SULIT
1
50/2 Matematik Kertas 2 Ogos 2006
1
3 4
50/2
Nama : …………………………….. Tingkatan : 3 ………...……………
jam
SEKTOR SEKOLAH BERASRAMA PENUH KEMENTERIAN PELAJARAN MALAYSIA
PEPERIKSAAN PERCUBAAN PMR SELARAS SBP 2006
MATEMATIK Kertas 2 Satu jam empat puluh lima minit
JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU
1. Tulis uliska kan n nama nama dan tingk tingkat atan an anda anda pada pada ruang yang disediakan 2. Kert Kertas as soala soalan n ini ini adal adalah ah dalam dalam bahas bahasa a Inggeris 3. Kertas Kertas soala soalan n ini ini menga mengandun ndungi gi 20 20 soala soalan. n. 4. Jawab semua soalan. 5. Jawa Jawapa pan n hend hendak akla lah h ditu dituli liss pada pada ruan ruang g yang yang disedi disediaka akan n dalam dalam kertas kertas soala soalan. n. Kertas Kertas soalan soalan ini hendakla hendaklah h diserahk diserahkan an pada akhir peperiksaan. 6. Tunjukk unjukkan an langka langkah-l h-lang angka kah h pent penting ing.. Ini boleh membantu anda untuk mendapatkan markah. 7. Rajah yang mengiringi soalan tidak dilukiskan mengikut skala kecuali dinyata. 8. Mark Markah ah yang yang dipe diperu runt ntuk ukka kan n bagi bagi seti setiap ap soalan ditunjukkan dalam kurungan. 9. Anda tidak bole boleh h meng me nggu guna naka kan n kalkulator.
Guru Pemeriksa Soalan
Markah Penuh
1
2
2
2
3
3
4
3
5
3
6
3
7
3
8
3
9
2
10
3
11
2
12
3
13
3
14
3
15
5
16
3
17
2
18
5
19
3
20
4
Markah Diperoleh
Jumlah
Kertas soalan ini mengandungi 17 halaman bercetak
50/2
© 2006 Hak Ha k Cipta Sektor SBP
[Lihat sebelah SULIT
SULIT
2
50/2
The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. RELATIONS
1
am an
a m n
2
am an
a mn
3
( a m )n
4
Distance =
5
Midpoint
a mn
( x, y ) =
( x2
x1 ) 2 ( y2 y1 )2
x1 x 2 2
,
y1 y 2 2
distance travelled
6
Average speed =
7
Mean =
8
Pythagoras Theorem c2 a 2 b2
time taken
sum of data number of data
SHAPE AND SPACE
1
Area of rectangle = length width
2
Area of triangle =
3
Area of parallelogram =
4
Area of trapezium =
50/2
1 2
1 2
base
height
base
height
sum of parallel sides
height
SULIT
SULIT
3
50/2
= 2π r
5
Circumference of circle = π d
6
Area of circle = π r 2
7
Curved surface area of cylinder = 2π rh
8
Surface area of sphere = 4π r 2
9
Volume of of ri right pr prism = cross se section ional area × length
10
Volume of of cu cuboid = length
11
Volume of cylinder = π r 2 h
12
Volume of cone =
13
Volume of sphere =
14
Volume of of ri right py pyramid =
15
Sum of in interi erior an angles of a polyg lygon = ( n − 2) × 180
16
17
1 3
4 3
2
3
circumference of circle area area of secto sectorr area of circle
=
h
π r
arc length
=
1 3
× base area × height o
angle subtended at centre o
360
angl anglee sub subten tende ded d at at cen centre tre o
360
PA′
18
Scale factor, k =
19
Area of image = k
50/2
π r
× width × height
PA 2
×
area of object
[Lihat sebelah SULIT
SULIT
4
50/2
For Examiner’s Use
Answer all questions. 1
Calculate the value of
3 3 ÷ 1 − and express the answer as a fraction in its lowest 16 8 4 3
term. [2 marks]
Answer:
1
2
2
Calculate the value of −
3 4
× 5.48 − ( −6)
and express the answer as a decimal. [2 marks]
Answer:
2
2
50/2
SULIT
SULIT 3
5
50/2 For Examiner’s Use
Find the value of 3 −0.343
(a )
Calculate the value of (3)3 169
(b)
2
[3 marks]
Answer: (a)
(b) 3
3
4
In Diagram 1, JKL and LMN are right angled triangles.
N
J x°
15 cm 10 cm
y° L 25 cm
K
DIAGRAM 1 Given that cos x
3
. 5 Find (a) the length of LM LM (b) tan y [3 marks]
Answer : (a) 4
(b)
50/2
3
[Lihat sebelah SULIT
SULIT For Examiner’s Use
5
6
50/2
In Diagram 2, triangle P ′ ′ is the image of the triangle P under a transformation V .
y 12
10
P ′ ′ 8
6
P
4
2
0
2
4
6
8
10
12
x
DIAGRAM 2 Describe in full the transformation V .
[3 marks]
Answer:
5
3
50/2
SULIT
SULIT 6
(a) (a)
7
50/2
Diag Diagra ram m 3 in the the answ answer er spac spacee sho shows J ′ ′ is the image of J under a certain
For Examiner’s Use
translation. State the translation.
(b)
On the the diagram diagram in the ans answer wer spac space, e, draw draw the the image image of quadr quadrilat ilatera erall ABCD under a 90° anticlockwise rotation about the point (4, 3). [3 marks]
Answer :
(a)
(b)
y
10
• J
8
6
A B
4
•
C
J ′ ′
D
2
0
2
4
6
8
10
x
DIAGRAM 3 6
3
50/2
[Lihat sebelah SULIT
SULIT For Examiner’s Use
7
8
Express
d 4e
d 2 6 12de
50/2
as a single fraction in its simplest form. [3 marks]
Answer :
7
3
8
The data below shows part of the number of goals scored by the 32 teams in the first rounds of the World Cup 2006. 1 2 0 2 2 3
2 1 3 0 0 0
0 2 1 0 1 2
3 1 2 1 3 1
0 1 3 0 1 2
2 0 3 0 1 3
1 2 3 0 1 1
(a)
Using Using the above above data, data, comp complete lete the tally tally chart chart in the answer answer space. space.
(b)
State the mode. [3 marks]
Answer : (a )
Score 0 1 2 3
Tally
Frequency
8
(b) 3
2 Simplify ( 2a 3) 3(3 4a)
9
[2 marks]
Answer : 50/2
SULIT
SULIT
9
50/2 For Examiner’s Use
9
2
List al all th the in integer va values of of m which satisfy both the inequalities 7 2m 3 and
10
2m 4 .
[3 marks]
Answer:
10
3
11
Given 4
1
2n
64
. Calculate the value of n. [2 marks]
Answer: 50/2
[Lihat sebelah SULIT
SULIT
10
50/2
For Examiner’s Use
11
2
1
12 Simplify (4 qp 4 ) 2
3
q
2
2 p .
[3 marks]
Answer :
12
3
13
Given that
18 F 2 m 2
T
2 . Express T in terms of F and m. [3 marks]
Answer: 50/2
SULIT
SULIT
11
50/2 For Examiner’s Use
13
3
14
Solve each of the following equations. (a) 7u 5 2u (b)
3 2
(4 w 8) 7 w [3 marks]
Answer: (a)
(b)
14
3
15
Diagram 4 in the answer answer space shows shows a rhombus. rhombus. S , X and Y are three moving points in the diagram. (a)
50/2
S is the point which moves such that its distance from point A and point C are the same. By using the letters in the diagram, state the locus of S . [Lihat sebelah SULIT
SULIT For Examiner’s Use
12
(b)
(c)
50/2
On the diagram, draw (i)
the loc locus for the point X that is constantly 2 cm from the line AC ,
(ii) ii)
the loc locus for the po point Y that is constantly 4 cm from the point A
Henc Hence, e, stat statee the the num numbe berr of of inte inters rsect ectio ion n poi point ntss of of the the locu locuss of of X X and the locus of Y .
[5 marks]
Answer: (a)
(b)
A
D
B `
C
DIAGRAM 4 15
(c)
5
16 Factorise completely :
(a) 4m 8m2 n 2 (b) y (3 y ) 4 2 y
50/2
SULIT
SULIT
13
50/2
[3 marks]
For Examiner’s Use
Answer: (a)
(b) 16
3
17 Diagram 5 in the answer space shows polygon ABCDEFG and straight line PQ drawn on a
grid of equal squares. Starting from the line P Q, Q, draw polygon PQRSTUV which is congruent to polygon
ABCDEFG.
[2 marks]
Answer:
E
G F
C
D A
B
P
17
Q Q
2
DIAGRAM 5
P are not allowed for this question . 18 Set squares and protractors
60
50/2
R
S DIAGRAM 6
[Lihat sebelah SULIT
SULIT
14
50/2
For Examiner’s Use
(a) (a)
Usin Using g onl only y a rul ruler er and and a pair pair of of comp compas asse ses, s, con const stru ruct ct qua quadr dril ilat ater eral al PQRS as shown in Diagram 6 using the straight lines PS and SR provided in the answer space.
(b) (b)
Based ased on on the the diag diagra ram m cons constr tru ucted cted in in (a), (a), con consstru truct QT , angle bisector of the ∠ PQR such that point T lies on the line PS . Measure the length QT . [5 marks]
Answer:
P
18
5
S 19
R
The pictograph below shows the number of cakes sold by a school canteen within a week. Monday Tuesday
50/2
SULIT
SULIT
15
50/2 For Examiner’s Use
Wednesday Thursday Friday Key Key :
repr repres esen ents ts 10 cake cakess
Draw a line graph in the answer space to represent all the information in the pictograph above. [3 marks]
Answer:
120
e k 100 a c f o r e b m u 80 N
60
40
20 19
MON
20
TUE
WED
THU
FRI
Day
3
Use the graph paper given to answer this proble m. Table 1 shows the value of two variables, x and y of a function.
x 50/2
−4
−3
−2
−1
0
1
2 [Lihat sebelah SULIT
19
3
SULIT For Examiner’s Use
16
y
5
0
−3
50/2
−4
−3
0
5
TABLE 1
By using using a scale of 2 cm to 1 unit unit on the x-axis and 2 cm to 2 unit on the y-axis, draw the graph of the function on the graph paper provided in the answer space. [4 marks]
Answer: (Refer to graph on page 17)
20
4
50/2
SULIT
