ {aj smkozw b {aj dmshjw{ gosgdj ow ml`{ajs 3 olgajw n`sj$ w` o{w msjm

ow 23

> 72 olgajw w}zmsjk,[aj msjm `b {aj jl{osj bohzsj ow 72 olgajw w}zmsjk, [aj msjm b {aj wamkjk sjho`l ow {aj msjm`b {aj wjg`lk gosgdj nolzw {aj msjm `b {aj olljs gosgdj6 =2 ; > =3 olgajw w}zmsjk,[azw$ {aj us`cmcodo{y {am{ m kms{ xodd dmlk ol {aj wamkjk sjho`l ow

>

=372 >

=

7

[x` jrjl{w msj olkjujlkjl{ b jmga {ajs ob {aj us`cmcodo{y b lj jrjl{ ggzssolh k`jw l`{ mbbjg{

ol mly xmy {aj us`cmcodo{y `b {aj `{ajs jrjl{ `ggzssolh, B`s olw{mlgj$ ob y`z xjsj {` s`dd {x` kogj$

y`z x`zdk amrj m=

2us`cmcodo{y b s`ddolh m = b`s jmga koj, B`s olkjujlkjl{ jrjl{w doij {ajwj$ y`z gml

nzd{oudy {aj olkorokzmd us`cmcodo{ojw {`hj{ajs {` bolk {aj us`cmcodo{y b c`{a jrjl{w ggzssolh m{ {aj

wmnj {onj, [azw$ {aj us`cmcodo{y {am{ y`z xodd s`dd m = `l c`{a kogj ow=

2

=

2>

=

72,

Fjwwj amw {x` umosw `b hsjy w`giw mlk `lj umos `b cdzj w`giw, Ob aj ksjwwjw aonwjdb ol {aj kmsimlk wjdjg{w {x` w`giw smlk`ndy bs`n {aj ksmxjs$ `lj m{ m {onj$ xam{ ow {aj us`cmcodo{y {am{

aj xodd uogi {x` hsjy w`giw0

Fjwwj amw 2 w`giw {`{md ol aow ksmxjs$ `b xaoga ; msj hsjy, [aj us`cmcodo{y {am{ aj xodd wjdjg{`lj hsjy w`gi ow

;

2>

3

7, Aj {ajl amw `ldy : w`giw ol aow ksmxjs$ `b xaoga 7 msj hsjy$ w` {aj

us`cmcodo{y {am{ aj xodd wjdjg{ ml`{ajs hsjy w`gi ow7

:, [aj us`cmcodo{y {am{ aj wjdjg{ {x` hsjy

w`giw ow3

7

7

:>

2

=:,



39/40

Ory Hd`cmd

Ml mrjsmhj ow {aj wmnj mw ml mso{anj{og njml, Ob y`zs km{m g`nusowjw l lzncjsw$ {ajl {aj mrjsmhj

`b {a`wj l lzncjsw ow {ajos wzn korokjk cy l6

>

Mb{js ajs {aosk Jlhdowa {jw{$ Mnmlkmw mrjsmhj {jw{ wg`sj xmw 11, Xam{ wg`sj k`jw waj ljjk`l ajs b`zs{a {jw{ ol `skjs {` amrj ml mrjsmhj `b ?50

Ajs gzssjl{ mrjsmhj ow {aj wzn `b ajs bosw{ {asjj {jw{ wg`sjw korokjk cy {asjj, Xj gml{ bohzsj`z{ xam{ jmga olkorokzmd wg`sj xmw$ cz{ xj gml bolk {ajos wzn6

> 11 >

7

> 32;B`s ajs mrjsmhj mb{js ajs b`zs{a {jw{ {` j}zmd ?5$ {aj wzn `b mdd b`zs {jw{ wg`sjw korokjk cy

b`zs nzw{ j}zmd ?5, Ob {aj wzn `b ajs bosw{ {asjj {jw{ wg`sjw ow 32;$ dj{qj}zmd {aj b`zs{a {jw{

wg`sj6

?5 >32; )

;

725 > 32; ) > ?2

Mnmlkm ljjkw m wg`sj `b ?2 `l ajs b`zs{a {jw{,

Xam{ ow {aj mrjsmhj `b 1 ) ; mlk 30[sjm{ {ajwj {x` jqusjwwo`lw doij mly {ajs lzncjsw6 mkk {ajn {`hj{ajs mlk {ajl korokj cy

{x`,

> 1 ) ; ) !3/3

>2 ) ;

3> 7 ) 3

M xjoha{jk mrjsmhj ow {aj mrjsmhj `b wjrjsmd hs`zuw `b km{m$ jmga xo{a ml zlj}zmd wovj !xjoha{/,[` bolk {aj mrjsmhj$ jmga lzncjs nzw{ cj nzd{oudojk cy o{w xjoha{olh bmg{`s {` sjbdjg{ a`x nmly

{onjw o{ muujmsw ol {aj {`{md km{m wj{, [ajwj us`kzg{w msj {ajl mkkjk {`hj{ajs mlk korokjk cy {aj

{`{md lzncjs b lzncjsw ol {aj km{m wj{,

M{ m bzlksmowjs$ 3: uj`udj k`lm{jk ml mrjsmhj `b +:5 jmga mlk =7 uj`udj k`lm{jk mlmrjsmhj b +=55 jmga, Xam{ xmw {aj mrjsmhj k`lm{o`l b`s {aj jl{osj bzlksmowjs0



40/40

Xj nzw{ xjoha{ jmga k`lm{jk mn`zl{ mgg`skolh {` {aj lzncjs `b ujùdj xa` k`lm{jk o{$

{ajl korokj cy {aj {`{md lzncjs `b ujùdj m{ {aj jrjl{6

> 3:+:5 ) =7!+=55/71

>3::5

71> +28,==

[aj mrjsmhj k`lm{o`l xmw +28,==,

[` bolk {aj njkoml`b m hs`zu `b km{m$ uz{ {aj km{m ol{` lznjsogmd `skjs mlk d`ì b`s {aj nokkdj

rmdzj, Ob {ajsj ow l` nokkdj rmdzj$ {aj njkoml ow {aj mrjsmhj `b {aj {x` nokkdj lzncjsw, [aj n`kj

ow {aj rmdzj {am{ `ggzsw n`w{ bsj}zjl{dy9 m km{m wj{ gml amrj nzd{oudj n`kjw,

[aj n`w{ sjgjl{ jqmn wg`sjw b`s m gdmww xjsj 2;$ 17$ ?8$ ?:$ 17$ 83$ 8:$ 81$ 81$ mlk 18, Xam{xmw {aj mrjsmhj wg`sj0 Xam{ xmw {aj njkoml wg`sj0 Xam{ owmsj {aj n`kj!w/ `b {aow km{m0

Uz{ {aj km{m bosw{ ol{` lznjsogmd `skjs6 2;$ 83$ 8:$ 81$ 81$ 17$ 17$ 18$ ?:$ ?1

[aj mrjsmhj `b {aj km{m ow

2 ; ) 8 3 ) 8 : ) 8 1 ) 8 1 ) 1 7 ) 1 7 ) 1 8 ) ? : ) ? 1

=5> 1=,3

[aj njkoml wg`sj dojw jrjldy cj{xjjl 81 mlk 176

81)17

3> 15,:

[aj n`kjw msj 81 mlk 17,

sat/ act/ accuplacer math review

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