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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://tutormansor.wordpress.com/

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 -

t2ll f )

l r l ={ . r -+}-

^ xi+ vi17t

Vx- + -Y-3412t2

-Y, +.Y: ')

' ) l

SULIT

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


SULIT

STATISTICS

3472/2

l_iI(-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

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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


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)

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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

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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

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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

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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,

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[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


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

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At oq 7

v 1 14.5 3925 trA


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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

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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


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 '

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)+ I : t . / "


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

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11 markl

11 markahJ

12 marks)

12 ma*ahl

12 marksJ12 markahl

(b)


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

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14

(a)

(b)

(d)


SULIT

14 Diagram 14 shows a triangle PQR.

Rajah 14 menuniukkan sebuah segiiga PQR

Diagram 14Rajah 14

(a) Calculate /.PQR,

Krakan {PQR,

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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


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

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Number of raw materialsBilanqan Bahan Mentah


SLILIT

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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


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


SULlT

[ ]"*_

2

BAHAGIAN A

Solution

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Submarks

roGimarks

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

2 l l

El iminate 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


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


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


*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 \

J t r- : ) ' +(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



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


SULIT 7

BAHAGIAN B

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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


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


3472t2

vx

I

7

6

5

4

3

2

: ir^"r,t'

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

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


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


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



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



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



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


3472t2

[Lihat sebelahSULIT

t5SULIT

\ rct )

\-\

z l 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



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


SULIT t7 3472t2

ii{i l

Y'1

l:

! l

t

t , :

-tt

$i

i


JANGAN BUKA KERTAS SOALAN INI SEHINGGA · PDF file · 2012-08-29STJLIT Additional...

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