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SEKTOR SEKOLAH BERASRAMA PENUH
BAHAGIAN SEKOLAH
KEMENTERIAN PELAJARAN MALAYSIA
PEPERIKSAAN PERTENGAHAN TAHUN
TINGKATAN LIMA 2008
MATEMATIK
Kertas 2
Dua jam tiga puluh minit
Pemeriksa
Bahagian SoalanMarkah
Penuh
Markah
Diperoleh
A
1 3
2 4
JANGAN BUKA KERTAS SOALAN INISEHINGGA DIBERITAHU
1. Kertas soalan ini mengandungi dua bahagian :
Bahagian A dan Bahagian B. Jawab semua
soalan daripada Bahagian A dan empat soalan
dalam Bahagian B.
2. Jawapan hendaklah ditulis dengan jelas dalam
ruang yang disediakan dalam kertas soalan.
Tunjukkan langkah-langkah penting. Ini boleh
membantu anda untuk mendapatkan markah.
3. Rajah yang mengiringi soalan tidak dilukis
mengikut skala kecuali dinyatakan.
4. Satu senarai rumus disediakan di halaman
2 & 3.
5. Anda dibenarkan menggunakan kalkulator
saintifik yang tidak boleh diprogram.
3 4
4 4
5 5
6 6
7 6
8 5
9 6
10 5
11 4
B
12 12
13 12
14 12
15 12
16 12
Jumlah
Kertas soalan ini mengandungi 23 halaman bercetak dan 1 halaman tidak bercetak
SULIT
1449/2
Matematik
Kertas 2
Mei 2008
212 jam
1449/2
1449/2 2008 Hak Cipta Sektor SBP [Lihat sebelahSULIT
NAMA :
TINGKATAN :
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SULIT 1449/2
1449/2 2008 Hak Cipta Sektor SBP [Lihat sebelahSULIT
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SHAPES AND SPACE
1 Area of trapezium =2
1 sum of parallel sides height
2 Circumference of circle = d= 2r
3 Area of circle = r2
4 Curved surface area of cylinder = 2rh
5 Surface area of sphere = 4r2
6 Volume of right prism = cross sectional area length
7 Volume of cylinder = r2
h
8 Volume of cone =3
1r
2h
9 Volume of sphere =3
4r3
10 Volume of right pyramid =3
1 base area height
11 Sum of interior angles of a polygon = ( n 2) 180
12arc length angle subtended at centre
circumference of circle 360
13area of sector angle subtended at centre
area of circle 360
14 Scale factor , k=PA
PA'
15 Area of image = k2
area of object
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Use
Section A
[52 marks]
Answerall questions in this section.
1 The Venn diagram in the answer space shows sets P, Q and R such that the universal set,RQP .
On the diagram in the answer space, shade
(a) the set QP .(b) the set ( P Q ) R .
[3 marks]
Answer:
(a) (b)
2 Calculate the value of v and ofw that satisfy the following simultaneous linear equations:
112 wv
733
2 wv
[4 marks]
Answer :
PQ
R
PQ
R
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Only3 Using factorisation, solve the following quadratic equation:
2
213
x
xx
[4 marks]
Answer :
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Use 4 Diagram 1 shows a right prism with a horizontal rectangular base PQRS. VUQR is a
trapezium.
Identify and calculate the angle between the plane QWR and the base PQRS.
[4 marks]
Answer :
T
U
W
V
P
Q
R
S
8 cm
6 cm
12 cm
5 cm
DIAGRAM 1
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Only5 In Diagram 2, straight line TU is parallel to straight line VWand O is the origin .
The equation of straight line VW is 02552 yx .
Find:
(a) the equation of the straight line TU.
(b) the x-intercept of the straight line TU.
[5 marks]
Answer:
(a)
(b)
DIAGRAM 2
y
x
W
U(1,5)
V
T
O
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Use
6 Diagram 3 shows two sectors of circle ORQ and OPS with centre O.
By 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)
OP
Q
R
S
1507 cm
12 cm
DIAGRAM 3
7 cm
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Only7 (a) State whether the following statements are true or false.
(i) 2.02
1and
3 aaaa
(ii) Number 5 is an odd number or number 2 is a prime number.
(b) State the antecedent and consequent of the implication:
(c) Complete the following argument.
Premise 1 : If y > 3, then 5y > 15.
Premise 2 : _________________________________________
Conclusion : 5y > 15.
[6 marks]
Answer :
(a) (i)
(ii)
(b) Antecedent : ______________________________
Consequent : ______________________________
(c) Premise 2 : ________________________________________________
If y is less than zero, then y is a negative number.
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Use 8 (a) Complete the following statement using the quantifier all or some, to make it a falsestatement.
(b) Write down two implications based on the following statement:
(c) Make a general conclusion by induction for the sequence of numbers 2, 14, 34,
which follows the following pattern.
2 = 4(1)2 2
14 = 4(2)2 2
34 = 4(3)2 2
62 = 4(4)2
2
= ..
[ 5 marks]
Answer:
(a) ____________ polygons have six sides.
(b) Implication 1:
____________________________________________________________
Implication 2 :
_____________________________________________________________
(c) _____________________________________________________________
______________________________________________________________
____________ polygons have six sides.
x > y if and only if x < y
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Only9 (a) The inverse matrix of
45
23is p
35
4 q
Find the value of p and of q.
(b) Hence, using matrices, calculate the value ofx and ofy that satisfy the following
simultaneous linear equations :
3x 2y = 8
5x 4y = 13
[6 marks]
Answer :
(a)
(b)
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Use
10 Diagram 4 shows the speed-time graph of a particle for a period of 50 seconds.
(a) Calculate the rate of change of speed, in ms-2
, in the first 10 seconds.
(b) Calculate the value of u, if the total distance traveled in the last 40 seconds is 750 m.
[5 marks]
Answer :
(a)
(b)
Speed (ms-1
)
Time (s)0
5
10 30
20
50
DIAGRAM 4
u
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Only11 Diagram 5 shows a solid formed by joining a prism to a right pyramid. Trapezium
ABGFis the uniform cross-section of the prism.
FG = GH= 7 cm. The height of the pyramid is 6 cm.
Calculate the volume, in cm3
, of the solid.
[ Use = 722 ]
[4 marks]
Answer:
DIAGRAM 5
8 cm
11 cmA B
CD
E
F G
H
V
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For
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Use Section B
[48 marks]
Answer four questions from this section.
12 (a) Complete Table 1 in the answer space for the equation y = 2x2
+ 4x + 16.
x 4 3 2 1 0 1 2 3 4
y 32 h 0 10 16 18 k 10 0
Calculate the values of h and of k.
[2 marks]
(b) For this part of the question, use the graph paper on pag 15 .
You may us flexible curve ruler.
By using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis ,
draw the graph of y = 2x2
+ 4x + 16 for 4 x 4.[4 marks]
(c) From your graph, find
(i) the value ofy when x = 2.2
(ii) the value of x when y = 5 [3 marks]
(d) Draw a suitable straight line on your graph to find all the values of x which satisfy the
equation 2x2
+ x 11 = 0 for 4 x 4.
State these values ofx.
[3 marks]
Answer:
(a) h =
k=
(b) Refer graph on page 15
(c) (i) y =
(ii) x = .
(d) x =
TABLE 1
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Graph for Question 12
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Use13 (a) Transformation T is a translation
3
2and transformation P is an anticlockwise
rotation of 90o
about the centre (5, 0).
State the coordinates of the image of point (9, 4) under each of the following
transformations:
(i) P,
(ii) TP,
(iii) T2
[4 marks]
(b) Diagram 6 shows three quadrilaterals A, B and C, drawn on a Cartesian plane.
(i) Cis the image ofA under the combined transformations WV.
Descibe in full,:
(a) the transformation V
(b) the transformation W
[5 marks]
(ii) It is given that B represents a region of area 180 cm2.
Calculate the area, in cm2, of the region represented by A.
[3 marks]
0 2 4 6 8 10 12x
2
4
8
y
C A
DIAGRAM 6
B
6
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1449/2 2008 Hak Cipta Sektor SBP [Lihat sebelahSULIT
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OnlyAnswer:
(a) (i)
(ii)
(iii)
(b) (i) (a)
(b)
(ii)
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Use
14 The data in Table 2 shows the mass, in kg, of a group of 32 members of Science and
Mathematics societies.
44 64 59 49 35 40 50 51
60 50 40 43 47 45 57 5354 49 58 54 48 47 53 45
51 52 62 59 56 46 51 56
(a) Based on the data in Table 2 and by using a class interval of 5 kg,
complete the following table.
[4 marks]
Answer:
(a)
Mass (kg) Frequency Midpoint
35 39
(b) Calculate the estimated mean of the mass of the members.
[3 marks]
(c) Using a scale of 2 cm to 5 kg on the x-axis and 2 cm to 1 member on the y-axis, draw
a frequency polygon for the above data.
[5 marks]
Answer:
(b)
(c) Refer graph on page 19
TABLE 2
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Graph for Question 14
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Use15 (a) Complete Table 3 in the answer space for the equation y =
x
2by writing down the
values ofy when x = 0.5 and x = 2. [2 marks]
(b) For this part of the question, use the graph paper provided on page 21.
You may use a flexible curve rule.
By using a scale of 2 cm to 1 unit on both the axes, draw the graph ofy = x
2for
4 x 4. [5 marks]
(c) From your graph, find
(i) the value ofx when y = 1.2 ,
(ii) the value ofy when x = 2.3. [2 marks]
(d) Draw a suitable straight line on your graph to find values of x which satisfies the
equation x + 1 =x
2for 4 x 4.
State these values ofx.
[3 marks]
Answer:
(a)
x 4 3 2 1 0.5 0.5 1 2 3 4
y 0.5 0.67 1 2 4 2 0.67 0.5
TABLE 3
(b) Refer graph on page 21
(c) (i) x = .
(ii) y = .
(d) x = ............................................................................
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Graph for Question 15
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Use16 (a) Transformation U is a translation
2
1.
Transformation V is a reflection in the straight line y = 1.
State the coordinates of the image of point (3, -2) under each of the following
transformations :
(i) U,
(ii) UV.
[3 marks]
(b) Diagram 7 shows three quadrilaterals ABCD, HGFE and KJIE on a
Cartesian plane.
J
K
I
H
G
B
DC
E
F
A
- 2
- 4
6
- 8
4
- 10
2
- 6 - 4 - 2 6420
DIAGRAM 7
HGFEis an image of ABCD under transformation W and KJIE is an image of
HGFE under transformation Z.
(i) Describe in full,
(a) the transformation W,
(b) the transformation Z.
[6 marks]
(ii) Given that quadrilateral HGFE represents a region of area 26 cm2,
calculate the area, in cm2, of the region represented by the shaded region.
[3 marks]
x
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