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SEKOLAH MENENGAH KEBANGSAAN
KOTA SAMARAHAN
PEPERIKSAAN AKHIR TAHUN 2008
MATEMATIK
TINGKATAN 4
MATEMATIK
Kertas 2
Dua jam tiga puluh minit
Pemeriksa
Bahagian SoalanMarkah
Penuh
Markah
Diperoleh
A
1 4
2 4
JANGAN BUKA KERTAS SOALAN INI
SEHINGGA DIBERITAHU
1.Kertas soalan ini mengandungi satu bahagian :Jawab semua soalan.
2.Jawapan hendaklah ditulis dengan jelas dalamruang yang disediakan dalam kertas soalan.
Tunjukkan langkah-langkah penting. Ini bolehmembantu anda untuk mendapatkan markah.
3.Rajah yang mengiringi soalan tidak dilukis
mengikut skala kecuali dinyatakan.
4.Satu senarai rumus disediakan di halaman
2.
5.Anda dibenarkan menggunakan kalkulator
saintifik yang tidak boleh diprogram.
3 4
4 5
5 4
6 6
7 6
8 3
9 12
10 12
Jumlah
Kertas soalan ini mengandungi 14 halaman bercetak
SULIT
1449/2
Matematik
Kertas 2
Oktober2008
2
12 jam
1449/2
[Lihat sebelah
SULIT
NAMA :
TINGKATAN :
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MATHEMATICAL FORMULAE
The following formulae may be helpful in answering the questions. The symbols given are the ones
commonly used.RELATIONS
1 am x an = a m+ n
2 am an = a m n
3 ( am )n = a mn
4 A-1 =bcad
1
ac
bd
5 P ( A ) =)(
)(
Sn
An
6 P ( A ) = 1 P(A)
7 Distance = 2 21 2 1 2( ) ( ) x x y y +
8 Midpoint, (x, y ) =
++
2,
2
2121 yyxx
9 Average speed =
10 Mean =
11 Mean =
12 Pythagoras Theorem
c2 = a2 + b2
13 m =12
12
xx
yy
14-intercept
-intercept
ym
x=
Answerall questions in this section.
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distance travelled
time takensum of data
number of data
sum of (class mark frequency)
sum of frequencies
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1 Solve the quadratic equation3
5 4 22
x
x
= . [4 marks]
Answer:
2 The Venn diagram shows set P, set Q and set R. Given that the universal set = P Q R,
shade the region which represents the set.
(a) Q R P
[4 marks]
P Q
R
(b) P Q R
P Q
R
3. Diagram 1 shows a right prism with a horizontal rectangular baseJKLM. TrapeziumJKQP
is the uniform cross-section of the prism. The rectangular surface QRLKis inclined.
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3
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Calculate the angle between the planeRSJand the vertical planeRSML.[4 marks]
Answer:
4. In Diagram 2, O is the origin.JK,KL andLMare straight lines.JKis parallel toLMandKL is
parallel to the x-axis.
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DIAGRAM 1
5 cmSR
Q
P
ML
KJ
8 cm
12 cm
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The equation ofLMis 2y =x + 4.
(a) State the equation of the straight lineKL.
(b) Find the equation of the straight lineJKand hence, state itsy-intercept.[5 marks]
Answer:
(a)
(b)
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5
DIAGRAM 2
2
L K
M
Ox
J(3, 2)
y
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5. Diagram 3 shows a solid that is a combination of a pyramid VPQRSand a semi cylinder
with diameter 7 cm. VS= 8 cm,PS= QR = 6 cm. Using7
22= , find the volume, in cm 3
of the solid.
[4 marks]
Answer:
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V
P
R
S
Q
DIAGRAM 3
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6. Diagram 4 shows two semicirlesAOBCEand OBCD, with the centre O andB respectively.
BFCis a sector with the centreB. AOBCis a straight line andAO = 2OB.
BC= 3.5 cm and FBC= AOE= 60. Using =7
22, calculate
(a) the perimeter, in cm, of the whole diagram,
(b) the area, in cm2
, of the shaded region. [6 marks]
Answer:
(a)
(b)
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7
A O B
F
C
D
E
DIAGRAM 4
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7. (a) Determine whether the following sentence is a statement.
9 is not a factor of 40
(b) Write two implications from the following statement.
R3 = 64 if and only ifR = 4
(c) Write down the conclusion in the following argument.
Premise 1 : If m = 7 , then 3m = 21Premise 2 : 3m 21
(d) 2 =(0)2 + 2
3 =(1)2 + 2
6 =(2)2 + 2
11=(3)2 + 2
[6 marks]
Answer:
a) ..
b) Implication 1 : ..
Implication 2 : .
(c) Conclusion :
(d) Conclusion :
8. Table 1 shows the results of a survey. The survey is on the mode of transport to SMK
Shahbandar on a particular day involving 200 students.
Boys Girls
Bus 60 30
Car 28 36
Bicycle 32 14
If a student is picked at random, find the probability that the student went to school by car.
[3 marks]
Answer:
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TABLE 1
Make a general conclusion by induction
based on the following number pattern.
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9. The data in Diagram 5 shows the number of telephone calls made by 40 students in a
month.
28 22 34 26 22 37 35 38
23 20 22 33 39 17 45 28
21 39 35 14 38 24 27 35
19 34 31 26 40 32 28 44
30 32 29 27 32 40 33 30
(a) Using data in Diagram 5 and a class interval of 5 telephone calls, complete Table 3
in the answer space.
[4 marks]
(b) For this part of the question, use the graph paper provided on page 11.
By using a scale of 2 cm to 5 telephone calls on the horizontal axis and 2 cm to
5 students on the vertical axis, draw an ogive based on Table 3.
[5 marks]
(c) Find the interquartile range from your ogive in (b), [3 marks]
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9
DIAGRAM 5
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Answer :
9.
(a)
TABLE 3
(b) Refer graph on page 12
(c)
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Number of telephone
calls
Upper
Boundary
Frequency CumulativeFrequency
6 10 10.5 0 0
11 15
16 20
10
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1449/2 [Lihat sebelah
SULIT
11
Graph for Question 9G
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10. You are not allowed to use graph paper to answer this question.
(a) Diagram 6(i) shows a solid right prism with rectangular base PQMN on a
horizontal table.The surfacePSTNis its uniform cross-section.The rectangle RSTU is an inclined plane. The edges UM, TN , SP and RQ arevertical edges.
Draw to full scale, the elevation of the solid on a vertical plane parallel to MNas
viewed from X.[4 marks]
Answers :
10 (a)
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P
S
N
T
M
Q
U R
3 cm
3 cm
5 cm
6 cm
X DIAGRAM 6(i)
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(b) Another solid right prism is joined to the solid in the Diagram 6 (i) at the vertical plane
MNWVUto form a combined solid as shown in Diagram 6 (ii).
The surfaceDEFGJis its uniform cross-section and GFNWis an inclined plane.
The rectangleDJKL is a horizontal plane.The baseEFNPQMis on a horizontal plane.
DEandJG are vertical.
JG =KW= 5 cm.
Draw to full scale,
(i) the elevation of the combined solid on a vertical plane parallel to FPas viewed
from Y,
[4 marks](ii) the plan of the combined solid. [4 marks]
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SULIT
13
3 cm
P
S
N
T
M
Q
U R
3 cm
D
E
F
G
5 cm
6 cm
7 cm
3 cm
L
K
DIAGRAM 6 (ii)
Y
W
V
J
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Answer:
10.
(b) (i)
(ii)
END OF QUESTION PAPER
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