Percubaan Pmr 09 Sabah Mtk Paper 2

8/14/2019 Percubaan Pmr 09 Sabah Mtk Paper 2

1/19

JABATAN PELAJARAN NEGERI SABAH

PENILAIAN MENENGAH RENDAH 2009 50/2

EXCEL 2

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

50/1 2009 Hak Cipta Jabatan Pelajaran Negeri Sabah [Lihat SebelahSULIT

1 Tulis nama, tingkatan, nombor kad pengenalan

dan angka giliran anda pada ruang yang

disediakan.

2 Kertas soalan ini adalah dalam dwi bahasa.

3 Calon dikehendaki membaca maklumat di halaman

belakang kertas soalan ini.

Untuk Kegunaan Pemeriksa

Soalan Markah

Penuh

Markah

Diperoleh

1 2

2 2

3 3

4 3

5 2

6 2

7 2

8 3

9 3

10 3

11 2

12 213 3

14 2

15 5

16 3

17 3

18 6

19 5

20 4

Jumlah

Kertas soalan ini mengandungi 18 halaman bercetak

NAMA : ___________________

KELAS : ___________________

SULIT

MATHEMATICS

OGOS 2009

1 JAM 45 MINIT SATU JAM EMPAT PULUH LIMA MINIT


2/19

CONFIDENTIAL 2

MATHEMATICAL FORMULAE

RUMUS MATEMATIK

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 a m a n = a m + n

2 a m a n = a mn

3 (am)n = am n

4 Distance /Jarak= 212

2

12 )()( yyxx +

5 Midpoint / Titik Tengah

(x , y) = 2

21 xx +

, 2

21 yy +

6 Average speed =

Purata laju =

7 Mean =

Min =

8 Pythagoras Theorem / Teorem Pithagoras

c2 = a2 + b2

SHAPES AND SPACE

50/2 2009 Copy right Sabah State Education Department [[Lihat SebelahSULIT

distance travelled

time taken

jarak yang dilalui

masa yang diambil

sum of data

number of data

hasil tambah nilai databilangan data


3/19

CONFIDENTIAL 3

BENTUK DAN RUANG

1 Area of rectangle = length width

Luas segiempat tepat = panjang lebar

2 Area of triangle =21 base height

Luas segitiga =2

1 tapak tinggi

3 Area of parallelogram = base height

Luas segiempat selari = tapak tinggi

4 Area of trapezium =2

1 sum of parallel side height

Luas trapezium =21 hasil tambah dua sisi selari tinggi

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 = 4 r2

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 =

r

2

h Isipadu silinder = j2t

12 Volume of cone =3

1r2h

Isipadu kon =3

1j2t



4/19

CONFIDENTIAL 4

13 Volume of sphere =3

4 r3

Isipadu sfera =3

4j3

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) 180

Hasil tambah sudut pedalaman poligon = (n 2) 180

16 =

=

17 =

=

18 Scale factor /Faktor skala, k =

19 Area of image = k2 area of object

Luas imej = k2 luas objek

Answerall questions.For


Area of sector

Area of circle

Arc length

CircumferenceAngle subtended at centre

360

PA

PA

Angle subtended at centre

360

Panjang lengkok

Lilitan bulatan

Sudut pusat

Luas sektorLuas bulatan

Sudut pusat


5/19

CONFIDENTIAL 5

1 Calculate the value of

9

2

3

2

6

1and express the answer as a fraction in its lowest

terms.

Hitung nilai bagi

9

2

3

2

6

1dan ungkapkan jawapannya sebagai satu pecahan

dalam sebutan terendah.[2 marks]

[2 markah]

Answer /Jawapan:

Examiners

Use

2 Find the value of 2.3 +4.0

36.0and express the answer as a decimal.

Hitung nilai bagi 2.3 +4.0

36.0dan ungkapkan jawapannya dalam nombor

perpuluhan.[2 marks]

[2 markah]Answer /Jawapan:

3

For

ExaminersUse


3

3

2

2

2

1


6/19

CONFIDENTIAL 6

(a) Find the value of 3125

1 .

Cari nilai bagi 3125

1 .

(b) Calculate the value of

2

168

3

.

Hitung nilai bagi

2

168

3

.

[3 marks]


4 Solve each of the following equations:Selesaikan tiap-tiap persamaan berikut:

(a) y 4 = 9

(b) x 3 =3

1 x

[3 marks]

[3 markah]

Answer /Jawapan:


3

4


7/19

CONFIDENTIAL 7

5 Diagram 1 in the answer space shows object A and a straight line PQ drawn on agrid of equal squares.

Rajah 1 di ruang jawapan menunjukkan objek A dan garis lurus PQ yang dilukis

pada grid segiempat sama yang sama besar.

Draw the image ofA under a reflection in the straight linePQ.

Lukis imej bagi A di bawah pantulan pada garis lurus PQ.[2 marks]

[2 markah]

Answer /Jawapan :

Diagram 1

Rajah 1

ForExaminers

Use

6 Diagram 2 shows two polygons, Mand M,drawn on a grid of equal squares with ForExaminers

Use


2

5

2

6

A

P

Q


8/19

CONFIDENTIAL 8

sides of 1 unit.

Rajah 2 menunjukkan dua poligon, M dan M, yang dilukis pada grid segiempat

sama bersisi 1 unit.

Diagram 2

Rajah 2

M is the image ofMunder transformationZ.

Mialah imej bagi M di bawah suatu penjelmaan Z.

Describe in full transformation Z.

Huraikan selengkapnya penjelmaan Z.

[2 marks][2 markah]

Answer /Jawapan:

7 Factorise completely 12x2 27. ForExaminers


M

M

Diagram 2Rajah 2

M

M


9/19

CONFIDENTIAL 9

Faktorkan selengkapnya12x2 27.

[2 marks]


Use

8 Expand each of the following expressions:

Kembangkan tiap-tiap ungkapan berikut:

(a) 3k(f 3 ).

(b) (k+ 3)2 2(3k 1)[3 marks]


9 Express 21 3

3 12

p

p p

+ as a single fraction in its simplest form.

Ungkapkan 21 3

3 12

p

p p

+ sebagai satu pecahan tunggal dalam bentuk termudah.

[3 marks]


10 List all the integer values ofkwhich satisfy both the inequalities

4 k> 2 and 2k 3 7 .

For

Examiners

Use


2

7

3

8

3

9

3

10


10/19

CONFIDENTIAL 10

Senaraikan semua nilai integer k yang memuaskan kedua-dua ketaksamaan4 k> 2 dan 2k 3 7 .

[3 marks]


11 In Diagram 3, y is the length ofCD and cos4

5x =o .

Dalam Rajah 3,y ialah panjang garisCDdan kos4

5x =o .

Diagram 3

Rajah 3Find the value ofy.

Cari nilai y.[2 marks]

[2 markah]

Answer /Jawapan:

12 Find the value of 21

2

3

33

.For

Examiners

Use


2

12

2

11

A

BC

Dx

y

Diagram 4

Rajah 4

12 13

20

12 cm 13 cm

20 cm

A

B C y cm

x

D


11/19

CONFIDENTIAL 11

Cari nilai bagi 21

2

3

33

.

[2 marks][2 markah]

Answer /Jawapan:

13 Simplify

21

32m n n

.

Permudahkan

21

32m n n

.

[2 marks][2 markah]

Answer /Jawapan:

14 Given that tqp = , expressp in terms ofq and t.

Diberi bahawa tqp = , ungkapkan p dalam sebutan q dan t.[2 marks]

[2 markah]

Answer/Jawapan:

15 Diagram 4 in the answer space is drawn on a square grid of sides 1 unit.

W,Xand Yare three moving points on the diagram.

For

ExaminersUse


5

15

2

14

2

13


12/19

CONFIDENTIAL 12

Rajah 4 di ruang jawapan yang dilukis pada segiempat grid yang bersisi 1 unit.W,Xdan Y adalah tiga titik yang bergerak dalam rajah itu.

(a) Wis a moving point such that it is always equidistant 2 units from the straightlineKN. Describe in full the locus ofW.

W ialah titik yang bergerak dengan keadaan sama jarak 2 unit dari garislurus KN.

Huraikan sepenuhnya lokus W.

(b) On the diagram, draw

Pada rajah itu, lukiskan

(i) the locus ofXsuch thatAX = AD,

lokus X dengan keadaan AX = AD,

(ii) the locus Ysuch thatBY = YD,

lokus Y dengan keadaan BY = YD.

(c) Hence, mark with the symbol all the intersection of the locus ofXand locusof Y.

Seterusnya, tandakan dengan simbol semua kedudukan bagi persilanganlokus X dan lokus Y itu.

[5 marks]

[5 markah]Answer/Jawapan:

Diagram 4 /Rajah 41

6

Diagram 5 shows a prism.

Rajah 5 menunjukkan sebuah prisma.

For

ExaminersUse


C

3

16

D

A

2 units

4 units

4 units

5 units

K

B

N


13/19

CONFIDENTIAL 13

Diagram 5

Rajah 5

Draw a full scale the net of the prism on the grid in the answer space. The grid

has equal squares with side of 1 unit.

Lukiskan skala penuh bentangan bagi prisma itu pada grid segiempat sama

yang bersisi 1 unit di ruang jawapan.

[3 marks][3 markah]

Answer /Jawapan:

17 Table 1 shows the number of motorcycles repaired in three workshops. There are 80

motorcycles in the three workshops.

Jadual 1 menunjukkan bilangan motosikal yang telah dibaiki bagi tiga buah bengkel.

Terdapat 80 buah motosikal di ketiga-tiga bengkel tersebut.

For

Examiners

Use


3

17


14/19

CONFIDENTIAL 14

Workshop

Bengkel

Number of motorcycles

Bilangan motosikal

K p

L 32

M 26

Table 1

Jadual 1(a) Find the value ofp.

Cari nilai bagi p.

(b) Hence, complete the bar chart to represent all the information in Table 1.

Seterusnya, lengkapkan carta bar untuk mewakili semua maklumat dalamJadual 1.

[3 marks][3 markah]

Answer /Jawapan:

Number of motorcycles

Bilangan motosikal

18 Set squares and protractors are not allowed to be used in section (a) of this question.

Sesiku dan protraktor tidak boleh digunakan untuk ceraian (a) soalan ini.

For

ExaminersUse


60

S R

QTP

6

18

Workshop

BengkelL0


15/19

CONFIDENTIAL 15

Diagram 6

Rajah 6

Diagram 6 shows a rhombusPQRS.

Rajah 6 menunjukkan sebuah rombus PQRS.

(a) By using only a ruler and a pair of compasses, construct Diagram 6, beginning

from the linePQ provided in the answer space.

Dengan menggunakan pembaris dan jangka lukis sahaja, bina Rajah 6, bermula

dengan garis lurus PQ yang disediakan di ruang jawapan.

(b) Based on the diagram constructed in (a), measure the length of line ST.

Berdasarkan rajah yang dibina di (a), ukur panjang garis lurus ST.

[6 marks]

[6 markah]Answer/Jawapan:

19 Table 2 shows the number of cars sold by a company in July 2009.

Jadual2 menunjukkan bilangan kereta yang telah dijual oleh sebuah syarikat

dalam bulan Julai 2009.

For

Examiners

Use


5

19

P Q


16/19

CONFIDENTIAL 16

Model

Model

Number of Cars

Bilangan Kereta

Angle of Sector

Sudut Sektor

Perdana 10

Waja 18 90

Wira 20 100

Iswara 24 Table 2

Jadual2

The information for Waja Model is shown fully in the pie chart in the answer

space.

Maklumat bagi model Waja ditunjukkan sepenuhnya dalam carta pai di ruang

jawapan.

Complete

Lengkapkan

(a) the angles of the sectors for Perdana Model and Iswara Model in Table 2.Sudut sektor bagi model Perdana dan model Iswara dalam Jadual 2.

(b) the pie chart represents all the information in Table 2.

carta pai itu untuk mewakili semua maklumat dalam Jadual2.[5 marks]

[5 markah]

Answer /Jawapan:

20 Table 3 shows the values of two variables,x andy of a function.

Jadual 3 menunjukkan nilai-nilai pembolehubah x dan y bagi satu fungsi.

For

ExaminersUse


Waja

4

20


17/19

CONFIDENTIAL 17

x 3 2 1 0 1 2 3 4

y 9 2 9 12 11 6 3 16Table 3

Jadual 3

Draw the graph of the function using a scale of 2 cm to 1 unit onx-axis and

2 cm to 5 units on y-axis.

Lukiskan graf fungsi itu dengan menggunakan skala 2 cm kepada 1 unit pada paksi-xdan 2 cm kepada 5 unit pada paksi-y.

[4 marks]

[4 markah]

Answer/Jawapan:

END OF QUESTION PAPER

INFORMATION FOR CANDIDATES



18/19

CONFIDENTIAL 18

1. This questions paper consists of20 questions.

2. Answerall questions.

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

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

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

write down the new answer.

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

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

8. A list of formulae is provided on pages 2 and 4.

9. The usage of calculator is not allowed.

10. Hand in this question paper to the invigilator at the end of the examination.

COORDINATOR



19/19

CONFIDENTIAL 19

BERNADETTE JOHN

Sektor Pengurusan Akademik

PANEL MEMBERS

1. Tan Boon Tiew (Leader) SMK Perempuan, Likas

2.Ag Mahmmud B Ag Tengah SMK Benoni, Papar

3. Felicity Ng SMK ST. Francis Convent (M), KK.

4.Flora Jimmy SM All Saints, Kota Kinabalu.

5. Johny Suah SMK Bandaraya, Kota Kinabalu.

6. Lee Tee Boo SMK Kolombong, Inanam.

7. Shim Lhi Shwo SMK Muhibbah, Sandakan.

8. Kellson Shim SMK ST. John, Tuaran.

9. Syed Razali Syed Dalbeh SMK Benoni, Papar


Percubaan Pmr 09 Sabah Mtk Paper 2

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