trial terengganu spm 2013 add math ques_scheme all paper

7/27/2019 Trial Terengganu SPM 2013 ADD MATH Ques_Scheme All Paper

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SULIT :' '>/!

N AMA

T INGKATAN :

PENTAKSIRAN SUMATIF 3 SPM 2013MATEMATIK TAMBAHANKer ta s 1Ogos 20132jam

JANGAN BUKA KERTAS SOALAN INIS EH INGGA D IBER ITAHU

1. Tulis Nama dan Tingkatan pada ruangyangdisediakan.

2. Kertas soalan in i adalah dalam dwibahasa.3. Soalan dalam bahasa Inggeris mendahului

soalan yang sepadan dalam bahasa Melayu.4. Calon dibenarkan menjawab keseluruhan

atau sebahagian soalan soma ada dalambahasa Inggeris atau dalam bahasa Melayu.5. Calon dikehendaki membaca maklumat di

halaman belakang kertas soalan ini.

Untuk Kegunaan PemeriksaSoalan MarkahPenuh

MarkahDiperoleh

1 22 33 24 35 36 37 38 39 310 411 412 31314 315 316 317 318 419 420 321 322 423 424 325 3

Jumlah 80

Kertas soalan ini mengandungi 28 halaman bercetak.TERENGGANU NEGERI ANJUNG ILMU

Disediakan 01eh :Kerajaan Negeri Terengganu

Dicetak oleh:Percetakan Yayasan Islam Terengganu Sdn. Bhd.Te/efon: 609-666 '8611/6652/8601 Faks: 609-666 0611/0063

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SULIT 3472/2

PENTAKS IRAN SUMAT IF 3 SPM 2013 3472/2MATEMAT IK TAMBAHANKer t a s 2Ogos 20132 Vi jam Dua jam tiga puluh minit

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1. Kertas soalan in i adalah dalam dwibahasa.2. Soalan dalam bahasa Inggeris mendahului soalanyang sepadandalamhahasaMelayu.3. Calondikehendaki membacamaklumat di halaman belakang kertassoalan ini.4. Calondikehendaki menceraikan halaman 23 dan ikat sebagai muka hadapanbersama-sama dengan kertas jawapan.

Kcrlas soalan ini mengandungi 24 halaman bercetak.

TERENGGANU NEGERI ANJUNG ILMUDisediakan Oleh:

Kerajaan Negeri TerengganuDicetak oleh:Percetakan Yayasan Islam Terengganu Sdn. Bhd.Tele/on: 609-666 8611/6652/8601 Faks: 609-666 0611/0063

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SULIT 2 3472/2BLANK PAGE

HALAMANKOSONG

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SULIT 3472/2

The following formulae may be helpful in answering the questions. The symbolsgivenare theones commonly used.Rumus-rumus berikut boleh membantu anda menjawah soalan. Simbol-simbolyangdiberiadalahyang biasa digunakan.

x =-byjb2 -Aac

2a

m n _ in * n2. am x a" = a

in . n _ m-n3. a'" + an = a

4. (cTf = a"5. logfl /w = logow + logo

w6. loga = logam-Iogatfn

7. log^ m" = n \oga m

1. y=uvdy dv du = a + v dx dx dx

du dv, V u 2. y=-, ^ = ^


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SULIT 3472/2

STATISTICS / STATIST IK

x = 2>N

- _ Z A2. x = If

3. a = lUx-x)2 _ N;*3 -CxfN N4. 9 = \ m ^ t ,m


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SULIT 3472/2

TR IGONOMETRY / TR IGONOMETR I

1. Arc length, s = rQPanjang lengkok, s = jQ

1 22. Area o f sector = - r 0

Luas sektor, L = - j22

3. sin2 A + cos2 A = 1sin2 A + kos2 A = 1

4. sec2^ = 1+ tan2 Asek2A = 1 + tan2 A

5. cosec2y4 = 1 + cot2^kosek2^ = 1+ kot2A

6. sin 2A = 2 slnA cosAsi n 2A = 2 s'mA kosA

1. cos 2A = cos2A - sin2A= 2 cos2.4-1

= 1 -2 sin2.4kos 2A = kos2A - sin2A

= 2 kos2.4-1= 1 - 2 sin2^

8. sin (.4 B) = s\nA cos/? cosA s'mBs'm(A B) = sinA kosB kosA s'mB

9. cos(A B) = cosA cosB + s'mA s'mBkos(A B) = kosA kosB + sin^ s'mB

10. ton(AB) = tan A tan B1 T tan A tan B

11 . t anZ4 = 2 tan .41-tan2^

12 . si n ,4 sin/? s inC

13. a2 = b2 + c2-2bccosAa2 = b2 + c2-2bc kosA

14. Area of triangle/ Luas segi tiga= - ab sin C

2

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Section A I Bahagian A[40 marks140 markah]Answer all questions.Jawab semua soalan.

1 Solve the simultaneous equation x+2y=3 and x2 +y2 +2xy =5Give your answers correct to two decimal places.Selesaikan persamaan serentak x+2y=3 dan x2 +y1 +2xy= 5 .Berikan jawapananda betul sehingga dua tempat perpuluhan.

2 (a) Sketch the graph of y = - 4 cos -x for 0


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SULIT 3472/2

Diagram 3 shows a part of a series of circular sectors drawn with an angle of 1-5 radianswith centre O. The radiusof the first sector is 4 cm. The radiusof each subsequentsector is 2 cm more than the preceding sector.Rajah 3 menunjukkan sebahagiandaripada siri sektor bulatan yang dilukisdengansudut 1-5 radianpada pusat O. Jejarisektor pertama ialah 4 cm. Jejaribagi sektoryang berturutan yang herikutnya ialah2 cm lebih daripada sektor yang sebelumnya.

Diagram 3 / Rajah 3

Given that the length of the arc of the nlb sector is30 cm, findDiberipanjang lengkokbagi sektorke-n ialah 30 cm, cari

(a) the radius of the n[h sectorjejari bagi sektorke-n

(b) the value of3?nilai n

(c) the sum of the length of arc arc of the first 20 sectors.hasil tambah panjang lengkok bagi 20 sektor yangpertama.

3472/2 'O 2013 SUMATIF 3 SPM Hak Cipta Jabatan Pelajaran Negeri Terengganu

[2 marks-][2 markah]

[3 marks][3 markah][2 marks][2 markah]

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SULIT ? 3472/2

4 Given that the curvey = x3 - 5x2 + 8 passes through P(-\, 2).Diberi lengkung y = x -5x + 8 melalui P(-\, 2).(a) Ifx decreases from 3 to 2-99,

Jika x menyusut daripada 3 kepada2-99,(i) find the small change in y,

cari perubahan kecil dalamy,(ii) Hence, find the approximate value ofy.Seterusnya, cari nilai hampirbagiy.

[4 marks][4 markah]

-l(b) Find the rate of change of v when the rate of change ofx is 0-4 unit s at point P.[3 marks]Cari kadarperubahanyjika kadarperubahan xpada titik P ialah 0-4 unit s~l .[3 markah]

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SULIT 10 3472/2

5 Table 5 shows the frequency distribution of the scores ofa group of students intheScience quiz.Jadual 5menunjukkan taburan kekerapan bagi skor sekumpulanpelajar dalam kuiz Sains.

ScoreSkor

Number of pupilsBilangan murid

11 - 15 316 - 2 0 421 - 25 326 - 3 0 631 - 3 5 436 - 40 5

Table 5 /Jadual 5

(a) Calculate the standard deviation of the distribution.Hitung sisihanpiawai bagitaburan markah itu. [4 marks][4 markah](b) Find the variance if the score ofeach pupil ismultiplied by 2 and then 5 is added to it.

[2 marks]imbah[2markah][2 marks]

Cari variansjika skor setiap murid didarabkan dengan 2dan kemudian ditambahdengan 5.

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SULIT II 3472/2

Diagram 6 shows a triangle ABC. D is the midpoint ofAC and E is a point onAB such-7>that AB= 4AE.The straight lines BD and C intersect at point F. It is given that BC = 4x

and AB - 87.itay'a/? 6menunjukkan segitigaABC. D adalah titik tengah ACdan titik E terletakpadaABdengan keadaan AB = 4AE. Garis lurus BDbersilang dengan garis lurus CEpada titik F.

-> , " t n ADiberi bahawa BC = 4x dan AB = 8y.

Rajah 6 / Diagram 6(a) Express the following in terms of x and y

Ungkapkan dalam sebutan x dan y(i) BD(ii) CE

[3 marks][3 markah]

-> -7> - > -> ->(/>) Given that BF = hBD and CF = A:CF(where h and A: are constants. Express BF-> -> -> ^Diberi BF = hBD dan CF = kCEtdengan keadaan h dan kadalahpemalar.

Ungkapkan BF(i) in terms ofh, x and y,

dalam sebutan h, x dany,(ii) in terms of k,x and y.

dalam sebutan k,x dan y

(c) Hence, find the value of/? and of &.Seterusnya, cari nilai h dan nilai k.

3472/2 2013 SUMATIF 3 SPM Hak Cipta Jabatan Pelajaran Negeri Terengganu

[2 marks][2 markah][3 marks][3 markah]

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SULIT 12 3472/2

Section B I Bahagian B[40 marks 140 markah]

Answer four questions from this section.Jawab empat soalan daripada bahagian ini.

7 Use graph paper to answer this question.Gunakan kertas grafuntuk menjawah soalan ini.

Table7 shows thevaluesof twovariables, x and^y, obtained from an experiment.kThevariables x andy are related by the equation y = hx2 + , whereh and kare constants.x

Jadual 1menunjukkan nilai-nilai bagi duapemboleh ubah, x dan y,yang diperolehdaripada satu eksperimen. Pemboleh ubah x dan y dihubungkan olehpersamaanky = hx~ + , dengankeadaan h dankadalahpemalar.x

X 0-8 1. 1 1-4 1-6 1-8 1-9y 6-28 6.02 6-18 7-62 8-55 9-47

Table IIJadual!

(a) Plot xy against x3, using a scale of2 cm to 1unit on the x3-axis and 2 cm to 2 units onthe x,y-axis. Hence, draw the line ofbest fit. [5 marks]Plot xy melawan x3, dengan menggunakan skala 2cm kepada 1unitpadapaksi-x3dan 2 cm kepada 2 unitpada paksi-xy. Seterusnya, lukis garis lurus penyuaianterbaik.

[5 markah](b) Use the graph in (a) to find the value ofGunakan grafdi (a) untukmencari nilai(i) h and k

h dan k(ii) y whenx= 1-518

ybila x= 1-518[5 marks][5 markah]

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SULIT 14 3472/2

9 Solutionbyscale drawing is not accepted.Penyelesaian secara lukisan berskala tidak diterima.Diagram 9 shows a straight line PQ.Rajah 9 shows a straightline PQ.

2x + 3^-12 = 0

Diagram 9 / Rajah9

(a) Find the equation of the straight line PR. [3 marks]Caripersamaan garis lurus PR. [3 markah](b) Find the coordinates ofP. n marks]Cari koordinat P. p markah](c) Calculate the area oftriangle PQR. [3 marks]Hitung luas segitiga PQR. [3 markah](d) PQ is extended to Tsuch that 2PQ=3QT. Find the coordinates ofT. [2 marks]PQ diperpanjangkan ke Tsupaya 2PQ= 3QT. Cari koordinat T. [2 markah]




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SULIT 15 3472/2

10 Diagram 10 shows a circle OMN, centre Owith radius 5 cm and a sector PQR centre P.The straight linesMP andNP, are tangents to the circle at pointM and point N respectively.Rajah 10menunjukkan sebuah bulatan OMN, berpusat Odenganjejari 5 cm dansektorPQRberpusatdi P. Garis lurusMP dangaris lurusNP adalah tangent kepada bulatanmasing-masing di titikM dan titikN

R12 cmA*

Diagram 10 / Rajah 10[Ust/Guna n= 3-142]Calculate / Hitung(a) ZMON and Z QPR in radian, [3 marks]

ZMON dan Z QPR dalam radian, t3 markah](b) the perimeter of the shaded region, [3 marks]perimeter kawasan berlorek, [3 markah](c) area of the shaded region. [4 marks]luas kawasan berlorek. [4markah]




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SULIT 16 3472/2

11 (a) In a company, 75% of the workers are over 40 years old.Dalam sebuahsyarikat, 75% daripadapekerjanya berumur lebihdaripada40 tahun.(i) Given that the mean numbers ofworkers over 40 years old is 2280, find the total

number ofworkers in the company.Diberi minbilanganpekerja yang berumur lebih daripada 40 tahun ialah 2280,carijumlah pekerja dalam syarikat tersebut.

(ii) If 8 workers are randomly chosen, find the probability that at least 2 of them areover 40 years old.Jika 8 orangpekerjadipilihsecara rawak, cari kebarangkalian bahawasekurang-kurangnya 2 daripadamereka berumur lebih daripada 40 tahun.

[4 marks][4 markah]

(b) The weight of the workers in biscuit factory follows a normal distribution with a mean64 kg and variance of 144 kg2.Berat bagipekerja di kilang biskut adalah mengikut taburan normal dengan min 64 kgdan varians 144 kg2.(i) Calculate the percentage ofworkers having weightbetween 58 kg and 67 kg.Hitungperatus pekerja yangmempunyai berat di antara 58 kg dan 61 kg.(ii) If 97-8%of the workersweightmore thanmkg, find the value ofm.Jika 97-8% daripada pekerja mempunyai berat lebih daripada mkg, cari nilaibagi m.

[6 marks][6 markah]

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SULIT 17 3472/2

Section CI Bahagian C[20 marks I 20 markah]

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

12 A particle moves along a straight line and passes through a fixed point O,with an initialvelocity of24 ms"1. Its acceleration, a ms~2, is given by a = 2t - 10, where t is thet ime in seconds.Suatuzarah bergerakdi sepanjang suatu garis lurus dan melalui titik tetap O, denganhalaju awal 24ms-1. Pecutannya, ams"", diberi oleh a = 2/ - 10 dengan keadaan t ialahmasa dalam saat.

Find / Cari

(a) the minimum velocity, in ms-1, of the particle, [4marks]halajuminimum, dalamms~ , zarah itu, [4 markah]

(h) the range of values oft during which the particle moves to the left. [3 marks]julat nilai t apabila zarah itu bergerak arah ke kiri. [3 markah]

(c) the total distance, in m, travelled by the particle in the first 6 seconds. [3 marks]jumlahjarak, dalamm.yang dilalui oleh zarah itu dalam 6 saat pertama. [3 markah]

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13 Table 13 shows the price indices and percentage expenditure for three items, A, B and Cused in making a certain kind of cake.Jadual 13menunjukkan indeks harga dan peratus perbelanjaan bagitiga bahan, A,B dan Cyang digunakanuntuk membuat sejenis kek.

I temBahan

Price index in the year 2010based on the year 2008Indeks hargapada

tahun 2010berasaskan tahun 2008

Price index in the year 2012based on the year 2008Indeks hargapada

tahun 2012berasaskan tahun 2008

PercentageexpenditurePeratus

perbelanjaanA 132 142 40B 116 h 25C k 150 35

Jadual 13 /Table 13(a) Find theprice index of item A in the year 2012 based on the year 2010. [2marks]Cari indeks harga bahan Apada tahun 2012 berasaskan tahun 2010. [2markah](h) Theprice of item B inthe year 2008 isRM12-10 andits price in the year2012is

RM14-60.Harga bahan Bpada tahun 2008 ialah RM12-10 dan harganyapada tahun 2012 ialahRM14-60.Find / Cari(i) the value of/?,

nilai h,(ii) the priceof itemB in the year2010.harga bahan Bpada tahun 2010.

[3 marks][3 markah]

(c) Given the composite index for the production cost ofmaking the cake in the year 2010based on the year 2008 is 120. Find the value ofk. [2 marks]Diberi indeks gubahan untuk kos membuat kekpada tahun 2010 berasaskan tahun 2008ialah 120. Cari nilai k. [2 markah]

(d) Given the price of the cake increases 10% from the year 2010 to the year 2012.If its price in the year 2008 is RM38, calculate the corresponding price of the cakein the year 2012. [3 marks]Diberi bahawa harga sebiji kek telah meningkat sebanyak 10% daripada tahun 2010kepada tahun 2012. Jika harganyapada tahun 2008 ialah RM38, hitung harga yangsepadan bagi kek itu pada tahun 2012. [3 markah]




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SULIT 19 3472/2

14 Usegraphpaper to answer this question.Gunakan kertasgrafuntuk menjawah soalan ini.A cooperative purchasing school uniforms and T-shirts from a supplier. Cooperatives havecapitalRMIO 000 to buyx school shirts and v T-shirts.Sebuah koperasi sekolah membeli baju sekolah dan kemeja-T daripada seorangpembekal.Koperasi itu mempunyai modal RMIO 000 untuk membeli x helai baju sekolah dany helaikemeja-T.Purchase of clothes is based on the following constraints:Pembelian baju adalah berdasarkan kekangan berikut:I : The cost of purchasing a school shirt is RM20 and a T-shirt is RM25.

Kos membelisehelai bajusekolah ialah RM20 dan sehelai bajukemeja-Tialah RM25.

II : The number of school shi rt s cannot exceed twice t he number of T-shirts.Bilangan baju sekolah tidak bolehmelebihi duakali hilangan baju kemeja-T.III : The number of T-shirts exceed the number of school shirts by at most 40.

Bilangan baju kemeja-Tmelebihi bilangan baju sekolah selebih-lebihnya40 helai.

(a) Write three inequalities that satisfy all the above constraints excluding x > 0 and v > 0.[3 marks]

Tulistiga ketaksamaan yang memenuhi semua kekangan di atas selain x > 0 dany > 0.[3 markah]

(b) Using a scale of 2 cm to 40 shirts purchased on both axes, construct and shade theregion Rwhich satisfies all the above constraints. [3 marks]Denganmenggunakan skala 2 cm kepada 40 helai baju yang dibelipada kedua-duapaksi, binadan lorekkan rantauRyang memenuhi semua kekangandi atas.

[3 markah](c) Use your graph in 14(b) to find

Gunakangrafanda di 14(b) untuk meneari(i) the maximum number of T-shirts purchased if the cooperative purchase 240

school shirts.bilangan maksimum bajukemeja-Tyang dibelijika koperasi membeli 240 helaibaju sekolah.

(ii) the maximum gross profit if the price of a school shirt and a T-shirt are RM30and RM40 respectively.jumlah keuntungan kasarmaksimum jika harga sehelai bajusekolah dan sehelaibaju kemeja-T ialahRM30danRM40 masing-masing.

[4 marks][4 markah]




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SULIT 20 3472/2

15 Diagram 15 shows a triangle ABC.Rajah 15menunjukkan sebuah segitigaABC.

12-2 cm

Diagram 15 / Rajah 15(a) Calculate / Hitung

(i) the length ofAC,panjangAC,

(ii) ZBCA.[5 marks][5 markah]

(b) Given that the line AB is extended toB' such that B'C = BC, while AC and Z BACremain unchanged.Diberi bahawa garis AB diperpanjangkan ke B' supaya B'C = BC, manakala ACdan Z BAC adalah kekal.

(i) Sketch the triangleAB'C.Lakar segitiga AB'C.

(ii) Find the area, in cm2, of the triangle AB'C.Cari luas, dalam cm2, bagi segitiga AB'C.

KERTAS SOALAN TAMA TEND OF QUESTION PAPER

3472/2 2013 SUMATIF 3 SPM Hak Cipta Jabatan Pelajaran Negeri Terengganu

[5 marks][5 markah]

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BLANK PAGE

HALAMAN KOSONG

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SULIT

x

NAMA :

T I NGKATAN :

23

Arahan Kepada Calon1. Tulis Nama dan Tingkatan anda.2. Tandakan (*/) untuk soalan yangdijawab.3. Ceraikan helaian ini dan ikat sebagai muka hadapan bersama-sama dengan

kertas jawapan.

3472/2

Bahagian Soalan SoalanDijawabMarkahPenuh

Markah Diperoleh(Untuk Kegunaan Pemeriksa)

A

1 52 73 74 75 66 8

B

7 108 109 1010 1011 10

C

12 1013 1014 1015 10Jumlah




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SULIT 24 3472/2INFORMATION FOR CANDIDATES

MAKLUMA T UNTUK CALON

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

2. Answer all questions in Section A, any four questions from Section B and any twoquestions from Section C.Jawab semua soalan dalam BahagianA, mana-manaempat soalan daripadaBahagianBdanmana-mana dua soalan daripadaBahagian C.

3. Write your answers on the foolscap papers provided.Tulis jawapan andapada kertas jawapanyang disediakan.

4. Show your working. It may help you to get marks.Tunjukkan langkah-langkahpenting dalam kerja mengiraanda. la boleh memhantu andauntuk mendapatkan markah.

5. The diagrams in the questions provided are not drawn to scale unless stated.Rajah yangmengiringi soalan tidak dilukis mengikut skalakecuali dinyatakan.

6. Themarksallocated for eachquestion and sub-part of a question are shown in brackets.Markah yangdiperuntukkan bagisetiap soalan dan ceraian soalan ditunjukkan dalamkurungan.

1. A list of formulae is provided on pages 3 to 5.Satu senarairumus disediakan di halaman 3 hingga 5.

8. Graph paper is provided.Kertas grafdisediakan.

9. You may use a non-programmable scientific calculator.Anda dibenarkan menggunakan kalkulator saintifikyang tidak boleh diprogram.

10. Tie the 'helaian tambahan' and the graph papers together with the answer sheets and hand into the invigilator at the end of the examination.Ikatkan helaian tambahan dan kertas grafbersama-sama dengan kertas jawapan danserahkankepadapengawas peperiksaanpada akhirpeperiksaan.

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1TilTtTTiVffiT f JABATAN PELAJARAN NEGERI TERENGGANU

PENTAKSIRAN SUMATIF 3 SPM 2013MATEMATIK TAMBAHANKer t a s 1Pe ra tu ran Pema r k ahanOgos 2013

Peraturanpemarkahan ininiengandungi 7 halaman bercetak.

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SULIT 2 3472/1 (PP)

INSTRUCTIONS FOR EXAMINERS

1. MARKING GUIDE

1.1 Mark all t he answers .1.2 Donotmark working / answer that hasbeen cancelled.1.3 Answer written in the answer space orat the end of the working isconsidered the final

answer.1.4 Full mark is given for the correct answer without referring to the working.1.5 If the final answer is wrong, award the corresponding maximum mark as stated in the

marking scheme.1.6 Ifmore then one final answer is given, choose the answer with the highest mark unlessstated otherwise in the marking scheme.

1.7 If the final answer is correct, but stated wrongly in theanswerspace, full mark isnotawarded.

2. NOTATION2.1 Full mark for eachquestion in this paper iseither2, 3 or4.2.2 If full mark is not awarded, the following system is used :

B3 - 3 marks is awarded if the answer at this stage is correct.B2 - 2 marks is awarded if the answer at this stage is correct.Bl - 1 mark is awarded if the answer at this stage is correct.

2.3 Only one out ofB3, B2 orB1 is awarded for each question orpart ofaquestion.3. Accept answers correct to 4 significant figures unless stated otherwise in the marking scheme.4. Accept other correct methods which are not given in the marking scheme.5. Accept answers in Bahasa Melayu.

6. Calculating total marks.EScore for Paper 1+Y Score for Paper 2- ^ - x 100%180

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SUL IT 3472/l(PP)

PENTAKSIRAN SUMATIF 3 SPM 2013PERATURAN PEMARKAHAN UNTUK MATEMATIK TAMBAHAN KERTAS 1

No. Mark Scheme(a) 1 dan 3 [11(b) {p, q, /', /} HI ignore the bracketW r t) T(b) o

HI[2]

1 - 2 Bl follow through

4.x- - 4x - 3 = 0

(2*+l)(2x-3) = 0[2]B l

m


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SUL IT 3472/l(PP)

No. Mark Scheme SM a r k8 / = 8 cm [3|

;- + / + 2r = 3 2 B2

2 or rO or 2r seen Bl3

9 (a ) - 4 111(b) 171 [2]

3^[5(10)-13]-1[5(4)-13] Bl10

(a) - [2]4I28r3=2 Bl

(b) ^ m 4j

12 8I 4

11 P-X- 14 ]2 + 2(1+/?) - 3-6y? B322+2(l+p) _ ^3-6/> g2 42..2a+/) i C123(2/;-l) D1

12

*=- PI

2k =22 B21 - 3* 39 Iklog2-^--2 OR log2-^- = log2221 3a: \-A Bl for lo,&2 13/r

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SUL IT

No.13

14

15

16

. Mark Scheme

x + 3y - 4log?m -: log2 nJ - log2 16

los2 w = x or log? /7 = y

[4]B2 for 1 logarithm law used

and (log? in= a or log? w= 7)B3 for 2 logarithm laws usedand (log2 m=a or log2 =J>)Bl (seen anywhere)

3- 58 - 4 - 5

Q,= 4-5 or Q3 =

[3B2Bl

k = 13]x =

6 x - 4 = 0&=6x-4dx

OR

A =

B2

B l

13|

31.- +yA +

- 42(3) + 5-

B2

Mr4(3) B l

dy__ 1_dx~ (\-2x)dy (l-2x)(l)-x(-2)dx~ (1-2a-)2

- or equivalent | 3 \

B2

*=1 , ^ =_2 (both) Blciv g&

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EMa r k

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SULIT

No.17

18

19

20

21

(a)

(b) 33 unit23 x 1 1

(a ) -309

(b) -

Ma r k Scheme

[21B l

[1][31

(3,11)

10- fc[1 B222 ->fjif(jt) c6c - k \x dx Bl (separate)

HI

a = 90, 180, 270 |4| Give B3 for any 2 correct answers givencosa-O, cos a =-1 (both) B32 cos a (cos a + 1) - 0 B22 cos2a- 1 + 2 cosx= -1 Bl

/ 7 - 8 , / t - 3 [3]fc = -2(l)+10 or 4 = -2k+]0 B2- = -2a + 10 and (m= -2, c = 10 used) BlA

Vektor unit = 5/+2y

OP = 5/+2y

131

B2

OP = OQ + QP = 7 /+6y + ( -2 / -4 /) B

3472/l(PP)

SM a r k

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SUL IT 3472/l(PP)

No. Mark Scheme ' - .' SMa r k22 (a) t 1215

2x15 3(b) g n 43 2 2 1 3 1 2 2x or x- or x- OR x 5 3 5 3 5 3 5 3 B l

23 (a) 700 [1]

(b) 1008 |3 |^2x8C4 +5C,x8C5 +5C0x8C6 B2 45C2x8CA or 5C{x*C5 or 5C0x*C6 Bl

24 (a) 5040 Ml(b) 720 |2 |

33/?3 or 5p4 or 5! or 3!or 5x4x3x2x1 or 3x2x1 B l

25(a) 0-762 in(b) 0-5516 [2] 3

0-2758 o r 2 x 0-2242 B l

END OF MARK S CH EME

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JABATAN PELAJARAN NEGERI TERENGGANU

PENTAKSIRAN SUMATIF 3 SPM 2013MATEMATIK TAMBAHANKer t a s 2Pera tu ran PemarkahanOgos 2013

Peraturan pemarkahan inimengandungi 15 halaman bercetak.

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SULIT 2 3472/2(PP)INSTRUCTIONS FOR EXAMINERS

1. MARKING GUIDE

1.1 Mark al l th e answers.1.2 Donot mark working / answer that has been cancelled.1.3 Give the mark P /K /N in line with steps ofcalculation given by thestudents.1.4 Give the mark PO / KO / NO for the incorrect working / answer.1.5 Ifmore than one final answer is given, mark all the solution and choose the answer with the

highest mark.1.6 Accept other corect methods which are not given in themarking scheme.

2. NOTATION

P - Themark is given ifthe working /answer in accordance with the Knowledge assessedas stated in the marking scheme.

K - The mark is given ifthe working / answer in accordance with the Skills assessed asstated in the marking scheme.

N - The mark is given if the working / answer in accordance with the Values assessed asstated in the marking scheme.

PA - Subtract 1mark (only once) from theNmark when students make an early rounding ofnumbers .

KP - Subtract 1mark (only once) from the Pmark orNmark when students do not write theimportant stepsof the calculations.3. Accept answers correct to 4 significant figures unless stated otherwise in the marking scheme.4. Accept other correct methods which are not given in the marking scheme.

5. Accept answers inBahasa Melayu.

6. Calculating total marks.EScore for Paper 1+Y Score for Paper 2! ^=* x 100%

18 0

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SULIT 3472/2(PP)

PENTAKSIRAN SUMATIF 3 SPM 2013PERATURAN PEMARKAHAN UNTUK MATEMATIKTAMBAHAN KERTAS 2

No.

SECTION A I40MARKSJMARK SCHEME

j -xx = 3 - 2y or y - PI

(3 - lyf + y2 +2(3 - 2y)y =5 or x2 +2x

/ -6y +4=0 or x2 +6x- 11 =0

j-x

v 2j-x

-(-6)x/(-6)2-4(l)(4) x=~ m :6J62-4(1)(-11)y = 2(1) 2(1)

;; = 5-24, 0-76 Nl (both)

x = -7-47, 1-47 Nl(both)

3472/2 (PP) 2013 SUMATIF 3 SPMHakCiptaJabatan PelajaranNegeri Terengganu

= 5

K l

SMARK

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SULIT 3472/2(PP)

No. MARK SCHEME EMARK

2 (a) jnd(b).V;4

3

*

s ^X 2" / - \ o x/ X y - 3 - -1 \ 7t

I 1 T *"

7

0 / n x

-4

- shape of cosinegraph PI- amplitude (max = 4) PI- negative graph PI- period/cycle i n 0


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SUL IT 3472/2(PP)

No. MARK SCHEME EM A R K3 (a) 4 + (-l)(2) Kl

2 + 2 Nl

(b )7>306+ (p -1)3=30 PI (d=3) Kl (useformula)n = 9 N l 7

(c)y[2(6)+(20-l)3] Kl690 cm Nl

4 (a) (i) ^ =3.r-10x Kl


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SULIT 3472/2(PP)

No. MARK SCHEME SMA RK5 (a) x = or 26-8 Klv ' 25

19670 Nl

6=-(2^? K,= 8-28 Nl

(b) (8-28 x 2)2 or (8-28)2 x (2)2 Kl= 274-2 Nl

6(a) (i) BD = BA + AD = -$y + -AC

= -8v + -(8y + 4x)2 ~

= -Ay + 2x

Use triangle law of vectorK l

-> -> ->(ii) CE = G4 + ;4 = -8>> - 4x + 2y= - 4 x - 6 y J

N l

(b) (i) F = hBD= h(-4y +2x) = 2hx - 4hy Nl(ii) CF = kCE =k(-4x-6y)= -4kx-6ky Nl

8

(c) BF = BC + CF = 4x-4kx-6ky= (4- 4*)x - 6y K1 for fmding BF

and compare2/7 = 4- 4

- 4/ j = -6ASolve K l

7A=6 Nl both

7

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No. 7| . . :_ j . .q4^H^^

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SULIT

No. MARK SCHEME

2x l(a) v = 8x + c Kl for integration9 - '(Give Kl for or -8x)2

2(1)39= vJ -8(l) +c Kl forsubstitution to find c2 v 'v = .y2-8.v + 16y - (*-4)2 N l

(b) -(7+9)(1) + \{x-4fdx Kl for area of trapezium= 8 + (*-4)3

-T

= 17 N l

(c) Volume = iv \{x-4)* dx= TV

(x-4f -4- 1

Kl for integration of curveKl for Al+A2

K li

for limit '

Kl for integration (Ignore tc)

= 48 -* Nl (Accept 152-7)

3472/2 (PP) 2013SUMATIF 3SPMHak Cipta Jabatan Pelajaran Negeri Terengganu

3472/2(PP)

IMARK

10

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SULIT

No. MARK SCHEME

(a) m = v } 2 PIy-X- = -(x-2) OR,2 22y= 3x-5 or equivalent

2 2N l

K l

(6) Tr>- to solve simultaneous equations :2x+ 3?-12 = 02>; = 3.x:-513^=26 Kl (until 1 unknown left)y2, x = 3(3,2) Nl

(c) Q(0, 4),R\ -, o] Both coordinates seen anywhere PIArea = 2

s0 33

04 2 0 4= |0(2)+3(0)+f(4)-3(4)--(2)-0| Kl

2 j Ji 1*3= 4-unit2 Nl (Accept4-333 or )3 J

{d) 3x+2& =o or 3y+2(2) =4 or equivalent Kl-2,yl

3472/2 (PP) 2013 SUMATIF 3 SPM Hak Cipta JabatanPelajaran Negeri Terengganu

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SUL I T 11

No.11

MARK SCHEME

(a) (i) 2280=(0-75) Kln = 3040 N l

(ii) P(X>2)= \ -P(X=0)-P(X=\)=1- 8C0 (0 -75) (0 -25)8 - 8C, (0 75)' (0 -25)*

= 0-9996 Nl

(b) (i) P(58


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SUL IT 12 3472/2(PP)

SECTION C |20 MARKS|No. MARK SCHEME SM A R K

12 (a) v= \2t-\0dt =r-\0t +c Kl24 = (0)2-I0(0) + c; c = 24 PIv = /2 -10 / + 24a = 0 , 2 /- 10 =0

t =5 s N lv = (5)2-10(5) + 24= -1 Nl

(b) v = /2-10/ + 24 < 0 PI v /( r -6)( / -4)


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SUL IT

No.13

13

MARK SCHEME

(a) l32xQ* =142 Kl100 , = 107-6 Nl

(b) (i)/7=ii^xl00 Klv J 12-10= 120-7 Nl

(ii)^xlOO =116 Kl [give once-(i) or (ii)|12-10

i>= RM14-04 Nl

(132x40)+(U6x25)+(A:x35) =m K1KC) 100

k = 109-1 N l

(^0 4012/ 120x110100= 132 N l

^xlOO = 132 Kl38

Pmi = RM50-16 Nl

3472/2 (PP) 2013 SUMATIF 3 SPMHakCiptaJabatan Pelajaran Negeri Terengganu

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SMARK

10

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y

400

360

320

280

240

200

160

120

MO

40

No. 14

(a )

(b)

(c)

14

20x + 25y< 10000 or equivalentN1x 40 or equivalent N1Iv IN lNl

(i)(ii)

drawcorrectlyat leastone straight linedraw correctly three straight linesshaded regiony maximum- 240 NlUse3Qx + 40> i.e.30(200) + 40(240) Kl Kl

= RM 15 600 N l

x400



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SULIT 15

No.15

MARK SCHEME(tf)(rMC2 = 8-72+ 12-22-2(8-7)(12-2) cos 125 Kl

= 18-61 cm N l

AC = 18-61 cm Nl, ,sinC _

12-2s in l25 K l18-61

ZBCA = 32-48 N lOR

12-22 = 8-72~ 18-612 2(8-7)(l 8-61) cos CZBCA = 32-48 N l

C(b) (i)

BB' 1-7( i ' )~sin 70 sin 55BB' = 9-98 cm Nl

Area = -(8-7)(9-98 + 12-2)sin 55 Kl= 79-03 cm2 Nl

K l

OR

BB'sin 70 - 87 K!s in55

BB' = 9-98 cm Nl

Area = - (18-61)(9-98 + 12-2)sin 22-52 K l= 79-05 cm2 Nl

ORArea = - (8-7)(18-61)sin (70 + 32-48) K l

K l

3472/2(PP)

2 MARK

10

trial terengganu spm 2013 add math ques_scheme all paper

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