SPM Sabah Math P2 2010 Q n A_2

download SPM Sabah Math P2 2010 Q n A_2

of 42

Transcript of SPM Sabah Math P2 2010 Q n A_2

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    1/42

    SULIT 1449/

    1449/2 [Lihat sebelahSULIT

    JABATAN PELAJARAN NEGERI SABAH

    SIJIL PELAJARAN MALAYSIA 1449/2EXCELMATHEMATICS Paper 2

    2 Hours 30 Minutes Two hours and thirty minutes

    JANGAN BUKA KERTAS SOALAN INISEHINGGA DIBERITAHU

    1. Tulis nombor kad pengenalan dan angka giliran anda pada ruangan

    yang disediakan.2. Kertas soalan ini adalah Bahasa

    Ingers. 3. Calon dikehendaki membaca

    maklumat di halaman 2.

    Kod Pemeriksa

    Bahagian Soalan MarkahPenuhMarkah

    Diperolehi

    A

    1 32 4

    3 4

    4 5

    5 3

    6 67 5

    8 5

    9 7

    10 4

    11 6

    B

    12 1213 12

    14 12

    15 12

    16 12Jumlah

    Kertas soalan ini mengandungi 29 halaman bercetak.

    NAMA : _______________________________

    KELAS : ______________________________

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    2/42

    SULIT 1449/2

    2

    INFORMATION FOR CANDIDATES

    1. This question paper consists of two sections : Section A and Section B ..2. Answer all questions in Section A and four questions from Section B .

    3. Write your answers clearly in the space provided in the question paper.

    4. Show your working. It may help you to get marks.

    5. If you wish to change your answer, neatly cross out the answer that you have done. Then write down thenew answer.

    .6. The diagram in the questions provided are not drawn to scale unless stated.

    7. The marks allocated for each question and sub-part of a question are shown in brackets.

    8. A list of formulae is provided on pages 3 to 4.

    9. A booklet of four-figure mathematical tables is provided.

    10. You may use a non-programmable scientific calculator.

    11. This question paper must be handed in at the end of the examination.

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    3/42

    SULIT 1449/2

    3

    MATHEMATICAL FORMULAERUMUS MATEMATIK

    The following formulae may be helpful in answering the questions. The symbols given are the ones commonlyused. Rumus-rumus berikut boloeh membantu anda menjawab soalan. Simbol-simbol yang diberi adalah yang biasadigunaan.

    1 nmnm aaa

    2 nmnm aaa

    3 mnnm aa )(

    4

    ac

    bd

    bcad A

    11

    5 Distance/ jarak

    = 2212

    21 )()( y y x x

    6 Midpoint/ Titik tengah

    2,

    2),( 2121

    y y x x y x

    7

    8 Mean =dataof number

    dataof sum

    9 Mean =sfrequencieof sum

    frequency)mark class(of ums

    10 Pythagoras Theorem / Teorem Pithagoras

    222 bac

    11

    12 )(1)'( AP AP

    1312

    12

    x x

    y ym

    14ercept xercept y

    mintint

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    4/42

    SULIT 1449/2

    4

    SHAPES AND SPACE

    1 Area of trapezium = heights21

    sides parallelof um

    Luas trapezium =

    2 Circumference of circle = r d 2 Lilitan bulatan = d = 2 j

    3 Area of circle = 2r Luas bulatan = j2

    4 Curved surface area of cylinder = rh 2 Luas permukaan melengkung silinder = 2 jt

    5 Surface area of sphere = 24 r Luas permuaan sfera = 4 j2

    6 Volume of right prism = cross sectional area length Isipadu prisma tegak = luas keratan rentas panjang

    7 Volume of cylinder = hr 2 Isipadu silinder = j2t

    8 Volume of cone = hr 2

    3

    1

    Isipadu kon =

    9 Volume of sphere = 33

    4r

    Isipadu sfera = 33

    4r

    10 Volume of right pyramid =3

    1 luas tapak tinggi

    Isipadu piramid tegak =

    11 Sum of interior angles of a polygon Hasil tambah sudut pedalaman poligon= 180)2(n

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    5/42

    SULIT 1449/2

    5

    12 360

    centreatsubtendedanglecircleof ncecircumfere

    lengtharc

    13 360

    centreatsubtendedanglecircleof areasectorof area

    14 Scale factor,PAPA

    k '

    Faktor skala, k =

    15 Area of image = 2k area of object Luas imej = k 2 luas objek

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    6/42

    SULIT 1449/2

    6

    Section A[52 marks ]

    Answer all questions in this section .

    1 The Venn diagram in the answer space shows sets, J , K and L such that the universalset, = J LK .

    Gambar rajah Venn di ruang jawapan menunjukkan set J, set K and set L dengankeadaan set semesta = J LK .

    On the diagram in the answer space, shadePada rajah di ruang jawapan, lorekkan

    (a) J L ,

    (b) ( ) ' J L K .[3 marks ]

    [ 3 markah ]

    Answer/ Jawapan :

    (a) J K L

    (b) J K L

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    7/42

    SULIT 1449/2

    7

    2 Calculate the value of p and of q that satisfy the following simultaneous linear equations:

    Hitung nilai p dan nilai q yang memuaskan persamaan linear serentak berikut:

    7612

    343

    q p

    q p

    [ 4 mar[4 marka

    Answer /Jawapan :

    3 Using factorization, solve the following quadratic equation. Menggunakan pemfaktoran, selesaikan persamaan kuadratik berikut.

    )1(3222

    x x [4 mar[4 marka

    Answer/ Jawapan :

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    8/42

    SULIT 1449/2

    8

    4 Diagram 4 shows a trapezium PQRS drawn on a Cartesian plane . SR is parallel to PQ . Rajah 4 menunjukkan sebuah trapezium PQRS yang dilukis pada suatu satah Cartesan.SR adalah selari dengan PQ.

    yS

    R ( 6, 1)

    xO

    P ( -1,-2)

    Q ( 4, - 3)

    Diagram 4 Rajah 4

    FindCari(a) the equation of the straight line SR

    persamaan garis lurus SR

    (b) the x-intercept of the straight line SR pintasan-x bagi garis lurus SR

    [ 5 mark[ 5marka

    Answer /Jawapan :

    (a)

    (b)

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    9/42

    SULIT 1449/2

    9

    5 Diagram 5 shows a pyramid. Base JKLM is a horizontal rectangle and VL is vertical. VLM is a rightangled triangle.

    Rajah 5 menunjukkan sebuah piramid. Tapak segiempat tepat JKLM adalah mengufuk dan VL adalahmenegak. VLM adalah sebuah segitiga bersudut tegak.

    V

    3 cm

    M L

    5 cm

    J 6 cm K

    Diagram 5 Rajah 5

    (a) Name the angle between the line KV and the plane LMV.

    Namakan sudut di antara garis KV dengan satah LMV.

    (b) Calculate the angle between the line KV and the plane LMV Hitung sudut di antara garis KV dengan satah LMV . [3 mar

    [3 marka

    Answer /Jawapan :(a)

    (b)

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    10/42

    SULIT 1449/2

    10

    6 In Diagram 6, OABC and ODE are two sectors of circles with centre O .

    Dalam Rajah 6, OABC and ODE ialah dua sektor bagi bulatan-bulatan berpusat O.

    Diagram 6

    Rajah 6

    It is given that OA = 7 cm, OE = 14 cm , 104 , AOE and 36 . EOD Diberi bahawa OA = 7 cm, OE = 14 cm, 104 , AOE dan 36 . EOD

    By using =7

    22 , calculate

    Dengan menggunakan =7

    22 , hitung

    (a) the area, in cm 2, of the whole diagram,luas , dalam cm 2, seluruh rajah itu ,

    (b) the perimeter, in cm, of the whole diagram. perimeter, dalam cm, seluruh rajah itu. [6 mar

    [6 markaAnswer /Jawapan :

    (a)

    (b)

    D

    C

    B

    A

    OE

    14cm

    7cm

    36o

    104 o

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    11/42

    SULIT 1449/2

    11

    7 (a) Determine whether the following statement is true or false.

    All multiples of 10 are multiples of 5

    Tentukan pernyataan berikut betul atau palsu.

    Semua nombor gandaan 10 merupakan nombor gandaan 5.

    (b) It is given the sum of all interior angle of a regular polygon of n sides is 0( 2) 180n .Make one conclusion by deduction on the size of the sum of all interior angle of a regularoctagon.

    Diberi bahawa jumlah sudut pedalaman sebuah polygon sekata dengan n sisi ialah0( 2) 180n .

    Buat satu kesimpulan secara khusus tentang saiz jumlah sudut pedalaman sebuah octagon.

    (c) State the premise in the following argument.Premise 1 : If x is a prime number, then x has two factors only.Premise 2 : . Conclusion : x is not a prime number.

    Nyatakan premis yang sesuai dalam hujah berikut:Premis 1 : Jika x ialah suatu nombor perdana, maka x mempunyai dua faktor sahaja.

    Premis 2 : . Conclusion : x bukan nombor perdana.

    [5 marks[5 markah

    Answer /Jawapan :

    (a) .

    (b)

    .

    (c) Premise 2 / Premis 2 ::

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    12/42

    SULIT 1449/2

    12

    8 The diagram 8 below shows six labeled cards in Box P and Box Q. Rajah 8 dibawah menunjukkan enam kad yang berlabel di dalam kotak P dan kotak Q.

    Diagram 8 Rajah 8

    A card is picked at random from each of the boxes.Sekeping kad dipilih secara rawak daripada setiap kotak itu.

    (a) List the sample space.Senaraikan ruang sampel.

    (b) List all the outcomes of the events and find the probability thatSenaraikan semua kesudahan peristiwa dan cari kebarangkalian bahawa

    (i) both cards are labelled with an odd number,kedua-dua kad dilabel dengan nombor ganjil.

    (ii) a card is labelled with number 7 or the card with an even number is picked.satu kad dilabel dengan nombor 7 atau kad berlabel nombor genap dipilih.

    [5 marks[5 markah

    Answer /Jawapan :

    (a)

    (b)(i)

    (ii)

    Box Q Kotak Q

    Box P Kotak P

    765 328

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    13/42

    SULIT 1449/2

    13

    9.The inverse of

    3 2

    6 7

    is7 21

    2 3mk

    Matrix songsang bagi3 2

    6 7

    ialah7 21

    2 3mk

    a) Find the value of m and of k Cari nilai m dan nilai k

    b) Using matrices, calculate the value of x and of y that satisfy the following matrix equation: Menggunakan kaedah matriks, hitung nilai x dan nilai y yang memuaskan persamaan matriksberikut:

    3 2 1

    6 7 8

    x

    y

    [7 marks

    [7 markah

    Answer/ Jawapan :

    (a)

    (b)

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    14/42

    SULIT 1449/2

    14

    10 Diagram 10 shows a solid mass in the shape of a half cylinder with a half cone taken out. The height of the cone is half of the length of the cylinder. The diameter of the half cylinder is 7cm and the length of cylinder is 12cm.

    Rajah 10 menunjukkan sebuah pepejal berbentuk separuh silinder dengan separuh kon dikeluarkan.Tinggi kon adalah separuh daripada tinggi silinder tersebut. Diameter separuh silinder adalah 7cm dan

    panjang silinder adalah 12cm.

    Diagram 10 Rajah 10

    Calculate the volume, in cm 3 , of the remaining solid. Hitung isipadu, dalam cm 3 , pepejal yang tinggal itu.

    [ Use /Guna =7

    22] [1

    marks ][10 markah

    Answer/ Jawapan :

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    15/42

    SULIT 1449/2

    15

    11 Diagram 11show the distance-time graph of a lorry and a taxi. Rajah 11 menunjukkan graf jarak masa bagi perjalanan sebuah lori dan sebuah taxi.

    Diagram 11 Rajah 11

    The graph ABCD represents the journey of the lorry from town Y to town X. Graph PQ represents the journey of the taxi from town X to town Y. The lorry and the taxi depart at the same time and travelalong the same road.

    Graf ABCD mewakili perjalanan lori dari bandar Y ke bandar X. Graf PQ mewakili perjalanan taxi daribandar X ke bandar Y. Lori dan taxi itu bertolak pada masa yang sama dan melalui jalan yang sama.

    (a) State the length of time, in minutes, during which the lorry is stationary. Nyatakan tempoh masa, dalam minit, lori itu berhenti.

    (b) (i) If the journey starts at 2.00 p.m., at what time do the vehicles meet? Jika perjalanan itu bermula jam 2.00 p.m., pukul berapakah kedua-dua kenderaan itubertemu?

    (b) (ii) Find the distance, in km, of the two vehicles from town Y when they meet.Cari jarak, dalam km, dari bandar Y bila kedua-dua kenderaan itu bertemu.

    (c) Calculate the average speed, in kmh -1 , of the lorry for the whole journey.Kirakan purata laju, dalam kmj -1 , lori itu bagi keseluruhan perjalanan. [6 marks

    [6 markahAnswer/ Jawapan :

    (a)

    (b)(i)

    (b) (ii)

    (c)

    Time / Masamin

    Town Y Bandar Y

    60

    40

    0 10 25 50 80

    A

    B C

    D

    Q

    P

    Town X Bandar X

    Distance/ Jarak km

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    16/42

    SULIT 1449/2

    16

    Section BBahagian B

    [ 48 marks/markah]Answer any four questions from this section.

    Jawab mana-mana empat soalan daripada bahagian ini.

    12 (a ) Complete Table 12 in the answer space for the equation 12 y x

    by writing down the values of y

    when x = 2 and x = 3.5. [2 marks ]

    Lengkapkan Jadual 12 di ruang jawapan bagi persamaan12

    y x

    dengan menulis nilai-nilai y

    apabila x = 2 dan x = 3.5 . [2 markah ]

    (b) For this part of question, use the graph paper provided on page 19.You may use a flexible curve rule.Untuk ceraian soalan ini, guna kertas graf pada halaman 19.

    Anda boleh guna pembaris flesible.

    Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 2 units on the y-axis, draw the graph of 12

    y x

    for . [4 marks ]

    Menggunakan skala 2 cm kepada 1 unit pada paksi-x dan 2 cm kepada 2 unit pada paksi-y, lukis

    graf 12

    y x

    untuk . . [4 markah ]

    (c) From the graph in 12 (b), find Dari graf di 12 (b) , cari

    (i) the value of y when x = 2.5,nilai y apabila x = 2.5,(ii) the value of x when y = 10.

    nilai x apabila y = 10. [2 marks ][2 markah ]

    (d ) Draw a suitable straight line on the graph in 12(b) to find the values of x which satisfy the equation24 12 0 x for . .

    State the values of x. [4 marks ] Lukis satu garis lurus yang sesuai pada graf di 12 (b) untuk mencari nilai-nilai x yang memuaskan persamaan 24 12 0 x untuk . . Nyatakan nilai-nilai x ini. [4 markah ]

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    17/42

    SULIT 1449/2

    17

    Answer / Jawapan :

    (a ) x -4 3 2 -1.2 1 2 3 3.5 4

    y 3 4 10 -12 -6 -4 -3

    Table 12 Jadual 12

    (b) Refer graph on page 19. Rujuk graf di halaman 19.

    (c) (i) y = .

    (ii) x = .

    (d ) x = , .

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    18/42

    SULIT 1449/2

    18

    Graph for Question 12Graf untuk Soalan 12

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    19/42

    SULIT 1449/2

    19

    13 (a ) Transformation R is a clockwise rotation of 90 o about the centre (0, 2).

    Transformation T is a translation2

    2

    .

    Penjelmaan R ialah putaran 90o ikut arah jam pada pusat (0, 2).

    Penjelmaan T ialah translasi 22

    .

    State the coordinates of the image of the point (-1, 5) under these transformations : Nyatakan koordinat imej bagi titik (-1 ,5) di bawah penjelmaan:

    (i) T 2

    (ii) TR [4 marks ][4 markah ]

    (b) Diagram 13 shows three pentagons, ABCDE, FGHIJ and FMNPQ , drawn on a Cartesian plane. Rajah 13 menunjukkan tiga pentagon , ABCDE, FGHIJ dan FMNPQ , dilukis pada suatu satahCartesan .

    Diagram 13 Rajah 13

    (i) FMNPQ is the image of ABCDE under a combined transformation WV . FMNPQ ialah imej bagi ABCDE di bawah gabungan penjelmaan WV .

    Describe in full the transformation Huraikan selengkapnya penjelmaan(a) V ,(b) W . [ 5 marks ]

    4

    y

    A

    B

    C

    D

    0

    M

    E F

    H

    G

    2 4

    2

    4 8

    2

    4

    6

    x

    I

    J Q

    P

    2 6

    N

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    20/42

    SULIT 1449/2

    20

    [5 markah ](ii) It is given that the region FMNPQ represents a region of area 20.5 m 2.

    Calculate the area, in m 2, of the shaded region. Diberi bahawa kawasan FMNPQ mewakili luas 20.5 m 2. Hitung luas , dalam m2, kawasan berlorek.

    Answer / Jawapan :

    (a ) (i)

    (ii)

    (b) (i) (a ) V :

    (b) W :

    (ii)

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    21/42

    SULIT 1449/2

    21

    14 The data below shows the life span, in hours, of 32 batteries tested.

    Data di bawah menunjukkan jangka hayat, dalam jam, 32 buah bateri yang telah diuji .

    20 40 37 26 30 42 28 35

    31 25 41 36 35 38 30 36

    35 39 32 48 33 27 44 22

    49 29 42 40 51 36 48 34

    (a ) Based on the data, complete Table 14 in the answer space. [5 marks ] Berdasarkan data itu, lengkapkan jadual 14 pada ruang jawapan. [5 markah ]

    (b) State the modal class. [1 marks ]Nyatakan kelas mod. [1 markah ]

    (c) For this part of the question, use the graph paper provided on page 24.Untuk ceraian soalan ini, gunakan kertas graf yang disediakan di halaman 24 .

    By using a scale of 2 cm to 5 hours on the x-axis and 2cm to 5 batteries on the y-axis, drawan ogive based on the data. [4 marks ]

    Dengan menggunakan skala 2cm kepada 5 jam pada paksi x and 2cm kepada 5 bateri pada paksi y, lukiskan satu ogif berdasarkan data yang diberi. [4 markah ]

    (d) From the ogive in (c) Dari ogif di (c)

    (i) Find the median [1 marks ]Cari median, [1 markah ]

    (ii) Find the third quartile, [1 marks ]Cari kuartil ketiga , [1 markah ]

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    22/42

    SULIT 1449/2

    22

    Answer / Jawapan :

    (a )

    Class

    intervalSelang kelas

    Upperboundary Sempadan

    atas

    Frequency Kekerapan

    CumulativeFrequency

    Kekerapan longgokan

    15-19 19.5 0 0

    20-24 24.5

    25-29

    30-34

    35-39

    40-4445-49

    50-54

    Table 14 Jadual 14

    (b)

    (c) Refer graph on page 24. Rujuk graf di halaman 24.

    (d ) (i)

    (ii)

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    23/42

    SULIT 1449/2

    23

    Graph for Question 14Graf untuk Soalan 14

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    24/42

    SULIT 1449/2

    24

    15 You are not allowed to use graph paper to answer this question. Anda tidak dibenarkan menggunakan kertas graf untuk menjawab soalan ini .

    (a ) Diagram 15(i) shows a solid right prism with a rectangular base ABCD on a horizontal plane. Thesurface ABRUFE is the uniform cross-section of the prism. The rectangle RBCS is an inclinplane. The rectangles EFGH and RSTU are horizontal planes. The edges EA and FU are vertical.

    Rajah 15(i) menunjukkan sebuah pepejal berbentuk prisma tegak dengan tapak segiempat tepat ABCD yang terletak di atas satah mengufuk. Permukaan ABRUFE ialah keratan rentasseragamnya. Segiempat tepat JRBCS ialah satah condong. Segi empat tepat EFGH dan RSTU ialah satah mengufuk. Tepi EA dan FU adalah tegak.

    Diagram 15(i) Rajah 15(i)

    Draw to full scale, the elevation of the solid on a vertical plane parallel to AB as viewed from X .

    Lukis dengan skala penuh, dongakan pepejal itu pada satah mencancang yang selari dengan ABsebagaimana dilihat dari X .

    [3 marks[3 markah

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    25/42

    SULIT 1449/2

    25

    Answer /Jawapan :(a )

    (b) A solid cuboid of length 4cm, width 3cm and height 2cm is removed from the prism and theremaining solid is shown in Diagram 15(ii). PQML is a horizontal plane. FP, JL, NM and RQ arevertical edges.

    Sebuah pepejal berbentuk kuboid dengan panjang 4cm, lebar 3cm dan tinggi 2cm, dikelaurkandaripada prisma itu . Pepejal yang tinggal seperti ditunjukkan pada Rajah 15(ii). PQML ialahsatah mengufuk. Tepi FP, JL, NM dan RQ adalah tegak .

    Diagram 15(ii) Rajah 15(ii)

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    26/42

    SULIT 1449/2

    26

    Draw to full scale, Lukis dengan skala penuh,

    (i) the plan of the remaining solid, pelan pepejal yang tinggal ,

    [4 marks[4 markah

    (ii) the elevation of the remaining solid on a vertical plane parallel to BC as viewed from Y .dongakan pepejal yang tinggal pada satah mencancang yang selari dengan BC sebagaimana dilihat dari Y. [5 marks

    [5 markahAnswer /Jawapan :(b) (i), (ii)

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    27/42

    SULIT 1449/2

    27

    16 P (42 oN, 65 oW), Q and R are three points on the surface of the earth. PQ is the diameter of the parallel of latitude 42 oN. PR is the diameter of the earth.P (42 oU, 65 oB), Q dan R adalah tiga titik pada permukaan bumi. PQ ialah diameter selarian latitud 42oU . PR ialah diameter bumi.

    (a ) State the position of Q. Nyatakan kedudukan Q.

    [3 marks[3 markah

    (b) Calculate the shortest distance, in nautical mile, from P to Q measured along the surface of theearth,

    Hitung jarak terpendek , dalam batu nautika, dari P ke Q diukur sepanjang permukaan bumi ,[2 marks

    [2 markah

    (c) An aeroplane took off from P and flew due east to Q along the parallel of latitude. It then flew duesouth to R.Sebuah kapal terbang berlepas dari P arah ke timur ke Q sepanjang selarian latitude dankemudian terbang arah ke selatan ke R.

    Calculate/ hitung (i) the distance, in nautical mile, from P to Q measured along the common parallel of latitude,

    jarak , dalam batu nautika, dari P ke Q diukur sepanjang selarian latitude sepunya ,[3 marks

    [3 markah

    (ii) The time, in hours, taken for the whole flight if its average speed is 630 knots. Masa, dalam jam, yang diambil bagi seluruh penerbangan itu jika purata lajunya ialah 63knot.

    [4 marks[4 markah

    Answer / Jawapan :(a )

    (b)

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    28/42

    SULIT 1449/2

    28

    (c) (i)

    (c) (ii)

    END OF QUESTION PAPERSOALAN TAMAT

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    29/42

    SULIT 1449/2

    29

    Question Solution and Mark Scheme Marks

    1 (a)

    (b)

    J KK L

    J KL

    P1

    P2

    32

    2

    12p 16q = 12 o r 9 p - 12 q= 9 or 24 p-12q = 14 or

    equivalent

    Note :Attempt to equate the coefficient of one of the unknowns, award K1

    -10q= 5 or -15p = -5 or equivalent

    OR

    p = 134

    q or q=43

    43

    p or p127

    21

    q or q =67

    2 p or

    equivalent

    Attempt to make one of the unknowns as the subject, award K1

    K1

    K1

    K1

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    30/42

    SULIT 1449/2

    30

    -10q= 5 or -15p = -5 or equivalent

    OR

    7

    3

    312

    46

    )12)(4(6)3(1

    q

    p

    Note :

    Award K1 if

    1.

    7

    3*

    Matrix

    Inverse

    q

    p or

    7

    3

    612

    43

    q

    p

    2. Do not accept

    *inverse

    matrix

    =

    612

    43 or

    1 0

    0 1

    31

    p

    21

    q

    Note :

    21

    3

    1

    q

    pas final answer, award N1

    K1

    K2

    N1

    N1

    4

    3 2 x2-3 x - 5=0 K1

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    31/42

    SULIT 1449/2

    31

    (2 x- 5) ( x + 1) =0 or equivalent

    x = 2.5 or 2

    5

    x = -1

    Note :

    1. Accept without =0

    2. Accept three terms on the same side, in any order

    3. Do not accept solutions solved not using factorization

    K1

    N1

    N1

    4

    4(a)M PQ =M SR =

    )1(4)2(3

    or5

    1

    =1 = * (6)SR M c or equivalent

    y =5

    1151

    x or equivalent

    P1

    K1

    N1

    4(b)0 =

    1 115 5

    x or equivalent

    11

    K1

    N1

    5

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    32/42

    SULIT 1449/2

    32

    5(a)

    (b)

    6(a)

    (b)

    Identify KVL or LVK

    tan KVL =3

    5or equivalent

    59.04 or 59 2

    777

    22360220

    or36 22

    14 14360 7

    777

    22360220

    +36 22

    14 14360 7

    32155

    45cm 2 or

    7007

    45cm 2 or 155.71 cm 2

    77

    222

    360220

    or36 22

    2 14360 7

    77

    222

    360220

    +36 22

    2 14 14 7 7360 7

    3163

    45cm or

    286645

    cm or 63.69 cm

    Note:

    1. Accept for K mark.2. Correct answer from incomplete working, award KK2

    P1

    K1

    N1

    K1

    K1

    N1

    KI

    K1

    N1

    3

    6

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    33/42

    SULIT 1449/2

    33

    8(a)

    (b) (i)

    (ii)

    {(5,2), (5,3),(6,2),(6,3),(7,2),(7,3),(8,2),(8,3)}

    {(5,3),(7,3)}

    2

    8 @ 1

    4

    {(5,2),(6,2),(6,3),(7,2),(7,3),(8,2),(8,3)}

    7

    8

    Note: Accept answer without working for K1N1

    P1

    K1

    N1

    K1

    N1

    9. (a)

    (b)

    k = 9

    2m = -6m= -3

    7 2 116 3 8(3)(7) (2)(6)

    x

    y

    1

    2

    x

    y

    x = -1 y = 2

    P1

    P2

    K2

    N1N1

    7 (a)

    (b)

    (c)

    True

    0(8 2) 180 1080 o

    x has more than two factors / x does not has two factors

    P1

    P1N1

    K2

    5

    5

    7

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    34/42

    SULIT 1449/2

    34

    Note:

    1. * 1

    8

    x inverse

    y matrix

    or7 2 116 3 8(3)(7) (2)(6)

    seen, award K1

    2. Do not accept*inverse

    matrix

    =

    3 2

    6 7

    or1 0

    0 1

    3.1

    2

    x

    y

    as final answer, award N1

    4. Do not accept any solutions solve not using matrices.

    10. 1 1 22 3.5 3.5 62 3 7

    OR 1 22 3.5 3.5 122 7

    1 223.5 3.5 12

    2 7 -

    1 1 223.5 3.5 6

    2 3 7

    96.25 cm 3 @ 96 cm 3

    K1

    K2

    N14

    11(a)

    (b)(i)

    (ii)

    (c)

    40 or 40 m or 40 min

    2.25pm or 1425 or 2.25

    20km or 20

    8060

    60

    45kmh -1 // 45 kmj -1 or 45

    P1

    P1

    P1

    K2

    N16

    12(a) (a) 6 K1

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    35/42

    SULIT 1449/2

    35

    3.43 K1 2

    (b) Graph1. Axes drawn in correct direction with uniform scales in

    3 x 4 and 12 y 82. All 6 points and *2 points correctly plotted or curve passes

    through all the points for 3 x 43. A smooth and continuous curve without any straight line and

    passes through all points

    Note :6 or 7 points correctly plotted award K1 N0

    P1

    K2

    N1

    4

    (c) (i)

    (ii)

    y = 4.8 4.5 5.1 y , and

    x = -1.21.1 1.3 x

    Note :

    1. Allow P mark if value of x and of y are shown on graph

    2. Value of x and of y obtained by calculation, award P0

    P1

    P1 2

    (d) Identify equation 24 y x

    Straight line 24 y x correctly drawn(Check any two points (-1,4), (0,0), (1,- 4),)

    1.65 1.85 x

    1.85 1.65 x

    Note:

    1. Allow N mark if value of x shown on graph

    2. Value of x obtained by calculation, award N0

    K1

    K1

    N1

    N1

    4

    12

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    36/42

    SULIT 1449/2

    3613(a)(i) (3,1) P2

    y

    x

    8

    -8

    -10

    -12

    Graph for Question 12Graf untuk Soalan 12

    -4 -3 -2 -1 0 1 2 3 4 x

    10

    8

    6

    4

    2

    -2

    -4

    -6

    -8

    -10

    -12

    y = -4x

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    37/42

    SULIT 1449/2

    37

    (ii) (5,1) P2 4

    (b) (i) (a) V : Reflection in the line x = 3

    Note :

    1. Reflection / Pantulan , award P1

    P2

    (b) W : Enlargement with scale factor1

    2at centre F/ (-3,1)

    Note :

    1. Enlargement with scale factor1

    2// Pembesaran dengan faktor skala

    1

    2

    or Enlargement at centre F (-3,1) // Pembesaran pada pusat F

    (-3,1), award P2

    2. Enlargement // Pembesaran, award P1

    P3 5

    (b) (ii) 22 20.5

    22 20.5 - 20.5

    61.5

    K1

    K1

    N1 3

    12

    14(a)

    Class Upper Frequency Cumulative

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    38/42

    SULIT 1449/2

    38

    intervalSelang kelas

    boundary Sempadan

    atas

    Kekerapan Frequency Kekerapanlonggokan

    15-19 19.5 0 0I 20-24 24.5 2 2II 25-29 29.5 5 7III 30-34 34.5 6 13IV 35-39 39.5 9 22V 40-44 44.5 6 28VI 45-49 49.5 3 31VII 50-54 54.5 1 32

    Upper boundary : (II to VII) P1Frequency : (I to VII) P2Cumulative Frequency : (I to VII) P2 5

    Note :1. Allow two mistakes in frequency for P12. Allow two mistakes in cumulative frequency for P1

    (b) 35-39 P1 1

    (c) Graph1. Axes drawn in correct direction with uniform scales in

    19.5 x 54.5 and 0 y 322. All points correctly plotted and curve passes through using at

    least correct 6 correct upper boundary

    3. Smooth and continuous curve without any straight line passesthrough all correct points using the given scales

    Note :5* points plotted correctly award K1 N0

    P1

    K2

    N1

    4

    (d) (i) 36 37 x P1 1

    (ii) 40.5 41.5 x P1 112

    Graph for Question 14Graf untuk Soalan 14

    CumulativeFrequency

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    39/42

    SULIT 1449/2

    39

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    40/42

    SULIT 1449/2

    40

    15(a)

    Correct shape with prism AEFURB.All solid lines .

    AE=AB>RB>RU=FU>EF

    Measurement correct to 0.2 cm (one way) and all angles at the verticesof rectangles = 90 o 1 o.

    K1

    K1

    N1 3

    15 (b) (i)

    Correct shape with rectangle ADGF, LTSN,FLNR,RSCB.All solid lines .

    CD=AB>AD=BC=FG=RS>FL=RN>ST=FR=JN>GJ=SN

    K1

    K1

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    41/42

    SULIT 1449/2

    41

    Measurement correct to 0.2 cm (one way) and angle A, angle B andangle K= 90 o 1 o.

    N2 4

    15 (b) (ii)

    Correct shape with rectangle REGS and ARSC.All solid lines.

    Note :Ignore dotted line NM and QM.

    N and M as well as Q and M joined with dotted line to form rectangleQRNM

    AE=DH>EG=RS=AC>RN>NS

    Measurement correct to 0.2 cm (one way) and all angle at the verticesof rectangles = 90 o 1 o.

    K1

    K1

    K1

    N2 5

    12

  • 8/8/2019 SPM Sabah Math P2 2010 Q n A_2

    42/42

    SULIT 1449/2

    16 (a) (42 oN, 115 oE) // (42 oU, 115 oT)

    Note :

    1. 42 oN // 42 oU or 115 oE // 115 oT, award P22. 42 o or 115 o, award P1

    P3 3

    (b) (180 o-42 o-42 o)x60=96 x 60=5760 n.m.

    K2

    N1 3

    (c)(ii) 180 60 cos 42 o

    Note : Using cos42 o or * cos42 o , award K1

    8025.96 n.m.

    K2

    N1 3

    (ii) (5760 8025.96)630

    21.88

    K2

    N1 3

    12