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SPM2008
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Mathematic
43
J A W A P A N b o l e h d i d a p a t i d
i l a m a n w e b h t t p : / / w w w
. t i m e s . m y
SOALAN ULANGKAJI SPM 2008
TOPICSPAPER 1
2004 2005 2006 2007
F
O
R
M
1-3
1
2
3
4
5
6
7
8
9
10
11
12
13
F
O
R
M
4
1
2
3
4
5
6
7
8
9
10
11
FO
R
M
5
1
2
3
4
5
6
7
8
9
10
TOTAL 40 40 40 40
Polygon 1 ,11
Transformations 1, 11
Trigonometry 1
Algebraic Expressions 1,11,111
Algebraic Formulae
Algebraic Fractions
Linear Equations 1,11
Indices
Linear Inequalities
Graph of Functions 1
Solid Geometry 1,11,111
Circles 1,11
Statistics 1,11
Standard Forms
Quadratic Expressions and Equations
Set
Mathematical Reasoning
The Straight Lines
Statistics III
Probability I
Circles III
Trigonometry II
Angles of Elevation and Depression
Lines and Plane in 3-Dimension
Number Base
Graph of Functions II
Transformations III
Matrices
Variations
Gradient and the Area under a Graph
Probability II
Bearing
The Earth as a Sphere
Plan and Elevation
7
19,10
13
20
21
19
22
23,24
25,26
-
-
-
27,28
1,2,3,4
-
30,31,32
-
33,34
-
-
8
11,12
15,16
14
5,6
28
-
40
38,39
-
35,36,37
18
17
-
6,7
9,10
-
-
21
20
22
23,24
25
-
-
-
27
1,2,3
19
29,30,31
-
32,33
26
-
8
11,12,13
15
14
4,5
28
-
39,40
36,37,38
-
34,35
16
17,18
-
7
9,10
-
19,20
21
-
22
23
24
-
-
-
25,26
1,2,3,4
-
29,30,31
-
32,33
27
34,35
8
11,12,13
15,16
14
5,6
28
-
39.40
36,37,38
-
-
17
18
-
6,7
9,10
-
19
20
21
22
23,24
25
-
-
-
26,27
1,2,3
-
29,30,31
-
32,33
-
34,35
8
11,12,13
15
14
4,5
28
-
39,40
36,37,38
-
-
16
17,18
-
Analysis Of Mathematic
(2004-2007)
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SPM2008
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Mathematic
SOALAN ULANGKAJI SPM 200844
TOPICSPAPER 1
2004 2005 2006 2007
F
O
R
M
1-3
1
2
3
4
5
6
7
8
9
10
11
12
13
F
O
R
M
4
1
2
3
4
5
6
7
8
9
10
11
FO
R
M
5
1
2
3
4
5
6
7
8
9
10
TOTAL 40 40 40 40
Polygon 1 ,11
Transformations 1, 11
Trigonometry 1
Algebraic Expressions 1,11,111
Algebraic Formulae
Algebraic Fractions
Linear Equations 1,11
Indices
Linear Inequalities
Graph of Functions 1
Solid Geometry 1,11,111
Circles 1,11
Statistics 1,11
Standard Forms
Quadratic Expressions and Equations
Set
Mathematical Reasoning
The Straight Lines
Statistics III
Probability I
Circles III
Trigonometry II
Angles of Elevation and Depression
Lines and Plane in 3-Dimension
Number Base
Graph of Functions II
Transformations III
Matrices
Variations
Gradient and the Area under a Graph
Probability II
Bearing
The Earth as a Sphere
Plan and Elevation
5
2
9
7
1
4
6
14
3
12
13
8
11
10
16
15
2
3
6
7
1
8
5
14
4
12
13
11
10
9
16
15
4
5
8
3
1
6
10
14
2
13
12
11
9
7
16
15
2
11
6
3
7
5
16
4
1,12
15
9
10
8
14
13
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TIMES HIGHER EDUCATION
SOALAN ULANGKAJI SPM 2008
MATHEMATICPaper 1
Nov./Dis
1 hour 15 minutes
DO NOT OPEN UNTILL INTSRUCTED TO
1. Answer all the questions
2. Think thoroughly before answering any of the questions. If you need to change your
answer, erase the answer properly and thoroughly before remarking the question sheet.
This question paper contains 6 printed pages and 0 non printed pages
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SOALAN ULANGKAJI SPM 200846
1. Round off 3.0364 correct to three signicant gures.
A 3.036
B 3.04
C 3.03
D 3.037
2 Express 1.354 x 10 – 5
as a single number
A 0.001354
B 0.0001354
C 0.00001354D 135400
3 =
A 5 x 102
B 5 x 10-2
C 5 x 10-4
D 5 x 10-6
4. Given 5 x 8
3
+ 6 x 8
2
+ 8k = 56708, nd the value of k.
A 0
B 6
C 7
D 561
5. 110102 + 11112 =
A 100112
B 110102
C 1010012
D 1100012
6.
Diagram 1, LMNTUV is a regular hexagon. KLM and HVL
are straight lines. Find the value of x + y .
MATHEMATICS
Paper 1
1 hour 15 minutes
Answer all question
0.35
70 000
DIAGRAM 1
HU
V
N
MLK
760
x y
A 64o
B 74o
C 104o
D 106o
7.
P Q R
In diagram 2, PQR is the tangent to the circle at Q.
Find the value of y.
A 30o
B 45o
C 55o
D 75o
S
750
8.
Diagram 3, PQRSTU is a regular hexagon. H and K are
midpoints of TS and UT respectively. The value of x is
A 106.5o
B 140o
C 150.5o
D 175o
DIAGRAM 2
DIAGRAM 3
27o
x
T H S
R
QP
U
K
T
y
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10
Diagram 5, UVWM is given a clockwise rotation of 270o
about point R, the coordinates of the image of point U are
A (4,3)
B (5,6)
C (7,2)
D (8,5)
9. Diagram 4 shows seven points on a square grid. L is the
image of K under a reection.
The axis of reection is the straight line that joins P and
A Q B R C S D T
DIAGRAM 4
P
L
Q
K
R
T
S
DIAGRAM 5
-2 -1 0 1 2 3 4 5 6 7 8 9 10 11
1
2
3
4
56
-1
-2
-3
-4
U
M
W
VR
y
x
11. It is given that cos = 0.3420 and 180º < < 360º,
nd the value of .
A 70º
B 110º
C 250ºD 290º
0 0
0
12. Diagram 6 shows the graph of y = - sin . The value of is
A 90º
B 180º
C 270º
D 360º
0 0
00
-1
1
DIAGRAM 6
13. Factorise k ( 3 + 2k ) – 35 completely
A ( 2k – 7 )( k – 5 )
B ( 2k – 7 )( k + 5 )
C ( 2k + 7 )( k – 5 )D ( 2k + 7 )( k + 5 )
14
DIAGRAM 7
Diagram 7 shows a cuboid. Name the angle between the
planes HKRT and PQKH.
A THK
B QRK
C QKR
D TRK
S T R
H K
P Q
M L
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26. Pictograph in Table 1 shows the total marks obtained by
four classes in a quiz.
15. Diagram 8, K and L are on a horizontal ground. H is 20 m
vertically above L. Find the angle of depression of K from
H.
A 38.7º
B 43º
C 50.7º
D 51.3º
DIAGRAM 8
20 m
H
K L25 m
16. Diagram 9 shows the position of points P and Q. Find the
bearing of point P from point Q
A 050º B 130º C 250º D 310º
DIAGRAM 9
230ºP
Q
North
North
17. P (37º N,76º W) and Q are two points on the earth`s surface.
PQ is the diameter of the earth. Find the location of Q .
A ( 37º S , 76º E )
B ( 143º S , 76º W )
C ( 37º S , 104º E )
D ( 143º S, 104º E )
18. H ( 50º N, 20º E) and K are two points on the surface
of the earth. K lies 3 600 nautical miles to the south of H.
The latitude of point K is
A 10º S B 60º S C 60º N D 110º S
19. ( 4k – 1 )² =
A 16k² + 8k – 1
B 16k² – 8k + 1
C 16k² – 8k – 1
D 16k² + 1
20. Given that m + = mn, express m in terms of n.
A C
B D
2
n
2
n²-1
2
1-n²
2
n²-n
2
n-n²
21. - =
A C
B D
h+3
3hk
2+3k
6k
2-hk
2hk
2+hk
2hk
hk-2
2hk
6+3hk
6hk
22. If y = 6 y -2, then y =
A C
B D
2
31
43
8
2
31
3
23. can be written as
A 3 x-7 C x7
B 3 x7 D x-7
3
x-7
2
3
2
3
24. It is given that 37
÷ 3n = 9 , nd the value of n.
A - 6 B 4 C 5 D 6
12
25. List all the integres x that satisfy the inequalities
3 < 2x – 4 ≤ 14 - x
A 4,5 B 3,4,5 C 4,5,6 D 3,4,5,6
5 Tauk * *5 Hidayah * * * *
5 Rahmah *
5 Ikhtiar * * *
* represents 25 marks
If the data in Table 1 is represented by a pie chart, nd theangle of a sector which represent the total marks obtained
by 5 Ikhtiar.
A 75 B 108 C 144 D 216
Table 1
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SOALAN ULANGKAJI SPM 2008
Score 1 2 3 4 5 6
Number
of pupils
5 8 2 20 4 6
Table 2
Table 2 shows scores obtained by a group of students in a
game. Number of pupils who get score less than the mode
score is
A 6 B 10 C 15 D 25
27
28. Diagram 10 shows the graph of the function y = x³ + 5
Find the value of k .
A 3 B 4 C 5 D 6
(1,k )
y = x³ + 5
y
x0
DIAGRAM 10
29. Diagram 11 is a Venn diagram which shows the number
of elements in set P, and set Q.
ξ
If ∩ (ξ) = 30, find ∩ ( P Q )′
A 12 B 15 C 14 D 18
∩
30. Given the universal set, ξ = K L, set K = {2,6,7} andset L = {3,5,6,7,8,9}. nd the value of ∩ (ξ).
A 2 B 3 C 7 D 9
∩
6 4 2
QP
DIAGRAM 11
31. List all the subsets of P = {h,k }
A {h},{k }B {},{h},{k }C {h},{k },{h,k }
D {},{h},{k },{h,k }
32. Find the y-intercept of the straight line 2 x + 4 y = 8
A - 4 B 2 C 4 D 8
33 Diagram 12 shows a straight line HK on a Cartesian lane.
0
12
H
-4
K
The gradient of HK is
A - 3 B - 2 C 3 D 4
24 12 33 48 52 60 19 76
DIAGRAM 13
34. Diagram 13 shows 8 cards . A card is picked at random.
State the probability that a number that is divisible by 6 is
picked.
A B C D1
2
1
4
1
8
3
8
35. A box contains of 10 blue marbles and 15 black marbles.
Two marbles are picked At random from the box. The
probability of picking two different colours of marbles is
A B C D1
41
2
2
5
3
5
36. If p α and p = 6, q = - 8 and h = 2 , nd the value of v
when p = 12 and q = 1.
A - B 6 C 15.5 D 18
1
2
√q
v
y
x
DIAGRAM 12
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37. Table 3 shows some value of the variables y , u and v
which satisfy the relationship vα u , nd the value of m.
A 10 B 20 C 25 D 30
√ y
y 9 36
u 3 12
v 5 m
Table 3
38. Diagram 14 shows two objects P and Q on a Cartesian plane. Q is the image of P under a reection.
The line of reection is
A the x-axis
B the y-axis
C x = 1
D y = x
DIAGRAM 14
-2 0 2 4 6 8
2
4
6
Q
y
x
8
P
39. It is given that (3 6) = (96), nd the value of h + k .
A - 1 B 2 C 4 D 8
( )4h
2k
40. Find the matrix P such that -2P =
A C
B D
( )1 32 -4 ( )3 -5
4 -2
( )-1 4
-1 1
( )-1 4
-1 -1 ( )-1 1
-1 -1
( )-2 8
-2 -2
END OF QUESTION PAPER
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TIMES HIGHER EDUCATION
SOALAN ULANGKAJI SPM 2008
MATHEMATICPaper 2
Nov./Dis
2 hour 30 minutes
DO NOT OPEN UNTILL INTSRUCTED TO
1. Read the instructions carefully
2. Think thoroughly before answering any of the questions. If you need to change your
answer, erase the answer properly and thoroughly before remarking the question sheet.
This question paper contains 8 printed pages and 0 non printed pages
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SOALAN ULANGKAJI SPM 200852
This question paper consists of two sections: Section A and Section B.
Answer all the questions in section A and four questions in Section B.
SECTION A
Answers all the questions in this section.
( 52 marks )
1. Using factorization, solve the following quadratic equation:
3x² = 4 ( 2 + x ) - 9 ( 4 marks )
2. Calculate the values of p and q that satisfy the following simultaneous linear equations:
4p – 3q = 10
2p – 5q = 12 ( 4 marks )
3. The Venn diagrams in the answer space show sets P, Q and R. The universal set, ξ = P Q R. On the diagrams providedin the answer space, shade
(a) P ∩ (Q R) ′ (b) (P Q) ∩ R ′
( 3 marks )
∩ ∩
∩ ∩
4. (a) State whether each of the following statements is true or false.
(i) 4² – 1 = 7 or 3 x 4 + 3 = 15
(ii) A square has two right angles and a square has 4 axes of symmetry.
(b) Write down two implications based on the following sentence.
`` 3k² – 5 > 7 if and only if k > 1
(c) Form a general conclusion by induction, given 4 , 7 , 12, 16,……. and
4 = 1² + 3
7 = 2² + 3
12 = 3² + 3
19 = 4² + 3
…………… ( 5 marks )
Q
P
R Q
P
R
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5.
Diagram 1 shows a solid consisting of a cylinder and cone. The diameter of the base of the cylinder is 28cm. The volume of
the solid is 16 632 cm³ and the height of the cylinder is 21cm.
By using П = , calculate the height, in cm , of the cone. ( 4 marks )22
7
21 cm
6.
Diagram 2 shows a cuboid with a horizontal rectangular base UVWT. Calculate the angle between the plane WUL and the
plane TWLM
( 4 marks )
DIAGRAM 1
DIAGRAM 2
M L
W
VU
H
T
K
8 cm
6 cm
7. Table 1 shows numbers of member in three societies from 4 Hidayah.
Table 1
(a) Two members are chosen at random from the Mathematics Society. Calculate the probability that both members are male.
(b) Two members are chosen at random from the Chemistry Society. Calculate the probability that they are from different
gender.
( 5 marks )
Students/ Society Mathematics Science Chemistry
Boy 10 82 4
Girl 5 6 7
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9.
Diagram 3, O is the origin and the point Q lies on the x-axis. The straight line PQ is parallel to the straight line ST.
Given that the equation of the straight line QT is y + x + 2 = 0 , nd
(a) the gradient of PS
(b) the equation of the straight line ST and hence state its x-intercept. ( 5 marks )
DIAGRAM 3
P (0,3)
S (12,6)
T
Q (-2,0)
y
x
8. It is given that = k
(a) Find the value of k .
(b) Using matrices, solve the following simultaneous equations:
5x + 6y = -1
2x + 3y = -1 ( 6 marks )
( )5 6
2 3 ( )3 -6
-2 5 ( )1 0
0 1
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SECTION B
Answer four questions from this section.
( 48 marks )
12.
Table 2
(a) Table 2 shows values of x and y which satisfy the equation y = x³ - 5x + 20 ( 2 marks )
x -3 -2 -1 0 1 2 3 4
y 22 24 20 16 32 64
(b) For this part of the question, use the graph paper . You may use a exible curve ruler.
By using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 10 units on the y-axis,
draw the y = x³ – 5x + 20 - 3 < x < 4 ( 3 marks )
(c) From your graph, nd(i) the value of y when x = - 1.5 ( 1 marks )
(ii) the value of x when y = 20 ( 2 marks )
(d) Draw a suitable line on your graph to nd the value of x which satises theequation x³ – 15x + 10 = 0 for - 3 < x < 4. State this values of x . ( 4 marks )
13 (a) Transformation T represents a translation and R represents clockwise rotation of 90 0 about the point (1,3). State
the coordinates of point ( 3,2 ) under the transformations
(i) R (ii) TR (iii) RT ( 5 marks )
(b) Diagram 6 shows a polygon ABCD being mapped to ABPQRD under a transformation M
(i) State
(a) the centre of enlargement
(b) the scale factor, k
DIAGRAM 6-1
3-2( )
(ii) If the area of ABCD is 8 unit², nd the area of BPQRDC ( 7 marks )
BA P
QR
-2 -1 0 1 2 3 4 5 6 7 8
1
2
3
4
5
y
x
-4 -3
D C
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14. The data in Diagram 7 shows the ages, in years, of 48 participants in a mathematics competition.
18 13 12 30 21 19 17 23 23 20
18 17 22 27 14 38 28 29 34 28
37 22 26 25 18 24 21 16 27 31
24 11 21 21 29 30 27 30 27 2322 35 25 22 14 10 18 25
DIAGRAM 7
(a) Based on the data in Diagram 7, complete the Table 3 provided in the answer space. ( 4 marks )
Age (years) Frequency Upper Boundary Cumulative frequency
5 - 9 0 9.5 0
10 - 14
(b) For this part of the question, use graph paper.
By using a scale of 2 cm to 5 years on the x-axis and 2 cm to 5 participants on the y-axis, draw the ogive for the data.
( 4 marks )
(c) From your ogive in (b),
(i) nd third quartile(ii) hence, explain briey the meaning at the third quartile. ( 4 marks )
15. (a) Diagram 8(i) shows a solid right prism with a rectangular base, PQRS, on a horizontal table. CDPST is the uniform
cross-section of the prism and BCTU is an inclined plane. Rectangle ABCD is a horizontal plane and AQ, DP, UR and TS
are vertical edges.
Draw to full scale, the plan of the solid. ( 3 marks )
U
T
B
C
R
S
Q
P
A
D
6 cm
8 cm
3 cm
3 cm
7 cm
DIAGRAM 8(i)
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