Spb Maths P2 Pmr 2009
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1 SULIT Nama: …………………………………………
Tingkatan: ……………
BAHAGIAN PENGURUSAN SEKOLAH BERASRAMA PENUH& SEKOLAH KLUSTER KEMENTERIAN PELAJARAN MALAYSIA
PEPERIKSAAN PERCUBAAN PENILAIAN MENENGAH RENDAH 2009 MATEMATIK Kertas 2 Ogos 2009 1
3 4
jam
50/2
Satu jam empat puluh lima minit JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU Untuk Kegunaan Pemeriksa
1.
Tuliskan nama dan tingkatan anda pada ruang yang disediakan.
2.
Kertas soalan ini adalah dalam bahasa Inggeris.
3.
Kertas soalan ini mengandungi 20 soalan.
4.
Jawab semua soalan.
5.
Jawapan anda hendaklah ditulis pada ruang yang disediakan dalam kertas soalan ini.
6.
Tunjukkan langkah-langkah penting dalam kerja mengira anda. Ini boleh membantu untuk mendapatkan markah.
7.
Jika anda hendak menukar jawapan, batalkan jawapan yang telah dibuat. Kemudian tulis jawapan yang baru.
8.
Rajah yang mengiringi soalan tidak dilukis mengikut skala kecuali dinyatakan.
9.
Markah yang diperuntukkan bagi setiap soalan ditunjukkan dalam kurungan.
10. Penggunaan kalkulator tidak di- benarkan. 11. Serahkan kertas soalan ini kepada pengawas peperiksaan pada akhir peperiksaan.
Kod Pemeriksa: Soalan 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Markah Penuh 2 2 3 3 3 3 3 2 5 5 2 2 2 3 3 3 4 3 3 4
Markah Diperoleh
Jumlah Kertas soalan ini mengandungi 17 halaman bercetak 50/2 © 2009 Hak Cipta SBP
www.tutormuruli.blogspot.com
[Lihat sebelah SULIT
2 The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. RELATIONS
1
a m a n a m n
2
a m a n a m n
3
(a m ) n a mn
4
Distance =
5
Midpoint
( x2 x1 ) 2 ( y2 y1 )2
y y2 x x2 , 1 ( x, y ) = 1 2 2
distance travelled time taken
6
Average speed =
7
Mean =
8
Pythagoras Theorem c2 a2 b2
sum of data number of data
SHAPE AND SPACE
1
Area of rectangle = length width
2
Area of triangle =
3
Area of parallelogram = base height
4
Area of trapezium =
5
Circumference of circle = d 2 r
1 base height 2
1 sum of parallel sides height 2
[Lihat sebelah SULIT
50/2 © 2009 Hak Cipta SBP www.tutormuruli.blogspot.com
3
6
Area of circle = r 2
7
Curved surface area of cylinder = 2 rh
8
Surface area of sphere = 4 r 2
9
Volume of right prism = cross sectional area length
10
Volume of cuboid = length width height
11
Volume of cylinder = r 2 h
12
Volume of cone =
13
Volume of sphere =
14
Volume of right pyramid =
15
Sum of interior angles of a polygon = (n 2) 180
16
arc length angle subtended at centre circumference of circle 360
17
area of sector angle subtended at centre area of circle 360
18
Scale factor, k =
19
Area of image = k 2 area of object
1 2 r h 3 4 3 r 3 1 base area height 3
PA PA
[Lihat sebelah SULIT
50/2 © 2009 Hak Cipta SBP www.tutormuruli.blogspot.com
4
SULIT
50/2
For Examiner’s Use
Answer all questions 1
Calculate the value of 48 ÷ 3 7 11 [2 marks] Answer:
1
2
2
2 Calculate the value of 0.48 1 0.2 5
[2 marks] Answer:
2
2
3
1
9 16
(a)
Find the value of
(b)
Calculate the value of
3
0.008 1
2
[3 marks] Answer: (a)
(b) 3
3
[Lihat sebelah SULIT 50/2 © 2009 Hak Cipta SBP
www.tutormuruli.blogspot.com
5
SULIT
4
50/2
For Examiner’s Use
2 3 6w k 3 4
(a)
Expand
(b)
Simplify ( 2x – 3 )( 3x + 2 ) – x( 3x – 3 ) [3 marks]
Answer: (a)
(b)
4
3 5
Factorise completely (a)
5gh – 10g2h2
(b)
p + pq – 2 – 2q [3 marks]
Answer: (a)
(b)
5
[Lihat sebelah SULIT 50/2 © 2009 Hak Cipta SBP
www.tutormuruli.blogspot.com
3
6
SULIT For Examiner’s Use
6
Express
50/2
3h h 2 2 as a single fraction in its simplest form. 2 2h [3 marks]
Answer:
6
3
7
Solve each of the following equations: (a)
e=7–e
(b)
3( a + 3 ) = a – 5 [3 marks]
Answer: (a)
(b) 7
3
8
Given b
bc . Express b in terms of a and c. 2a
[2 marks]
Answer:
8
[Lihat sebelah SULIT
2
50/2 © 2009 Hak Cipta SBP
www.tutormuruli.blogspot.com
7
SULIT 9
50/2 For Examiner’s Use
Diagram 9 shows a quadrilateral ABCD. D 45o C 7 cm 120o B
A Diagram 9
[5 marks] Using only a ruler and a pair of compasses, construct Diagram 1 beginning from the diagram provided in the answer space. Based on the diagram constructed, measure the length, in cm, of CD. Answer:
B
A
9
CD = ………………………. 5
[Lihat sebelah SULIT 50/2 © 2009 Hak Cipta SBP
www.tutormuruli.blogspot.com
8
SULIT 10 For Examiner’s Use
50/2
Diagram 10 in the answer space shows a rectangle PQRS. K, L, M and N are midpoints of PQ, QR, RS and PS respectively. X, Y and Z are three moving points in the diagram. (a) (b)
X is the point which moves such that it is equidistant from PQ and SR. By using the letters in the diagram, state the locus of X. On the diagram, draw (i)
the locus of the point Y which moves such that its distance is constantly 4 cm from point K.
(ii)
the locus of the point Z which moves such that it is equidistant from straight lines PQ and PS.
(c)
Hence mark with the symbol the intersections of the locus of Y and the locus of Z. [5 marks]
Answer: (a) (b) (i), (ii) P
N
S
K
O
M
Q
L
R
Diagram 10
10
5
[Lihat sebelah SULIT 50/2 © 2009 Hak Cipta SBP
www.tutormuruli.blogspot.com
SULIT 11
9
50/2
For Examiner’s Use
Diagram 11 in the answer space shows a quadrilateral R drawn on a square grid. 5 Draw the image of the quadrilateral R under a translation . 3
R
Diagram 11 [2 marks]
11
2
[Lihat sebelah SULIT 50/2 © 2009 Hak Cipta SBP
www.tutormuruli.blogspot.com
10
SULIT For Examiner’s Use
12
50/2
Diagram 12 in the answer space shows two triangles drawn on a grid of equal squares. S is the image of S under an enlargement.
y 10 8 6 S
4 2
-2
0
S
2
4
6
8
10
x
-2
Diagram 12 [2 marks] State (a) the centre of the enlargement. (b) the scale factor of the enlargement. Answer: (a)
(b)
12
[Lihat sebelah SULIT 2
50/2 © 2009 Hak Cipta SBP
www.tutormuruli.blogspot.com
11
SULIT 13.
50/2 For Examiner’s Use
Diagram 13 shows a polygon. 32 m 12 m 24 m
28 m Diagram 13 On the grid in the answer space, redraw the polygon using the scale 1 : 400. The grid has equal squares with side of 1 cm. [2 marks] Answer:
13
2
[Lihat sebelah SULIT 50/2 © 2009 Hak Cipta SBP
www.tutormuruli.blogspot.com
12
SULIT For Examiner’s Use
14.
1 2
Find the value of 5 20
50/2
1 2
[3 marks] Answer:
14
3
15
27 3 x 3 Calculate the value of x
Given that 3x =
[3 marks]
Answer:
15
3
16
Given 3 > 2 – p and
2 p4 3
Solve the simultaneous linear inequalities above and represent the common values of p which satisfy both the inequalities on a number line. [3 marks] Answer:
16
3
[Lihat sebelah SULIT 50/2 © 2009 Hak Cipta SBP
www.tutormuruli.blogspot.com
13
SULIT 17
50/2
For Examiner’s Use
Table 17 shows the sale of books at Kedai Buku Utara over 5 months. Month Number of books sold
Jan
Feb
Mar
800
2 400
Apr
May
2 600 2 200
3 000
Table 17 On Diagram 17 in the answer space, complete the scale and draw a line graph to represent all the information in Table 17. [4 marks] Answer: Number of books sold
3000
17
4
Jan
Feb
Mar
Apr
May Month
Diagram 17 [Lihat sebelah SULIT 50/2 © 2009 Hak Cipta SBP
www.tutormuruli.blogspot.com
For Examiner’s Use
14
SULIT 18
50/2
In Diagram 18, PQR and RST are right-angled triangles. [3 marks] Q
xo P
R 10 cm
S
yo T Diagram 18 Given that cos xo =
3 3 and RT = PR. 5 2
(a)
Find the length, in cm, of ST.
(b)
Tan yo.
Answer: (a)
(b) 18
[Lihat sebelah SULIT
3
50/2 © 2009 Hak Cipta SBP
www.tutormuruli.blogspot.com
15
SULIT 19
50/2
Diagram 19 is a pie chart which shows the sale of 4 types of cars in a month. Given that the number of car C sold is twice the number of car B.
For Examiner’s Use
D C o 75o 30
A B
Diagram 19 (a)
State the value of angle D
(b)
By using the data from the pie chart, complete Table 19. [3 marks]
Answer : (a)
(b) Type of car
A
Number of cars sold
B
C
60
Table 19
19
3
[Lihat sebelah SULIT 50/2 © 2009 Hak Cipta SBP
www.tutormuruli.blogspot.com
16
SULIT
50/2
For Examiner’s Use
20
Use the graph paper provided to answer this question. Table 20 shows the values of two variables, x and y of a function. x
–3
–2
–1
0
1
2
y
–7
0
5
8
9
8
Table 20 (a)
By using the scale of 1 cm to 1 unit on the y-axis, complete and label the y-axis.
(b)
Based on Table 20, plot the points on the graph paper.
(c)
Hence, draw the graph of the function. [4 marks]
20
[Lihat sebelah SULIT
4
50/2 © 2009 Hak Cipta SBP
www.tutormuruli.blogspot.com
Tingkatan: ……………
BAHAGIAN PENGURUSAN SEKOLAH BERASRAMA PENUH& SEKOLAH KLUSTER KEMENTERIAN PELAJARAN MALAYSIA
PEPERIKSAAN PERCUBAAN PENILAIAN MENENGAH RENDAH 2009 MATEMATIK Kertas 2 Ogos 2009 1
3 4
jam
50/2
Satu jam empat puluh lima minit JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU Untuk Kegunaan Pemeriksa
1.
Tuliskan nama dan tingkatan anda pada ruang yang disediakan.
2.
Kertas soalan ini adalah dalam bahasa Inggeris.
3.
Kertas soalan ini mengandungi 20 soalan.
4.
Jawab semua soalan.
5.
Jawapan anda hendaklah ditulis pada ruang yang disediakan dalam kertas soalan ini.
6.
Tunjukkan langkah-langkah penting dalam kerja mengira anda. Ini boleh membantu untuk mendapatkan markah.
7.
Jika anda hendak menukar jawapan, batalkan jawapan yang telah dibuat. Kemudian tulis jawapan yang baru.
8.
Rajah yang mengiringi soalan tidak dilukis mengikut skala kecuali dinyatakan.
9.
Markah yang diperuntukkan bagi setiap soalan ditunjukkan dalam kurungan.
10. Penggunaan kalkulator tidak di- benarkan. 11. Serahkan kertas soalan ini kepada pengawas peperiksaan pada akhir peperiksaan.
Kod Pemeriksa: Soalan 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Markah Penuh 2 2 3 3 3 3 3 2 5 5 2 2 2 3 3 3 4 3 3 4
Markah Diperoleh
Jumlah Kertas soalan ini mengandungi 17 halaman bercetak 50/2 © 2009 Hak Cipta SBP
www.tutormuruli.blogspot.com
[Lihat sebelah SULIT
2 The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. RELATIONS
1
a m a n a m n
2
a m a n a m n
3
(a m ) n a mn
4
Distance =
5
Midpoint
( x2 x1 ) 2 ( y2 y1 )2
y y2 x x2 , 1 ( x, y ) = 1 2 2
distance travelled time taken
6
Average speed =
7
Mean =
8
Pythagoras Theorem c2 a2 b2
sum of data number of data
SHAPE AND SPACE
1
Area of rectangle = length width
2
Area of triangle =
3
Area of parallelogram = base height
4
Area of trapezium =
5
Circumference of circle = d 2 r
1 base height 2
1 sum of parallel sides height 2
[Lihat sebelah SULIT
50/2 © 2009 Hak Cipta SBP www.tutormuruli.blogspot.com
3
6
Area of circle = r 2
7
Curved surface area of cylinder = 2 rh
8
Surface area of sphere = 4 r 2
9
Volume of right prism = cross sectional area length
10
Volume of cuboid = length width height
11
Volume of cylinder = r 2 h
12
Volume of cone =
13
Volume of sphere =
14
Volume of right pyramid =
15
Sum of interior angles of a polygon = (n 2) 180
16
arc length angle subtended at centre circumference of circle 360
17
area of sector angle subtended at centre area of circle 360
18
Scale factor, k =
19
Area of image = k 2 area of object
1 2 r h 3 4 3 r 3 1 base area height 3
PA PA
[Lihat sebelah SULIT
50/2 © 2009 Hak Cipta SBP www.tutormuruli.blogspot.com
4
SULIT
50/2
For Examiner’s Use
Answer all questions 1
Calculate the value of 48 ÷ 3 7 11 [2 marks] Answer:
1
2
2
2 Calculate the value of 0.48 1 0.2 5
[2 marks] Answer:
2
2
3
1
9 16
(a)
Find the value of
(b)
Calculate the value of
3
0.008 1
2
[3 marks] Answer: (a)
(b) 3
3
[Lihat sebelah SULIT 50/2 © 2009 Hak Cipta SBP
www.tutormuruli.blogspot.com
5
SULIT
4
50/2
For Examiner’s Use
2 3 6w k 3 4
(a)
Expand
(b)
Simplify ( 2x – 3 )( 3x + 2 ) – x( 3x – 3 ) [3 marks]
Answer: (a)
(b)
4
3 5
Factorise completely (a)
5gh – 10g2h2
(b)
p + pq – 2 – 2q [3 marks]
Answer: (a)
(b)
5
[Lihat sebelah SULIT 50/2 © 2009 Hak Cipta SBP
www.tutormuruli.blogspot.com
3
6
SULIT For Examiner’s Use
6
Express
50/2
3h h 2 2 as a single fraction in its simplest form. 2 2h [3 marks]
Answer:
6
3
7
Solve each of the following equations: (a)
e=7–e
(b)
3( a + 3 ) = a – 5 [3 marks]
Answer: (a)
(b) 7
3
8
Given b
bc . Express b in terms of a and c. 2a
[2 marks]
Answer:
8
[Lihat sebelah SULIT
2
50/2 © 2009 Hak Cipta SBP
www.tutormuruli.blogspot.com
7
SULIT 9
50/2 For Examiner’s Use
Diagram 9 shows a quadrilateral ABCD. D 45o C 7 cm 120o B
A Diagram 9
[5 marks] Using only a ruler and a pair of compasses, construct Diagram 1 beginning from the diagram provided in the answer space. Based on the diagram constructed, measure the length, in cm, of CD. Answer:
B
A
9
CD = ………………………. 5
[Lihat sebelah SULIT 50/2 © 2009 Hak Cipta SBP
www.tutormuruli.blogspot.com
8
SULIT 10 For Examiner’s Use
50/2
Diagram 10 in the answer space shows a rectangle PQRS. K, L, M and N are midpoints of PQ, QR, RS and PS respectively. X, Y and Z are three moving points in the diagram. (a) (b)
X is the point which moves such that it is equidistant from PQ and SR. By using the letters in the diagram, state the locus of X. On the diagram, draw (i)
the locus of the point Y which moves such that its distance is constantly 4 cm from point K.
(ii)
the locus of the point Z which moves such that it is equidistant from straight lines PQ and PS.
(c)
Hence mark with the symbol the intersections of the locus of Y and the locus of Z. [5 marks]
Answer: (a) (b) (i), (ii) P
N
S
K
O
M
Q
L
R
Diagram 10
10
5
[Lihat sebelah SULIT 50/2 © 2009 Hak Cipta SBP
www.tutormuruli.blogspot.com
SULIT 11
9
50/2
For Examiner’s Use
Diagram 11 in the answer space shows a quadrilateral R drawn on a square grid. 5 Draw the image of the quadrilateral R under a translation . 3
R
Diagram 11 [2 marks]
11
2
[Lihat sebelah SULIT 50/2 © 2009 Hak Cipta SBP
www.tutormuruli.blogspot.com
10
SULIT For Examiner’s Use
12
50/2
Diagram 12 in the answer space shows two triangles drawn on a grid of equal squares. S is the image of S under an enlargement.
y 10 8 6 S
4 2
-2
0
S
2
4
6
8
10
x
-2
Diagram 12 [2 marks] State (a) the centre of the enlargement. (b) the scale factor of the enlargement. Answer: (a)
(b)
12
[Lihat sebelah SULIT 2
50/2 © 2009 Hak Cipta SBP
www.tutormuruli.blogspot.com
11
SULIT 13.
50/2 For Examiner’s Use
Diagram 13 shows a polygon. 32 m 12 m 24 m
28 m Diagram 13 On the grid in the answer space, redraw the polygon using the scale 1 : 400. The grid has equal squares with side of 1 cm. [2 marks] Answer:
13
2
[Lihat sebelah SULIT 50/2 © 2009 Hak Cipta SBP
www.tutormuruli.blogspot.com
12
SULIT For Examiner’s Use
14.
1 2
Find the value of 5 20
50/2
1 2
[3 marks] Answer:
14
3
15
27 3 x 3 Calculate the value of x
Given that 3x =
[3 marks]
Answer:
15
3
16
Given 3 > 2 – p and
2 p4 3
Solve the simultaneous linear inequalities above and represent the common values of p which satisfy both the inequalities on a number line. [3 marks] Answer:
16
3
[Lihat sebelah SULIT 50/2 © 2009 Hak Cipta SBP
www.tutormuruli.blogspot.com
13
SULIT 17
50/2
For Examiner’s Use
Table 17 shows the sale of books at Kedai Buku Utara over 5 months. Month Number of books sold
Jan
Feb
Mar
800
2 400
Apr
May
2 600 2 200
3 000
Table 17 On Diagram 17 in the answer space, complete the scale and draw a line graph to represent all the information in Table 17. [4 marks] Answer: Number of books sold
3000
17
4
Jan
Feb
Mar
Apr
May Month
Diagram 17 [Lihat sebelah SULIT 50/2 © 2009 Hak Cipta SBP
www.tutormuruli.blogspot.com
For Examiner’s Use
14
SULIT 18
50/2
In Diagram 18, PQR and RST are right-angled triangles. [3 marks] Q
xo P
R 10 cm
S
yo T Diagram 18 Given that cos xo =
3 3 and RT = PR. 5 2
(a)
Find the length, in cm, of ST.
(b)
Tan yo.
Answer: (a)
(b) 18
[Lihat sebelah SULIT
3
50/2 © 2009 Hak Cipta SBP
www.tutormuruli.blogspot.com
15
SULIT 19
50/2
Diagram 19 is a pie chart which shows the sale of 4 types of cars in a month. Given that the number of car C sold is twice the number of car B.
For Examiner’s Use
D C o 75o 30
A B
Diagram 19 (a)
State the value of angle D
(b)
By using the data from the pie chart, complete Table 19. [3 marks]
Answer : (a)
(b) Type of car
A
Number of cars sold
B
C
60
Table 19
19
3
[Lihat sebelah SULIT 50/2 © 2009 Hak Cipta SBP
www.tutormuruli.blogspot.com
16
SULIT
50/2
For Examiner’s Use
20
Use the graph paper provided to answer this question. Table 20 shows the values of two variables, x and y of a function. x
–3
–2
–1
0
1
2
y
–7
0
5
8
9
8
Table 20 (a)
By using the scale of 1 cm to 1 unit on the y-axis, complete and label the y-axis.
(b)
Based on Table 20, plot the points on the graph paper.
(c)
Hence, draw the graph of the function. [4 marks]
20
[Lihat sebelah SULIT
4
50/2 © 2009 Hak Cipta SBP
www.tutormuruli.blogspot.com
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