Peperiksaan Percubaan Maths Paper 1 PMR · Cari hasil tambah semua nombor perdana di antara 20 hingga 30. A 44 B 50 ... Kira beza di antara suhu yang tertinggi dengan suhu yang terendah

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SULIT 50/1

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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 biasa digunakan.

RELATIONS

PERKAITAN

1. m n m na a a +× =

2. m n m na 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 = jarak yang dila lu i

masa yang diambil

7. Mean = sum of data

number of data

Min = hasil tambah nilai data

bilangan data

8. Pythagoras’ Theorem / Teorem Pithagoras

c a b= +2 2 2

1. Area of rectangle = length × width Luas segiempat tepat = panjang × lebar

2. Area of triangle = ×1

2base × height

Luas segitiga = ×1

2tapak × tinggi

3. Area of parallelogram = base × height Luas 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 = πd = 2πr

Lilitan bulatan = πd = 2πj

6. Area of circle = πr

2

Luas bulatan = πj2

7. Curved surface area of cylinder = 2πrh

Luas permukaan melengkung silinder = 2πjt

8. Surface area of sphere = 4πr

2

Luas permukaan sfera = 4πj2

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 = πr

2h

Isipadu silinder = πj2t

12. Volume of cone = 3

1 πr2h

Isipadu kon = 3

1 πj2t

13. Volume of sphere = 3

4 πr

3

Isipadu sfera =

3

4 πj

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 pusa t

L ilitan bula tan =

°

17. =°

A re a o f se c to r A n g le su b te n d e d a t ce n tre

A re a o f c irc le 3 6 0

L u a s s e k to r S u d u t p u s a t

L u a s b u la ta n=

°

3 6 0

18. Scale factor / Faktor skala, PAk

PA=

'

19. Area of image = k2 × area of object

Luas imej = k2 × Luas objek

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Answer all questions

Jawab semua soalan

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

A thousands ribu

B ten thousands puluh ribu

C hundred thousands ratus ribu

D millions juta

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

A 2

1

B 3

2

C 5

6

D 8

7

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

Student Pelajar

Height Ketinggian

Abu 1m 68cm

Ben 1.72m

Chin 1m 75cm

Table 1 Jadual 1 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. Rajah 1 menunjukkan suatu urutan nombor

Diagram 1/ Rajah 1

The value of m + n is Nilai m + n ialah

A – 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 by 3

4 hour. What time did the singing competition start?

Satu pertandingan nyanyian dijangka bermula pada 6.50pm tetapi dilewatkan

3

4 jam. Pada pukul berapakah pertandingan menyanyi itu bermula?

A 7.15 pm

B 7.35 pm

C 7.45 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 antara 20 hingga 30.

A 44 B 50

C 52

D 56

7 Table 2 shows the temperature for three towns P, Q and R in Australia. Jadual 2 menunjukkan suhu bagi tiga buah Bandar P, Q dan R di Australia.

Town Bandar

P Q R

Temperature Suhu

–11 o

C –17 oC –26

oC

Table 2 Jadual 2

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

A –37 o

C

B –15 o

C

C 9 oC

D 15 o

C

8 Asiah has 1 kilogramme of sugar. She needs 350g to make a cake and 235g to make pudding. Find the

mass in g, of the remaining sugar. Asiah ada 1 kilogram gula. Dia menggunakan 350g untuk membuat kek dan 235g untuk membuat puding. Cari jisim, dalam g, baki gula itu.

A 325

B 415

C 595

D 695 9 In Diagram 2, PQR is a straight line.

Dalam Rajah 2, 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 2 Rajah 2

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10 Diagram 3 shows a regular octagon with centre O.

Rajah 3 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, ABCDEF is a regular hexagon. GAC and GFE are straight lines.

Dalam Rajah 4, 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˚

D x˚

A

B C

G F E

Diagram 4 Rajah 4

A

Diagram 3 Rajah 3

E

F

G

H

O

D

C

B

q°

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12 In Diagram 5, A, B, C and D are some of the vertices of a regular polygon. BCE is a straight line.

Dalam Rajah 5, 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, JKLM is a trapezium. Dalam Rajah 6, 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. Rajah 7 menunjukkan sebuah trapezium.

Calculate the area, in cm2

, of the trapezium.

Hitungkan luas, dalam cm2

, trapezium itu.

A 24 B 30 C 36 D 45

Diagram 5 Rajah 5

A

B C E

D

4x° x°

10cm

13cm

6cm 7cm

K

J

L

M

N

Diagram 6 Rajah 6

12cm

6 cm

9 cm

4 cm 5 cm

Diagram 7 Rajah 7

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15 Diagram 8 shows two congruent squares ABEF and BCDE. ABF and EBD are two quadrants with centres A and E respectively. Rajah 8 menunjukkan dua buah segiempat sama sisi kongruen ABEF dan BCDE. ABF dan EBD adalah dua sukuan dengan pusat A dan E masing-masing. Calculate the area, in cm², of the shaded region.

Hitung luas, dalam cm², kawasan yang berlorek. [ Use / Guna π = 7

22 ]

A 10.5

B 21

C 22.5

D 25

16 Diagram 9 shows a cuboid. Rajah 9 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 ialah 120 cm2

. Cari jumlah luas permukaan kuboid itu dalam cm2

.

A 700

B 800

C 1000

D 1200

8 cm

Diagram 9 Rajah 9

10 cm

E D

C B A 7 cm

7 cm

F Diagram 8

Rajah 8

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

Rajah 10 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 ialah 12 cm dan panjang silinder itu ialah 10 cm.

Hitung isi padu, dalam cm3, pepejal gabungan itu.

A 396π

B 408π

C 468π

D 504π

18 The distance between two bus stations, P and Q is 120 km. The bus leaves P to Q at 0845. If it travels at an average speed of 80 km/h, calculate the time of its arrival.

Jarak di antara dua stesen bas, P dan Q adalah 120 km. Sebuah bas meninggalkan P ke Q pada pukul 0845. Jika ia bergerak dengan purata laju 80 km/j, kirakan masa bas itu tiba.

A 1015

B 1115

C 1135

D 1225

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

The radius of the cone is 7 cm and the height is 12 cm. Calculate, in cm

3, the volume of water needed to

fill up the cone. Jejari kon itu ialah 7 cm dan tingginya ialah 12 cm. Hitung, dalam cm

3, isi padu air yang diperlukan untuk

memenuhi kon itu. (Use/Guna 22

7π = )

A 308

B 616

C 1848

D 2002

Diagram 10 Rajah 10

Diagram 11 Rajah 11

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20

Diagram 12 shows a circle ABCD with centre O. ∠ ABD = 54° and ∠ CDB = 22°.

Rajah 12 menunjukkan sebuah bulatan ABCD berpusatkan O. ∠ ABD = 54° dan ∠ 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. OPQ and MPR are straight lines.

Dalam Rajah 13, MNOP ialah sebuah sisi empat kitaran. OPQ dan MPR ialah garis lurus. Find the value of z.

Cari nilai bagi z.

A 118

B 62

C 59

D 52

B

C A

D

O

x°

54°

22°

Diagram 12 Rajah 12

N

O

P

Diagram 13 Rajah 13

R

Q M

z° 118°

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

Find the value of x. Cari nilai x.

A 40

B 50

C 55

D 110

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

Calculate the area, in cm², of the shaded region. Hitung luas, dalam cm², kawasan yang berlorek.

A 6

B

8

C 12

D 16

100° 2x°

80°

P Q

R S Diagram 14 Rajah 14

110°°

Diagram 15 Rajah 15

P

12 cm

Q R 4 cm

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

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

A 4

B 5

C 6

D 7

25

The value of x + y + z is Nilai x + y + z ialah

A 235 º

B 295 º

C 305 º

D 345 º

N

12 cm

9 cm

M

K L Diagram 16

Rajah 16

x y

z

55°

Diagram 17 Rajah 17

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

Rajah 18 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 nilai integer x = 5, 6, 7, …?

A 3x < 15

B 3x > 18

C 3x – 3 > 9

D 3x + 3 > –9

Diagram 18 Rajah 18

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28

In the diagram, Q is the midpoint of PR. The values of x and y are Dalam 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. Rajah 20 menunjukkan tiga titik P, Q dan R pada suatu satah Cartesian. If P, Q, R and S are 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

y 0

Diagram 19 Rajah 19

x

4

-4 4 0

-4

y

Q

P

R

Diagram 20 Rajah 20

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30 Diagram 21 shows the arc PQ of a circle with centre O.

Rajah 21 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 / Guna 7

22=π ]

A 33

B 44

C 55

D 66

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

Find the value of x. Cari nilai x.

A 8

B 9

C 11

D 12

32 The mass of box P is 250 g and the mass of box Q is 1 kg 50 g. State the ratio of mass P to mass Q. Jisim kotak P ialah 250 g dan jisim kotak Q ialah 1 kg 50 g. Nyatakan nisbah jisim P kepada jisim Q.

A 1 : 2

B 1 : 6

C 5 : 3

D 5 : 21

Q R

20 cm

P

S

U T x cm

5 cm

3 cm

Diagram 22 Rajah 22

150°

O

P

Q

18 cm

Diagram 21 Rajah 21

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16 33 Diagram 23 is a bar graph showing the number of visitors at a museum for the first 5 month of the year.

Rajah 23 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 pelawat tertinggi 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 in

Diagram 24. Jadual 3 menunjukkan bilangan pelajar dari lima buah bandar. Semua maklumat ditunjukkan dalam Rajah 24. Which sectors are correct? Sektor-sektor yang manakah adalah betul?

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

C D

E

A 100°

40° 70°

120°

30°

Diagram 24 Rajah 24

Table 3 Jadual 3

Jan April May Mac Feb

Nu

mb

er

of

peo

ple

B

ilan

ga

n o

ran

g

Month Bulan

Diagram 23 Rajah 23

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35 Table 4 shows the number of Hari Raya cards received by a group of student.

Jadual 4 menunjukkan bilangan kad Hari Raya yang diterima oleh sekumpulan pelajar.

Number of cards Bilangan kad

5 6 7 8 9

Number of students Bilangan 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. Jadual 5 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, C and D represents the image of W under the translation

4

3

−

?

Dalam Rajah 25, di antara garis bertanda A, B, C dan D yang manakah mewakili imej bagi W di bawah

translasi 4

3

−

?

.

Table 4 Jadual 4

Table 5 Jadual 5

W

A

B

C

D

Diagram 25 Rajah 25

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18 38 The triangles are drawn on square grids as shown in Diagram 26.

Segitiga-segitiga dilukis pada petak segi empat sama seperti yang ditunjukkan dalam Rajah 26. Which of the image A, B, C or D is not an image of T under certain reflections? Di antara imej A, B, C atau D, yang manakah bukan imej bagi T di bawah pantulan tertentu?

39 Given that y = 3x2 − x + 6, calculate the value of y when x = − 3.

Diberi bahawa y = 3x2 – x + 6 , kirakan nilai y apabila x = − 3.

A 12

B 27

C 30

D 36

T

A B

C

D

Diagram 26 Rajah 26

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

line AB is always 5 cm?

Antara berikut, yang manakah lokus bagi satu titik x yang bergerak dengan keadaan jarak tegaknya sentiasa 5 cm dari garis AB?

A

B

C

D

5 cm 5 cm

A

B

x x

5 cm

A 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.

RELATIONS

PERKAITAN

1. m n m na a a +× =

2. m n m na 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 = jarak yang dila lu i

m asa yang diambil

7. Mean = sum of data

number of data

Min = hasil tambah nilai data

bilangan data

8. Pythagoras’ Theorem / Teorem Pithagoras

c a b= +2 2 2

1. Area of rectangle = length × width Luas segiempat tepat = panjang × lebar

2. Area of triangle = ×1

2base × height

Luas segitiga = ×1

2tapak × tinggi

3. Area of parallelogram = base × height Luas 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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SULIT 3 50/2

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

SULIT

5. Circumference of circle = πd = 2πr

Lilitan bulatan = πd = 2πj

6. Area of circle = πr

2

Luas bulatan = πj2

7. Curved surface area of cylinder = 2πrh

Luas permukaan melengkung silinder = 2πjt

8. Surface area of sphere = 4πr

2

Luas permukaan sfera = 4πj2

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 = πr

2h

Isipadu silinder = πj2t

12. Volume of cone = 3

1 πr2h

Isipadu kon = 3

1 πj2t

13. Volume of sphere = 3

4 πr

3

Isipadu sfera =

3

4 πj

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 bu latan =

°

17. =

°

A re a o f se c to r A n g le su b te n d e d a t ce n tre

A re a o f c irc le 3 6 0

L u a s s e k to r S u d u t p u s a t

L u a s b u la ta n=

°

3 6 0

18. Scale factor / Faktor skala, PAk

PA=

'

19. Area of image = k2 × area of object

Luas imej = k2 × Luas objek

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For Examiner’s

Use

1

Answer all questions. Jawab semua soalan.

Calculate the value of 14

9 ÷ (

5

1 +

4

1 ) and express the answer as a fraction in its

lowest term.

Hitungkan nilai bagi 14

9 ÷ (

5

1 +

4

1 ) dan ungkapkan jawapannya sebagai satu

pecahan terendah.

Answer / Jawapan:

[3 marks] [3 markah]

2

Calculate the value of

Hitungkan nilai bagi

7.38

0.2 0.3×

Answer / Jawapan:


3

(a)

Find the value of (0.7 )² Carikan nilai bagi (0.7 )²

(b) Calculate the value of

3

2 12

8

×

Hitungkan nilai bagi 3

2 12

8

×


Answer / Jawapan: (a)

(b)

1

3

2

2

3

3

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4

In Diagram 4, ∆ABC and ∆PQR are similar. Given that 2

5=

AB

PQ, calculate the length in

cm, of PR.

Dalam Rajah 4, ∆ABC dan ∆PQR adalah serupa. Diberi 2

5=

AB

PQ, kira panjang, dalam

cm, bagi PR.


For Examiner’s

Use

Answer / Jawapan:

5

In Diagram 5, ABC and BDE are right-angled triangles. D is the midpoint of AB. Dalam Rajah 5, ABC dan BDE ialah segi tiga bersudut tegak. D ialah titik tengah garis AB. Given that BC = 13 cm. Diberi BC = 13 cm.

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

(b) Calculate the length, in cm, of DE. Hitung panjang, dalam cm, bagi DE.



(b)

A

100°

C

B

40°

8 cm

R

Q

100°

40°

P

Diagram 4 Rajah 4

Diagram 5 Rajah 5

4

2

5

3

5 cm A C

B

=

= E

D

X o

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For Examiner’s

Use

6

Diagram 6 in the answer space shows two quadrilaterals P and Q, which are drawn on a Cartesian plane. Q is the image of P under a rotation. Rajah 6 di ruang jawapan menunjukkan dua buah sisi empat P dan Q, yang dilukis pada 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 K as the centre of rotation. Tandakan titik K sebagai pusat putaran.


Answer / Jawapan:

(a)

(b)

Diagram 6 Rajah 6

6

3

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SULIT 7 50/2


SULIT

7

Diagram 7 shows ∆ABC and its image ∆PQR under an enlargement at centre S. Rajah 7 menunjukkan ∆ABC dan imejnya ∆PQR di bawah satu pembesaran di pusat S

For Examiner’s

Use (a) Mark the centre of enlargement S.

Tandakan pusat pembesaran S.

(b)

State the coordinates of S. Nyatakan koordinat S.

[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 7 Rajah 7

R Q

C B

A P

0 x

10 8 6 4 2

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:

For Examiner’s

Use

(a)

18 – 12t

(b) 75p

2 – 12


Answer / Jawapan:

(a)

(b)

10

Diagram 10 shows a regular pentagon PQRST. J, K, L, M and N are the midpoints of QR, PQ, PT, ST and SR respectively. W, Y and Z are three moving points in the diagram. Rajah 10 menunjukkan sebuah pentagon PQRST. J, K, L, M dan N ialah titik tengah bagi QR, PQ, PT, ST dan SR masing-masing. W, Y dan Z adalah tiga titik yang bergerak dalam rajah itu.

(a) W is a point which moves such that it is equidistant from PT and 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 Rajah 10, lukis

(i) the locus of Y such that YP = PT.

lokus Y supaya YP = PT.

(ii) the locus of Z such that it is equidistant from point P and 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 Y and Z.

Seterusnya, tandakan dengan simbol ⊗ titik persilangan lokus Y dan lokus Z itu.


Answer / Jawapan:

(a)

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

J

Q

R S

T

K

P

N

M

L

Diagram 10 Rajah 10

10

4

9

3

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SULIT 9 50/2


SULIT

A

B

11 (a) Diagram 11.1 shows a triangle EFG. Rajah 11.1 menunjukkan sebuah segi tiga EFG. Measure EFG using a protractor. Ukur EFG menggunakan protraktor.

For Examiner’s

Use

(b) Diagram 11.2 shows triangle ABC. Using only a ruler and a pair of compasses, construct Rajah 11.2 menunjukkan segi tiga ABC. Menggunakan pembaris dan jangka lukis sahaja, bina

(i) the triangle ABC, beginning from the straight line AB provided in the answer space. segi tiga ABC, bermula dari garis lurus AB yang disediakan di ruang jawapan.

(ii) the perpendicular line BD to the straight line AC from the point B. garis serenjang BD kepada garis lurus AC yang dari titik B.


(c) Measure the length, in cm, of BD. Ukur panjang, dalam cm, bagi BD.

Answer / Jawapan:

(a)

(b) (i), (ii)

Diagram 11.2 Rajah 11.2

A

B

7 cm

300

C

F

G

Diagram 11.1 Rajah 11.1

E

11

5

(c)

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SULIT 10 50/2


For Examiner’s

Use

12 Express 4 1

3 12

+−

x

xy y as a single fraction in its simplest form.

Ungkapkan 4 1

3 12

+−

x

xy y sebagai satu pecahan tunggal dalam bentuk termudah.


Answer / Jawapan:

13

Given that 3

22

+− =

qp , express q in terms of p.

Diberi bahawa 3

22

+− =

qp , ungkapkan q dalam sebutan p.


Answer / Jawapan:

14

Solve : Selesaikan:

(a)

x – 2 = – 3

(b)

3

42

+=−

xx


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

For Examiner’s

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.

Diberi n 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

For Examiner’s

Use

17 Given 4y − 1 ≥ 7 and y is an even number which is less than 9, list all the integer values of y. Diberikan 4y − 1 ≥ 7 dan y ialah nomber genap yang kurang daripada 9, senaraikan semua nilai integer bagi y.


Answer / Jawapan:

18

Diagram 18 shows a polygon. On the 1cm square grid below, redraw the polygon using the scale 1:200. Rajah 18 menunjukkan sebuah poligon. Lukis semula poligon itu pada grid segi empat sama bersisi 1 cm menggunakan skala 1:200.

[ Assume 1 unit = 1 cm ] [ Anggap 1 unit = 1 cm ]


Answer / Jawapan:

17

3

4 m

Diagram 18 Rajah 18

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. Rajah 19 ialah carta pai yang menunjukkan hobi bagi 120 orang pelajar di sebuah sekolah.

For Examiner’s

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.



(b)

(c)

20

Use the graph paper on page 14 to answer this question. Gunakan kertas graf di mukasurat 14 untuk menjawab soalan ini. Table 20 shows the values of two variables, x and y, of a function. Jadual 20 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 20 Jadual 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 skala 2 cm kepada 5 unit, lengkap dan labelkan paksi-y.

(b) Based on the Table 20, plot all the points on the graph paper. Berdasarkan Jadual 20, plot semua titik pada kertas graf itu.

(c) Hence, draw the graph of function. Seterusnya, lukiskan graf fungsi itu.


19

3

PlayingTennis Bermain Tenis

Playing Soccer Bermain Bola Sepak

Diagram 19 Rajah 19

5

Playing Badminton Bermain Badminton

Cycling Berbasikal

Reading Membaca

20

2x

5

25

30

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SULIT 14 50/2


y For

Examiner’s Use

END OF QUESTION PAPER

KERTAS SOALAN TAMAT

x

─ 1 ─ 2 ─ 3 0

2 3 1 ─ 3 ─ 2 ─ 1 0 1 2 3

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

20

4

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SULIT 15 50/2


SULIT

INFORMATION FOR CANDIDATES

MAKLUMAT UNTUK CALON

1. This question paper consists of 20 questions.

Kertas soalan ini mengandungi 20 soalan.

2. Answer all questions.

Jawab semua 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 mendapatkan markah.

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

answer. 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 halaman 2 hingga 3.

9. The usage of calculator is not allowed.

Penggunaan kalkulator tidak 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 5

14 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) 0.49 3

2

3

3

1( ) 2

8

1 4

8

1

2

1

8

b

×

= ×

=

=

1

1

1

3

Note :

See 4 5

20

+

or 9

20 award 1 mark

Note:

See 0.06 or 738

6 award 1 mark

Note:

see 1

2, award 1 mark

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3



4 8 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

b DE

DE =

DE =

DE

( ) =

×

=

1

1

1

3

6

(a) 90o

clockwise direction

2

1

3

Note : Also accept

PR = 4 × 5}

PR=20

1 mark 8 ÷ 2 = 4

1 mark

Note:

Also accept 2.3 .

(b) The point K plotted 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

C B

A P

0 x

10 8 6 4 2

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 ± 1

o

(b)

30°A

B

C

1

1

1

1

1

5

Construct a 30o angle at A correctly

Construct point C correctly.

Construct the triangle ABC correctly..

Construct the perpendicular line BD from B to AC correctly.

BD = 3.0 (± 0.1) cm

J

N R

M

S

L

T

K

P

Q

(a) The straight line PN

(b) (i) Locus Y drawn

Correctly

(ii) Locus Z drawn

Correctly

(c) Intersection of locus Y and

locus Z marked 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

+− =

− = +

+ = −

= − −

= −

qp

p q

q p

q p

q p

32

2

2 4 3

3 2 4

2 3 4

2 7

1

1

1

3

14 (a) x – 2 = –3

x = 2 – 3

x = –1

1

1

1

3

Note : See 2p – 4 award 1 mark

1 mark

1 mark

1 mark

4b 2

3

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

4y ≥

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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9

Answer for question 20

××××

y

-2 -3 x 0 2 3 1

─ 5

5

10

15

20

25

30

35

××××

××××

-1 ×××× ××××

××××

××××

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Documents

Peperiksaan Percubaan Maths Paper 1 PMR · Cari hasil tambah semua nombor perdana di antara 20 hingga 30. A 44 B 50 ... Kira beza di antara suhu yang tertinggi dengan suhu yang terendah