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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
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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
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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
50/2 2009 Copy right Sabah State Education Department [[Lihat SebelahSULIT
8/14/2019 Percubaan Pmr 09 Sabah Mtk Paper 2
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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
50/2 2009 Copy right Sabah State Education Department [[Lihat SebelahSULIT
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
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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
50/2 2009 Copy right Sabah State Education Department [[Lihat SebelahSULIT
3
3
2
2
2
1
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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]
[3 markah]Answer /Jawapan:
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:
50/2 2009 Copy right Sabah State Education Department [[Lihat SebelahSULIT
3
4
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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
50/2 2009 Copy right Sabah State Education Department [[Lihat SebelahSULIT
2
5
2
6
A
P
Q
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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
50/2 2009 Copy right Sabah State Education Department [[Lihat SebelahSULIT
M
M
Diagram 2Rajah 2
M
M
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CONFIDENTIAL 9
Faktorkan selengkapnya12x2 27.
[2 marks]
[2 markah]Answer /Jawapan:
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]
[3 markah]Answer /Jawapan:
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]
[3 markah]Answer /Jawapan:
10 List all the integer values ofkwhich satisfy both the inequalities
4 k> 2 and 2k 3 7 .
For
Examiners
Use
50/2 2009 Copy right Sabah State Education Department [[Lihat SebelahSULIT
2
7
3
8
3
9
3
10
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CONFIDENTIAL 10
Senaraikan semua nilai integer k yang memuaskan kedua-dua ketaksamaan4 k> 2 dan 2k 3 7 .
[3 marks]
[3 markah]Answer /Jawapan:
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
50/2 2009 Copy right Sabah State Education Department [[Lihat SebelahSULIT
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
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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
50/2 2009 Copy right Sabah State Education Department [[Lihat SebelahSULIT
5
15
2
14
2
13
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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
50/2 2009 Copy right Sabah State Education Department [[Lihat SebelahSULIT
C
3
16
D
A
2 units
4 units
4 units
5 units
K
B
N
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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
50/2 2009 Copy right Sabah State Education Department [[Lihat SebelahSULIT
3
17
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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
50/2 2009 Copy right Sabah State Education Department [[Lihat SebelahSULIT
60
S R
QTP
6
18
Workshop
BengkelL0
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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
50/2 2009 Copy right Sabah State Education Department [[Lihat SebelahSULIT
5
19
P Q
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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
50/2 2009 Copy right Sabah State Education Department [[Lihat SebelahSULIT
Waja
4
20
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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
50/2 2009 Copy right Sabah State Education Department [[Lihat SebelahSULIT
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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
50/2 2009 Copy right Sabah State Education Department [[Lihat SebelahSULIT
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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
50/2 2009 Copy right Sabah State Education Department [[Lihat SebelahSULIT