add._maths_trial_spm_johor_2009_[banksoalanspm.blogspot.com].pdf

62
SULIT NO. KAD PENGENALAN ANGKA GILTRAN 3472/l JABATAN PELAJARAN NEGERI JOHOR PEPERIKSAAN PERCUBAAN SPM 2OA9 ADDITIONAL MATIIEMATICS Kertas I Sept. 2 Jam 3472/l Dua iam JANGAN BUKA KBRTAS SOALAN 1. Tulis nombor kad pengenalan danangka giliran andapada petak yangdisediakan. 2. Kertas soalan ini adalah dalam dwibahasa. 3. Soalandalam bahasa Inggerismendahului soalan yang sepadan dalambahasa Melayu. 4. Calon dibenarkanmenjawab keseluruhan atau sebahagian soalan sama ada dalam bahasa lnggeris ataubahasa Melayu. 5. Calon dikehendaki membaca maklumatdi halaman belakang kertas soalan . INI SEHTNGGA DIBERITAHU Untuk Kegunaan Pemeriksa Soalan Markah Penuh Markah Dioerolehi I 2 2 4 3 3 4 3 5 3 6 3 7 3 8 3 9 2 10 J 2 2 3 4 J 5 2 6 4 7 A 8 A 9 A 20 , 2l A 22 J 23 A + 24 ! 25 A Jumlah 80 Kertas soalan ini 347211 2oo9 Hak Cipta JpNJ mengandungi 20 halarnan bercetak [Lihat sebelah SULIT http://banksoalanspm.blogspot.com/

Upload: carolyne-chang

Post on 19-Feb-2016

38 views

Category:

Documents


12 download

TRANSCRIPT

Page 1: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SULIT

NO. KAD PENGENALAN

ANGKA GILTRAN

3472/l

JABATAN PELAJARAN NEGERI JOHOR

PEPERIKSAAN PERCUBAAN SPM 2OA9ADDITIONAL MATIIEMATICSKertas ISept.2 Jam

3472/l

Dua iam

JANGAN BUKA KBRTAS SOALAN

1. Tulis nombor kad pengenalan dan angkagiliran anda pada petak yang disediakan.

2. Kertas soalan ini adalah dalam dwibahasa.

3. Soalan dalam bahasa Inggeris mendahuluisoalan yang sepadan dalam bahasa Melayu.

4. Calon dibenarkan menjawab keseluruhanatau sebahagian soalan sama ada dalambahasa lnggeris atau bahasa Melayu.

5. Calon dikehendaki membaca maklumat dihalaman belakang kertas soalan .

INI SEHTNGGA DIBERITAHU

Untuk Kegunaan PemeriksaSoalan Markah Penuh Markah Dioerolehi

I 22 43 34 35 36 37 38 39 210 J

2234 J

5 26 47 A

8 A

9 A

20 ,2l A

22 J

23 A+

24 !

25 A

Jumlah 80

Kertas soalan ini

347211 2oo9 Hak Cipta JpNJ

mengandungi 20 halarnan bercetak

[Lihat sebelahSULIT

http://banksoalanspm.blogspot.com/

Page 2: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SULIT 3472t1

T'he f|ltov,ing -formulae may be hetpfut in onsw-ering the qttestions The synbols giren are lhe ones

commonly used.

-b + r lh ' -4ac1 x=

2a

2 r ! ' x L l '= Lt" 'n

3 t ! '+on- ai l 'n

4 (u" ' )n=a'" '

5 log. mn = log am + laga n

nl6 log"

' = log sn - log'nn

7 log"m': n logom

ALGEBRA

8loc.b

lOe"D = ' -log. a

fn:6r(n- l )d

s"= l lzr+(n- l )d l2 '

Tn = a"r n-t

a(r ' - l \ u( l - r ' ) . .Sn= =--J, l . r+t)' r - l l - r

S_ = d l ' l . r" l - r "

10

l l

t2

CALCULUS

. dy tly du

dx du dx

dv dv dul=tw, - ;=t t ;+v;

dx ax ax

du dv.v

tt clx dr dx,

=- 1

rdyv

Area under a curve

I: lY. l r or

f= lx t tV

Votume generated

t t= | /w" ctr oroo

lt= l l r { - dy) -

GEOMETRY

1 Distancc =

2 Midpoint

5 A point dividing a segment of a l ine( ra,

- mr, nv, +.y, )

( r , .v)= i - ' i\ t l r n nt+t t /

6 Area of triangle

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

(x.+x-(r , r )= l

\ , .t , ;

l r l ={ . r -+.r , -

^ xt+y. ll )7

V-r- +.Y-

-Yr + .Y: )'1)

341211 2oo9 IIak Cipta JPNJSULIT

- -'r, )' + (jr,

http://banksoalanspm.blogspot.com/

Page 3: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SULIT

STATISTIC

3472t1

x

x

=IIN

=21Zr

Zw,I,Lw,

=,!(n - r) l

nl

7-

3o=,F:, t r ;4-,ry=ffi;

5 m=

6 I =&x100Qo

[1r-" ]r+l2-lg

l ' ' l

1)

IJ

l4

l0

t l

' (n - ry.vl

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

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

Mean p- np

o = J;pqx- u

o

TRIGONOMETRY

I Arclength,s=r0

2 Areaofsector,L=!r '02

3 sinzA + cos 2l : I

4 sec2A= | +tan2A

5 cosec2A-l+cot2A

6 sinZA:2 sinA cosA

7 cos2A = cos2l -sin2 A:2 cos2A - |=|-2sin2A

g tan2A - Ztan 4

1-tan'A

3472/1 2oo9 Hak Cipta JnNJ

sin (l t B) : siM cosB t cosl sin.B

cos (l t 13) = coM cosB T sinl sin3

tan A+ tan BIan (.{ +lT tanAtan B

o =b =,sin,4 sin B sin C

a2 = b2 + c2 - 2bc cos"4

IArea of t r iangle = :absin C-2

9

t0

1l

I2

l3

t4

I Lihat sebelahSULIT

http://banksoalanspm.blogspot.com/

Page 4: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SULIT 34721r

12 marksl12 markahl

Answer lJawaPan: (a) . . . . . .

(b)

Answer all questfbns

Diagram 1 shows tne graph of the funct ion . f (x) =l x+ i i , for the domain

-2<x<5.

Raiah 1 menuniukkan graf f (x) = l.r + | l, untuk domain -2<x<5 '

State:Nyatakan'.

(a) the / - ' (5)(b) f |Q)

Forexomrner's

use only

I

I r---I l2 l

2. Giventhefunct ions g:-r+7.v+l and h' .x-+{- t f inO,3

Diber i fungsi g ' .x-+7x+1 dan h:x-+!* t Car i ,

(a) g- ' (8)(b) sh(x)

Answer/JawaPan'. (a)

. (b)

14 marksl14 ma*ah)

34721t 2oa9 Hak cipta JPNISULIT

http://banksoalanspm.blogspot.com/

Page 5: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

Forexaminer's

use only

3

| ---lI l3 l

4

I r-lI t3 l

( )

SULIT 3472t1

3.a

Given the functions .f(x) =-:; and gf(x) = 5x - 4.Find g(.r).

-Diberi fungsi "f (x) = -:; dan gf (x) = 5x * 4 . Cari g(x) .x- l

4.

[3 marksj13 maftahl

Answerl Jawapan:

Given that 3 and k are the roots of the quadratic equation x' +.r = p. Find the valueof k and p.Diberi bahawa 3 dan k ialah punca-punca wrsamaan kuadratik. cai nilai k dan p .

13 marksl[3 markah]

347211 2009 Hak Cipta lpNJ I Lihat sebelahSULTT

http://banksoalanspm.blogspot.com/

Page 6: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

347211SULIT

A Diagram 5 shows the graph of /(x) = a(x - b)2 + c' State the value ol a 'b and c '

Rajah 5 menunjukkan graf f (x) = alx - b)'1 + c'Nyatakan nilai a 'b dan c

Diagram 5Rajah 5

x-b)2 + c

Answer/ Jawaqan'.

[3 marks][3 markah]

Forexaminer's

use only

6

I r--1I l3 l

t ,

6. Given the quadratic function f (x) = 2x' - 7' find the range of r if

Diberi fungsi kuadratik -f (x) = 2x' -7, cari julat bagi x jika f (x) >

Answer/ Jawapan :

347211 2ooe Hah ciptd JPNJ

/ (x) > I l .

l l .

[3 marks]13 ma*ahl

SULIT

http://banksoalanspm.blogspot.com/

Page 7: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

Forexaminer's

use only

1

I r--1I l r l

9

[JI t2 l

r )

SULIT

7. Solve the equation 3'*'Se/esaikan persamaan

3472/l

[3 marks][3 markah]

Answer/ Jawapan:

Given that log3 x = loge 4, f ind the value of x.Diberi log3 x = Iogg 4, cari nilai x.

[3 marks][3 markah]

Answer/ Jawapan.

Find the sum to infinig of the geometric series 1 * I * -!- *..24

Carihasiltambah hingga ketakterhinggaan bagisirijanjang geometri t *] *1*....) , r

12 marksl12 markah)

Answer/ Jawapan

347211 2oo9 Hok ciDra JnNJ I Lihat sebelahSULIT

http://banksoalanspm.blogspot.com/

Page 8: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SULIT

10. Find the least number of terms in the arithmetic progression

sum exceeds 200.Cari bilangan sebufan te*ecil dalam ianiang arithmetic -5,

tambah sebutan melebihi 200.[3 marks]

13 markahl

Answer/ Jawapan

11 , The first three consecutive positive terms of a geometric progression are 2 , y and 1 8.

Find the common ratio of the progression.

Tiga sebutan peftama suatu ianiang geometri ialah 2 , y dan 18'

Cari nisbah sepunya bagi ianiang tersebut.12 ma*sl12 maftahl

Answer/ Jawapan: .....,

347211 2oo9 Hah cipta JPNJ

347211

- 5, - l, 3, ... so that its

- 1,3, ... supaya hasil

Forexaminer's

use only

l0

| .--lI l r l

l lr-=I l2 l

t ,

http://banksoalanspm.blogspot.com/

Page 9: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

Forexaminer's

we only

t2

l r -I l3 l

SULTT

12.

3472tt

[3 marks ][3 markah]

The variables x and ), are related by the equatio n y = +, where m and n aren

constants. Diagram '1 2 snows the straight l ine obtained by plotting logr y

against x.

Pembolehubah x dan y dihubungkan oleh persamzotl y = 4'0, mana m dann

n adalah pemalar. Raiah 12 menuniukkan garis lurus yang diperolehi dengan

memplot log, y melawan x .

Diagram 12Rajah 12

Find the value of m and of n.Cari nilai m dan n.

3472/1 2oo9 Hak cipta JPNJ

Answer/ Jawaoan

Lihat sebelahSULIT

http://banksoalanspm.blogspot.com/

Page 10: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SULIT 3472tL

Diagram 13 shows a straight line PMQ.

Rajah 13 menunjukkan garis lurus PMQ.

P1-s + l,-4t)

QQ +7,s -21

Diagram 13Rajah 13

Given that a point M(4,4) divides the l ine segment joining the points P(s + t '-4t)

and QQ +7,s - 2) in the ralio 2: l Find the value of s and f.

Diberi titik M(4, 4) membahagi tembereng garis yang menyambungkan titikP(s + t,-4t) dan QQ + 7,s - 2) dalam nisbah 2:1. Cari nilai s dan t.

[ 4 marks ]14 markahl

Answer/JawapSl? i s =

t -

347211 2oo9 Hak ciDtd JPNJSULIT

t0

13

Forexaminer's

use only

l3

I r---i l4 l

r \

http://banksoalanspm.blogspot.com/

Page 11: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

Forexaminer's

use onlv

t4

I r---1I l3 i

( )

SULIT 3472/l

14. Diagram 14 shows a straight line AB which intersects to the straight line CD at the pointT(2,3)

Raiah 14 menuniukkan garis lurus AB bersilang dengan garis lurus CD pada titik T(2,3)).

*1"*q2

Diagram 14Rajah 14

The equat ion of the straight l ine ABisy=-1r+4 and the equat ion of the straight2

l ine CD is y=2y-1.

Persamaan garis lurus AB iatah y = *1, + 4 dan persamaan garis lurus CD ialahL

Y=2x- l

Calculate the area of the triangle l7D .

Kirakan luas segitiga ATD .

[3 marks]l3 markah I

Answer / Jawapan :

347211 2oo9 Hak cipto JpNJ I Lihat sebelahSULIT

http://banksoalanspm.blogspot.com/

Page 12: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SULIT l2 347Zt l

15. Diagram 15 shows vectors 4 and ! . Draw the resul tant vector of 2g- b.

Rajah 1 5 menunjukkan vektor a dan \. Lukiskan vektor paduan bagi 2a - b.

12 marks)[2 markah]

Diagram 15Rajah'15

Answer / Jawapan

3472/1 2oo9 IIok cir)to JPNJST]I , IT

/

,/g

Irorexuminer's

use only

http://banksoalanspm.blogspot.com/

Page 13: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

Forexaminer's

use only

t6

I r-iI l4 l

r \

PQ= 2?- 3! and

-) -> ->VeKor PQ dan RS adalah selai. Diberi bahawa PQ =-tqRS=

2-FindCari

(a) the value of /rNilai bagi k

(b) the ratio of PQ: RS

Nisbah bagi PQ: RS

SULIT

347211 2oo9 Hak cipta JPNJ

-+aThe vectors PQ and Rf are parallel. lt is given that-+onS = (t +Ds-;b..

3472t1l3

16.

2a -3b dan

[4 marks]14 ma*ahl

Answer/Jawapan:(a'1

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

I Lihat sebelahSULIT

http://banksoalanspm.blogspot.com/

Page 14: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SULIT IAla['or

examiner'suse onlv

17. Given that coS I = p and 0 is an acute angle, express in terms of p .

Diberi bahawa kos 0 = p, dan 0 adalah suatu sudut tirus, ungkapkan dalamsebutan p bagi

(a) tan d

e(b) s in;

z

Answer/Jawapan: (a)

.A

Given y = :j , find the approximate value of y , when ;r changes lrom 2 to 2.02.x

)4Diberi y =:, , cari perubahan nilai bagi y , apabila x berubah daripada 2 kepada

x2.02.

14 marksl14 markahl

Answer / Jawaoan .

3472/1 2oo9 Hak Cipta JPNJSULIT

t7

I r--I l4 l

18.

18

I l4 l

r )

http://banksoalanspm.blogspot.com/

Page 15: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

Forexaminer's

use only

l9

t-lI la l

t t

l53472/l

Diagram 18 shows a seclor OPQ with centre O and radius 5 cm.Rajah 18 menunjukkan seldorOPQ yang berpusatO dan jejari 5 cm.

O Rlcm O

Diagram 18Rajah 18

Given QR =1 cm and IPRO = 900, f ind the area in cm2 , of the shaded region.

Diberi QR=1 cm dan ./.PRO = 900 , kirakan luas datam cm2 bagi kawasan bedorek.

14 marksl14 matuahl

Answer / Jawapan

347211 2oo7Ha*ciptuIPNJ [Lihat sebelahSULIT

http://banksoalanspm.blogspot.com/

Page 16: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

t6SULIT 3472t1 For

examiner'suse only

20.I

Find the coordinates of the turning points on the curve / = 4x + - and determine thex

maximum Doint.

I

Cari koordinat bagi titik-titik pusingan bagi tengkung y = 4x + i- dan tentukanx

titik maksimum.14 marksl

14 markahl

Answer / Jawapan . ' . . . . . . . . .

20

t--JI l4 l

Given y =# andx-

!,s@)a'

1- _1Diberi y=2-: dan

Isi)ax '

dy

= 3g(r) where g(r) is a function of x. Find the value of

= 3g(x) di mana g(x) ialah fungsi bagi x . Cari nilai

347211 2oo9 Hak cipto JPNJ

Answer / Jawapan :

14 marks)14 markahl

SULIT

2l

I r--I l4 l

t l

http://banksoalanspm.blogspot.com/

Page 17: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SULIT1l

3472t1

Table 22 shows the marks of a group of students in an examination.

Jadual 22 menunjukkan markah sekumpulan pelajar yang diperolehi dalam suatupeperiksaan.

Marks 1i?

Number of students 4 6 8 7

Iable22Jadual 22

FindCari

(a) the maximum value of x if the mode mark is 8.nilai markah bagi x jika markah mod ialah 8.

(b) the minimum value of x if the mean of the marks is greater than 3nilai minimum bagi x jika markah min lebih daripada 3.

[3 marks]13 markahJ

Answer / Jawapan

Find the number of ways in which 4 boys and 5 girls can be seated in a row ifCari bilangan cara susunan 4 budak lelaki dan 5 budak perempuan boleh duduk.

(a) there is no restrictiontiada syarat dikenakan

(b) the boys and the girls are seated allernatelypelajar lelaki duduk berselang seli dengan pelajar perempuan.

14 marks)14 markahl

Answer/Jawapan: (a)

317211 2007 llok Ciota JPNJ

(b) . , . . .

IL ihat sebelahSULIT

22.

22

t--_lI r---I l r l

)7

t lI r-1I l4 l

\ l

(a)

(b)

23.

http://banksoalanspm.blogspot.com/

Page 18: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

l8SULIT

24. f abire 24 shows the number of coloured marbles in a bag.Jadual 24 menunjukkan bilangan guli bervvarna di dalam satu beg.

3472t1

Colour Number of marblesRed 4

Green x+2Purple 2

Table24Jadual 24

A marble is drawn at random from the bag. Given that the probability of getting aI

green marble is -. Find the value of -t.

Sebiji gulidikeluarkan sscara rawak daripada beg. Diberi kebarangkalian mendapatI

sebij i guli hijau ialah ;. Cari nilai x.J

[2 marksl12 markahl

Answer /JawaDan : . . . . . . . . .

347211 2ao9 Hak cipta JpNJ

Forexaminer's

use only

24

I r'l

rl

http://banksoalanspm.blogspot.com/

Page 19: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

Forexonriner

use onlr-

25

[JI l4 l

( )

l9SULIT 3472/l

Diagram 25 shows a standard normal distribution graph

Rajah 25 menunjukkan graf taburan normal piawai.

The probabil ity represented by the shaded region is 0.7514.Kebarangkalian kawasan bedorek ialah 0.7514.

(a) Find the value of & ,Carinilai k.

(b) X is a continuous random variables which is normally distributed with a mean80 and a variance of 9. Flnd the value of X when the z-score is t .

X ialah pembolehubah rawak selaniar yang beftabur secara normal denganmin 80 dan varians 9. Cari nilai X iika skor'z ialah k .

14 marksl14 markahl

Answer/Jawapan: (a)

th ltv, , . . ' .

END OF QUESTION PAPER

341211 2oo7 Huk c'ipra JI'NJ ILihat sebelahSULIT

25.

1(x)

http://banksoalanspm.blogspot.com/

Page 20: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SULIT

L This question paper consists of25 questionsKertas soakn ini mengandungi 25 soalan

2. Answer all questions.Jawab semua soalan

3. Write your answers in the spaces provided in the question paper.Tulis jawapan anda dalam ruang yang disediakan dalsm kertas soalan.

4. Show your working. It may help you to get marks.Tunjukkan langkah-langkah penting dalam kerja mengira anda. Ini boleh membantu andauntuk mendapatkan markah.

5. If you wish to change your answer, cross out the answer that you have done.Then write down the new answer.Sekiranya anda hendak menukar jawapan, batalkan jawapan yang telah dibuat.Kemudian tttlis jcwapan yang baru.

6. The diagrams in the questions provided are not drawn to scale unless stated.Rajah yang mengiringi soalan tfulak dilukis mengihtt skala kecuali dinyatakan.

1. The marks allocated for each question are shown in brackes.Markah yang diperuntukkan bagi setiap soalan ditunjukkan dalam kurungan-

8. A list of formulae ls provided on pages 3 to 5.Satu senarai rumus disediakan di halaman 3 hingga 5.

9. A booklet of four-figure mathematical tables is provided.Sebuah buku sifr matematik empat angka disediakan.

10. You may use a non-prograrnmable scientific calculator.Anda dibenarkan meng,gunakan kalkulator saintifk yang tidak boleh diprogram.

I l. Hand in this question paper to the invigilator at the end of the examination.Serahkan kertas soalan ini kepada pengawas peperilcsaan di akhir peperiksaan.

3472/1 2oo9 Hak Cipta JPNJ

20

INFORMATION FOR CANDIDATESMAKLUMAT UNTAK CALON

3472t1

http://banksoalanspm.blogspot.com/

Page 21: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

suLlr

3472t1AdditionalMathematicsKertas 1September 20092 Jam

347211

JABATAN PELAJARAN NEGERI JOHORPEPERIKSAAN PERCUBAAN SPM 2OO9

ADDITIONAL MATHEMATICSKertas 1

JANGAN BTJKA BUKU JAWAPAN SEHINGGA DIBERITAHU

MARKING SCHEME I------J

l(ertas soalan ini mengandungi 6 halaman bercetak

[Lihat sebelahSULIT

347211 tlak Cipta JPNJ 2009

http://banksoalanspm.blogspot.com/

Page 22: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

Solution(a) 4

(b) 5

Sub marks

(4 s18) = 1g- ' (x) = " = '

/

lv(b) gh(x) = -^ - 6@ equivalent

J

qh(x) =z(!-1) + 1' 'a

^)(- \l^ . l

9l ; - r I\J )

g(x) =

p=12k=-4

3+k=-1 @3k=p@equivalent

2

B1

rJ l

3

B2

1(

-TU

x11 )

5l' - l

\v )I .

- i=) \ -4) l

i

_1

9(Y) = j

la

rt l ----1..-*

\x-rJ

x-

J

82

B1

(a) a=1

(b) b=3

(c) c= -3

6 x<-3 , x>3

\, /' t /

*--\ / -:\-- zi -:+-3 \-/ 3

@equivalent

_l

82

B1

'-L

fotal marks

i'L__

(x+3)(x-3)"0 @ x=t3

http://banksoalanspm.blogspot.com/

Page 23: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

Sub marks Total marks

82

B1

2

B1

.x IJ =*-

9l8(3- ) = 2

27(3' , ) -g(3.1= 23*.33 - 3*.32 =2

I

I f-/ "

l--:I 'l81

I a i " : ,l iI i

rog, x = los, zqlu,g, +

i i log, x = 19"sJ- or any baseI I log19

i tt-- T-_-I I l t

l l "i l^ lI l )oo=-. . - . -

i i r li l1

t-*-f"--- :i

,o i n=12

i t

I i ,,' t:*ol_:5rli?_og

i i , , - 2(2)i j ; [ : r -s)+( i?- l )4 j ,2ooi1-I is"200i--]*-i t r 1, .=:I i l , 18t ti i2 vi tf--T-_-i 12 j m=16 andn=1.7411

i ii l tos,m=4or

- loez r=-! or log

t li I

log, ),= logz at _ "rlog, nl ii lL_t_ _-

J

82

B1

ATlog, n

L__-,-.----_-L

http://banksoalanspm.blogspot.com/

Page 24: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

S[b marks T- ; - | Total marks

l=6ands=-20

t=6 or s=--20

s + 3/ = -2,2s - 4t =16(Solve simultaneous equation)

s+l+2t+14

1' l . r o l- l - L-ol2 ' l

ol4l

?

82

1lo 2 oI

-_* ' Ia l i a I

t l+ r - r

A(0,4) or D(0,-1)

2

B1either 2a or

-b

(a) k=2a

' ) * -2

qk +7 =2)@,: =3),

"2

g( f t + l )q - : :h= l (2q-3[) @ equivalent

2-nS = .1.pQ

. - - ]

/

,l/

\\

. ( l t,

\!

\\

http://banksoalanspm.blogspot.com/

Page 25: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

IIIIIIIt_

t. 1r l l - O-

(a) v ' -p

l r - p '

.e r : ;(01 srn--=^l '?\ l )Ll

^( g\o: l - 2sin ' l - |' \2)

2.044 cmz1^1: (5) '(0.6435) - _ (aX3)2' ' 2

l1

1$)' (0.643s) or

1{+X3)

Shaded region = Apon - Apon

IPOR = 36.870 or 0.6435 racl

.V = 1.44

-0.06-96

6y=-- :x0.02- aa

3Z

) , ,? = - 4(21)x'5 or -4(24) x 5dx

( - t \| -: .4 I\2 )d'y 2 . d2, ,-;* = -; ?r.rd -=4 ,= -16dx' x'' dx'

, l4-L- '

2

Q- = q- --1- ro equivatentclx x'

4

B3

82

4

B3

82

I

II4

B3

82

B1

http://banksoalanspm.blogspot.com/

Page 26: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

4.;J

ZA:i--J

2(--1) - 3

, - . ]l?r"-11't - " " ll r lIx- l

t Izx-: l; t ? Ir l_ x- I

B1

(a) 7

(b) . r=1x>0

I*:31:J":!l , s25+x

x t -2

8+x

L

2

B1

I

B1

Ia

(a) k-0,679 2

B1P(Z>k;= A.2486

I I (b) . r=8203'i lI lo67e=tj lo

(b) .r = 82..031

IIII

__i_L _i__

http://banksoalanspm.blogspot.com/

Page 27: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

STJLIT

Additional MathematicsKertas 2Sept 2009

^l/ - lam2'

3472/2

JABATAN PELAJARAN NEGERI JOHORPEPERIKSAAN PERCUBAAN SPM 2OO9

ADDITIONAL MATHEMATICSKERTAS 2

Dua jam tiga puluh minit

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1. Kertqs soalan ini adalah dalan dt,ihahasa.

2. Soalan dalam baha,sa Inggeris mendohului soalun yung, sepadun dalcnn bahal;a llfelayu.

3. Calon dikehendaki rnembace maklumal di halarnan belakang kertas ,soalan ini.

4. Culon dikehendaki menceraikan lwlamctn I9 dan ikat sehagai tnuka hadapanhers ama- s am a de, ngan j atv apan awla..

Kertas soalan ini mengandungi t9 halaman bercetak dan I halarnan kosong

J+ LLt,1. SULIT

http://banksoalanspm.blogspot.com/

Page 28: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

sulrT 2 347212

The followingformulae may be helpful in answering the questions. The symbols given are

the ones commonly wed.

-b+ "[Y 4o;x=

2a

2 q^ xan= e^* '

3 a^ +t{=a^'n

4 (am)" = ann

5 logo mn = log um * loga n

6 log"m:bggn- logonn

7 log at tn : n logum

tog,a : fo8'blQgc a

T,:a+.(n- l )d

s^: l tza+(n-r)el l

Tn = Qt 'n ' l

;= a(r"- l ) =a(!-r") , r *1" r- l l - r

s- = o l r l . t" l - r "

ALGEBRA

8

t0

l l

t2

IJ

CALCULUS

n

" dy d), du

dx du dr

dv dv duv=uv. L=u-+v-'&drd\

du dv

. .uqYdxdr--:_=-._*-;-'vdxu-

Area under a curye

l= lvdx orJ'

b

= lxdyJ'

Volume generated

-- llry' aY orJ-

b

-- l|d.- dv

GEOMETRY

'l Distance =

2 Midpoint

A point dividing a segment of a l ine( tu,

- .* . , rv, , mv"\

lx, v) =\ f r r+ n m+n )

Area of triangle =

l ,

; l (x,1, + x2y3 + x. ! , , ) - (xry, + xry, + x,yt) l

(x,+x,(x.y)= l -

t2l l f )

l r l ={ . r -+}-

^ xi+ vi17t

Vx- + -Y-3412t2

-Y, +.Y: ')

' ) l

SULIT

- r , ) t + (.Y, - Y,) '

http://banksoalanspm.blogspot.com/

Page 29: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SULIT

STATISTICS

3472/2

l_i I ( - r -x)23o=tr t_-=

l= ' .l ) x-

v1/

; zI,'w,Lw,

, , _ n!

" {n - r1''.

n^ nl| =_--r fu* r) ! r r '

P (A w B) -- P (A) + P (B) - P (A a B)

P(X=r) = 'C,P'qn- ' , P+ q = |

Mean, p : np

o =.[rW

__x-po

, - &t/

zf,Zr

[ . !"-r lr+l2 lc

l f " l

4 o=

5 m=

6 I =9x100O"

l0

11

12

t4

TRIGONOMETRY

I Arclength,s=r0

2 Areaof'sector. ,e = ! ,'e

3 s in 2l * "or 'A:

| 2

4 sec2A: | +tan2A

5 cosecz A=1+cot2A

6 sinM = 2 s iM cosl

7 cos2A: cos'A - sin2 A=2cos2A-r= l- 2 sin2A

) tqn /

8 tan2A: ' *" : 'l - Ian'A

3412t2

sin (l + 8) : siM cos8 + cosl sin-B

cos (l + B) : cosl cosB F sinl sinB

tnn l*1911$f l tan(A+ B) = '*" '

I + tan ltan B

abc

9

l0

t2

t3

14

sinA sinB sinC

a2 = b2 + c2 - 2bc cosl

Area of triansle = f aDsin C-2

I Lihat sebelahSULIT

http://banksoalanspm.blogspot.com/

Page 30: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SULIT )L+ILIL

Section ABahagian A

140 marksl

140 markahl

Answer all questions ln this secfion.

Jawab semua soalan.

1 Solve the following simultaneous equations:Give your answers correcl to three decimal places.

Selesaikan persamaan serentak berikut :Berikan jawapan anda betul kepada tiga titik perpuluhan.

P+2q =l

p ' -3p+2q' =3

[5 marks]15 markahl

2 A curve has a gradient function co.t -2x, where a is a constant. The tangent to

the curve at the point (1,3) is perpendicular to the straight line 2y = *x +3 ,

Satu lengkung mempunyai fungsi kecerunan axt -2x , di mana a adalah pemalar.Tangen kepada lengkung pada titik (1,3) adalah bersereniang dengan garis lurus2Y=-x+3'

FindCari

(a) the value of a, [3 marks]

nilai bagi a , 13 markah)

(b) the equation of the curve. 13 marksl

persamaan lengkung tersebut. 13 markah)

3472t2SULIT

http://banksoalanspm.blogspot.com/

Page 31: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SULIT 347212

Ahmad has 1000 chickens in his poultry farm. Every week, he willsell40 of his chickens.

Ahmad mempunyai 1000 ekor ayam di ladang ayamnya.Setiap minggu, dia akan menjua! 40 ekor ayamnya.

(a) Find the total number of chicken left in his poultry farm after 21't week.

Cari bilangan ayam yang masih tinggal di ladang ayamnya se/epas minggu ke-21 .

{4 marksl

14 markahl

(b) The cost of feeding each chick is RM2 per week.Find the total amount of money that he spent on the remaining chicken for the firsttwelve weeks.

Perbelanjaan atas makanan seekor ayam adalah RM2 seminggu.Kirakan jumlah perbelanjaan yang dibelanjakan atas jumlah ayam yang tinggaluntuk duabelas minggu yang pertama..

[3 marks]13 markahl

HeightTinggi(cm)

Number of plantsBilangan tanaman

20 -29 4

30-3940-4950-5960-69 5I ! .J_ IY 1

Table 4Jadual 4

Table 4 shows the distribution of the heights of plants in a gardenGiven the median is 47.5, f ind the value of a

Jadual 4 menunjukkan taburan tinggi tanaman di sebuah taman.Diberi median adalah 47.5, carikan nilai a .

Hence, find the variance of the distribution.Seterusnya, cari varians taburan tinggi tanaman tersebut.

13 marksl

13 markahl

13 marksl13 markahl

I Lihat sebelah3412t2SULIT

http://banksoalanspm.blogspot.com/

Page 32: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SULIT 347212

5 Solutions by scale drawing will not be accepted'Penyelesaian secara lukisan berskala tidak diterima.

Diagram 5 shows rhombus PQRS. The equation of PS is 3y +7 x = 33 and the

equation of PR is .Y = -r + I I '

Rajah 5 menunjukkan rombus PQRS. Persamaan garis lurus PS ialah 3y +7x =33

dan persamaan gais lurus PR ialah y = -'r + I I

Diagram 5Rajah 5

(a) Find

Cari

(i) the equation of QS,

persamaan garis /urus QS,

(ii) the coordinates of S.

koordinat bagi S.

[3 marks]

13 markahl

[2 marksl

12 markahl

(b) A point f moves such that Sf :IQ = 2'.1 . Find the equation of the locus of f,

Satu titik T bergerak dengan keadaan Sf :fQ = 2'.1 . Cari persamaan lokus T.

[3 marks]13 markahl

3472t2SULIT

http://banksoalanspm.blogspot.com/

Page 33: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SULIT 3472/2

6 (a) prove that tos 2l = cos ,4 - sin I . t2 marksl

cosl+sinl

Bukt ikan bahawa kos2A =kosA-sinl t2markahl

kosA+sinA

(b) ( i ) Sketchthe graph of /=sin2r+2 for 0<x<n.

Lakarkan graf y= sin2x +2 untuk 0 < x < n .

(ii) Hence, using the same axes, sketch a suitable straight line to find the

number of solutions for the equation Lsin2x = J- br 0 < x < n .

Seterusnya, dengan menggunakan paksi yang sama, lakar garis lurus yangsesuai untuk mencari bilangan penyelesaian bagi persamaan

lsin2x=x untuky<x<n. [6marks]22r

16 markahl

I Lihat sebelah3472t2SULTT

http://banksoalanspm.blogspot.com/

Page 34: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SULIT

Section B

Bahagian B

140 marksl

140 markahl

Answer any four questions from this section.

Jawab mana-mana empat soalan daripada bahagian ini.

7 Diaoram 7 shows the curve y=x2 +2 and the straight l iney =-x+8 '

Diagram 7Raiah 7

Find

Cari

(a) the value of k,

nilaibagi k,

(b) the area of the shaded region,

luas rantau berlorek,

3472t2SULIT

34',7212

[3 marks]

13 markahl

14 marksl

14 markahl

(c) the volume generated In terms of a, when the region bounded by the curve'

the y-axis and y = 6 is revolved 360' about the y-axis' [3 marks]

tsipadu janaan, dalam sebutan n , apabila rantau yang dibatasi oleh lengkungitu, paski-y dan y = 6 dikisarkan melalui 360' pada paksi-y,

B markahl

,=x2+2

http://banksoalanspm.blogspot.com/

Page 35: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SUI,IT 3472t2

8 Table B shows the values of two variables, x and y , obtained from an experiment.

Variables.r and y are related by the equation .y = 2ox) + bx, where aand b are

constants.

Jadual 8 menunjukan nilaidua pembolehubah, x dan y didapatidaripada satu

eksperimen. Pembolehubah x dan y dihubungkan dengan persamaan y =2qx2 + bx,

dengan keadaan a dan b adalah pemalar.

Table 8Jadual I

v(a) Plot i against .r, using a scale of 2 cm to 1 unit on both axes.

Hence, draw the line of best fit. 14 marksi

Ptotkan graf ! lawan x , dengan menggunakan skala 2 cm kepada '1 unit pada

kedua-dua paksi.

Seterusnya, lukiskan garis lurus penyuatan terbaik. 14 markahJ

(b) Use your graph in 8(a), to f ind the value of

Gunakan graf anda di 8(a), untuk mencari niilai

( i ) a,

( i i ) b,

( i i i ) y when x= 1.2.

), apab1a x = 1.2. [6 marks]

16 markahl

f Lihat sebelah

3472t2SULIT

At oq 7

v 1 14.5 3925 t rA

http://banksoalanspm.blogspot.com/

Page 36: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SULIT 3472t2

Diagram I shows a semicircle OADEB, centre O and sector fOFC with centre L

Given that OB = 5 cm and fO = 15 cm.

Rajah 9 menunjukkan sebuah semibulatan AADEB berpusat a dan sebuah sektorTOFC berpusat T. Diberi bahawa OB = 5 cm dan fO = 15 cm.

10

AOBDragram 9Rajah 9

[Use/Guna r =3.142)CalculateHitung

(a) 4.TCO,

4TCO,

(b) the perimeter, in cm, of the shaded region,

perimeter, dalam cm, kawasan berlorek.

(c) the area, in cm2, of the shaded region.

luas, dalam cm2, kawasan berlorek.

11 markl

11 markah)

[5 marks]

l5 markahl

14 marksl

14 markahl

3472/2SULIT

http://banksoalanspm.blogspot.com/

Page 37: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SULIT l l 3472/2

10 Diagram 10 shows triangle oPQ. The point r lies on QP and the point s lies on opThe straight line Of intersects the straight line QS at the point R.

Rajah 10 menunjukkan segitiga OPQ. Titik T tertetak pada eP dan titik S tertetakpada OP. Garis lurus OT bersilang dengan garis lurus eS dl t/tk R.

Diagram 10Rajah 10

1rI t is g iventhat O"S =-OP, Qf =:QP, OP = p and OQ = q

t .

Diberi bahawaos = lrlr , gr =\e, , oF = p dan Og = qz)

(a) Express in terms of p and

U ngkapkan dalam sebutan

( r or ,( i l ) gJ,

(ii i) .5. 14 marks)14 markah)

(b) Giventhat On =n(f i andQF.=16 ,where rr and n are constants,f indthevalue of m and of n . [6 marks]

Diberi OR=rrOT aan QR=nQS , dengan keadaan m dann adatah pemalar,cari nilai m dan nilai rt. 16 markahl

I L ihat sebelah

(1 .

pdan q"

34',72t2STILIT

http://banksoalanspm.blogspot.com/

Page 38: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

l2

1 1(a) ln a survey carr ied out in a school , i t is found that 2 out of 3 students passedtheir Mathematics Test.

Dalam satu tinjauan yang dijalankan ke atas murid-murid di sebuah sekolahdidapati 2 daripada 3 orang murid lulus dalam ujian Matematik.

(i) If 7 students from that school are chosen at random, calculate the probabil itythat exactly 6 students passed their Mathematics Test [3 marks]

JikaT orang murid daripada sekolah itu dipilih secara rawak, hitungkebarangkalian bahawa tepat 6 orang murid lulus dalam ujian Matematik.

13 markahl

( i i ) l f there are 600 students in the school, f ind the number of students who fai ledthe Mathematics Test. 12 marksl

Jika terdapat 60A orang murid dalam sekolah itu, cari bilangan orang murrdyang gagal dalam ujian Matematik 12 markahl

(b) A survey on body-mass is done on a group of teachers. The mass of the teachershas a normal distr ibut lon wi th a mean of 45 kg and standard deviat ion of 10 kg

Satu kajian terhadap berat badan sekumpulan guru telah drlakukan. Berat Badanguru- guru adalah mengikut taburan normal dengan ntrn 45 kg dan sisihanpiawai 10 kg.

( i ) A teacher is chosen at random from the groupFind the probabi l i ty that the body-mass of the teacher is less than 42.5 kg.

Seorang guru dipilih secara rawak darrpada kumpulan tersebut.Cari kebarangkalian bahawa guru tersebut rnentpunyai berat badan kurangdari 42 5 kg.

( i i ) l l 12.3% of the teachers have a body-mass of more than k kg, f ind thevalue of k.

Jika 12.3% guru tersebul mempunyai berat badan lebih dari k kg, cari nilaibagi k.

[5 marks]15 markahl

SULI ' I '

3172/2SULI'T

)+ I : t . / "

http://banksoalanspm.blogspot.com/

Page 39: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

t3

Section C

Bahagian C

[20 marksl

l2A markahJ

Answer two questions from this section.Jawab dua soalan daripada bahagian ini.

12 A particle P moves along a straight line and passes through a fixed point O.l ts veloci ty, vms-t, is given by r '= 6t ' -4t-2, where r is the t ime, in seconds,after passing through O.

Suatu zarah bergerak di sepanjang suatu garis Iurus dan melalui satu titik tetap OHalajunya, u ms-t ,diber i oleh t '=6t2-4t-2,dengankeaclaan t ia lahmasa,dalam saaf, selepas melalui O.

(a) Find

Cari

(i) the initial velocity of the particle P,

halaju awalzarah P,

(ii) its velocity at the instant when the acceleration is zero,

halajunya pada ketika pecutan adalah sifar,

(ii i) the time interval during which the pafticle moves towards the left,

Julat masa apabila zarah itu bergerak arah ke kiri,

the distance, in m, travelled by the particle during the first three seconds,[3 marks]

jarak, dalam m, yang dilalui oleh zarah dalam tiga saat pertama, 13 markahl

Sketch the velocitytime graph of the motion of the particle for 0 < I < 312 marks)

Lakar graf halaju melawan masa bagi pergerakan zarah itu untuk 0 < I < 3.[2 markah]

I Lihat setrelah

sut_t'f

3172/2SULIT

3412t2

11 markl

11 markahJ

12 marks)

12 ma*ahl

12 marksJ12 markahl

(b)

http://banksoalanspm.blogspot.com/

Page 40: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SULIT )+I : IL

13 Table 13 shows the pr ice indices intheyear 2009 based on the year 2007 offour i tems, A, B, C, and D, used in the product ion of a cake.

Jaclual 13 menunjukkan indeks harga bagi tahun 2009 berasaskan tahun2007

bagi empat item A, B, C dan D, yang digunakan untuk membuat kek

Item Price Index in the year 2009

based on the year 2007

weightage

130 1

B 144

(, 115 2n

U 120

Table 13

Jadual 13

Given the pr ice of A is RM 2.60 in the year 2009, calculate i ts pr ice in2007.[2 marks]

Diberi harga untuk A adalah RM 2.60 dalam tahun 2009, kirakan harganyadalam tahun 2Q07, 12 markahl

Given that the composite index for the year 2009 based on the year 2007 is125, find the value of n. 13 marksl

Diberi indeks gubahan bagi tahun 2009 berasaskan tahun 2007 ialah125, carikan nilai n 13 markahl

Find the price of the cake in the year 2007 rt its corresponding price in theyear 2009 is RM 46. 00. l2 marksl

Cari harga kek dalam tahun 2007 lika harga yang sepadan dalam tahun20A9 iatah RM46. 00. 12 markah)

Given that the pr iceof i tem D is est imatedtoincreaseby 10% fromtheyear 2009 to 2010, whi le the other i tems remain unchanged.calculate the composite index of the cake for the year 2010 based on theyear 2007. t3 marksl

Diberi harga item D diiangka meningkat sebanyak 10ok dari tahun2009 ke 2010, manakala item-item lain tidak berubah.Kirakan nombor indeks gubahan pada tahun 2010 berasaskan tahun 2007 .

13 markahl

3472t2SULIT

14

(a)

(b)

(d)

http://banksoalanspm.blogspot.com/

Page 41: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SULIT

14 Diagram 14 shows a triangle PQR.

Rajah 14 menuniukkan sebuah segiiga PQR

Diagram 14Rajah 14

(a) Calculate /.PQR,

Krakan {PQR,

3472t2SULIT

15 3472/2

[2 marksl

12 markahl

12 marksl

(c)

(b) Sketch and label a triangle PQ'R which has a different shape from triangle PQRsuch that length of PQ, PR and IPRQ remain unchanged.

State lPp'R,

Lakar dan labetkan sebuah segitiga PQ'R yang berlainan daripada segttlga PQRdalam rajah di atas, dengan keadaan panjang PQ , PR dan IPRQ dikekalkan'

Nyatakan /.PQ'R,

Hence, calculate

Seferusnya, kirakan

(i) the length of Q'Q, in cm,panjang Q'Q, dalam cm,

(ii) the area of the triangle PRQ', in cm2.luas segitiga PRQ', dalam cm'.

12 markahl

[6 marks]16 markahl

I Lihat sebelah

http://banksoalanspm.blogspot.com/

Page 42: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SLTLIT l ( ) 34'.12t2

15 Use graph paper to answer this quest ion.Gunakan kerlas graf untuk meniawab soalan ini.

Afactory producestwo types offurni ture, A and B.Each furniture needs 2 types of raw materials , P and Q and the number of each rawmaterials needed for each furniture are presented in the Table '1 5 below.

Sebttah kilang mengeluarkan dua ienis perabott iaitu A dan B.Setiap perabot memerlukan bahan mentah P dan Q dan bilangan bahan mentahyang diperlukan bagi setiap perabot ditunjukkan dalam jadual 15 di bawah.

Table 15Jadual 15

The number of raw mater ials P lef t in the factory rs 30 and the number of rawmaterials Q left is 24.I t is given that the number of furni ture A produced is at most twice the number offurniture I produced and the factory produces x unlts oT furniture A and y units offurniture B.

Bekalan bahan mentah P yang tinggal dalam kilang adalah 30 manakala bekalanbahan mentah Q yang tinggal dalam kilang adalah 24. Diberi bahawa bilanganperabot A adalah selebih-lebihnya dua kali bilangan perabot B dan kilang itumengeluarkan x unit perabot A dan y unit perabot B.

(a) Write three inequalities, other than x > 0 and y > 0, which satisfy all the constraintsaoove. 13 marksj

Tulis tiga ketaksamaan, selain x > A dan y > 0, yang memenuhi semuakekangan di atas. l3 markah)

(b) By using the scale of 2 cm to 2 units on the x-axis and 2 cm to I unit on the y-axis,construct and shade the region Rwhich sat isf ies the above constraints.

[3 marks]

Dengan menggunakan skala 2 cm kepada 2 unit pada paksi-x dan 2 cm kepada1 unit pada paksi-y, bina dan lorek rantau R yang memenuhi semLta kekangandi atas.

13 markahl

3472t2ST]I,IT

Number of raw materialsBilanqan Bahan Mentah

http://banksoalanspm.blogspot.com/

Page 43: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SLILIT

3472t2SUI,IT

t7

(c) Use your graph in '15(b), to findGunakan graf anda di 15(b), untuk mencari

(i) the maximum number of units of furniture,B produced if 4 units of furniture Aare produced

Bitangan maksimum unit perabot B yang dihasilkan jika bilangan unit perabot Ayang dihasilkan adalah 4.

(ii) the maximum profit obtained by the factory if the profit from the sale of a unitof furniture A /'s RM 200 and the profit from the sale of a unit of furniture I isRM 2s0.

Keuntungan maksimum yang diperoleh jika keuntungan daripada jualanseunit perabot A adalah RM 200 dan keuntungan daripada jualan seunitoerabot B adalah RM 254.

14 marksl14 markahl

END OF QUESTTON PAPER

I Lihat sebelah

J+tztz

http://banksoalanspm.blogspot.com/

Page 44: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

Jq/Zl !l9

Nama:

Kelas:

Arahan Kepada Calon

I Tulis nama dan kelas anda pada ruang yang disediakan.2 Tandakan ( { ) untuk soalan yang dijawab,3 Ceraikan heiaian ini dan ikat sebagai muka hadapan bersama-sama dengan buku

jawapan.

I Lihat sebelah3472t2SULIT

Bahagian Soalan SoalanDijawab

Markah Penuh Markah Diperolehi(Untuk Ke gunaan Pemeriksa)

A 5

2 6

J 7

4 6

5 8

6 I

B 7 10

8 10

9 l0

t0 t0

1i 10

L 12 10

13 t0

T4 10

l5 10

Jumlah

http://banksoalanspm.blogspot.com/

Page 45: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SULIT 3472/2

INFORMATION FOR CANDIDATESMAKLUMAT UNTUK CALON

l. This question paper consists of three sections: Section A, Section B and Section C.Kertas soalan ini mengandungi tiga bahagian: Bahagian A, Bahagian B danBahagian C.

2. Answer all questions in Section A, four queslions from Section B and two qucstionsfrom Secfion C.Jala,ab semua soalqn dalam Bahagian A, empot soalan daripada Bahagian B dandua soalan daripada Bahogian C.

3. Show your working. It may help you to get narks.Tttnjukkan langkah-langknh penting dalam kerja mengiro anda. Ini boleh membantuanda untuk mendapatkan markah .

4. The diagrams in the questions provided are uot drawn to scale unless stated.Rajah yang mengiringi soalan tidak dilukis mengikut skala kecuali dinyatakan.

5. The marks allocated for each question and sub-part of a question are shown inbrackets.Markah yang diperuntukkan bagi setiap soolctn dttn kraian soalan ditunjukkandalam kurungan.

6. A list of formulae is provided on pages 2 to 3.Satu senarei rttmus disediakan di halarnan 2 hinggo 3 .

7. Graph papers are provided.Ke r t as gr af di s e di akan.

8. You may use a non - progralnmable scientific calculator.Anda dihenarkan menggunakan kalkulutor saintifk yang, tidak boleh diprogram.

20

3472t2SULIT

http://banksoalanspm.blogspot.com/

Page 46: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SULIT

3472t2AdditionalMathematicsKertas 2September 20092'h Jam

3472t2

JABATAN PELAJARAN NEGERI JOHORPEPERIKSAAN PERCUBAAN SPM 2OO9

ADDITIONAL MATH EMATICSKertas 2

JANGAN BUKA KERTAS SOALAN IN! SEHINGGA DIBERITAHU

RKING SCHEUIE

Kertas soalan ini mengandungi 17 halaman bercetak

[Lihat sebelahSULIT

347212 Hak Cipta JPNJ 2009

http://banksoalanspm.blogspot.com/

Page 47: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SULlT

[ ]"*_

2

BAHAGIAN A

Solution

3472t2

Submarks

roGimarks

1- np=1-2q Orq=-- ' . lPl I

2 l l

Eliminate p or q"(1 - 2q) ' - 3.(1 *2q) + 2q2- 3 = OOrp2-3p +2"( \P )2-3*-0

?_or eouivalent

6q'+2q-5=03p'-8p-5=0

Solve t lre quadraticequation by using thefactorization @quadratic formula @completinq the sq

-z r J+ -"(oX-sj2(6)

ri i&4:ll3&t2(3)

q=0.761,-1.095or

p=-0.523,3.189

Ip: - 0.523, 3.189 (9q = 0.761, - 1.095

if the working clf solving quadratic equation is not shown

ILihat sebelahSULIT

347212 llak Cipta JPNJ 2009

http://banksoalanspm.blogspot.com/

Page 48: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

t_

Jt*+"' - 2x)rtx

a=4

Solution

SULIT 347212

2

a)

i , ,

"/ - axt -zxdx

2y=-y+J

II

fl'ln = - -2

*1r=2 E]

substitute x = 1 in to axo -2x = 2a (1) ' - 2(1) '= 2

Submarks

[Lihat sebelahSULIT

Totalmarks

PFI

Integrate y=

4xo 2x'v - -----.--'A.)

+L

{-c

Substitute x = 1, y= 3 into4xa 2x2

y = :.i + c, to find the

value of c.

y=x4-x2+3.

Nqte:

.y: J(*4x'' - Zx)h must have at least 1 ter"m with power increased by

At .

347212 t{ak Cipta JPNJ 2009

http://banksoalanspm.blogspot.com/

Page 49: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

A"t

- -Solulion

347212

tr_lUseTn-a+(n_1)d

721=40+20"(40)

1000-*840=160

b)

OR other val id method

l.Jse Sn = !; tz^ + (n - 1 )dl

I rrrooo) + (11x- 40)l

l , lfl-ihat sebelah

rUILI

Sutrmarks

Totalmarks

3472t2 Hak Cipta.JPNJ 2009

http://banksoalanspm.blogspot.com/

Page 50: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

*L=39.5or*F=7or " f r=d lPl I

Use median formula

47.5 =.39.5 + (

al ' \ ,^I r ' -Y-- 1 l -* (7\2\ 1 '

Zf*= 1425 or Zl*- 72917smFfr,

'tGt" f 4- | ---

st- t -

Submarks

Using the formuia distance ,,n7

- - - - . -

/ t r t \

Jtr- :) ' +(y-4) ' = 2JG-7) ' + (r ' -8) ' \ :_ l

\-_,

9r1rqv1-qql_- PPvJ l?7-- q --]=Y

SULIT {

- --olution ---

347212

[Lihat sebelahSULIT

*a

With "f, and F corresponding to "L

/+-"1'Zf - t-J

72917.5 ,1425,2*-30-- ' -30- ' '

i i ) 3y+7x=33y=x+1

y=x+1

s (3, 4)ST = 2TQ

Can be implied as formula. I Pl I

347212 Hak Cipta JPNJ 2009

http://banksoalanspm.blogspot.com/

Page 51: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

9UUr

[_i-- m347212

Solution

Use identityCos2A-Sin2A=Cos2A

LHS = RHSNs mistake allowed

b) i )

Graph Sin

l per ioCin 0sxs n

Amplitude 1

Drawing of the straight l ine from the equation involvingX and y, either gradient OR y intercept of straightl-ine must be correct.

Fr*ltir*lE]

[Lihat sebelahgUL[

( r r

347212 |'lak Cipta JPNJ 2009

http://banksoalanspm.blogspot.com/

Page 52: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SULIT 7

BAHAGIAN B

3472t2

Submarks

[Lihat sebelahSULIT

Totalmarks

c)

Solve the simultaneous

lntegrate x2 +2

lntegrate (x'+2)+ area of triangie

T +rc3

lntegrate z x2

n t tt'- 2),1t,

x?'+2=*x+8

x2+x-6x=2,x=-3

F2 u '1

Use l imi t I ' in to . [ \x)- +2xJJ

Or f ind the area tr iangle% (6)(6)

in. , rQ)|-2yl

I

iL

-n

(24.667)

l imi tUse/ \\ Kl /\*__r/

\I\

3472t? Hak Cipta JPNJ 2009

http://banksoalanspm.blogspot.com/

Page 53: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SULIT

Frcm graplr ): againt x

b=- 2.45

[-2.S0<---+ -2.30]

3472t2

Submarks

[Lihat sebelah$uur

Solution

Note:lf table is not shown award F,l mark if all the points are plotted correcily.

vlJlot j- agatnst x

x(Correct axes and uniform scales)

6 *points plotted correctly

Line of best fit

Totalmarks

8a)

b)

\K] /

-rl--r\ r'ir )

-r(xr \\*-"

/I/ liIIi

(* ' )

Use *m = t" /-)8-2 \5!,

c) ! =zax"oLl]_lx

Or implied.

i )

i i )

a="tL( 0.7<---),0.8)

i i ) t-x

=-0.6

= -0.6

y=-0.72

Note:ss-1i f ,

Part of the scale is not uniform at the x-axis and/0r the I -axis.x

OR not using the given scales. OR not using graph paper.

Nl , /

_i

M

\1/

347212 Hak Cinta JPN.| 2009

10

http://banksoalanspm.blogspot.com/

Page 54: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

3472t2

vx

I

7

6

5

4

3

2

: ir^"r,t'

I.4i ir{r i. .^ t; !1i, l

7212 " Hak" ei$t5 J]rNru''20f.rs

http://banksoalanspm.blogspot.com/

Page 55: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SULIT 10 347212

Totalmarks

9a)

b)

< TCO = 45" OR 0.7855 rad OR v

4

Use S = r 0 la find the length of arc BEor ODFC

1s(?-) or 5(i)KI

4azasr// 48 706 // aazt

Use Y, f g to find the area of sector TODFCOr sector OEB

Area of shaded region(176.7375 - 112.5) + I 8188 )

Use Pytho. Teorem to find CO

16.2132

Perimeter of the shaded region"23.565 + *16.2132 + *3.927 5 + 5

' / roaua//74.06

ILihat sebelahsULlr

347212 Hak Cipta JPI'IJ 2009

http://banksoalanspm.blogspot.com/

Page 56: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SULIT 3472t2l t

Solution

10a)i )i i )i i i )

Use the triangle lawfor Of or g..t or .V

1)or = lo. io

2;q)J

I

;0

t2- -p+;Q

OJN1

f f i=6q1p*

IQR=n1-c+1n)

Use the triangle law to findoQ=on*nO171jtPo Jn,q-ntp*nq=q

1arJ

n=--- .m=--1A.4- a

{Both are correctl

,.-*\ Compare the coefficient/ Kt )\*-/ of p and q.

l 1̂rn. n=0JL

2-m+n;1_)

af

- ( -n)+n=1J1-

Jm= --n

2

[Lihat sebelahLULlT

347212 Hak Cipta JPNJ 2009

http://banksoalanspm.blogspot.com/

Page 57: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SULIT t2 347212

[Lihat sebelahSULII

Solution

11a)i )

2 ----1I lpr I

0.2048

Use nqI

600(: ). " ) .J

/^\\ Kr )

b)i ) r-\

\Kr/

- \

o aorsl_rur I

k-45 = 1.16l0

Submarks

Totalmarks

-\-____,

zoo I !!1 |

Use Z

P(2. *#",

P(Xtk)=0.123

p(z> L:45 )=0.123' i0

347212 Hak Cipta JPNJ 2009

http://banksoalanspm.blogspot.com/

Page 58: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SULIT 13

BAHAGIAN C

3472t2

[Lihat sebelahSULIT

Totalmarks

$olution Subrng$s

12a) i )

i i ) ,1, ,

Use al = 0. to find tdt

1

t= laI

- | , ,y=tr(- ) -J

6=.---

J

1I*4G) -2

a_)

i i i )

b)

v<0 G)( t - . lx3t+l)<0

\--

0<t<rh

lntegrate t = Jlott - 1t -2) (tt

2t3 -2.t2 -2t

Subst i tutet= l or t=3Find Sr or 53.

*2+2+30=34

c)

L{ Forshapeofthesraph

Ipr I| " ' I y- intercept and x-intercept

K1

Ditance traveled

347212 Hak Cipta JPNJ 2009

http://banksoalanspm.blogspot.com/

Page 59: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

Ztw = (130)1 + (140)3 + (115)2n + (120)n t - t , I

- \ tw r--rUse ,= T,

= 125 \ .KIJt\1_Nl n=2

,,=-13,: tt l100

t32

I :{tl r!$;) +' l:():!_?g)l0

sur=rT

2'60 x I00 = 130

X \_,

Ll!]_] x = RM2.0o

347212

[Lihat sebelahsuLlI

14

Solution

13a)

User =9- x loo ( l )eo

n rvv \ -K{

347212 Hak Cipra JPNJ 2009

http://banksoalanspm.blogspot.com/

Page 60: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

3472t2

[Lihat sebelahSULIT

t5SULIT

\ rct )

\-\

zl xrr I

SinQ Sin45"

62.12' il 62'

Submarks

r__--.1LNI I <e,obtuse

<RpQ = 180 -62.12" - 17.12' = 55.76" [1J

_ Qg' _ ____6 __Sin55.76 Sin62.12"

QQ' = 5.6115 f ; -.-fll

30---=---_-7-l- c,SinlT.12 ,Sur I 17^8y

t - f

a

RQ'= 2.4977

Area of tr iangle PRQ' = % (V.5)(2.4977)sin45"

6.6230

347212 Hak Cipta JPNJ 2009

http://banksoalanspm.blogspot.com/

Page 61: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SULIT t6 347212

Submarks

15(a) 2x + 5y < 30 or equivalent

3x + 2y s 24 or equivalent

x < 2,! or equivalent

Draw correctly at least one straight line froni the*inequalit ies which invoves x and y.

Draw correctly all three "straight linesNote : Accept dotted lines.

The correct region R shaded

Furniture A = 4(fromx=4intheregion)

Maximum point at (5, 4)

Use 200x + 250y*region R

for point in the

ss-1i f

c) i)

@trr:l

RM2000

In (a) the symboi " - " is not used at al i or more than threeInequalit ies are given.

In (b) does not use the scale given or does not use graphpaper Or interchange between the x-axis and the y-axis'

[Lihat sebelahSULIT347212 Hak Cipta JPNJ 2009

http://banksoalanspm.blogspot.com/

Page 62: Add._Maths_Trial_SPM_Johor_2009_[banksoalanspm.blogspot.com].pdf

SULIT t7 3472t2

ii {i l

Y'1

l :

! l

t

t , :

-tt

$i

i

http://banksoalanspm.blogspot.com/