additional mathematics project work 2/2011 spm

8/6/2019 additional mathematics project work 2/2011 spm

1/45

:

ThfkejmOhnhncjmFhgjnctjj

n Jcjoj Ojqjnc


2/45

7

Jaa`q`knje Ojqmhojq`dtRwkihdq Skwf

Phjw9 72::

Rwkihdq Skwf9 7

Q`qeh9 Djfh Gjf`nc jna Ahdkwjq`ncNjoh9 Okmjooja TkeehmjnGkeemjttjn

Dejtt9 8 Jgx Gjfjw

@+D Nxoghw9 01:72


3/45

4

DJFH

GJF@NC

JNA

AHDKWJQ@NC


4/45

1

DknqhnqtQ@QEH 4

DKNQHNQT 1

JDFNKSEHACHOHNQ 8

@NQWKAXDQ@KN 3

KGIHDQ@\H ::

QJTF :4

ZXHTQ@KN :8

RWKGEHO TKE\@NC 7:

:.RJWQ : 777.RJWQ 7 784.

RJWQ 4 47

LXWQMHW H]REKWJQ@KN 4 18 do

Qm`t `t ghdjxth jnp mh`cmqt ekshw qmjn 3 do sèe whtxeq `n qmh a`johqhw

kl qmh djfh gh`nc qkk g c qk l`q nqk qmh gjf`nc k|hn sm eh jnp mh cmqt m`cmhw

qmjn 18 do s eedjxth qmh djfh gh`nc qkk qjee qk l q nqk qmh gjf`nc k|hn` ) @ skxea txcchtq qmh aòhnt`knt kl qmh djfh qk gh 70 do n mh`cmq jna

jrrwk}òjqhep70 do n a`johqhw. Qm`t t ghdjxth j djfh s qm qmhth aòhnt`knt

`t okwhtpoohqw`dje jna hjt`hw qk ahdkwjqh.

d) ) \ ? wm

\ ? :0222 do

w ?

:0222 ? 4.:17 } -)} m

?

a?

a ? :88.84 } m^

? / &

: :.


28/45

7=


29/45

70

4)j) m ? 70 do

w ? :1.11 do

:1.11do

70do

A`jcwjo :9 djfh s qmkxq dwhjo

:do :8.11do

:do 42do

A`jcwjo 79 djfh s`qm dwhjo

Qk djedxejqh |kexoh kl dwhjo xtha% qmh dwhjo `t tpogke`tha jt qmhejwchw dpe`nahw jnaqmh djfh `t tpogke`tha jt qmh tojeehw dpe`nahw.

\dwhjo? 4.:17 } :8.11} 42 / :0222

? 7713: /:0222

? 413: do


30/45

42


31/45

4:

1)g) `) Tzxjwh tmjrha djfhHtq`ojqha |kexoh kl dwhjo xtha

? 42 } 73.< } 73.< :0222

? 77=87.= / :0222

? 4=87.= do

g) ``) Qw`jnceh tmjrha djfh

Htq`ojqha |kexoh kl dwhjo xtha

? } 40.3 } 40.3 } 42 / :0222? 74


32/45

47

Rjwq 4


33/45

44

Ohqmka :9 Gp dkorjw`nc |jexht kl mh`cmq jcj`ntq |kexoh kl dwhjo xtha

m+do \kexoh

kl dwhjo

xtha+do

m+do \kexoh

kl dwhjo

xtha+do

m+do \kexoh

kl dwhjo

xtha+do

: :00=4.


34/45

41

Ohqmka 79 Xt`nc a`llhwhnq jq kn

Jttxo`nc qmjq qmh txwljdh jwhj kl qmh djfh `t rwkrkwq`knjqh qk qmh

jokxnq kl lwhtm dwhjonhhaha qk ahdkwjqh qmh djfh.

Lkwoxej lkw txwljdh jwhj

? w & 7wm

m ? :0222 + 4.:17w

Txwljdh jwhj `n dknqjdq s`qm dwhjo

? w & 7w-:0222 + 4.:17w )

? w & -4=222+w)

Qmh |jexht% smhn rekqqha nqk j cwjrm s ee lwko j o`n`oxo |jexh qmjq djn gh

kgqj`nhaqmwkxcm a`llhwhnq`jq`kn.

? 2

? 7w / -4=222+w )

2 ? 7w / -4=222+w )

2 ?


35/45

48

Qmh aòhnt`knt kl qmh djfh qmjq whzx`wht qmh o`nòxo jokxnq kllwhtm dwhjo qk ahdkwjqh `tjrrwk}òjqhep :=.7 do `n mh`cmq jna :=.7 do `n

wja`xt.@ skxea gjfh j djfh kl txdm aòhnt`knt ghdjxth qmh djfh skxea nkq gh

qkk ejwch lkw qmhdxqq nc kw hjq nc kl tjà djfh% jna q skxea nkq gh qkk g`c qk

gjfh `n j dkn|hnq knje k|hn.

Qmh jgk|h dknihdqxwh t rwk|hn gp qmh lkeeks`nc

Smhn w ? :2%~qmh qkqje txwljdh jwhj kl qmh djfh `t 1::1.7 do

~qmh jokxnq kl lwhtm dwhjo nhhaha qk ahdkwjqh qmh djfh t 14=:.7 do

~qmh wjq`k kl qkqje txwljdh jwhj kl djfh qk jokxnq kl lwhtm dwhjo

nhhaha `t 2.01

Smhn w ? 72%

~qmh qkqje txwljdh jwhj kl qmh djfh `t 4:8


36/45

4


37/45


38/45

4=

? 2.=:

g)Tn? ? :8 fc ? 83222 do

83222 >

::122 > :=:: / 2.=

2.43: 5 2.=

ekc 2.43: 5 n ekc 2.=

5n

1.111 5 n

n ? 1


39/45

40

\hw`l`djq`kn kl jntshw

@l n ? 1

Qkqje |kexoh kl 1 djfht

? :=::


40/45

12

Dkndext`kn


41/45

1:

Jlqhw ak`nc whthjwdm% jntshw`nc zxhtq knt% awjs`nc cwjrmt% jna tkoh

rwkgeho tke|`nc% @ tjs qmjq qmh xtjch kl chkohqwp% djedxext jna

rwkcwhtt`knt jwh òrkwqjnq `n ajèp e`lh.

p Chkohqwp t qmh tqxap kl jnceht jna qw`jnceht% rhwòhqhw% jwhjjna|kexoh. @q a`llhwt lwko jechgwj `n qmjq knh ah|hekrt jekc`dje tqwxdqxwh

smhwh ojqmhojq`dje whejq`kntm`rt jwh rwk|hajna jrre`ha.

p Jn jw qmohq d rwkcwhtt`kn -JR) kw jw qmohq d thzxhndh t jthzxhndh klnxoghwt txdm qmjq qmh a`llhwhndh kl jnp qsktxddhtt`|h ohoghwt kl qmh

thzxhndh t j dkntqjnq.

p J chkohqw`d rwkcwhtt`kn -CR)% jetk fnksn jt jchkohqw`dthzxhndh% t j thzxhndh kl nxoghwt smhwh hjdm qhwo jlqhw

qmhl`wtq `t lkxna gp oxeq`rep`nc qmh rwh|`kxt knh gp j l`}ha nkn/

yhwknxoghw djeeha qmh dkookn wjq`k.

p A`llhwhnq`jq`kn `t htthnq`jeep qmh rwkdhtt kl l`na`nc jnhzxjq`knsm`dm sèe c`|h pkx qmh cwja`hnq -tekrh% 'w`th k|hw wxn'%

hqd.) jqjnp rk`nq jeknc qmh dxw|h. Tjp pkx mj|h p ? }^7.Qmh

hzxjq`knp# ? 7} sèe c`|h pkx qmh cwja`hnq kl p jq jnp rk`nq jeknc

qmjqdxw|h.

Jt qmh dkndext`kn% chkohqwp% djedxext jna rwkcwhtt`knt jwh rjwqkl kxw

nhdhtt`q`ht. Qmxt% sh tmkxea gh qmjnflxe kl qmh rhkreh smkdknqw`gxqh

`n qmh àhj kl chkohqwp% djedxext jna rwkcwhtt`kntghdjxth s`qmkxq

qmho% sh djnqaknhqmh oxeq`/tqkwhp djfh% jna `qtmjwa qk l`na kxq qmh

|kexoh kl `ncwha`hnqt nhhaha lkw qmh djfh.


42/45

17

Whlhwhndh


43/45

14

Jlqhw trhna`nc dkxnqehtt mkxwt% ajp jna n`cmq qk l`n`tm qm`t

rwkihdqskwf jna jetk tjdw`l`d`nc op qòh lkw dmjqq`nc jna sjqdm`ncok|`ht `nqm`t mkeàjp% qmhwh jwh th|hwje qm`nct qmjq @ djn tjp

Jaa`q`knje Ojqmhojq`dt

Lwko qmh ajp @ gkwn

Lwko qmh ajp @ sjt jgeh qk mkea`nc rhnd e

Lwko qmh ajp @ tqjwq ehjwn`nc

Jna

Lwko qmh ajp @ mhjwa pkxw njoh

@ jesjpt qmkxcmq qmjq

pkx sèe gh op cwhjqhtq kgtqjdeh jna w`|je `n

h}dhee`nc `n op e`lh

Gxq jlqhw dkxnqehtt kl mkxwt

Dkxnqehtt kl ajpt

Dkxnqehtt kl n`cmqt

Jlqhw tjdw`l`d`nc op rwhd`kxt qòh ixtq lkw pkx

Tjdw`l`d`nc op rejp qòh

Tjdw`l`d`nc op dmjqq`nc

Tjdw`l`d`nc op @nqhwnhq

Tjdw`l`d`nc op jnòh

Tjdw`l`d`nc op ok|`ht

@ whje`yha tkohqm`nc whjeep òrkwqjnq `n pkx

@ whjeep ek|h pkx

Pkx jwh whje lw`hnaPkx jwh op rjwqnhw

Pkx jwh op tkxe ojqh

@ EK\H PKX JAA@Q@KNJE OJQMHOJQ@DT


44/45

11

G`ge`kcwjrmp


45/45

additional mathematics project work 2/2011 spm

Documents