SULIT 1449/

1449/2 [Lihat sebelah

SULIT

JABATAN PELAJARAN NEGERI SABAH

SIJIL PELAJARAN MALAYSIA 1449/2

EXCEL

MATHEMATICS Paper 2

2 Hours 30 Minutes Two hours and thirty minutes

JANGAN BUKA KERTAS SOALAN INI

SEHINGGA DIBERITAHU

1. Tulis nombor kad pengenalan dan

angka giliran anda pada ruangan

yang disediakan.

2. Kertas soalan ini adalah Bahasa

Ingerís.

3. Calon dikehendaki membaca

maklumat di halaman 2.

Kod Pemeriksa

Bahagian Soalan Markah

Penuh

Markah

Diperolehi

A

1 3 2 4 3 4 4 5 5 3 6 6 7 5 8 5 9 7 10 4 11 6

B

12 12 13 12 14 12 15 12 16 12

Jumlah

Kertas soalan ini mengandungi 29 halaman bercetak.

NAMA : _______________________________

KELAS : ______________________________

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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 the

new 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.

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MATHEMATICAL FORMULAE

RUMUS MATEMATIK

The following formulae may be helpful in answering the questions. The symbols given are the ones commonly

used.

Rumus-rumus berikut boloeh membantu anda menjawab soalan. Simbol-simbol yang diberi adalah yang biasa

digunaan.

1 nmnm aaa

2 nmnm aaa

3 mnnm aa )(

4

ac

bd

bcadA

11

5 Distance/ jarak

= 2

21

2

21 )()( yyxx

6 Midpoint/ Titik tengah

2,

2),( 2121 yyxx

yx

7

8 Mean = data ofnumber

data of sum

9 Mean = sfrequencie of sum

frequency)mark class ( of um s

10 Pythagoras Theorem /

Teorem Pithagoras

222 bac

11

12 )(1)'( APAP

13 12

12

xx

yym

14 erceptx

erceptym

int

int

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SHAPES AND SPACE

1 Area of trapezium = height s2

1 sidesparallelofum

Luas trapezium =

2 Circumference of circle = rd 2

Lilitan bulatan = d = 2j

3 Area of circle = 2r

Luas bulatan = j2

4 Curved surface area of cylinder = rh2

Luas permukaan melengkung silinder = 2jt

5 Surface area of sphere = 24 r

Luas permuaan sfera = 4j2

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 = 3

3

4r

Isipadu sfera = 3

3

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

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12 360

centreat subtended angle

circle ofncecircumfere

length arc

13 360

centreat subtended angle

circle of area

sector of area

14 Scale factor, PA

PAk

'

Faktor skala, k =

15 Area of image = 2k area of object

Luas imej = k2 luas objek

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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 universal

set, = J LK .

Gambar rajah Venn di ruang jawapan menunjukkan set J, set K and set L dengan

keadaan set semesta = J LK .

On the diagram in the answer space, shade

Pada 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

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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

qp

qp

[ 4 marks]

[4 markah]

Answer/Jawapan :

3 Using factorization, solve the following quadratic equation.

Menggunakan pemfaktoran, selesaikan persamaan kuadratik berikut.

)1(322 2 xx

[4 marks]

[4 markah]

Answer/Jawapan:

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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.

y

S

R ( 6, 1)

x

O

P ( -1,-2)

Q ( 4, - 3)

Diagram 4

Rajah 4

Find

Cari

(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 marks ]

[ 5markah]

Answer/Jawapan :

(a)

(b)

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

angled triangle.

Rajah 5 menunjukkan sebuah piramid. Tapak segiempat tepat JKLM adalah mengufuk dan VL adalah

menegak. 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 marks]

[3 markah]

Answer/Jawapan :

(a)

(b)

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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 π =7

22, calculate

Dengan menggunakan π =7

22, hitung

(a) the area, in cm2, of the whole diagram,

luas, dalam cm2, seluruh rajah itu,

(b) the perimeter, in cm, of the whole diagram.

perimeter, dalam cm, seluruh rajah itu. [6 marks]

[6 markah]

Answer/Jawapan :

(a)

(b)

D

C

B

A

O E

14cm

7cm

36o

104o

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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 regular

octagon.

Diberi bahawa jumlah sudut pedalaman sebuah polygon sekata dengan n sisi ialah 0( 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:: …………………………………………………………………………

…………………………………………………………………………………………………

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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 that

Senaraikan 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

7 6 5 3 2 8

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9. The inverse of

3 2

6 7

is 7 21

2 3mk

Matrix songsang bagi 3 2

6 7

ialah 7 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 matriks

berikut:

3 2 1

6 7 8

x

y

[7 marks]

[7 markah]

Answer/Jawapan:

(a)

(b)

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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 ] [10

marks]

[10 markah]

Answer/Jawapan :

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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 travel

along the same road.

Graf ABCD mewakili perjalanan lori dari bandar Y ke bandar X. Graf PQ mewakili perjalanan taxi dari

bandar 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 itu

bertemu?

(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 markah]

Answer/Jawapan:

(a)

(b)(i)

(b) (ii)

(c)

Time / Masa

(min)

Town Y

Bandar Y 60

40

0 10 25 50 80

A

B C

D

Q

P

Town X

Bandar X

Distance/ Jarak

(km)

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Section B

Bahagian 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

12y

x by writing down the values of y

when x = –2 and x = 3.5. [2 marks]

Lengkapkan Jadual 12 di ruang jawapan bagi persamaan

12y

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

12y

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

yx

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 equation 24 12 0x 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 0x untuk . .

Nyatakan nilai-nilai x ini. [4 markah]

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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 = …………………… , ……………………………….

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Graph for Question 12

Graf untuk Soalan 12

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

Transformation T is a translation 2

2

.

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

Penjelmaan T ialah translasi 2

2

.

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) T2

(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 satah

Cartesan.

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

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20

[5 markah]

(ii) It is given that the region FMNPQ represents a region of area 20.5 m2.

Calculate the area, in m2, of the shaded region.

Diberi bahawa kawasan FMNPQ mewakili luas 20.5 m2.

Hitung luas, dalam m2, kawasan berlorek.

Answer / Jawapan :

(a) (i)

(ii)

(b) (i) (a) V :

(b) W :

(ii)

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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, draw

an 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]

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Answer / Jawapan :

(a)

Class

interval

Selang kelas

Upper

boundary

Sempadan

atas

Frequency

Kekerapan

Cumulative

Frequency

Kekerapan longgokan

15-19 19.5 0 0

20-24 24.5

25-29

30-34

35-39

40-44

45-49

50-54

Table 14

Jadual 14

(b)

(c) Refer graph on page 24.

Rujuk graf di halaman 24.

(d) (i)

(ii)

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Graph for Question 14

Graf untuk Soalan 14

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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. The

surface ABRUFE is the uniform cross-section of the prism. The rectangle RBCS is an incline

plane. 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 rentas

seragamnya. 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 AB

sebagaimana dilihat dari X.

[3 marks]

[3 markah]

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25

Answer/Jawapan :

(a)

(b) A solid cuboid of length 4cm, width 3cm and height 2cm is removed from the prism and the

remaining solid is shown in Diagram 15(ii). PQML is a horizontal plane. FP, JL, NM and RQ are

vertical edges.

Sebuah pepejal berbentuk kuboid dengan panjang 4cm, lebar 3cm dan tinggi 2cm, dikelaurkan

daripada prisma itu . Pepejal yang tinggal seperti ditunjukkan pada Rajah 15(ii). PQML ialah

satah mengufuk. Tepi FP, JL, NM dan RQ adalah tegak.

Diagram 15(ii)

Rajah 15(ii)

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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 markah]

Answer/Jawapan :

(b) (i), (ii)

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16 P(42oN, 65

oW), Q and R are three points on the surface of the earth. PQ is the diameter of the parallel of

latitude 42oN. PR is the diameter of the earth.

P(42oU, 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 the

earth,

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 due

south to R.

Sebuah kapal terbang berlepas dari P arah ke timur ke Q sepanjang selarian latitude dan

kemudian 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 630

knot.

[4 marks]

[4 markah]

Answer /Jawapan:

(a)

(b)

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(c) (i)

(c) (ii)

END OF QUESTION PAPER

SOALAN TAMAT

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29

Question Solution and Mark Scheme Marks

1 (a)

(b)

J K

K L

J K

L

P1

P2

3

2

2

12p – 16q = 12 or 9p - 12q= 9 or 24p-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 = 13

4q or q=

4

3

4

3p or p

12

7

2

1 q or q =

6

72 p or

equivalent

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

K1

K1

K1

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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

3

1p

2

1q

Note :

2

13

1

q

pas final answer, award N1

K1

K2

N1

N1

4

3 2x2-3x - 5=0

K1

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31

(2x- 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

or

5

1

=

1 = * (6)SRM c or equivalent

y = 5

11

5

1 x or equivalent

P1

K1

N1

4(b) 0 =

1 11

5 5x or equivalent

11

K1

N1

5

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32

5(a)

(b)

6(a)

(b)

Identify KVL or LVK

tan KVL = 3

5 or equivalent

59.04 or 592’

777

22

360

220 or

36 2214 14

360 7

777

22

360

220 +

36 2214 14

360 7

32155

45 cm

2 or

7007

45 cm

2 or 155.71 cm

2

77

222

360

220 or

36 222 14

360 7

77

222

360

220 +

36 222 14 14 7 7

360 7

3163

45cm or

2866

45 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

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 = -6

m= -3

7 2 11

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

x

y

1

2

x

y

x = -1

y = 2

P1

P2

K2

N1

N1

7 (a)

(b)

(c)

True

0(8 2) 180

1080o

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

P1

P1

N1

K2

5

5

7

SULIT 1449/2

34

Note:

1. * 1

8

x inverse

y matrix

or

7 2 11

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

seen, award K1

2. Do not accept *inverse

matrix

=3 2

6 7

or 1 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 1 223.5 3.5 6

2 3 7 OR

1 223.5 3.5 12

2 7

1 223.5 3.5 12

2 7 -

1 1 223.5 3.5 6

2 3 7

96.25 cm3 @ 96 cm

3

K1

K2

N1

4

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

N1

6

12(a) (a) 6

K1

SULIT 1449/2

35

3.43

K1 2

(b) Graph

1. Axes drawn in correct direction with uniform scales in

−3 ≤ x ≤ 4 and −12 ≤ y ≤ 8

2. All 6 points and *2 points correctly plotted or curve passes

through all the points for −3 ≤ x ≤ 4

3. 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 5.1y , and

x = -1.2 1.1 1.3x

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 24y x

Straight line 24y x correctly drawn

(Check any two points (-1,4), (0,0), (1,-4),……)

1.65 1.85x

1.85 1.65x

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

SULIT 1449/2

36

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

y

x

8

-8

-10

-12

Graph for Question 12

Graf 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

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 factor

1

2 at centre F/ (-3,1)

Note :

1. Enlargement with scale factor 1

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

SULIT 1449/2

38

interval

Selang

kelas

boundary

Sempadan

atas

Kekerapan Frequency

Kekerapan

longgokan

15-19 19.5 0 0

I 20-24 24.5 2 2

II 25-29 29.5 5 7

III 30-34 34.5 6 13

IV 35-39 39.5 9 22

V 40-44 44.5 6 28

VI 45-49 49.5 3 31

VII 50-54 54.5 1 32

Upper boundary : (II to VII) P1

Frequency : (I to VII) P2

Cumulative Frequency : (I to VII) P2 5

Note :

1. Allow two mistakes in frequency for P1

2. Allow two mistakes in cumulative frequency for P1

(b) 35-39

P1 1

(c) Graph

1. Axes drawn in correct direction with uniform scales in

19.5 ≤ x ≤ 54.5 and 0 ≤ y ≤ 32

2. 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 passes

through all correct points using the given scales

Note :

5* points plotted correctly award “K1 N0”

P1

K2

N1

4

(d) (i) 36 37x P1

1

(ii) 40.5 41.5x P1 1

12

Graph for Question 14

Graf untuk Soalan 14

Cumulative

Frequency

SULIT 1449/2

39

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 vertices

of rectangles = 90o ± 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

SULIT 1449/2

41

Measurement correct to ± 0.2 cm (one way) and angle A, angle B and

angle K= 90o ± 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 rectangle

QRNM

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

Measurement correct to ± 0.2 cm (one way) and all angle at the vertices

of rectangles = 90o ± 1

o.

K1

K1

K1

N2

5

12

SULIT 1449/2

42

16 (a) (42oN, 115

oE) // (42

oU, 115

oT)

Note :

1. 42oN // 42

oU or 115

oE // 115

oT, award P2

2. 42o or 115

o, award P1

P3 3

(b) (180o-42

o-42

o)x60

=96 x 60

=5760 n.m.

K2

N1

3

(c)(ii) 180 60 cos42o

Note : Using cos42o or * cos42o , award K1

8025.96 n.m.

K2

N1

3

(ii) (5760 8025.96)

630

21.88

K2

N1

3

12