PMR Trial 2010 Math Q&A (Swk)

8/8/2019 PMR Trial 2010 Math Q&A (Swk)

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50/1 2010 Hak Cipta Jabatan Pelajaran Sarawak

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2

sides height

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

Rumus-rumus berikut boleh membantu anda menjawab soalan. Simbol-simbol yang diberi adalah yang biasadigunakan.

RELATIONS

PERKAITAN

1. m n m n a a a + =

2. m n m n a a a =

3. ( )n

m mna a=

4. Distance /Jarak = ( ) ( )x x y y + 2 2

2 1 2 1

5. Midpoint /Titik tengah

( )y yx x

x y+ +

=

1 21 2, ,2 2

6. Average speed = distance travelled

time taken

Purata laju = ja rak yang d ila lu i

m a sa y an g d ia m bil

7. Mean = sum of data

number of data

Min = hasil tambah nila i data

bilangan data

8. Pythagoras Theorem /Teorem Pithagoras

c a b= +2 2 2

1. Area of rectangle = length widthLuas segiempat tepat = panjang lebar

2. Area of triangle = 1

2base height

Luas segitiga= 1

2tapak tinggi

3. Area of parallelogram = base heightLuas segiempat selari = tapak tinggi

4. Area of trapezium = 1

2sum of parallel

Luas trapezium = 1

2hasil tambah dua sisi selari tinggi

SHAPE AND SPACE

BENTUK DAN RUANG

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5. Circumference of circle = d = 2r

Lilitan bulatan= d = 2j

6. Area of circle = r2

Luas bulatan = j2

7. Curved surface area of cylinder = 2rhLuas permukaan melengkung silinder = 2jt

8. Surface area of sphere = 4r2

Luas permukaan sfera = 4j2

9. Volume of right prism = cross sectional area length

Isipadu prisma tegak = luas keratan rentas panjang

10. Volume of cuboid = length width height

Isipadu kuboid = panjang lebar tinggi

11. Volume of cylinder = r2h

Isipadu silinder = j2t

12. Volume of cone =3

1 r2h

Isipadu kon=3

1 j2t

13. Volume of sphere =3

4r

3

Isipadu sfera =3

4j

3

14. Volume of right pyramid =3

1 base area height

Isipadu piramid tegak=3

1 luas tapak tinggi

15. Sum of interior angles of a polygon = ( n 2 ) 180o

Hasil tambah sudut pedalaman poligon = ( n 2 ) 180o

16.360

=

Arc length Angle subtended at centre

Circumference of circle

36 0

Panjang lengkok Sudu t pusa t

Lil itan bulatan=

17. =

A rea o f s ec to r A ng le su bte nde d a t ce ntreA rea o f c irc le 3 60

L u a s se k to r S u d u t p u sa t

L u a s b u l a ta n =

3 6 0

18. Scale factor /Faktor skala, PAkPA

='

19. Area of image = k2

area of object

Luas imej = k2

Luas objek

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4

Answerallquestions

Jawab semuasoalan

1 What is the place value of digit 6 in the number 680 912 ?Apakah nilai tempat bagi digit6 dalam nombor680 912 ?

Athousandsribu

B

ten thousands

puluh ribu

Chundred thousandsratus ribu

Dmillionsjuta

2 Which of the following has the smallest value?Antara berikut, yang manakah mempunyai nilai terkecil?

A2

1

B3

2

C

5

6

D8

7

3 Table 1 shows the height of three students.Jadual1 menunjukkan ketinggian bagi tiga orang pelajar.

StudentPelajar

HeightKetinggian

Abu 1m 68cm

Ben 1.72m

Chin 1m 75cm

Table 1Jadual1

What is the total height in metre?Berapakah jumlah ketinggian dalam meter?

A 0.515

B 5.15

C 51.5

D 515

4 Diagram 1 shows a sequence of numbers.Rajah1 menunjukkan suatu urutan nombor

Diagram 1/Rajah1The value of m+ nisNilai m + n ialahA 6

B 4

C 3

D 3

m, 2, n, 4, 7,

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5 A singing competition was supposed to start at 6.50pm but was delayed by3

4hour. What time did the singing competition start?

Satu pertandingan nyanyian dijangka bermula pada 6.50pm tetapi dilewatkan3

4jam. Pada pukul berapakah pertandingan menyanyi itu bermula?

A 7.15 pm

B 7.35 pm

C7.45 pm

D 8.15 pm

6 Find the sum of all the prime numbers between 20 and 30.Cari hasil tambah semua nombor perdana di antara20 hingga30.

A 44

B 50

C 52

D 56

7 Table 2 shows the temperature for three towns P, Qand Rin Australia.Jadual2 menunjukkan suhu bagi tiga buah Bandar P, Q dan R di Australia.

TownBandar P Q R

TemperatureSuhu

11oC 17

oC 26

oC

Table 2Jadual2

Calculate the difference between the highest and the lowest temperature.Kira beza di antara suhu yang tertinggi dengan suhu yang terendah.

A 37oC

B 15oC

C 9oC

D 15oC

8Asiah has 1 kilogramme of sugar. She needs 350g to make a cake and 235g to make pudding. Find themass in g, of the remaining sugar.Asiah ada1 kilogram gula. Dia menggunakan350g untuk membuat kek dan 235g untuk membuatpuding. Cari jisim, dalamg, baki gula itu.A 325

B 415

C 595D 695

9 In Diagram 2, PQRis a straight line.Dalam Rajah2, PQR ialah garis lurus.

Find the value of x.Cari nilai x.

A 10

B 15

C 35

D 85

P

50

Q

R

35

x

Diagram 2Rajah2

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10 Diagram 3 shows a regular octagon with centre O.

Rajah3 menunjukkan sebuah oktagon sekata berpusat O.

Find the value of q.

Cari nilai q.

A 135

B 235

C 330

D 400

11 In Diagram 4, ABCDEFis a regular hexagon. GACand GFE are straight lines.

Dalam Rajah4, ABCDEF ialah sebuah heksagon sekata. GAC and GFE adalah garis lurus.

Find the value of x+ y.

Cari nilai x + y.

A 150

B 180

C 200

D 240

y

Dx A

B C

G F EDiagram 4

Rajah4

A

Diagram 3Rajah3

E

F

G

H

O

D

C

B

q

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12 In Diagram 5, A, B, Cand Dare some of the vertices of a regular polygon. BCEis a straight line.Dalam Rajah5, A, B, C dan D ialah beberapa bucu sebuah poligon sekata. BCE ialah garis lurus.

Find the number of sides of the regular polygon.

Cari bilangan sisi poligon sekata itu.

A 8

B 9

C 10

D 12

13 In Diagram 6, JKLMis a trapezium.Dalam Rajah6, JKLM ialah sebuah trapezium.

Find the perimeter, in cm, of the shaded region.Cari perimeter, dalam cm, bagi kawasan yang berlorek.

A 46

B 48

C 52

D 56

14 Diagram 7 shows a trapezium.Rajah7 menunjukkan sebuah trapezium.

Calculate the area, in cm2

, of the trapezium.

Hitungkan luas, dalam cm2

, trapezium itu.

A 24B 30C 36D 45

Diagram 5Rajah5

A

B C E

D

4xx

10cm

13cm

6cm7cm

K

J

L

M

N

Diagram 6Rajah6

12cm

6 cm

9 cm

4 cm5 cm

Diagram 7Rajah7

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15 Diagram 8 shows two congruent squares ABEFand BCDE.ABFand EBDare two quadrantswithcentres A and Erespectively.Rajah8 menunjukkan dua buah segiempat sama sisi kongruen ABEF dan BCDE.ABF dan EBD adalahdua sukuan dengan pusat A dan E masing-masing.

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

Hitung luas, dalam cm, kawasan yang berlorek. [ Use /Guna =7

22]

A 10.5

B 21

C 22.5

D 25

16 Diagram 9 shows a cuboid.Rajah9 menunjukkan sebuah kuboid.

The area of the shaded face is 120 cm2

. Find the total surface area of the cuboid in cm2

.

Luas bagi permukaan berlorek ialah120 cm2

. Cari jumlah luas permukaan kuboid itu dalamcm2

.

A 700

B 800

C 1000

D 1200

8cm

Diagram 9Rajah9

10 cm

E D

CBA 7 cm

7 cm

FDiagram 8

Rajah8

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17 Diagram 10 shows a composite solid of a cylinder and a hemisphere.

Rajah10 menunjukkan pepejal gabungan sebuah silinder dan sebuah hemisfera.

Given that the diameter of the hemisphere is 12 cm and the length of the cylinder is 10 cm.

Calculate the volume, in cm3, of the composite solid.

Diberi diameter hemisfera ialah12 cm dan panjang silinder itu ialah10 cm.

Hitung isi padu, dalamcm3, pepejal gabungan itu.

A 396

B 408

C 468

D 504

18The distance between two bus stations, Pand Qis 120 km. The bus leaves Pto Qat 0845. If it travelsat an average speed of 80 km/h, calculate the time of its arrival.

Jarak di antara dua stesen bas, PdanQadalah120 km. Sebuah bas meninggalkanPkeQpada pukul0845. Jika ia bergerak dengan purata laju80 km/j, kirakan masa bas itu tiba.

A 1015

B 1115

C 1135

D 1225

19 Diagram 11 shows a cone.Rajah11 menunjukkan sebuah kon.

The radius of the cone is 7 cm and the height is 12 cm. Calculate, in cm3, the volume of water needed to

fill up the cone.Jejari kon itu ialah7 cm dan tingginya ialah12 cm. Hitung, dalamcm

3, isi padu air yang diperlukan untuk

memenuhi kon itu. (Use/Guna 22

7 = )

A 308

B 616

C 1848

D 2002

Diagram 10Rajah10

Diagram 11Rajah11

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20 Diagram 12 shows a circle ABCDwith centre O. ABD= 54and CDB= 22.

Rajah12 menunjukkan sebuah bulatan ABCD berpusatkan O. ABD= 54dan CDB= 22.

Find the value of x.

Cari nilai x.

A 98

B 100

C 102

D 104

21 In Diagram 13, MNOP is a cyclic quadrilateral. OPQand MPRare straight lines.

Dalam Rajah13, MNOP ialah sebuah sisi empat kitaran. OPQ dan MPR ialah garis lurus.

Find the value of z.

Cari nilai bagi z.

A 118

B 62C 59

D 52

B

CA

D

O

x

54

22

Diagram 12Rajah12

N

O

P

Diagram 13Rajah13

R

Q M

z118

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22 In Diagram 14, PQRS is a quadrilateral.Dalam Rajah14, PQRS ialah sebuah sisi empat.


A 40

B 50

C 55

D 110

23 Diagram 15 shows a right angled triangle PQR.Rajah15 menunjukkan sebuah segitiga bersudut tegak PQR.

Calculate the area, in cm, of the shaded region.Hitung luas, dalam cm, kawasan yang berlorek.

A 6

B 8

C 12

D 16

1002x

80

P Q

RS Diagram 14Rajah14

110

Diagram 15Rajah15

P

12 cm

Q R4 cm

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24 In Diagram 16, LKNis a right-angled triangle and NML is a straight line.Dalam Rajah16, LKN ialah segitiga bersudut tegak dan NML ialah garis lurus.

Calculate the length, in cm, of NMHitungkan panjang, dalam cm, NM

A 4

B 5

C 6

D 7

25

The value of x+ y+ z isNilai x + y + z ialah

A 235

B 295

C 305

D 345

N

12 cm9 cm

M

K LDiagram 16

Rajah16

xy

z

55

Diagram 17Rajah17

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26 Diagram 18 shows the graph of a function on a Cartesian plane.

Rajah18 menunjukkan satu graf fungsi pada satah Cartesan.

What is the equation of the function?Apakah persamaan fungsi itu?

A y= 2x + 3

B y= 2x + 3

C y x1

32

= +

D y x1

32

= +

27 Which of the following inequalities has a solution of integer values x= 5, 6, 7, ?

Antara ketaksamaan berikut, yang manakah mempuyai penyelesaiaan nilaiinteger x= 5, 6, 7, ?

A 3x< 15

B 3x> 18

C 3x 3 > 9

D 3x+ 3 > 9

Diagram 18

Rajah18

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28

In the diagram, Qis the midpoint of PR. The values of xand yareDalam rajah, Q ialah titik tengah PR. Nilai untuk x dan y ialah

A x= 4, y= 4

B x= 5, y= 4

C x= 5, y= 5

D x= 6, y= 5

29 Diagram 20 shows three points, P, Q and R on a Cartesian plane.Rajah20 menunjukkan tiga titik P, Q dan R pada suatu satah Cartesian.

If P, Q, Rand Sare vertices of a parallelogram, find a possible coordinates of S.Jika P, Q, R dan S ialah bucu-bucu sebuah segiempat selari, cari koordinat yang mungkin bagi S.

A ( 0, 3 )

B ( 1, 3 )

C ( 1, 4 )

D ( 2, 4 )

P(2, 8)

Q(4, y)

R(x, 2)

x

y0

Diagram 19Rajah19

x

4

-4 40

-4

y

Q

P

R

Diagram 20Rajah20

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30 Diagram 21 shows the arc PQof a circle with centre O.Rajah21 menunjukkan lengkok PQ bagi sebuah bulatan berpusat O.

Calculate the length, in cm, the major arc PQ.Hitung panjang, dalam cm, lengkok major PQ.

[Use / Guna7

22= ]

A 33

B 44C 55

D 66

31 Diagram 22 shows two similar triangles PQRand STU.Rajah22 menunjukkan dua segitiga serupa, PQR dan STU.


A 8

B 9

C 11

D 12

32 The mass of box Pis 250 g and the mass of box Qis 1 kg 50 g.State the ratio of mass Pto mass Q.Jisim kotak P ialah250g dan jisim kotak Q ialah1 kg 50 g.Nyatakan nisbah jisim P kepada jisim Q.

A 1 : 2

B 1 : 6

C 5 : 3

D 5 : 21

QR

20 cm

P

S

U Txcm

5cm

3 cm

Diagram 22Rajah 22

150

O

P

Q

18cm

Diagram 21Rajah21

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1633 Diagram 23 is a bar graph showing the number of visitors at a museum for the first 5 month of the year.

Rajah23 ialah carta palang yang menunjukkan bilangan pelawat bagi 5 bulan pertama dalam satu tahun.

The number of visitors in January is 400 people. What is the difference between the highest number of

visitors and the lowest number of visitors?

Bilangan pelawat bagi bulan Januari ialah 400 orang. Berapakah perbezaan antara bilangan pelawattertinggi dengan bilangan pelawat terendah?

A 480

B 720

C 1200

D 1440

34 Table 3 shows the number of students from five towns. All the information in the table is represented inDiagram 24.Jadual3 menunjukkan bilangan pelajar dari lima buah bandar. Semua maklumat ditunjukkan dalam

Rajah24.

Which sectors are correct?Sektor-sektor yang manakah adalahbetul?

Town No. of students

A 10

B 8

C 5

D 7

E 6

A A and B

B B and C

C A and D

D D and E

B

CD

E

A100

4070

120

30

Diagram 24Rajah24

Table 3Jadual3

Jan April MayMacFeb

Numberofpeop

le

Bilanganorang

MonthBulan

Diagram 23Rajah23

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35 Table 4 shows the number of Hari Raya cards received by a group of student.Jadual4 menunjukkan bilangan kad Hari Raya yang diterima oleh sekumpulan pelajar.

Number of cardsBilangan kad

5 6 7 8 9

Number of studentsBilangan pelajar

4 5 6 3 2

Find the median.Cari median.

A 6

B 6.5

C 7

D 7.5

36 Table 5 shows the students scores in a game.Jadual5 menunjukkan skor pelajar-pelajar dalam suatu permainan.

Score /Skor 0 1 2 3 4

Frequency/Kekerapan 3 6 4 4 3

Find the mean score.Cari skor min.

A 1.9

B 2.1

C 2.9

D 3.1

37 In Diagram 25, which of the lines marked A, B, Cand Drepresents the image of Wunder the translation

4

3

?

Dalam Rajah25, di antara garis bertandaA, B, CdanDyang manakah mewakili imej bagiWdi bawah

translasi4

3

?

.

Table 4Jadual4

Table 5Jadual5

W

A

B

C

D

Diagram 25Rajah25

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1838 The triangles are drawn on square grids as shown in Diagram 26.

Segitiga-segitiga dilukis pada petak segi empat sama seperti yang ditunjukkan dalam Rajah26.

Which of the image A, B, C or D is notan image of T under certain reflections?Di antara imejA, B, C atauD, yang manakahbukanimej bagiT di bawah pantulan tertentu?

39Given that y = 3x

2

x + 6, calculate the value of ywhen x= 3.Diberi bahaway = 3x

2x+ 6 , kirakan nilaiyapabila x = 3.

A 12

B 27

C 30

D 36

T

AB

C

D

Diagram 26Rajah26

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40 Which of the following is the locus of a point xthat moves such that its perpendicular distance from the

line ABis always 5 cm?

Antara berikut, yang manakah lokus bagi satu titik x yang bergerak dengan keadaan jarak tegaknyasentiasa5 cm dari garis AB?

A

B

C

D

5 cm5 cm

A

B

xx

5 cmA B

x

A

B

5 cm

5 cm

x

A

B

5 cm 5 cm

5 cm 5 cm

x

x

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SULIT 2 50/2

50/2 2010 Hak Cipta JABATAN PELAJARAN SARAWAK SULIT

sides height

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

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

digunakan.

RELATIONSPERKAITAN

1.m n m n

a a a+

=

2.m n m n a a a =

3. ( )n

m mna a=

4. Distance /Jarak = ( ) ( )x x y y + 2 2

2 1 2 1

5. Midpoint /Titik tengah

( )y y

x xx y+ +

=

1 21 2, ,2 2

6. Average speed = distance travelled

time taken

Purata laju = ja rak yang d ila lu i

m a sa y an g d ia m bil

7. Mean = sum of data

number of data

Min = hasil tambah nila i data

bilangan data

8. Pythagoras Theorem /Teorem Pithagoras

c a b= +2 2 2

1. Area of rectangle = length widthLuas segiempat tepat = panjang lebar

2. Area of triangle = 1

2base height

Luas segitiga= 1

2tapak tinggi

3. Area of parallelogram = base heightLuas segiempat selari = tapak tinggi

4. Area of trapezium = 1

2sum of parallel

Luas trapezium = 1

2hasil tambah dua sisi selari tinggi

SHAPE AND SPACEBENTUK DAN RUANG

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50/2 2010 Hak Cipta JABATAN PELAJARAN SARAWAK [Lihat sebelah

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5. Circumference of circle = d = 2r

Lilitan bulatan= d = 2j

6. Area of circle = r2

Luas bulatan = j2

7. Curved surface area of cylinder = 2rh

Luas permukaan melengkung silinder = 2jt

8. Surface area of sphere = 4r2

Luas permukaan sfera = 4j2

9. Volume of right prism = cross sectional area length

Isipadu prisma tegak = luas keratan rentas panjang

10. Volume of cuboid = length width height

Isipadu kuboid = panjang lebar tinggi

11. Volume of cylinder = r2h

Isipadu silinder = j2t

12. Volume of cone =3

1 r2h

Isipadu kon=3

1 j2t

13. Volume of sphere =3

4r

3

Isipadu sfera =

3

4j

3

14. Volume of right pyramid =3

1 base area height

Isipadu piramid tegak=3

1 luas tapak tinggi

15. Sum of interior angles of a polygon = ( n 2 ) 180o

Hasil tambah sudut pedalaman poligon = ( n 2 ) 180o

16.360

=

Arc length Angle subtended at centre

Circumference of circle

360

Panjang lengkok Sudut pusat

Lilitan bulatan=

17.=

A re a o f s ec to r A ng le s ub te nd ed a t c en tre

A re a o f c irc le 36 0

L u a s s e k to r S ud u t p u sa t

L u a s b u l a ta n =

3 6 0

18. Scale factor /Faktor skala, PAkPA

='

19. Area of image = k2

area of object

Luas imej = k2

Luas objek

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ForExaminers

Use

1

Answerallquestions.Jawabsemuasoalan.

Calculate the value of14

9 (

5

1+

4

1) and express the answer as a fraction in its

lowest term.

Hitungkan nilai bagi14

9 (

5

1 +

4

1) dan ungkapkan jawapannya sebagai satu

pecahan terendah.

Answer /Jawapan:

[3 marks][3 markah]

2 Calculate the value ofHitungkan nilai bagi

7.38

0.2 0.3

Answer /Jawapan:

[2 marks][2 markah]

3 (a) Find the value of (0.7 )Carikan nilai bagi(0.7 )

(b)Calculate the value of

3

2 128

Hitungkan nilai bagi3

2 128

[3 marks][3 markah]

Answer /Jawapan:

(a)

(b)

1

3

2

2

3

3

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4 In Diagram 4, ABCand PQRare similar. Given that 2

5=

AB

PQ, calculate the length in

cm, of PR.

Dalam Rajah4, ABC danPQR adalah serupa. Diberi 2

5=

AB

PQ, kira panjang, dalam

cm, bagi PR.

[2 marks][2 markah]

ForExaminers

Use

Answer /Jawapan:

5 In Diagram 5, ABCand BDEare right-angled triangles. Dis the midpoint of AB.Dalam Rajah 5, ABCdan BDE ialah segi tiga bersudut tegak. D ialah titik tengah garisAB.

Given that BC= 13 cm.Diberi BC=13 cm.(a) Find the value of tan x.

Cari nilai bagi tan x.(b) Calculate the length, in cm, of DE.

Hitung panjang, dalamcm, bagi DE.

[3 marks]

[3 markah]Answer /Jawapan:(a)

(b)

A

100C

B

40

8 cm

R

Q

100

40

P

Diagram 4Rajah4

Diagram 5Rajah5

4

2

5

3

5 cmA C

B

=

= E

D

Xo

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SULIT 6 50/2


ForExaminers

Use

6 Diagram 6 in the answer space shows two quadrilaterals Pand Q, which are drawn ona Cartesian plane. Qis the image of Punder a rotation.Rajah6 di ruang jawapan menunjukkan dua buah sisi empat P dan Q, yang dilukispada satah Cartesan. Q ialah imej bagi P di bawah suatu putaran.

(a) State the angle and direction of rotation.

Nyatakan sudut dan arah putaran itu.

(b) Mark point Kas the centre of rotation.Tandakan titik K sebagai pusat putaran.

[3 marks][3 markah]

Answer /Jawapan:

(a)

(b)

Diagram 6Rajah6

6

3

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SULIT 7 50/2


SULIT

7 Diagram 7 shows ABCand its image PQRunder an enlargement at centre S.Rajah7 menunjukkanABC dan imejnyaPQR di bawah satu pembesaran di pusat S

ForExaminers

Use(a) Mark the centre of enlargement S.

Tandakan pusat pembesaran S.

(b) State the coordinates of S.Nyatakan koordinatS.

[2 marks][2 markah]

Answer /Jawapan:

(a)

(b)

8 Simplify each of the following expressions:Permudahkan tiap-tiap ungkapan berikut:

(a)3 ( p+ 2 )

(b) 4 ( 2p 3 ) + ( p 2 )2

[3 marks][3 markah]

Answer /Jawapan:

(a)

(b)

Diagram 7Rajah7

R Q

CB

AP

0x

108642

2

4

6

8

10

y

8

3

7

2

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SULIT 8 50/2


9 Factorise completely each of the following expressions:Faktorkan selengkapnya tiap-tiap ungkapan berikut:

ForExaminers

Use(a)

18 12t

(b) 75p2

12[3 marks]

[3 markah]

Answer /Jawapan:

(a)

(b)

10 Diagram 10 shows a regular pentagon PQRST. J, K, L, Mand Nare the midpoints ofQR, PQ, PT, STand SRrespectively. W, Yand Zare three moving points in thediagram.Rajah10 menunjukkan sebuah pentagon PQRST. J, K, L, M dan N ialah titik tengahbagi QR, PQ, PT, ST dan SR masing-masing. W, Y dan Z adalah tiga titik yangbergerak dalam rajah itu.(a) Wis a point which moves such that it is equidistant from PTand PQ. By using

the letters in the diagram, state the locus of W.W adalah satu titik yang bergerak dengan keadaan sama jarak dari PT dan PQ.Dengan menggunakan huruf-huruf dalam rajah, nyatakan lokus W.

(b) In Diagram 10, draw

Pada Rajah10, lukis

(i) the locus of Ysuch that YP= PT.

lokus Y supaya YP = PT.(ii) the locus of Zsuch that it is equidistant from point Pand point S.

lokus Z supaya jaraknya sentiasa sama dari titik P dan titik S.

(c) Hence, mark with the symbol the intersection of the loci of Yand Z.

Seterusnya, tandakan dengan simboltitik persilangan lokus Y dan lokus Z itu.

[4 marks][4 markah]

Answer /Jawapan:

(a)

(b) (i), (ii), (c)

J

Q

RS

T

K

P

N

M

L

Diagram 10Rajah10

10

4

9

3

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SULIT 9 50/2


SULIT

A

B

11 (a) Diagram 11.1 shows a triangle EFG.Rajah11.1 menunjukkan sebuah segi tiga EFG.

Measure EFGusing a protractor.Ukur EFG menggunakan protraktor.

ForExaminers

Use

(b) Diagram 11.2 shows triangle ABC. Using only a ruler and a pair of compasses,constructRajah11.2 menunjukkan segi tiga ABC. Menggunakan pembaris dan jangkalukis sahaja, bina

(i) the triangle ABC, beginning from the straight line ABprovided in the answerspace.segi tiga ABC, bermula dari garis lurus AB yang disediakan di ruangjawapan.

(ii) the perpendicular line BDto the straight line ACfrom the point B.

garis serenjang BD kepada garis lurus AC yang dari titik B.

[5 marks]

[5 markah](c) Measure the length, in cm, of BD.

Ukur panjang, dalamcm, bagi BD.

Answer /Jawapan:

(a)

(b) (i), (ii)

Diagram 11.2Rajah11.2

A

B

7

30

C

F

G

Diagram 11.1Rajah11.1

E

11

5

(c)

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SULIT 10 50/2


ForExaminers

Use

12Express 4 1

3 12

+

x

xy yas a single fraction in its simplest form.

Ungkapkan 4 1

3 12

+

x

xy y sebagai satu pecahan tunggal dalam bentuk termudah. [3 marks]

[3 markah]

Answer /Jawapan:

13 Given that3

22

+ =

qp , express qin terms of p.

Diberi bahawa3

22

+ =

qp , ungkapkan q dalam sebutan p.

[3 marks][3 markah]

Answer /Jawapan:

14 Solve :Selesaikan:

(a) x 2 = 3

(b)

3

42

+=

xx

[3 marks][3 markah]

Answer /Jawapan:

(a)

(b)

12

3

13

3

14

3

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SULIT 11 50/2


SULIT

15 Simplify each of the following:Permudahkan tiap-tiap yang berikut:

(a)(2 k

3)

3

ForExaminers

Use

(b) b b

b

5 3

4

[3 marks][3 markah]

Answer /Jawapan:

(a)

(b)

16 (a) Find the value of

Cari nilai bagi

4 52 2

(b)Given that

n 13 81+ = , calculate the value of n.

Diberin 13 81+ = , cari nilai n.

[3 marks][3 markah]

Answer /Jawapan:

(a)

(b)

15

3

16

3

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SULIT 12 50/2


4 m

12 m

8 m

ForExaminers

Use

17 Given 4y 1 7 and y is an even number which is less than 9, l ist all the integervalues of y.Diberikan 4y 1 7 dan y ialah nomber genap yang kurang daripada9,senaraikan semua nilai integer bagi y.

[3 marks][3 markah]

Answer /Jawapan:

18 Diagram 18 shows a polygon. On the 1cm square grid below, redraw the polygonusing the scale 1:200.Rajah18 menunjukkan sebuah poligon. Lukis semula poligon itu pada grid segiempat sama bersisi1 cm menggunakan skala1:200.

[ Assume 1 unit = 1 cm ][ Anggap1 unit= 1 cm ]

[2 marks][2 markah]

Answer /Jawapan:

17

3

4 m

Diagram 18Rajah18

18

2

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SULIT 13 50/2


SULIT

19 Diagram 19 is a pie chart which shows the hobbies of 120 students in a school.Rajah19 ialah carta pai yang menunjukkan hobi bagi120 orang pelajar di sebuahsekolah.

ForExaminers

Use

(a) Find the value of x.Cari nilai bagi x.

(b) Calculate the angle of the sector representing the students playing badminton.Hitung sudut sektor yang mewakili pelajar yang bermain badminton.(c) State the mode of the data.

Nyatakan mod bagi data itu.[3 marks]

[3 markah]Answer /Jawapan:(a)

(b)

(c)

20 Use the graph paper on page 14 to answer this question.Gunakan kertas graf di mukasurat14 untuk menjawab soalan ini.Table 20 shows the values of two variables, xand y, of a function.Jadual20 menunjukkan nilai-nilai dua pembolehubah, x dan y, bagi suatu fungsi.

x 3 2 1 0 1 2 3

y 31 11 1 5 1 11 31

Table 20Jadual 20

The x-axis and the y-axis are provided on the graph paper.Paksi-x dan paksi-y telah disediakan pada kertas graf.(a) By using a scale of 2 cm to 5 units, complete and label the y-axis.

Dengan menggunakan skala2 cm kepada5 unit, lengkap dan labelkan paksi-y.(b) Based on the Table 20, plot all the points on the graph paper.

Berdasarkan Jadual20, plot semua titik pada kertas graf itu.(c) Hence, draw the graph of function.

Seterusnya, lukiskan graf fungsi itu.[4 marks]

[4 markah]

19

3

PlayingTennisBermain Tenis

Playing SoccerBermain Bola Sepak

Diagram 19Rajah19

5

Playing BadmintonBermain Badminton

CyclingBerbasikal

ReadingMembaca

202x

5

25

30

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SULIT 14 50/2


yFor

ExaminersUse

END OF QUESTION PAPER

KERTAS SOALAN TAMAT

1230

2 313 2 1 0 1 2 3

Answer /Jawapan(a), (b), (c)

20

4

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SULIT 15 50/2


SULIT

INFORMATION FOR CANDIDATESMAKLUMAT UNTUK CALON

1. This question paper consists of 20 questions.

Kertas soalan ini mengandungi20 soalan.

2. Answer all questions.

Jawabsemua soalan.

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

Tulis jawapan anda pada ruang yang disediakan dalam kertas soalan ini.

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

Tunjukkan langkah-langkah penting dalam kerja mengira anda. Ini boleh membantu anda untuk mendapatkanmarkah.

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

Jika anda hendak menukar jawapan, batalkan jawapan yang telah dibuat. Kemudian tulis jawapan yang baru.

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

Rajah yang mengiringi soalan tidak dilukis mengikut skala kecuali dinyatakan.

7. The marks allocated for each question are shown in brackets.

Markah yang diperuntukkan bagi setiap soalan ditunjukkan dalam kurungan.

8. A list of formulae is provided on pages 2 to 3.

Satu senarai rumus disediakan di halaman2 hingga3.

9. The usage of calculator is not allowed.

Penggunaan kalkulatortidak dibenarkan.

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

Serahkan kertas soalan ini kepada pengawas peperiksaan pada akhir peperiksaan.

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1

JABATAN PELAJARAN SARAWAK

PEPERIKSAAN PERCUBAAN PMR 2010

Answers For Mathematics Paper 1

Question Answer Question Answer

1 C 21 B

2 A 22 C

3 B 23 A

4 B 24 C

5 B 25 C

6 C 26 D

7 D 27 C

8 B 28 D

9 B 29 B

10 A 30 D

11 B 31 D

12 C 32 D

13 A 33 A

14 B 34 C

15 B 35 C

16 A 36 A

17 D 37 A

18 A 38 D

19 B 39 D

20 D 40 A

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2

JABATAN PELAJARAN SARAWAK

PEPERIKSAAN PERCUBAAN PMR 2010

Marking Scheme For Mathematics Paper 2

Question Scheme Marks

1 9 1 1

14 5 4

9 4 514 20 20

9 9

14 20

9 20

14 9

10=

14

10=

7

3=1

7

+

= +

=

=

1

1

1 3

2 7.38

0.2 0.3

7.38

0.06

738

6

123

=

=

=

1

1 2

3 (a) 0.493

2

3

3

1( ) 2

8

14

8

1

2

18

b

=

=

=

1

1

1 3

Note :

See

4 5

20

+

or

9

20 award 1 mark

Note:

See 0.06 or738

6award 1 mark

Note:

see1

2, award 1 mark

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3



48 2

5

2 8 5

40

2

20

PR

PR=

PR=

PR

=

=

1

1 2

5(a)

5

12

5 13

6

13 5 6

30

13

42

13

bDE

DE =

DE =

DE

( ) =

=

1

1

1 3

6 (a) 90o clockwise direction 2

1 3

Note : Also accept

PR = 4 5}PR=20

1 mark8 2 = 4

1 mark

Note:

Also accept 2.3 .

(b) The point Kplotted correctly.

K

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4



7 (a)

S as seen or any 2 or 3 intersecting lines at S

(b) (10,10 )

1

1 2

8 (a) 3p + 6

(b) 4 ( 2p 3 ) + (p 2 )

= 8p 12 + (p 2 ) ( p 2 )

= 8p 12 + p 2 2p 2 p + 4 or 8p 12 + p 2 4p + 4

= p2 + 4 p 8

1

1

1 3

9 (a) 6 ( 3 2t)

(b) 3 ( 25p2

4 )

= 3 ( 5p + 2 )( 5p 2 )

1

1

1 3

R Q

CB

AP

0x

108642

2

4

6

8

10

y

S

Note :

See 8p 12 or p2

4p + 4 award 1 mark

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5


10

1

1

1

1 4

11 (a) 70o 1o

(b)

30A

B

C

1

1

1

1

1 5

Construct a 30o

angle atA correctly

Construct point Ccorrectly.

Construct the triangleABCcorrectly..

Construct the perpendicular line BD fromB toACcorrectly.

BD = 3.0 ( 0.1) cm

J

N R

M

S

L

T

K

P

Q

(a) The straight line PN(b) (i) Locus Ydrawn

Correctly(ii) LocusZdrawn

Correctly

(c) Intersection of locus YandlocusZmarked correctly ( )

locus Y

locus Z

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6



12 4 1

3 12

4( 4) (1)

12

x

xy y

x x

xy

+

+ =

=

4 16

12

x x

xy

+

=3 16

12

x

xy

+

or

12 ( 4) 3 (1)

3 (12 )

y x xy

xy y

+

=2

12 48 3

36

xy y xy

xy

+

=2

9 48

36

xy y

xy

=2

3 ( 3 16 )

36

y x

xy

=3 16

12

x

xy

+

1

1

1 3

13

+ =

= +

+ =

=

=

q

pp q

q p

q p

q p

3

2 22 4 3

3 2 4

2 3 4

2 7

1

11

3

14 (a)x 2 = 3x = 2 3

x = 11

1

1 3

Note : See 2p 4 award 1 mark

1 mark

1 mark

1 mark

4b 23

3 6 4

3 6 4

2 10

x+x =

x =x+

x x

x

x=5

= +

=

( )

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7



15 (a) 8k9

5 3

4

5 3 4

5 3 4

6

b bb

b

b

b

b

( ) ( )

( )

+

+

=

=

=

1

1

1 3

16(a)

1

2

(b) 3n+1

= 81

3n+1

= 34

Hence,n+1 = 4

n = 4 1

n = 3

1

1

1

3

17 4 1 7y 4 7 1y +

4 8y

8

4

y

2y

y = 2 , 4 , 6 , 8

1

2 3

18

2

2

Note :

Any three integers correct, award 1 mark

Image draw correctly

Note :

3 or 4 sides drawn

correctly, award 1

mark

c m c m

c m c m

c m c m

11 2 0 0 6

2 0 0

14 0 0 2

2 0 0

18 0 0 4

2 0 0

=

=

=

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8



19

1

1

1 3

20 The y-axis is drawn with the correct scales.

All the points plotted correctly.

The curve is drawn correctly. ( Passing through all the points )

1

2

1 4

Note :

5 or 6 points plotted correctly, award 1 mark

(a) 2x = 120 5 20 30 25 or 80 + 2x = 120

2x = 40

x = 40

2

x = 20

(b)20

360120

= 60o

(c) Reading

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Answer for question 20

y

-2-3 x0 2 31

5

5

10

15

20

25

30

35

-1

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PMR Trial 2010 Math Q&A (Swk)

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Transcript of PMR Trial 2010 Math Q&A (Swk)