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8/4/2019 Pmr Trial 2011 Mm2 Q&A (Swk)
1/24
SULIT 2 50/2
50/2 2011 Hak Cipta JABATAN PELAJARAN SARAWAK SULIT
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
PERKAITAN1. nmnm aaa +=
2. nmnm aaa
=
3. ( ) mnnm aa =
4. Distance /Jarak = ( ) ( )2122
12 yyxx +
5. Midpoint /Titik tengah
( )
++=
2,
2,
2121yyxx
yx
6. Average speed =takentime
travelleddistance
Purata laju =jarak yang dilalui
masa yang diambil
7. Mean =dataofnumber
dataofsum
Min =hasil tambah nilai data
bilangan data
8. Pythagoras Theorem /Teorem Pithagoras
222 bac +=
1. Area of rectangle = length width
Luas segiempat tepat = panjang lebar
2. Area of triangle = 2
1base height
Luas segitiga = 2
1tapak tinggi
3. Area of parallelogram = base height
Luas segiempat selari = tapak tinggi
SHAPE AND SPACE
BENTUK DAN RUANG
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SULIT 3 50/2
50/2 2011 Hak Cipta JABATAN PELAJARAN SARAWAK [Lihat halaman sebelah
SULIT
4. Area of trapezium = 2
1 sum of parallel sides height
Luas trapezium = 2
1 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 = 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 /Isipadu silinder = r2h
12. Volume of cone /Isipadu kon =3
1 j2h
13. Volume of sphere =3
4r
3
Isipadu sfera =3
4j
3
14. Volume of right pyramid =3
1 base area height
Isipadu piramid=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.Arc length Angle subtended at centre
Circumference of circle 360=
360
Panjang lengkok Sudut pusat
Lilitan bulatan=
17.Area of sector Angle subtended at centre
Area of circle 360=
360
Luas sektor Sudut pusat
Luas bulatan=
18. Scale factor /Faktor skala,PA
PAk
'=
19. Area of image = k2
area of object
Luas imej = k2
Luas objek
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SULIT 4 50/2
50/2 2011 Hak Cipta JABATAN PELAJARAN SARAWAK SULIT
For
Examiners
Use
Answerallquestions.
Jawabsemuasoalan
1 Calculate the value of :
Hitung nilai bagi:
3 ( 18 + 20 4 ) [2 marks]
[2 markah]
Answer /Jawapan:
2 Calculate the value of ( 4 0.22 ) 2
11 and express the answer as a decimal. [2 marks]
Hitung nilai bagi ( 4 0.22 ) 2
1
1 dan ungkapkan jawapan sebagai nombor
perpuluhan. [2 markah]
Answer /Jawapan:
3 (a) Find the value of :Cari nilai bagi :
4
16
(b) Calculate the value of:Hitung nilai bagi :
1
64
81 3
[3 marks]
[3 markah]
Answer / Jawapan:
(a)
(b)
2
2
3
3
1
2
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SULIT 5 50/2
50/2 2011 Hak Cipta JABATAN PELAJARAN SARAWAK [Lihat halaman sebelah
SULIT
4 Solve each of the following linear equations :
Selesaikan tiap-tiap persamaan linear berikut:
(a) 4 x = 1
(b)4
x 3 = x + 3
[3 marks]
[3 markah]Answer / Jawapan
(a)
(b)
For
Examiners
Use
5 Diagram 5 in the answer space shows quadrilateral PQRS and straight lineMNdrawn on a
grid of equal squares.RS is the image ofRS under a reflection in the straight lineMN. On
Diagram 5, complete the image of quadrilateral PQRS.
Rajah 5 di ruang jawapan menunjukkan sisi empat PQRS dan garis lurus MN yang dilukis
pada grid segi empat sama yang sama besar. RS ialah imej bagi RS di bawah pantulan
pada garis lurus MN. Pada Rajah 5, lengkapkan imej bagi sisi empat PQRS.
[2 marks]
[2 markah]
Answer /Jawapan:
Diagram 5Rajah 5
4
3
5
2
P
Q R
S
R
SM
N
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SULIT 6 50/2
50/2 2011 Hak Cipta JABATAN PELAJARAN SARAWAK SULIT
For
Examiners
Use
6 Diagram 6 shows two quadrilaterals, PQRS and PQRS, drawn on a Cartesian plane.
PQRS is the image ofPQRS under an enlargement.
Rajah 6 menunjukkan dua sisi empat, PQRS dan PQRS, yang dilukis pada satah
Cartesan. PQRSialah imej bagi PQRS di bawah suatu pembesaran.
Diagram 6Rajah 6
(a) State the coordinates of the centre of enlargement. [1 mark]
Nyatakan koordinat bagi pusat pembesaran itu. [1 markah]
(b) State the scale factor of the enlargement. [1 mark]
Nyatakan faktor skala bagi pembesaran itu. [1 markah]
Answer /Jawapan:
(a)
(b)
6
2
y
xO2 2
2
P
S
Q
R
Q
S
R
P
4
4
2
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SULIT 7 50/2
50/2 2011 Hak Cipta JABATAN PELAJARAN SARAWAK [Lihat halaman sebelah
SULIT
7 Diagram 7 in the answer space shows a parallelogram PQRS drawn on a grid of equal
squares with sides of 1 unit.MandNare the midpoints of straight lines PQ andRS
respectively. X, YandZare three moving points inside the parallelogram.
Rajah 7 di ruang jawapan menunjukkan sebuah segi empat selari PQRS yang dilukis pada
grid segi empat sama bersisi 1 unit. M dan N adalah titik tengah bagi garis lurus PQ dan RS
masing-masing. X, Y dan Z adalah tiga titik yang bergerak di dalam segi empat selari itu.
(a) Xis the point which moves such that it is always equidistant from pointR and S.
By using the letters in Diagram 7, state the locus ofX.
X ialah titik yang bergerak dengan keadaan jaraknya adalah sentiasa sama dari titik R
dan S.
Dengan menggunakan huruf di dalam Rajah 7, nyatakan lokus bagi X.
(b) On Diagram 7, drawPada Rajah 7, lukis
(i) the locus of the point Ywhich moves such that its distance is constantly 4 units
from point S.
lokus bagi titik Y yang bergerak dengan keadaan titik itu sentiasa berjarak4 unit
dari titik S.
(ii) the locus of the pointZwhich moves such that it is always equidistant from the
straight lines PS and SR.
lokus bagi titik Z yang bergerak dengan keadaan jaraknya adalah sentiasa sama
dari garis lurus PS dan SR.
(c) Hence, mark with the symbol the intersections of the locus ofYand the locus ofZ.
Seterusnya, tandakan dengan simbol kedudukan bagi semuapersilangan lokus Y dan
lokus Z itu.
[5 marks]
[5 markah]
Answer /Jawapan:
(a)
(b)(i), (ii)(c)
Diagram 7
Rajah 7
For
Examiners
Use
7
5
P Q
S RN
M
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SULIT 8 50/2
50/2 2011 Hak Cipta JABATAN PELAJARAN SARAWAK SULIT
For
Examiners
Use
8 Table 8 shows the number of students obtaining 8As in the PMR examinations of a school.
Jadual 8 menunjukkan bilangan murid yang memperolehi 8A dalam peperiksaan PMR di
sebuah sekolah.
Year /Tahun 2006 2007 2008 2009 2010
Number of students
Bilangan murid6 11 18 14 20
Table 8
Jadual 8
On Diagram 8 in the answer space, draw a line graph to represent all the information in
Table 8. Use the scale 2 cm to 5 students on the vertical axis.
[3 marks]
Pada Rajah 8 di ruang jawapan, lukiskan suatu graf garis untuk mewakili semua
maklumat dalam Jadual 8. Gunakan skala 2 cm kepada 5 orang murid pada paksi
mencancang.
[3 markah]
Answer /Jawapan :
Diagram 8
Rajah 8
8
3
Number of students
Bilangan pelajar
2006 2007 2008 2009 Year
Tahun
2010
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SULIT 9 50/2
50/2 2011 Hak Cipta JABATAN PELAJARAN SARAWAK [Lihat halaman sebelah
SULIT
9 (a) Expand :
Kembangkan :
4(t 2) + 3
(b) Simplify:
Permudahkan:
( ) ( )mm 2355 2 [3 marks]
[3 markah]
Answer /Jawapan:
(a)
(b)
For
Examiners
Use
10 Factorize completely each of the following expressions:
Faktorkan selengkapnya tiap-tiap ungkapan berikut:
(a) 10g 2gk(b) 12 27p2
[3 marks]
[3 markah]
Answer /Jawapan:
(a)
(b)
.
10
3
9
3
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SULIT 10 50/2
50/2 2011 Hak Cipta JABATAN PELAJARAN SARAWAK SULIT
For
Examiners
Use
11 Diagram 11 shows a right prism with a rectangular base.
Rajah 11 menunjukkan sebuah prisma bertapak segi empat tepat.
Complete the net of the prism in Diagram 11. [3 marks]
Lengkapkan bentangan prisma itu dalam Rajah 11 [3 markah]
Answer /Jawapan:
11
3
6 units
6 unit
3units
3 unit
4 units
4 unit
Diagram 11
Rajah 11
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SULIT 11 50/2
50/2 2011 Hak Cipta JABATAN PELAJARAN SARAWAK [Lihat halaman sebelah
SULIT
12 (a)Diagram 12.1 shows a quadrilateral PQRS drawn not to scale.
Rajah 12.1 menunjukkan sebuah sisi empat PQRS yang dilukis tidak mengikut skala.
Diagram 12.1
Rajah 12.1
Diagram 12.2 in the answer space shows two straight lines PQ and QR.
Rajah 12.2 dalam ruang jawapan menunjukkan dua garis lurus PQ dan QR.
Use only a ruler and a pair of compasses, construct
Menggunakan pembaris dan jangka lukis sahaja, bina
(i) quadrilateral PQRS to the measurements shown in Diagram 12.1,sisi empat PQRS menggunakan ukuran seperti yang ditunjukkan dalam Rajah
12.1,(ii) the perpendicular line to the straight line QR which passes through the point S.garis serenjang kepada garis lurus QR yang melalui titik S.
[4 marks]
[4 markah]
(b) Measure the perpendicular distance, in cm, between straight line QR and point S.
Ukur jarak tegak, dalam cm, di antara garis lurus QR dan titik S.
[1 mark]
[1 markah]
Answer /Jawapan:
(a) (i), (ii)
Diagram 12.2
Rajah 12.2
(b)
For
Examiners
Use
12
5
Q R
P
60
4 cm
S
Q R
P
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SULIT 12 50/2
50/2 2011 Hak Cipta JABATAN PELAJARAN SARAWAK SULIT
For
Examiners
Use
13 Given ddc 32 =+ , express c in terms ofd.
Diberi ddc 32 =+ , ungkapkan c dalam sebutan d.
[3 marks]
[3 markah]
Answer /Jawapan
14 (a) Evaluate:
Nilaikan:
2
35
p
pp .
(b) Given 9 43 3+
=xx , calculate the value ofx .
Diberi 9 43 3 + = xx , cari nilaix.
[3 marks][3 markah]
Answer /Jawapan
(a)
(b)
13
3
14
3
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SULIT 13 50/2
50/2 2011 Hak Cipta JABATAN PELAJARAN SARAWAK [Lihat halaman sebelah
SULIT
15 The data in Table 15 shows the grades obtained by 20 candidates in an examination.
Data dalam Jadual 15 menunjukkan gred yang diperolehi oleh 20 orang calon dalam
suatu peperiksaan.
B D B B C B A C D C
E A C C D B D B B B
Table 15
Jadual 15
(a) Using the data above, complete the frequency table in the answer space.Dengan menggunakan data di atas, lengkapkan jadual kekerapan pada ruang
jawapan.
(b) State the mode.
Nyatakan mod.
[3 marks]
[3 markah]
Answer /Jawapan :
(a)
Grades
GredA B C D E
Frequency
Kekerapan
(b)
For
Examiners
Use
16 Express26
65
2
3
p
p
p
as a single fraction in its simplest form.
Ungkapkan26
65
2
3
p
p
p
sebagai satu pecahan tunggal dalam bentuk termudah.
[3 marks]
[3 markah]
Answer /Jawapan :
15
3
16
3
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SULIT 14 50/2
50/2 2011 Hak Cipta JABATAN PELAJARAN SARAWAK SULIT
For
Examiners
Use
17 Solve each of the following inequalities :
Selesaikan tiap-tiap ketaksamaan berikut:
(a) 3 + q 7
(b) 6x 2 2 ( 3 + x )
[3 marks]
[3 markah]
Answer /Jawapan :
(a)
(b)
18 In Diagram 18, triangles PQR and TSR are similar.
Dalam Rajah 18, segi tiga PQR dan TSR adalah serupa.
Diagram 18
Rajah 18
Given that PQ = 2 cm, calculate the length, in cm, ofST.
DiberiPQ = 2cm, hitung panjang, dalam cm, bagi ST.
[2 marks]
[2 markah]
Answer /Jawapan:
17
3
S
T
Q
2 cm
P
R
3 cm
8 cm
18
2
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SULIT 15 50/2
50/2 2011 Hak Cipta JABATAN PELAJARAN SARAWAK [Lihat halaman sebelah
SULIT
19 In Diagram 19, PQR and PSTare right-angled triangles. PRS is a straight line.
Dalam Rajah 19, PQRdan PST adalah segi tiga bersudut tegak. PRS ialah garis lurus.
Diagram 19
Rajah 19
(a) Find the value of cosxo.
Cari nilai bagi kos xo
(b) Calculate the length, in cm, ofRS.
Hitung panjang, dalam cm, bagi RS.
[3 marks][3 markah]
Answer /Jawapan:
(a)
(b)
For
Examiners
Use
20 Use the graph paper on page 16 to answer this question.
Gunakan kertas graf di halaman 16 untuk menjawab soalan ini.Table 20 shows the values of two variables,x andy, 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 10 5 8 5 2 5 20
Table 20
Jadual 20
Thex-axis and they-axis are provided on the graph paper on page 16.
Paksi-x dan paksi-y telah disediakan pada kertas graf di halaman 16.
(a) By using a scale of 2 cm to 5 units, complete and label they-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 the function.
Seterusnya, lukiskan graf fungsi itu.
[4 marks]
[4 markah]
19
3
17 cm
10 cm 8 cm
8 cm
RP
Q
S
T
x
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SULIT 16 50/2
50/2 2011 Hak Cipta JABATAN PELAJARAN SARAWAK SULIT
20
4
For
Examiners
Use
x
y
3 2 1 1 2 3O
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SULIT 17 50/2
50/2 2011 Hak Cipta JABATAN PELAJARAN SARAWAK [Lihat halaman sebelah
SULIT
INFORMATION FOR CANDIDATES
MAKLUMAT UNTUK CALON
1. This question paper consists of20 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 untukmendapatkan 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 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 -
PEPERIKSAAN PERCUBAAN PMR 2011
MATHEMATICS PAPER 2
ANSWER
No Solution and Mark SchemeSub
Mark
Full
Mark1
3 ( 18 + 20 4 )
= 3 ( 18 + 5 )
= 3 ( 13 )
= 39
1
1 2
2
(4 0.22) 1
2
1
= 3.78 2
3
= 5.67
11 2
3
. a.4
16
=4
25
=25 OR 2
21
b. . (64
81 1 )
3
= (8
9 1 )
3
= (8
1)3
=512
1
1
1
1
3
Note:
Award 1 mark for 13 seen
Note:
Award 1 mark for3.78 seen
Note:
Award 1 mark for8
9or
8
1seen
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- 2 -
4
a. 4 x = 1 x = 1 4
x = 3
x = 3
b.4
x 3 = x + 3
.4
x x = 3 + 3
.4
3x= 6
3x = 24
x = 8
1
1
1 3
5
Complete diagram drawn 2
6
(a) (4,3)
(b)3
1
1
2
P
Q R
S
R
SM
N
QP
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- 3 -
7 (a)PN
Note: Award 1 mark forPNdrawn on the diagram.
(b)
Locus Y drawn correctly
Locus Z drawn correctly
marked correctly
2
1
1
1 5
8
Uniform scale marked correctly on vertical axisAll the five points marked correctly
All the points joined with straight line
Note: If scale is not written or different scale used, but allthe points plotted correctly, award 1 mark.
If scale is not written or different scale used, but line
graph drawn correctly, award 2 marks.
11
1
3
Number of
students
2006 2007 2008 2009 Year
Tahun
2010
25
20
15
10
5
P Q
S RN
M
Locus Z
Locus Y
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- 4 -
9
a) 4t + 5
b) mmm 101525102
= 102m
1
1
1
310 (a) 2g( 5 k)
(b) 12 27p2
= 3 ( 4 9p2)
= 3 ( 2 + 3p ) ( 2 3p)
1
1
1
3
11
Complete diagram drawn
Note: Any 2 sides drawn correctly, award 1 mark
Any 3 sides drawn correctly, award 2 marks
3
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- 5 -
12 (a) (i), (ii)
Correct construction of 60.
Line SR = 4 cm correctly drawn.Complete quadrilateral drawn.
Correct construction of perpendicular line from point Sto QR.
(b) 3.5 cm 0.1
1
11
1
1 5
1322 )3()2( ddc
2
92 ddc OR2
232 ddc
ddc 2
92
2
92 dd
c
OR2
19 )(
ddc
1
1
1
3
14a) 235
= 0
= 1
b) 4)3(2 33 xx
4)3(2 xx
462 xx
642 xx
10
1
1
1
3
Q R
P
S
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- 6 -
15 a)
GradesGred
A B C D E
FrequencyKekerapan
2 8 5 4 1
Note: 3 or 4 answers in the frequency table correctlyfilled, award 1 mark.
b) Grade B
2
1 3
162
6
65
2
3
p
p
p
26
659
p
pp
2
6
64
p
p
26
322
p
p )(
23
32
p
p
1
1
1 3
17
a. 3 + q 7q 7 3
q 4
b. 6x 2 2(3 + x )
6x 2 6 + 2x
6x 2x 6 + 24x 8x 2
1
1
1 3
18
ST
PQ=
SR
QR
ST
2=
8
3
ST =3
82
=3
16OR 5
3
1cm
1
1 2
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- 7 -
19(a) cosx
o=
10
6=
5
3
(b) PS= 22 817 = 15 OR PR = 22 810 = 6
RS =PS PR
=15 6
= 9 cm
Note : If 15 or 6 is marked correctly in the diagram, award 1 mark
1
1
1 3
20
x
y
5
10
15
20
1 2 3O 1 2 3
5
10
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1. Uniform scale ony-axis marked correctly in the
range 2010 y
2. All 7 points correctly plotted.
Note:
5 or 6 points marked correctly or curve passes through 5or 6 points, award 1 mark.
3. Smooth curve passes through all the 7 points.
Note:If scale is not written but all the points plotted correctly,
award 2 marks.
For other scale on they-axis, deduct 1 mark from the
total marks obtained.
12
1 4
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