ADD. MATHEMATICS PAPER 1

8/7/2019 ADD. MATHEMATICS PAPER 1

http://slidepdf.com/reader/full/add-mathematics-paper-1 1/18

TILUS 6 1/2743

: amaN

:natak gniT

AK ALEM NAR AJALEP NATABAJSAR ALES NAASK IR EPEP NUHAT NAHAGNETR EP

02 AISYALAM NAR AJALEP LIJIS 01

SCITAMEHTAM LANOITIDDA

1 satr eK

maJ auD

UHATIR EBID AGGNIHES INI NALAOS SATR EK AK UB NAGNAJ

.1 sil uT aman nad natak gnit gnay gnaur adap adna

nak aidesid .

2 . hal ad a nad nal aos 52 ig nud nag nem ini nal aos sat r eK

.asahabiwd mal ad

.3 bawaJ aumes nak ir eb nal aos pait es ig aB .nal aos U T AS .ajahas napawaj

.4 g nay g naur ad ap sil ut id hal k ad neh napawaJ .nal aos sat r ek mal ad nak aid esid

.5

hak g nal nak k ujnuT - ajr ek mal ad g nit nep hak g nal k ut nu ad na ut nabmem hel ob inI .ad na ar ig nemak r am nak t apad nem .h

.6 nak l at ab ,napawaj r ak unem k ad neh ad na aynar ik eS

.t aubid hal et g nay ar ig nem ajr ek sil ut naid umeK .ur ab g nay napawaj

.7 nak sik ul id k ad it ini nal aos ig nir ig nem g nay hajaR.nak at aynid il aucek al ak s t uk ig nem

.8 uat a nal aos pait es ig ab nak k ut nur epid g nay hak r aM .nag nur uk mal ad nak k ujnut id nal aos naiar ec

.9 5 ag g nih 3 namal ah id nak aid esid sumur iar anes ut aS

.01 .nak anug id hel ob ak g na t apme k it amet am r if is uk uB.

11 hel ob k ad it g nay k if it nias r ot al uk l ak naanug g neP nak r anebid hal ad a nak mar g or pid

21 r ihk a ad ap nak har esid hal k ad neh ini nal aos sat r eK . naask ir epep

doK

ask ir emeP

nalaoShak r aM

huneP

hak r aM

helor epiD

1 2

2 2

3 3

4 3

5 3

6 3

7 3

8 3

9 4

01 3

11 4

21 4

31 4

41 4

51 3

61 3

71 3

81291 3

02 3

12 4

22 4

32 3

42 4

52 3

halmuJ

TILUS

1/2743

lanoitiddA

scitamehtaM

1 satreK 0102 ieM

maj 2

1 ignudnagnem ini nalaos satreK 8 .k atecreb namalah

/2743 1 halebes tahiL[



TILUS 2 1/2743

DNAC R OF NOITAMR OFNI SETADI

.1 f o st sisnoc r epap noit seuq sihT 52 .snoit seuq

.2 r ewsnA l l a . snoit seuq

.3 yl no eviG eno .noit seuq hcae r of r ewsna

.4 .r epap noit seuq eht ni d ed ivor p secaps eht ni yl r ael c sr ewsna r uoy et ir W

.5 nik r ow r uoy wohS .sk r am t eg ot uoy pl eh yam t I .g

.6 nwod et ir w nehT .enod evah uoy t aht k r ow eht t uo ssor c ,r ewsna r uoy eg nahc ot hsiw uoy f I

.r ewsna wen eht

.7 .d et at s ssel nu el acs ot nwar d t on er a d ed ivor p snoit seuq eht ni smar g aid ehT

.8 a noit seuq hcae r of d et acol l a sk r am ehT .st ek car b ni nwohs er

.9 .5 ot 3 seg ap no d ed ivor p si eal umr of f o t sil A

.01 r uof f o t el k oob A ..d ed ivor p si sel bat l acit ameht am er ug if

.11 non a esu yam uoY .r ot al ucl ac cif it neics el bammar g or p

.21 .noit animaxe eht f o d ne eht t a ni d ed nah eb t sum r epap noit seuq sihT



TILUS 3 1/2743

eht er a nevig slobmys ehT .snoitseuq eht gnir ewsna ni luf pleh eb yam ealumr of gniwollof ehT.desu ylnommoc seno

sumuR - .nal aos bawajnem ad na ut nabmem k ut nu nak anug id hel ob t uk ir eb sumur l obmiS - .nak anug id asaib g nay hal ad a ir ebid g nay l obmis

AR BEGLA

.1a

cabbx

2

42

.2nmnm aaa

.3nmnm aaa

.4 mnnm aa )(

.5 nmnm aaa golgolgol

.6 nmn

maaa golgolgol

.7 mnm an

a golgol

.8a

bb

c

ca

gol

golgol

.9 d naT n )1(

.01 ])1(2[2

d nan

S n

.11 1 nn r aT

.21r

r a

r

r aS

nn

n

1

)1(

1

)1(( , r )1

.31r

aS

1 , r 1<

)SULUK LAK ( SULUCLAC

.1 y = vu , xd

ud v

xd

vd u

xd

yd

.2 v

u

y , 2v

xd

vd u

xd

ud v

xd

yd

,

.3xd

ud

ud

yd

xd

yd

.4 evr uc a r ednu aer A

)gnuk gnel hawab id sauL(

= b

a

y xd = uata b

a

x yd

5 detar eneg emuloV

)naanaj udapisI(

= b

a

y 2 xd = )uata( r o b

a

x2 yd



TILUS 4 1/2743

SCITSITATS )K ITSITATS(

.1 x =

N

x

.2 x =

f

xf

.3 = N

xx 2)( =

2_ 2

xN

x

.4 =

f

xxf 2)( =

22

xf

xf

.5 M = C f

F N

Lm

2

1

.6 0010

1 Q

QI

.71

11

w

I wI

.8!)(

!

r n

nP r

n

.9 !!)(

!

r r n

nC r

n

.01 A(P )B(P+)A(P=)B - A(P )B

.11 = )r =X(Pr nr

r

n qpC 1 = q + p ,

.21 = )niM( naeM pn

.31 qpn

.41 = z

x

( YR TEMOEG )IR TEMOEG

.1 )k ar aJ( ecnatsiD

= 2

21

2

21 )()( yyxx

.2 )hagnet k itiT( tniopdiM

(x , y = )

2

21 xx ,

2

21 yy

.3 enil a f o tnemges a gnidivid tniop A

utaus igahabmem gnay k itiT(

)sir ag gner ebmet

( y ,x = ) ,21

nm

xmxn

nm

ymyn 21

.4 )agitiges sauL( elgnair t f o aer A

= )()(2

1312312133221 1

yxyxyxyxyxyx

.5 22 yxr

.622 yx

jyixr



TILUS 5 1/2743

( YR TEMONOGIR T IR TEMONOGIR T )

.1 ,htgnel cr A s = r

,k ok gnel gnajnaP s = j

.2 = A ,r otces f o aer A 2

2

1r

= L , r otk es sauL 2

2

1j

.3 nis2

soc + A2

1 = A

nis2

sok + A2

1 = A

.4 ces2

nat + 1 = A2

A

k es2

nat + 1 = A2

A

.5 cesoc2

toc + 1 = A 2

A

k esok 2

tok + 1 = A 2

A

.6 s A soc A nis 2 = A2 ni

A sok A nis 2 = A2 nis

.7 A2 soc soc =2

A – nis 2

A

soc 2 =2

A – 1

1 = – nis 2 2

A

A2 sok sok =2

A – nis 2

A

sok 2 =2

A – 1

1 = – nis 2 2

A

.8 A( nis B soc A nis = )B nis A soc B

A( nis B sok A nis = )B B nis A sok

.9 A( soc B soc A soc = )B B nis A nis

A( sok B sok A sok = )B B nis A nis

1 A( nat .0 = )BBA

BA

natnat1

natnat

.11 = A2 natA

A2nat1

nat2

.21C

c

B

b

A

a

nisnisnis

.31 cbcba 2222 A soc

cbcba 2222 A sok

)agitiges sauL( elgnair t f o aer A .41

= C ba nis

2

1



TILUS 6 1/2743

.1 tes neewteb noitaler eht swohs 1 mar gaiD A tes dna B .

.2 B t es nad A t es ar at na id nag nubuh nak k ujnunem 1 hajaR

etatSnak at ayN

3 f o tcejbo eht )a(

ig ab k ejbo 3

noitaler eht f o egnar eht )b(

nag nubuh t al uj [ hak r am 2 ]

r ewsnA ...……………………… )a( :

..……………………… )b(

.2 noitcnuf eht neviG g : x 4 x dna 3 + h : x x2

– 6 x dnif ,5 + g h (x ]sk r am 2[ )

x : g isg nuf ir ebiD x : h nad 3 + x4 x 2 – nak ir ac ,5 + x6 )x( g h [ hak r am2 ]

r ewsnA ………………………… :

2

2

sk r am 2

1 margaiD1 haj aR

3 •

2 •

1 •0 •

• -2

x x+c

• 2

• 0

- • 3

2

1



TILUS 1/2743 7

.3 taht neviG f : x → 4x – 1 dna x: g → x – 2x2

dnif ,x :f isg nuf ir ebiD x4→ – x: g nad 1 x → – x2 2 . ir aC

)a( f 2

)b( f o eulav eht f 2 g )2( [3 sk r am ]

ialin f 2 g )2( [ hak r am 3 ]

r ewsnA : (a) …………………

(b) …………………

.4 - noitauqe citar dauq eht f o stoor eht f o eno si 2 83 2 xpx

k it ar d auq naamasr ep ig ab acnup ad apir ad ut as hal ai 2− 83 2 xpx

dniF

ir aC

) a ( f o eulav eht ,pn ,p ial i

) b ( .toor r ehto eht f o eulav eht ]sk r am 3[

n ig al ut as g nay acnup ial i [ hak r am 3 ]

r ewsnA : )a( …………………………

.........................................)b(

3

3

3

4



TILUS 1/2743 8

.5 noitauqe citar dauq eht f o stoor eht f o eno taht neviG 242 xpx semit eer ht si

f o eulav eht dniF .stoor r ehto eht p. ]sk r am 3[

acnup ad apir ad ut as awahab ir ebiD - k it ar d auk naamasr ep acnup 242 xpx hal ad a

.ig al ut as g nay ad nag il ak ag it .p ial in ir aC [ hak r am 3 ]

………………………: r ewsnA ……

.6 f o seulav eht egnar eht dniF x ytilauqeni r of ( x 2()4 + x- + 4 <)1 x x2( )4 + x( naamask at ek ig ab x ial in t al uj ir aC - x + 4 <)1

]sk r am 3[

[ hak r am 3 ]

: r ewsnA ..........................

3

5

3

6



TILUS 1/2743 9

7. mar gaiD 7 noitcnuf citar dauq f o hpar g swohs =)x( f 61 – x( – )s 2

htiw , s a sa

.tnatsnochajaR 7 6 1=)x( f k it ar d auk isg nuf ig ab f ar g nak k ujnunem – x( – )s

2 s nag ned ,

r al amep hal ad a

evr uc ehT )x( f =y ( tniop mumixam sah s,t taht hcus ,) t .tnatsnoc a si ,)t ,s( amisk am k it it iaynupmem )x( f =y g nuk g neL nag ned r al amep hal ad a t

etatSnak at ayN

f o eulav )a( s , s ial in

f o eulav )b( t ,t ial in

f o eulav )c( u u ial in

]sk r am 3[

[ hak r am 3 ]

: r ewsnA )a( ..………………………

.......................)b( ..............

.....................................)c(

.8 neviG gol taht 9 gol = x2 3 .x f o eulav eht dnif ,4 ]sk r am 3[g ol awahab ir ebiD 9 g ol = x2 3 .x ial in ir ac ,4 [ hak r am 3 ]

…… :r ewsnA ..……… ……………

3

8

7 margaiD7 hajaR

y

x

)t ,s(

)x ( f = y

)0 ,7 ( B( A - )0 ,1

u

3

7



TILUS 1/2743 01

9. noitauqe eht evloS 2 gol 2

(m- )1 - gol 2 ( m- )2 = 2 . [ 4 sk r am ]

naamasr ep nak iasel eS g ol 2 2

m( - )1 - g ol 2 m( - 2 = )2 [ 4 hak r am ]

…… :r ewsnA ..……… ……………

.01 noitauqe eht evloS nn 18)3(9 4 . ]sk r am 3 [

naamasr ep nak iasel eS nn 18)3(9 4

. [ hak r am 3 ]

……….………………… :r ewsnA

4

9

3

01



TILUS 1/2743 11

.11 5 er a noisser gor p citemhtir a na f o mr et thgie eht dna mr et htr uof ehT

dniF .ylevitcepser 12 dnanad 5 hal ai k it emt ir a g najnaj ut aus napal ek nat ubes nad t apmeek nat ubeS

g nisam 12 - am ir aC .g nis

)a( mr et tsr if eht dna ecner ef f id nommoc eht ]sk r am 2[

amat r ep nat ubes nad aynupes az eb [ hak r am 2 ]

)b( .noisser gor p eht f o mr et thgie tsr if eht f o mus eht ]sk r am 2[

h t i g najnaj amat r ep nat ubes napal ig ab habmat l isa u. [ hak r am 2 ]

(: r ewsnA … )a .……… ….… .……

)b( … .….……… ..……

.21 si mr et tsr if eht taht neviG .smr et 6 sah noisser gor p cir temoeg A 3

1 mr et tsal eht dna

si 18

g g najnaj ut auS hal ai amat r ep nat ubes ir ebiD .nat ubes 6 iaynupmem cir t emoe3

1 nad

.18 hal ai r ihk ar et nat ubes

dniFir aC

)a( noisser gor p eht f o oitar nommoc ehtini g najnaj ig ab aynupes habsin

)b( .smr et xis tsr if eht f o mus eht [ sk r am 4 ]ab habmat l isah .amat r ep nat ubes 6 ig [ hak r am 4 ]

r ewsnA : )a( ………………… ................

...........................................)b(

4

11

4

21



TILUS 1/2743 21

31 . sa nevig si noisser gor p cir temoeg a f o smr et n tsr if eht f o muShal ad a ir t emoeg g najnaj yt aus ig ab amat r ep nat ubes n habmat l isaH

S n 1[9 = -

n

3

2]

dniFnak ar iK

mr et htf if eht )a(

amil ek nat ubes

mus eht )b( ot .ytinif ni

h l isa it inif ni ag g nih habmat

]sk r am 4[[ hak r am 4 ]

(: r ewsnA … )a .……… ….… .……

)b( … .….……… ……

.41 mar gaiD 41 enil thgiar ts f o hpar g eht swohs x

y tsniaga x

hajaR 41 sur ul sir ag f ar g nak k ujnunem x

yem x nawal

x

y

(k )9,

,2( h)

0 x

taht neviG y 4 = x + x2

f o eulav eht etaluclac , h f o dna k . ]sk r am 4[

x + x4 = y awahab ir ebiD2

n nak ar ik , .k ig ab ial in nad h ig ab ial i [ hak r am 4 ]

r ewsnA : h …………………… =

k …………………… =

4

31

4

41

41 margaiD4 1 haj aR



TILUS 1/2743 31

………………… r ewsnA .…… .

.61 er a elgnair t a f o secitr ev ehT P ,)4 ,0( Q dna )t ,6( R elgnair t f o aer a eht neviG .)7 ,4(

RQP tinu 52 si 2

f o seulav eht dnif , t .] sk r am 3 [

ucuB awahab ir ebiD .)7 ,4( R nad )t ,6 ( Q ,)4 ,0( P hal ai ag it ig es haubes ig ab ucub−t inu52 hal ai RQP ag it ig es ig ab saul 2

ial in ir ac , .t ig ab ial in−[ hak r am3 ]

r ewsnA : t ……………… =

enil thgiar ts eht swohs 51 mar gaiD .51 BA enil thgiar ts eht ot r alucidnepr ep si hcihw

BC tniop eht ta B.hajaR 15 sur ul ir ag nag ned g najner esr eb BA sur ul sir ag nak k ujnunem hawab id

.B k it it id BC

51 margaiD51 haj aR

iG enil thgiar ts eht f o noitauqe eht nev BC si y 3 = x tniop f o setanidr ooc eht dnif ,8 B

]sk r am 3 [ C sur ul sir ag naamasr ep ir ebiD x3 = y hal ai B – B k it it t anid r ook ir ac ,8 [ hak r am 3 ]

y

A)4,0(

B

x

C

O

3

61

3

51



TILUS 1/2743 41

.71 taht neviG 32 )34()( xxxg dnif , g )2(’ [ sk r am 3 ]

ir ebiD32)34()( xxxg )2( ’ g ir ac , [ hak r am 3 ]

: r ewsnA …………………

,evr uc eht ot tnegnat ehT .81 xxy 62 2 tniop ta M eht ot r alucidnepr ep si

enil thgiar ts 32

1 xy eht dniF . f o setanidr ooc tniop .M

[2 ]sk r am

g nuk g nel ut aus ad apek neg nat sir aG xxy 62 2 nag ned g najner esr eb hal ad a M k it it ad ap

sur ul sir ag 321 xy . ir aC ig ab t anid r ook .M k it it [2m hak r a ]

………………… : r ewsnA ........... ....

2

81

3

71



TILUS 1/2743 51

.91 taht neviG y 4 = x3

– 7 x2

, x4 = y awahab ir ebiD 3 – x7 2 ,

dnif )a( f o eulav ehtxd

yd ,)4 ,2( tniop ta

ir ac ial inxd yd ,)4 ,2( k it it ad ap

ni tnemer cni etamixor ppa eht dnif ,ecneh )b( x nehw y mor f sesaer cni

50.4 ot 4nahabmat nak ut net nak ut net ,aynsur et es y al ibapa x mal ad nar ipmah

m 50.4 ot 4 ad apir ad t ak g nine

]sk r am 3[

[ hak r am 3 ]

....……………………… )a( :r ewsnA

. )b( ........................................

.02 f I 6

2)( xd xf dnif ,01 =

ir ebiD

6

2)(

xd xf ir ac ,01 =

f o eulav eht )a( xd xf 2

6)(

ial in xd xf 2

6)(

f i m f o eulav eht )b( 6

2])([ xd xf xm 41 =

n ak ij m ial i 6

2])([ xd xf xm 41 = ]sk r am 3[

[ hak r am 3 ]

…………………… )a( :r ewsnA ..… ..

... )b( ......................................

3

02

3

91



TILUS 1/2743 61

.12 neviG 3)21( xpxd

yd , 3y dna 1 = x nehw 95y nehw 1x if , eulav eht dn

f o p er ehw p .tnatsnoc a si ] sk r am 4 [

ir ebiD ,)21(3xp

xd

yd 3 = y al ibapa 1 = x nad 95 = y al ibapa 1x , b ial in ir ac ig a

p anamid p r al amep hal ai . k r am4 [ ha ]

: r ewsnA ……………………………

.22

E

DC B

margaiD 2222 haj aR

mar gaiD 22 r otces a swohs E C A er tnec htiw A tnar dauq a dna E DB er tnec htiw B .taht neviG BA ,mc8= E A etaluclac ,mc01=

hajaR 5 A t asupr eb E C A r ot k es ut as nak k ujnunem .B t asupr eb E DB nauk us ut as nad c01=E A ,mc8=BA awahab ir ebiD nak g nut ih ,m

f o eulav eht )a( .naidar ni ,

n ial i .naid ar mal ad ,mc ni ,r etemir ep eht )b(

2.noiger dedahs eht f o ,

p mc mal ad ,r et emir e2

.k er ol r eb nasawak ig ab ,]sk r am 4[

[ hak r am4 ]

)a( :r ewsnA …………………… ………

……………………………)b(

4

12

4

22



TILUS 1/2743 71

Q

P

O

mc 01

margaiD 32

32 haj aR

mar gaiD .32 32 er tnec htiw elcr ic a swohs O r otces r ojam eht f o aer a eht taht neviG . QP O si

mc 5222

elgna eht dniF . .snaidar ni esU( )241.3 = [ sk r am 3 ]

hajaR 32 hal ai QP O r ojam r ot k es saul ir ebiD .O t asupr eb nat al ub haubes nak k ujnunem

mc 522 2 t ud us ial in ir ac , .naid ar mal ad nak anuG( )241.3 = [ hak r am 3 ]

:r ewsnA ……………………………

ni atad ehT .42 T elba 42 r edr o gnidnecsa ni degnar r a siat aD mal ad J l aud a 42 k ianem nat ur u t uk ig nem nususid

er ocSr ok s 1 m-2 7 m 3+ 31 51

ycneuqer Fisneuk er F

3 2 3 4 3 2

42 elbaTl aud aJ 4 2

.3 si atad f o egnar elitr auqr etni ehT 3 hal ai at ad ig ab l it r auk ar at na t al uJ

)a( f o eulav eht dniF m m ial in ir aC

)b( naem eht dniFnim ial in ir aC

[4 ]sk r am

[4 hak r am ]

r ewsnA ( : a …………………………………)

(b …) ………………………………

3

32

4

42



TILUS 1/2743 81

,02 si r edr o gnidnecsed ni degnar r a sr ebmun f o tes A .52 r ,q ,p .8 ,31 ,

1 er a naidem eht dna edom eht ,naem eht neviG 5.4 1 dna 61 , 5

f o seulav eht dniF .ylevitcepser q ,p dna r .

r obmon t es ut auS i nur unem nat ur u t uk ig nem nususid ir ebiD .8 ,31 ,r ,q ,p ,02 hal a1 hal ai naid em nad d om ,nim 5.4 1 nad 6 1 , 5 g nisam - q ,p ig ab ial in ir aC .g nisam

.r nad

]sk r am 3[

]hak r am 3[

r ewsnA p : ……= ………… .…

q .………………… =

r .………………… = .

R EPAP NOITSEUQ FO DNET AM AT N ALAOS S AT RE K

3

52

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ADD. MATHEMATICS PAPER 1