Add Mth P1 Spm Johor 09

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3472/l

NO. KAD PENGENALAN ANGKA GILTRAN

JABATAN PELAJARAN NEGERI JOHOR

PEPERIKSAAN PERCUBAAN SPM 2OA9

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ADDITIONAL MATIIEMATICS Kertas I Sept. 2 Jam

D ua i am

JANGAN BUKA KBRTAS SOALAN INI SEHTNGGADIBERITAHU 1. Tulis nombor kad pengenalandan angka giliran andapadapetakyangdisediakan.

UntukKegunaan Pemeriksa Soalan I

Markah Penuh

2. Kertassoalanini adalahdalamdwibahasa.

2 3

3. Soalan dalam bahasaInggerismendahului soalanyang sepadandalambahasaMelayu.

4

4 3 3 3 3 3

4. Calon dibenarkan menjawab keseluruhan atau sebahagiansoalan sama ada dalam bahasalnggerisataubahasaMelayu. 5. Calon dikehendakimembacamaklumatdi halamanbelakangkertassoalan.

5 6 7 8 9 10

Markah Dioerolehi

2

3 2 J

2 2 3 4 5 6 7 8 9 20 2l 22 23 24 25 Jumlah

J

2 4 A

A A

, A J A

+ ! A

80

Kertassoalanini mengandungi 20 halarnanbercetak 347211

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giren are lhe ones T'hef|ltov,ing -formulae may be hetpfut in onsw-eringthe qttestions The synbols commonly used. ALGEBRA 1

-b + r lh' - 4ac

x=

l oc.b

l Oe"D= 'l og. a

8

2a

fn:6r(n-l )d

2

r!' x Ll'= Lt "' n

3

t!'+on-

4

(u"')n=a'"'

ll

n-t Tn = a"r

5

log. mn = log am + laga n

t2

S'n=

6

log"

a il' n

10 s"= llzr+(n-l)dl

2'

7

nl'

= log sn - log'n

n log"m':

a(r' -l \ r-l

d S"_= l -r

n lo g o m

u(l -r' ) l -r

=--J,l .r+t)

..

l' " l. r

C AL C ULU S

l=tw,

dv dv -;=t t ; + v ; dx ax

du

du

dv

ax

Area undera curve I

: .v clx

tt

rd yv .

,

=-

dy

tly

du

dx

du

dx

dx

dr 1

or

lY.lr f

=

lx ttV

Votumegenerated

= |tt /w " ctr or oo =

lt l l r {)-

dy

GEOMETRY

1 Distancc =

- -'r,)' + (jr,

2 Midpoint

(x.+xl \,. t r, - + .;r , = { . lr l

(r,r)=

+ -Yr .Y:) ' 1)

5 A pointdividinga segmentof a line ( ra, mr, nv, + .y, ) (r,.v)= i -' i nt+ tt / \ tl r n 6 Areaof triangle

:Jl,,r,r, +,r,-)/3 + r;/', ) - (t,.v,+ r',y,+'t,y',)l

xt+y.l

^

l) 7

V-r-+.Y-

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3472t1 STATISTIC

x

x

= II

7- Zw,I,

N

Lw,

=21 Zr

=,! (n- r)l nl

3o= ,F:,tr ;

'

4-,ry=ffi;

l0

P(Av B) = P(I)+P(B)-P(AnB)

tl

P (X = r) = nC ,p' qn-' ,p+ q:

1)

Meanp- np

[1r-"]

5 m= r+l2-lg

IJ

l'' l

(n - ry.vl

l4

o = J;pq x- u o

6

I =&x100 Qo

TRIGONOMETRY I A r c lengt h ,s = r0 2 A r eaof s e c to r,L = !r' 0 2 3 sinzA + cos 2l : I

9 sin (l t B) : siM cosB t cosl sin.B t0 cos(l t 13)= coM cosB T sinl sin3 1l

4 sec2A=| +tan2A 5 c os ec 2A - l + c o t2 A 6 sinZA:2

3472/1

tanA+ tanB lT tanAtanB

o =b =, sin,4 sinB sinC

sinA cosA

7 cos2A = cos2l -sin2 A :2 cos2A- | = |- 2 s i n 2 A g tan2A -

I2

Ian(.{ +

l3 a2= b2+ c2 - 2bc cos"4 I

t4 A reaof tri angl e = :absi n C -2

Ztan4 1-ta n ' A

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Answerall questfbns Diagr a m1 s h o w stn e g ra p ho f th efu n c ti on.f (x) = l x+ i i , forthe domai n - 2< x < 5 . graf f (x) = l.r + | l, untukdomain-2<x<5 ' Raiah1 menuniukkan

S t at e: Nyatakan'. ( a) t he / -' (5 ) ( b) f |Q )

12marksl 12markahl (a) ...... lJawaPan: Answer

I I

(b)

2.

G iv ent h e fu n c ti o ngs :-r+ 7 .v + l Diberfi un g s gi ' .x -+ 7 x + 1 ( a) (b)

a n d h ' . x-+ { -t 3

d a nh :x -+ !* t

fi nO,

C ari ,

g- ' (8 )

14marksl 14ma*ah)

sh(x)

(a) Answer/JawaPan'. .

34721t

(b)

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3472t1 a

3.

Giventhefunctions .f(x) =-:; Diberifungsi"f(x) = -:;x-l

and gf(x) = 5x- 4.Find g(.r).

dan gf (x) = 5x* 4 . Carig(x) . [3 marksj 13maftahl

3

| I

l---l 3l

AnswerlJawapan:

4.

Giventhat3 and k aretherootsof thequadratic equation x' +.r = p. Findthevalue of k andp. Diberibahawa3 dank ialahpunca-punca wrsamaankuadratik.cai nilai k dan p . 13marksl [3 markah]

4 I I

r-l t3l

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c Diagram5 showsthe graphof /(x) = a(x - b)2 + c' Statethe value ol a 'b and ' Rajah5 menunjukkangraf f (x) = alx - b)'1+ c'Nyatakannilai a 'b dan c

A

[3 marks] [3 markah] x-b)2 + c

5 Diagram Rajah5 Jawaqan'. Answer/

6.

functionf (x) = 2x' - 7' findtherangeof r if /(x) > I l . Giventhequadratic (x) = 2x' -7, carijulatbagix jika f (x) > l l . Diberifungsikuadratik -f

[3 marks] 13ma*ahl

6 I

I

Answer/Jawapan :

t, 347211

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l3l

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7.

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Solvethe equation3'*' Se/esaikan persamaan

[3 marks] [3 markah]

1

I I

r--1 lrl

Answer/Jawapan:

Giventhat log3x = loge4, findthe valueof x. Diberi log3x = Iogg4, cari nilai x.

[3 marks] [3 markah]

Answer/Jawapan.

Findthesumto infinigof thegeometric series 1 * I * -!-*.. 24 Carihasiltambah hinggaketakterhinggaan bagisirijanjang geometri t *] ) , *1*.... r 12marksl 12markah) 9

[J

I

t2l Answer/Jawapan

r) 347211

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progression - 5, - l, 3,... sothatits of termsinthearithmetic 10. Findtheleastnumber sumexceeds200. Caribilangansebufante*ecil dalamianiangarithmetic-5, - 1,3,...supayahasil tambahsebutanmelebihi200. [3 marks] 13markahl

l0 |

Answer/Jawapan

11,

.--l

I lr l

progression are2 , y and18. positive termsof a geometric Thefirstthreeconsecutive Findthecommonratioof theprogression. Tiga sebutanpeftamasuatuianianggeometriialah2 , y dan 18' Cari nisbahsepunyabagiianiangtersebut.

1 2ma * s l 12maftahl

r-= ll

I

....., Jawapan: Answer/

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l2 l

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12.

n y = +, wherem andn are bytheequatio x and ), arerelated Thevariables n constants.Diagram'12 snowsthe straightlineobtainedby plottinglogr y aga i n s tx .

manam dan y = 4'0, x dany dihubungkanolehpersamzotl Pembolehubah n n adalahpemalar. Raiah 12 menuniukkangarislurus yang diperolehidengan memplot log, y melawan x .

D i a gram12 Rajah12

Findthe valueof m and of n. Cari nilaim dan n.

[3 marks] [3 markah]

t2 lrI l3l Answer/Jawaoan

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Diagram13 showsa straightline PMQ. Rajah 13 menunjukkangaris lurus PMQ.

P1-s+ l,-4t)

QQ + 7,s -21 D i a g ram13 Rajah13

Giventhat a point M(4,4) dividesthe linesegmentjoiningthe pointsP(s + t'-4t) and QQ +7,s - 2) in the ralio 2: l Findthe valueof s and f. Diberi titik M(4, 4) membahagitemberenggaris yang menyambungkantitik P(s + t,-4t) dan QQ + 7,s - 2) dalamnisbah2:1. Cari nilais dan t. [ 4 marks ] 14markahl

l3 I i Answer/JawapSl?i s =

r\

t-

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14. Diagram 14showsa straight lineABwhichintersects to thestraight lineCDat thepoint T(2,3) Raiah14menuniukkan garislurusAB bersilang dengangarislurusCD padatitikT(2,3)).

*1"*q 2 Diagram 14 Rajah14 Theequation of thestraightline ABisy=-1r+4 2

andtheequation of thestraight

line CD is y = 2y - 1.

Persamaangarislurus AB iatahy = *1, + 4 dan persamaangarislurus CD ialah L

Y=2x-l Calculatethe areaof the trianglel7D . Kirakan luas segitiga ATD .

[3 marks] l3 markahI

t4 I I ()

r---1 l3i

Answer/ Jawapan:

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15.

vectorof 2g- b. Diagr am1 5 s h o w sv e c to rs4 a n d !. D ra wthe resul tant Rajah15 menunjukkanvektor a dan \. Lukiskanvektorpaduanbagi 2a - b. 12 marks) [2 markah]

/ g

,/

D i a gram15 R aj ah' 15 Answer/ Jawapan

3472/1

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16.

-+a

The vectors PQ and Rf are parallel.lt is giventhat PQ= 2?- 3! and -+o

nS = (t +Ds-;b..

-> -> -) VeKor PQ dan RS adalah selai. Diberi bahawa PQ = 2a -3b dan -tq RS = 2Find Cari (a)

the value of /r Nilaibagi k

(b)

the ratioof PQ: RS Nisbahbagi PQ: RS

[4 marks] 14ma*ahl

t6 I

I

r\

r-i

Answer/Jawapan:(a'1

l4l

(b)............. 347211

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Giventhat coSI = p and0 is an acuteangle,expressin termsof p . Diberibahawa kos0 = p, dan 0 adalahsuatusuduttirus,ungkapkandalam sebutanp bagi (a) tan d e (b) sin; z

t7 Answer/Jawapan:(a)

I I

r-l4 l

.A

18.

Given y = :j , find the approximatevalueof y , when ;r changeslrom 2 to 2.02. x )4

Diberiy =:, , cariperubahannilaibagi y , apabilax berubahdaripada2 kepada x 2.02. 14marksl 14markahl

18

I Answer/ Jawaoan. 3472/1

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r)

l5 For examiner's useonly

3472/l Diagram18showsa seclorOPQwithcentreO andradius5 cm. Rajah18menunjukkan seldorOPQyangberpusatOdanjejari5 cm.

O

Rl cm

O

Diagram18 R a jah18 Given QR =1 cm and IPRO = 900,findthe areain cm2 , of the shadedregion. Diberi QR=1 cm dan ./.PRO= 900 , kirakanluasdatamcm2 bagi kawasanbedorek.

14marksl 14matuahl

l9

t-l I l al

Answer/ Jawapan

tt

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I

20.

Findthe coordinatesof the turningpointson the curve / = 4x + - and determinethe x maximumDoint. I

Cari koordinatbagi titik-titikpusinganbagi tengkungy = 4x + i- dan tentukan x titik maksimum. 14marksl 14markahl

20

t--J l4 l

A nsw er/ Jaw apan.'.........

I Giveny =#

x-

= 3g(r) whereg(r) is a function of x. Findthevalueof

and

!,s@)a' 1- _1

Diberi y=2-:

dan

dy

= 3g(x) di mana g(x) ialahfungsibagi x . Cari nilai

Isi)ax' 14marks) 14markahl

2l

I I Answer/ Jawapan : 347211

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Table22 showsthe marksof a groupof studentsin an examination.

22.

Jadual 22 menunjukkanmarkah sekumpulanpelajar yang diperolehidalam suatu peperiksaan. Marks Numberof students

1i?

4

6

7

8

Iable22 Jadual22 F ind Cari (a)

the maximumvalueof x if the modemarkis 8. nilai markah bagi x jika markahmod ialah 8.

(b)

the minimumvalueof x if the meanof the marksis greaterthan 3 nilai minimumbagi x jika markah min lebih daripada3. [3 marks] 13markahJ

22

t--_l I r--I

Answer/ Jawapan (a) (b)

lrl

23.

Findthe numberof waysin which4 boysand 5 girlscan be seatedin a row if Cari bilangancara susunan4 budaklelakidan 5 budakperempuanboleh duduk. (a)

thereis no restriction tiada syarat dikenakan

(b)

the boysand the girlsare seatedallernately pelajar lelaki duduk berselang selidenganpelajar perempuan. 14 marks) 14markahl

)7 tl

I I

r-1 l4l Answer/Jawapan:(a)

\l

(b) . 317211

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24.

For examiner's use only

f abire24 shows the numberof colouredmarblesin a bag. Jadual 24 menunjukkanbilanganguli bervvarnadi dalam satu beg.

Colour

Numberof marbles

Red

4

Green Purple

x+2 2 Table24 Jadual24

A marbleis drawnat randomfrom the bag. Giventhat the probabilityof gettinga I

greenmarbleis -. Findthe valueof -t. Sebijigulidikeluarkan sscara rawak daripadabeg. Diberi kebarangkalianmendapat I

sebijiguli hijau ialah;. Cari nilai x. J

[2 marksl 12markahl

24

I r'l A nsw er /Jaw aD an: ......... 347211

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S ULI T For exonriner

25.

graph Diagram25 showsa standardnormaldistribution

useonlr-

Rajah25 menunjukkangraf taburannormalpiawai. 1 (x )

represented by the shadedregionis 0.7514. The probability Kebarangkaliankawasanbedorekialah0.7514. (a)

Findthe valueof & , Carinilaik.

(b)

with a mean whichis normallydistributed X is a continuousrandomvariables 80 and a varianceof 9. Flndthe valueof X whenthe z-scoreis t . X ialahpembolehubahrawakselaniaryang beftabursecaranormaldengan min 80 dan varians9. CarinilaiX iikaskor'z ialah k .

14marksl 14markahl

25

[J I

Answer/Jawapan:(a)

l4 l

thl tv,

,..'.

EN D O F QU ES TIONP A P E R

()

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