sbp p1 2008 (2)
TRANSCRIPT
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SEKTOR SEKOLAH BERASRAMA PENUH
BAHAGIAN SEKOLAH
KEMENTERIAN PELAJARAN MALAYSIA
PEPERIKSAAN PERTENGAHAN TAHUN
TINGKATAN 5 2008
MATEMATIK
Kertas 1
Satu jam lima belas minit
JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU
1. Kertas soalan ini adalah dalam Bahasa Inggeris.2. Calon dikehendaki membaca maklumat di halaman 2.
Kertas soalan ini mengandungi 24 halaman bercetak.
1449/1
Matematik
Kertas 1
Mei 2008
14
1jam
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INFORMATION FOR CANDIDATES
1. This question paper consists of 40 questions.2. Answerall questions.3. Answer each question by blackening the correct space on the answer sheet.4. Blacken only one space for each question.5. If you wish to change your answer, erase the blackened mark that you have done.
Then blacken the space for the new answer.
6. The diagrams in the questions provided are not drawn to scale unless stated.7. A list of formulae is provided on page 3 to 4.8. You may use a non-programmable scientific calculator.
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MATHEMATICAL FORMULAE
The following formulae may be helpful in answering the questions. The symbols given are theones commonly used.
RELATIONS
1 a
m
v
a
n
= a
m+ n
2 amzan = a m n
3 (am )n = a mn
4 A-1
=bcad
1
ac
bd
5 P(A ) =)(
)(
Sn
An
6 P(Ad ) = 1 P(A)
7 Distance = 2212
21 yyxx
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 m =
distance travelled
time taken
sum of data
number of data
sum of (class mark frequency)
sum of frequencies
y-intercept
x-intercept
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SHAPES AND SPACE
1 Area of trapezium =2
1 sum of parallel sides height
2 Circumference of circle = Td= 2Tr
3 Area of circle = Tr2
4 Curved surface area of cylinder = 2Trh
5 Surface area of sphere = 4Tr2
6 Volume of right prism = cross sectional area length
7 Volume of cylinder = Tr2h
8 Volume of cone =31Tr
2h
9 Volume of sphere =3
4Tr
3
10 Volume of right pyramid =3
1 base area height
11 Sum of interior angles of a polygon = (n 2) 180
12Q
360
centreatsubtendedanglecircleofncecircumfere
lengtharc !
13Q360
centreatsubtendedangle
circleofarea
sectorofarea!
14 Scale factor , k=
A
A'
15 Area of image = k2
area of object
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1
Round off 0.05078 correct to three significant figures.
A 0.05
B 0.0508
C 0.051
D 0.508
2
Express 410305.2 v as a single number.
A 0.0002305
B 0.002305
C 0.02305
D23050
3
61032.8 v + 5106.7 v
A510432.8
v
B610432.8
v
C51008.9 v
D 61008.9 v
4 !22
100110011
A 100112
B 10101 2
C 211010
D 11100 2
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6
In Diagram 1, JKLMN is a regular pentagon. MNFandLEFare straight lines.
The value ofx +y =
A 57
B 42
C 36
D 21
5
2m4 8 = 10156 , find the value ofm.
A 0
B 1
C 2
D 3
K
L J
E
NFM
x
y
15
Diagram 1
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7
Diagram 2 shows a regular pentagonPQRSTand an isosceles trianglePUM.
Calculate the value ofx +y
A 108
B 120
C 144
D 180
8
In Diagram 3,RSis a tangent to the circlePTSQ at SandPQR is a straight line.
The value of m is
A 54o
B 50o
C 46o
D 40o
TP
Q
R
S
U
M
xo
yo
Diagram 2
Diagram 3
y P
T
S
Q
50
86
m
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9 Diagram 4 shows two pentagons,R and Son a Cartesian plane. Sis the image ofRunder a reflection in the linePQ.
Find the equation of the line PQ.
A 1!x
B 1!y
C 2!x
D 0!y
y
-4
-3
-2
-1 0 1 2 3 4
4
3
2
1
-1
-2
-3
-4
x
R
Diagram 4
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10 Diagram 5 shows an incomplete triangle KdLdMd , which is the image oftriangleKLMunder an enlargement.
Find the coordinates of point Ld.
A ( 3, -3 )
B ( 4, -2 )
C ( 2, -4 )
D ( 6, 2 )
Diagram 5
y
1 2 3 4 5 7
4
3
2
1
-1
-2
-3
-4
x
K
ML
M
d
Kd
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11
In Diagram 6,PQSandRSTare straight lines. Given that tan x =2
1and
cos y =5
4 .
Find the length ofRQ.
A 12 cm
B 16 cm
C 20 cm
D 24 cm
Diagram 6
P
TR
Q
S
y
x
8 cm
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13
Diagram 8 shows the graph ofy = cos x.
Find the value ofx.
A 60
B 120
C 300
D 330
12
In Diagram 7, PQRS is a rectangle, STR is a straight line and ST=3
1SR.
Find the value of tan PTR .
A 23
B 3
2
C 2
1
D3
2
1 1
y
x
1
1
1
1
Diagram 8
12 cm
Diagram 7
P Q
RS T
6 cm
1
y(x, 0.5)
-1
0
x
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14
Diagram 9 shows a right pyramid with an isosceles triangle basePQR. Eia a midpoint
ofQR.
Calculate the angle between the lineESand the planePQR.
A '04133
B '02435
C '01438
D '02441
15
In Diagram 10,PTand QRSare two vertical poles on a horizontal plane.
Determine the angle of elevation ofQ fromP.
A QRP
B PRS
C PQR
D QPR
Diagram 9
Diagram 10
10cm
8cm
13 cm
S
R
Q
PyE
Q
P R
ST
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16
!
3
12
4
2
A
1
3
B
1
4
C
1
4
D
2
4
17 In Diagram 11, JMNand JKL are tangents to the circle FKM.
Find the value ofx.
A 54
B 62
C 64
D 72
Diagram 11
L
MJ N
K F72
x
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19
!2)3()3(2 yxyxx
A 22 963 yxyx
B 22 9122 yxyx
C 22 9123 yxyx
D 22 9123 yxyx
18
Diagram 12 shows the graph of y = 8 x3.
Find the value of k.
A -2
B -8
C 2
D 8
y
Diagram 12
x
y = 8 x3
y 0,k O
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22 Given that nnn ! 8243 , find the value of n.A 3
B 4
C 5
D 6
20
Given that, 33
2!
t
express t in terms ofm.
A
3
)32( 2m
B2
3
32
m
C 9
922
m
D2
9
32
m
21
Express22
1
p
p
p
6
3 as a single fraction in its simplest form.
A2
2
6
33
p
pp
B 2
2
6
33
p
pp
C 2
2
6
31
p
pp
D
2
2
2
13
p
pp
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23
3
214
a
acan be written as
A58
a
B18 a
C516 a
D a16
24
Simplify 983322 nmnm
A26 m
B26m
C28m
D148
m
25
The solution for 131219 e mm is
A2010 m
B 1410 e m
C 1410 e m
D 1210 e m
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26
Diagram 13 is a pictograph showing the number of laptops sold on Monday and
Tuesday. The number of laptops sold on Wednesday is not shown.
Monday
Tuesday
Wednesday
The sale on Tuesday was 20% of the total sale for the three days. The number oflaptops sold on Wednesday was
A 90
B 150
C 180
D 450
represents 30 laptops
Diagram 13
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27
Diagram 14 is a bar chart which is incomplete, showing the number of fruit trees in anorchard.
The ratio of the number of Mango trees to the number of Durian trees is 5 : 3.
Find the total number of fruit trees in the orchard.
A 240
B 280
C 300
D 320
Type of tree
Diagram 11
20
40
60
80
100
Number of fruit trees
Dragon
fruit
Mango Durian
Diagram 14
0
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29
Given \ = {a, b, c, d, e, i, o, u}, X= {a, i, u}, Y= {a, b, d} andZ= { b, c, d}.
Find ? AZYXn '
A 2
B 3
C 4
D 5
28 Diagram 15 shows a graph of a function .
The equation of the function is
A xy
5!
B5
xy !
Cx
y5
!
D5
xy !
y
O
5
1 5
1
x
Diagram 15
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30
Diagram 16 is a Venn diagram with the universal set \ = X Y Z.
It is given that ][2 YXn
n ! . Find the value of k.
A 5
B9
C 10
D 12
31
Diagram 17 is a Venn diagram which shows the universal set \, setP, set Q and setR.
The shaded region in the Venn diagram represents the set
A QRP
B (P R )d Q
C (PdRd) Q
D (P R )d Q
Diagram 17
X Y
Z
62k
10
5
7 + k
7 6
Diagram 16
P Q
R
\
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32
In Diagram 18 below, the gradient of the straight line3
4!TV .
Find the coordinates of point N.
A ( 4, 3 )
B ( 3, 4 )
C ( 3, 5 )
D ( 4, 5 )
33
Find they-intercept of the straight line 1056 ! yx
A 5
6
B3
5
C6
5
D 2
y
Diagram 18
V(3,0)
N
Tyy
O
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34
Table 1 shows the distribution of teachers in three schoolsR, Sand T.
If a teacher is chosen at random from the three schools, what is the probability that a
male teacher from school Sis chosen?
A139
74
B139
44
C139
42
D139
20
35 A box contains a few good eggs and 15 rotten eggs. If an egg is chosen at random from
the box and the probability of getting a rotten egg is7
3, find the total number of eggs
in the box.
A 12
B 20
C 35
D 56
Table 1
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36 Table 2 shows the relationship between three variables w, tand h.
w t h
2 2 4
4 m 9
Table 2
Given that w wh
t , calculate the value ofm.
A 3
B 6
C 12
D 18
37
Given that xy w and 32 ! zx . If 10!y when 4!z , calculate the value of z
when 8!y .
A 0.5
B 1.5
C 2.5
D 3.5
38
F varies directly as the square root of m and inversely as the square of n. Given that
5
4!F when 64!m and 5!n , express Fin terms ofm and n.
A22
3
n
mF !
B22
5
n
mF !
Cm
nF
3
2 2!
Dm
nF
4
3 2!
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END OF QUESTION PAPER
39 Given that
x
4 5y =
11
2020, calculate the value ofx and ofy.
A x =5
1 , y = 5
B x =5
1, y = 5
C x = 5, y =5
1
D x = 5, y =5
1
40
M is a 22 v matrix where
1
0
2
32 M =
0
1
3
4
Find the matrix ofM.
A
2
1
7
2
B
2
1
7
2
C
2
1
7
2
D
2
1
7
2
S