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8/3/2019 Check! Duplicate Pages Xxx Maths f4 Sbp 2008 Full Paper and Ans
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SULIT
BAHAGIAN PENGURUSAN
SEKOLAH BERASRAMA PENUH / KLUSTER
KEMENTERIAN PELAJARAN MALAYSIA
PEPERIKSAAN AKHIR TAHUN SELARAS SBP 2008 1449/1TINGKATAN EMPAT
MATHEMATICS
Kertas 1
Oktober
1 jam 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 belakang kertas soalan ini.
Kertas soalan ini mengandungi 20 halaman bercetak.
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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 a
n= a
m+ n
2 ama
n= a
m n
3 ( am
)n
= amn
4 A-1
=bcad
1
ac
bd
5 Distance = 2 22 1 2 1( ) ( ) x x y y
6 Midpoint, ( x, y ) =
2,
2
2121 yyxx
7 Average speed =
8 Mean =
9 Mean =
10 Pythagoras Theorem
c2
= a2
+ b2
11 P ( A ) =)(
)(
Sn
An
12 P ( A ) = 1 P(A)
13 m =12
12
xx
yy
14 m =
sum of data
number of data
sum of (class mark frequency)
sum of frequencies
y-intercept
x-intercept
distance travelled
time taken
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SULIT
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
12360
centreatsubtendedangle
circleofncecircumfere
lengtharc
13360
centreatsubtendedangle
circleofarea
sectorofarea
14 Scale factor , k=PA
PA'
15 Area of image = k2
area of object
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INFORMATION FOR CANDIDATES
1. This question paper consists of 40 questions.
2. Answer all questions.
3. Each question is followed by four alternative answers, A, B, C or D. For each
question, choose one answer only. Blacken your answer on the objective answer
sheet provided.
4. If you wish to change your answer, erase the blackened mark that you have done.
Then blacken the space for the new answer.
5. The diagrams in the questions provided are not drawn to scale unless stated.
6. A list of formulae is provided on page 2 to 3.
7. You may use a non-programmable scientific calculator.
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1. Round off 37 285 correct to three significant figures.
A 37 000
B 37 200
C 37 290
D 37 300
2. Express 2937 105
as a single number.
A 2 937
B 29 370
C 293 700
D 2 937 000
3.144
0160
=
A 28572
10
B 563
10
C 2857 410
D 56 210
4 136
10 52 710 =
A 12 710
B 12 6
10
C 1057
10
D 105 6
10
5. A rectangular floor has a width of 2700 cm and a length of 3200 cm. The floor
will be covered with tiles. Each tile is a square of side 24 cm. Calculate the number
of tiles required to cover the floor fully.
A 15 104
B 36 104
C 15 105
D 36 105
Answer all questions.
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6. )3()2(5 yxyx
A yx 92
B yx 112
C yx 8
D yx 38
7. xxx 31432 2
A 9882 xx
B 98162 xx
C 9816
2
xxD 9128
2 xx
8. List all the subsets of set H= { p, q}.
A {p}, {q}
B {p}, {q}, { }
C {p}, {q},{p, q}
D {p}, {q}, {p, q},{ }
9. Given the universal set, = TN , set N= {a, b, c} and set T= {b, c, d, e, f},
find the value ofn().
A 2
B 4
C 6
D 8
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10. Diagram 1 is a Venn diagram showing the universal set, = {Form Four students},
set G = {Students who play badminton} and set H={Students who play tennis}.
Given n() = 50, n(G) = 23, n(H) = 9 and n 6 HG , find the number of students
who do not play the two games.
A 44
B 30
C 24
D 18
11. Diagram 2 shows a straight line PQ on a Cartesian plane.
The distance of OQ is 2 units.
Find the gradient ofPQ.
A2
1
B4
3
C 1
D 2
O
y
Q
x
(8, 6P
G
H
DIAGRAM 1
DIAGRAM 2
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12. In Diagram 3, MNis a straight line on a Cartesian plane.
Find the gradient ofMN.
A 2
B 4
3
C4
3
D 2
13. Find the x-intercept of the straight line xy 23 = 12.
A 6
B61
C 4
D4
1
14. Diagram 4 shows the score obtained by a group of five pupils in a quiz where x is an
integer. The mode score is 6.
2 x x 4 9
Then another three pupils with scores of 3, 3 and 8 joins the group.
Find the median score of the group.
A 35
B 5
C 5125
D 6
N
M
8
6
0
y
x
DIAGRAM 3
DIAGRAM 4
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15. Diagram 5 is a bar chart showing the number of Mathematics textbooks sold in four
months. The number of textbooks sold in March and May are not shown.
DIAGRAM 5
The total number of books sold in four months is 140. The ratio of books sold in
March to books sold in May is 3 : 2. Find the number of books sold in May.
A 14
B 16
C 24
D 40
16. Diagram 6 is a pie chart which shows the combined results of a time trial race taken
by two groups of pupils. Table 1 shows the results obtained by the two groups but it
is incomplete.
Calculate the number of pupils in the Yellow Group.
A 140
B 146
C 160
D 194
Month
Numberoftextbook
10
20
30
40
50
60
Feb Mar Apr May
TABLE 1
156
Qualify
Do not
qualify
DIAGRAM 6
GroupNumber of pupils
Qualify Do not qualify
Yellow
Blue 60 80
Total 130
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17 A number is chosen at random from set P = {x: x is an integer , 2 x 12}.
Find the probability that the number chosen is a prime factor of 15.
A10
1
B5
1
C10
3
D5
2
18. Table 2 shows the types of food bought by 60 students at the canteen.
If a student is chosen at random from the group, the probability of the student
buying fried noodles is1
4. Calculate the value ofq.
A 11
B 13
C 15
D 26
19. A container holds 28 red marbles and a number of blue marbles. A marble is picked
at random from the container. The probability of picking a red marble is8
7.
How many blue marbles are there in the container?
A 4
B 8
C 21
D 24
Type of food Number of students
Fried noodles m
Nasi lemak 24
Bread q
Roti canai 10
TABLE 2
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20. A student puts 20 cards with serial number 21 to 40 in a box. A card is drawn at
random. Find the probability of drawing a card with a serial number which is a
multiple of 5.
A 4
1
B5
1
C10
1
D20
1
21. In Diagram 7, EFG is a tangent to the circle FJHat F.
Find the value of x.
A 64
B 58
C 52
D 26
DIAGRAM 7
J
64
x
GF
H
E
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22. In Diagram 8, KLMis a tangent to the circle centre O, at L. KJPO and NPL are
straight lines.
Find the value of y.
A 28
B 34
C 56
D 62
23. In Diagram 9, FGH is a tangent to the circle centre O, at G.
Find the value of z.
A 77
B 55
C 45
D 35
F G H
PQ
O
13
68 z
M
N
O
28
yJ
L
K
P
DIAGRAM 8
DIAGRAM 9
O
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24. In Diagram 10, PQRS is a rectangle and PM= NR = 3 cm.
Find the value of tan .
A12
5
B12
5
C13
5
D135
25. It is given that sin x =25
24and 90 x 180.
Find cos x.
A25
7
B25
7
C7
24
D7
24
P
S
M
N R
Q
13 cm
M
15 cm
DIAGRAM 10
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26. Diagram 11 shows the graph ofy = sin x .
Find the value of m.
A 190
B 210
C 240
D 300
27 In Diagram 12, PQ and RS are two vertical poles on a horizontal plane.
Calculate the angle of depression of vertex R from vertex P.A 26 34
B 41 59
C 48 01
D 63 26
1
1
(m, 50 )
DIAGRAM 11
P
Q
R
S
20 m
45 m
50 m
DIAGRAM 12
O
y
x
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29. Diagram 14 shows a cuboid with a horizontal base PQRS.
Name the angle between the line NMand the plane PQM.
A NQP
B NQM
C NMP
D NMQ
28 Diagram 13 shows a steel frame LKPMNplaced on a horizontal plane.
KL and PMNare vertical while KMis horizontal.
The angle of elevation of point Mfrom point L is 68.
Calculate the height, in m, of PN.
A 9
B 11
C 1342
D 258
P S
Q
M
K
R
N
L
DIAGRAM 14
P
N
M
L
K
8 m
10 m
DIAGRAM 13
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30. Diagram 15 shows a pyramid with rectangular base TUVW.
Vertex S is vertically above W. Name the angle between the plane STUand the
base TUVW.
A USW
B TSW
C SUW
D STW
31 Diagram 16 shows a regular pentagon PQRST. PRUand VWUare straight lines.
PRUis parallel to TS.
DIAGRAM 16
Calculate the value of x + y .
A 69
B 87
C 94
D 112
S
TW
VU
DIAGRAM 15
P
Q
R
ST V
U
xy
2257
W
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32 In Diagram 17, JKLM is a parallelogram. VWis parallel to JK.
DIAGRAM 17
Calculate the value ofp + q .
A 175
B 140
C 135
D 100
33 Diagram 18 shows five pentagons drawn on square grids.
DIAGRAM 18
Which of the pentagons A, B, C or D, is an image of pentagon Kunder a rotation?
K
A
B
C
D
J K
LM
VW
70150
q
p
80
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34 Diagram 19 shows two quadrilaterals, L and M, drawn on square grids.
DIAGRAM 19
Mis the image ofL under an enlargement.
Which of the point, A, B, C, or D, is the centre of the enlargement?
35. Choose a suitable linear equation in one unknown for the following statement.
A 3(x + 7 ) = 34
B 3 + x + 7 = 34
C 3 + 7x = 34
D 3x + 7 = 34
36. Given thatqr
rp
4 , express q in terms ofp and r.
A
2
4
1
r
p
rq
B 24
1prrq
C
r
p
rq
2
1
D prrq 21
A
B
C D
M
L
When a number is multiplied by 3 and increased by 7, the result is 34.
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37.
2
2
5
32
1
25
57
=
A7
1
B7
5
C 7
D 35
38. Simplify3
82
3
2 )(
n
nm .
A nm3
B53
nm
C nm 43
D
54
3
nm
39 Solve the inequalities 8 3x x + 16 and 5 2x > x 10.
A
B
C
D
2
2
2
2
5
6
5
6
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40. Given that x is an integer, find all the values of x that satisfy both of the
inequalities2
4x
5 and x32 > 3 .
A 1,0,1
B 2,1,0,1
C 1,0,1,2
D 2,1,0,1,2
END OF QUESTION PAPER
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QUESTION ANSWER QUESTION ANSWER
1 D 21 C
2 C 22 B
3 C 23 D
4 D 24 A
5 A 25 B
6 A 26 B
7 C 27 A
8 D 28 D
9 C 29 D
10 C 30 D
11 A 31 B
12 C 32 B
13 A 33 D
14 B 34 C
15 B 35 D
16 C 36 A
17 B 37 B
18 A 38 A
19 A 39 A
20 B 40 C
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SMS MUZAFFAR SYAH , MELAKA
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1449/2 Form Four
[T
1
NAMA : ___________________________________
TINGKATAN : _____________________________
BAHAGIAN PENGURUSAN
SEKOLAH BERASRAMA PENUH / KLUSTERBAHAGIAN SEKOLAH
KEMENTERIAN PELAJARAN MALAYSIA
PEPERIKSAAN AKHIR TAHUN SELARAS SBP 2008 1449/2TINGKATAN EMPAT
MATHEMATICS
Kertas 2
Oktober
2 jam Dua jam tiga puluh minit
MATEMATIK
Kertas 2
Dua jam tiga puluh minit
Pemeriksa
Bahagian SoalanMarkah
Penuh
Markah
Diperoleh
A
1 3
2 8
JANGAN BUKA KERTAS SOALAN INI
SEHINGGA 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 4
6 4
7 4
8 6
9 6
10 4
11 5
B
12 12
13 12
14 12
15 12
16 12
Jumlah
Kertas soalan ini mengandungi 23 halaman bercetak dan 1 halaman tidak bercetak1449/2 2008 Hak Cipta Sektor SBP [Lihat sebelah
SULIT
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1449/2 Form Four2
MATHEMATICAL FORMULAE
The following formulae may be helpful in answering the questions. The symbols given are the
ones commonly used.
RELATIONS
1 am an = am + n 12 Pythagoras Theorem
c2
= a2
+ b2
2 am an = am n 13
12
12
xx
yym
3 (am
)n
= am n
14
intercept
intercept
x
ym
4
ac
bd
bcadA
11
5
)(
)()(
Sn
AnAP
6 )(1)'( APAP
7 Distance =2
12
2
12 )()( yyxx
8Midpoint,
2,
2),( 2121
yyxxyx
9
takentime
travelleddistancespeedAverage
10
dataofnumber
dataofsumMean
11
sfrequencieofsum
frequency)marks(classofsumMean
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1449/2 Form Four
[T
3
SHAPES AND SPACE
1heightsidesparallelofsum
2
1trapeziumofArea
2 Circumference of circle = d= 2 r
3 Area of circle = r2
4 Curved surface area of cylinder = 2 r h
5 Surface area of sphere = 4 r2
6 Volume of right prism = cross sectional area length
7 Volume of cylinder = r2
h
8Volume of cone hr
2
3
1
9Volume of sphere
3
3
4r
10Volume of right pyramid heightareabase
3
1
11 Sum of interior angles of polygon = (n 2)180
12o360
centreatsubtendedangle
circleofncecircumfere
lengtharc
13o360
centreatsubtendedangle
circleofarea
sectorofarea
14
PA
PA'k,factorScale
15 Area of image = k2 area of object
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1449/2 Form Four4
For
Examiners
Use
Section A
[52 marks]
Answerall questions in this section.
1 The Venn diagram in the answer space shows sets K, L and Msuch that the
universal set, = K L M.
On the diagrams in the answer space, shade
(a) L M ,
(b) ( K M) L.
[3 marks]
Answer:
(a)
(b)
L
KM
L
KM
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1449/2 Form Four
[T
5
2(a) Diagram 1 shows a right prism. The base GMND is a horizontal rectangle.
Right angled triangle MFG is the uniform cross-section of the prism.
S is the midpoint of ND.
DIAGRAM 1
Identify and calculate the angle between the line FS and the base GMND.
[4 marks]
Answer:
F
Exam
U
E
G
D
M
S
F
N
5 cm
16 cm6 cm
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1449/2 Form Four6
For
Examiners
e 2(b) Diagram 2 shows a right prism with a horizontal rectangular base JKLM .
The isosceles triangle KLHis the uniform cross-section of the prism.
N is the midpoint ofKL.
DIAGRAM 2
Identify and calculate the angle between the plane KLG and the plane KLH.
[4 marks]
Answer:
J
K L
H
G
N
M
6 cm
5 cm
12 cm
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1449/2 Form Four
[T
7
3 Diagram 3 shows a solid, formed by joining a half cylinder to a half cone.
The height of the cone is 6 cm.
By using7
22 , calculate the volume, in cm3 , of the combined solid.
[4 marks]
Answer:
F
Exam
U
7 cm
12 cm
DIAGRAM 3
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1449/2 Form Four8
For
Examiners
Use
4 Using factorisation, solve the quadratic equation 3x (2x 1) + 8x = 1.
[4 marks]
Answer:
5 Using factorisation, solve the quadratic equation pp
5
23 2.
[4 marks]
Answer:
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1449/2 Form Four
[T
9
6 Calculate the value ofm and ofn that satisfy the following simultaneous
linear equations:
1223
166
nm
nm
[4 marks]
Answer:
Fo
Exami
Us
7 Calculate the value ofh and ofkthat satisfy the following simultaneous
linear equations:
273
644
3
hk
hk
[4 marks]
Answer:
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1449/2 Form Four10
For
Examiners
Use 8 Diagram 4 shows two sectors OPQ and ORS, both with centre O.
It is given that POQ = 60.
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)
T
Q 14 cm
7 cm
R
S
O
PDIAGRAM 4
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1449/2 Form Four
[T
11
9(a) Write down two implications based on the following statement:
m > 6 if and only if m 6 > 0
(b) State the converse of the following statement and hence determine whether the
converse is true or false.
Ifx is a factor of 5, then x is a factor of 10.
(c) Make a general conclusion by induction for the sequence of numbers
1 , 6 , 15 , 28, . . . which follows the following pattern.
1 = 2 ( 1 )2 1
6 = 2 ( 2 )2 2
15 = 2 ( 3 )2 3
28 = 2 ( 4 )2 4
=
[6 marks]
Answer:
(a) Implication 1:
Implication 2:
(b)
...
(c) ...
Fo
Exami
Us
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1449/2 Form Four12
For
Examiners
Use 10 In Diagram 5 , OPQR is a parallelogram and O is the origin.
Find
(a) the equation of the straight line PQ,
(b) y intercept of the straight line PQ.
[4 marks]
Answer:
(a)
(b)
x
R ( 4 ,12)
DIAGRAM 5
y
P ( 3 , 6 )
O
Q
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1449/2 Form Four
[T
13
11 In Diagram 6 , O is the origin. KL, PQ and RS are straight lines.
PQ is parallel to RS.
The equation of the straight line KL is 62 xy .
Find
(a) the gradient of the straight line PQ,
(b) the equation of the straight line RS.
[5 marks]
Answer:
(a)
(b)
Fo
Exami
Us
xO
K
R
S
L
DIAGRAM 6
y
P
Q (3, 3)
3
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1449/2 Form Four14
For
Examiners
Use
Section B
[48 marks]
Answer any four questions from this section.
12(a) The Venn diagram in the answer space shows the universal set , sets P, Q
and R. On the diagram in the answer space, shade the region for
(i) P Q ,
(ii) ( P Q ) R.
[3 marks]
Answer:
(i)
(ii)
P
Q
R
P
Q
R
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1449/2 Form Four
[T
15
12(b) In Diagram 7 , O is the origin. Straight line NR is parallel to straight line OQ .
Find
(i) the equation of the straight line RN,
(ii) the x intercept of the straight line RN.
[5 marks]
Answer:
(i)
(ii)
Fo
Exam
Us
y
x
R
N( 4,9 )
Q (3, 4)
O
DIAGRAM 7
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1449/2 Form Four16
For
Examiners
Use
12(c) Diagram 8 shows a right prism. The base PQRS is a horizontal rectangle.
Trapezium PQGF is the uniform cross-section of the prism.
U, V, and Ware midpoints ofPS, FEand QR respectively.
DIAGRAM 8
Identify and calculate the angle between the plane QRVand the base PQRS.
[4 marks]
Answer:
E
P
G
H
Q
R
F
V
U
S
W8 cm
12 cm
5 cm
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1449/2 Form Four
[T
17
13(a) (i) State whether the following sentences is a statement or
non-statement.
(a) 2x + 5y 6
(b) 4 is a prime number.
(ii) Combine the two statements below to form a false statement.
Statement 1 : 3 13 = 39
Statement 2 : 39 is a prime number.
(iii) Write down Premise 1 to complete the following argument:
Premise 1 :
Premise 2 : 3 is a factor of 15
Conclusion : 3 is a factor of 30
(iv) Fill in the blanks with < or > to form
(a) a true statement,
6 3
(b) a false statement.
8 24
[6 marks]
Answer:
(i)(a) _________________________________
(b) _________________________________
(ii) ______________________________________________________
(iii) Premise 1 :______________________________________________
(iv) (a) 6 3
(b) 8 24
F
Exam
U
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1449/2 Form Four18
For
Examiners
Use
13(b) In Diagram 9, ORSTis a quadrant and KL is an arc of another circle both
with centre O. ORKand OSL are straight lines.
DIAGRAM 9
OR = RK= 7 cm.
Using7
22 , calculate
(i) the perimeter, in cm, of the whole diagram,
(ii) the area, in cm 2 , of the shaded region.
. [6 marks]
Answer:
(i)
(ii)
60
R
S
T
L
K
O
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1449/2 Form Four
[T
19
14(a) Using factorisation, solve the quadratic equation mm
6
52.
[4 marks]
Answer:
14(b) Calculate the value ofdand ofe that satisfy the following simultaneous linear
equations:
144
102
13
ed
ed
[4 marks]
Answer:
F
Exam
U
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1449/2 Form Four20
For
Examiners
Use
14(c) Diagram 10 shows a solid cuboid. A semi cylinder is taken out of the solid.
The volume of the remaining solid is 292 cm3
.
Calculate the width, in cm, of the remaining solid.
(Use =7
22)
[4 marks]
Answer:
2 cm
2 cm
8 cm
7 cm
DIAGRAM 10
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1449/2 Form Four
[T
21
15. The data in Diagram 11 shows the ages of 50 runners who took part in a charity run
event.
14 36 12 16 27 31 27 28 30 28
16 18 23 18 24 32 23 14 18 31
22 30 23 20 25 30 31 22 20 37
12 26 36 23 28 30 34 38 33 36
11 23 27 27 34 38 25 12 17 29
DIAGRAM 11
(a) Based on the data in Diagram 11 and by using a class interval of 5, complete
Table 1 in the answer space.
[4marks]
(b) Based on Table 1 in (a),
calculate the estimated mean of the age of the runners.
[3marks]
(c) For this part of the question, use the graph paper provided on page 23.
By using a scale of 2 cm to 5 years on the horizontal axis and 2 cm to 1
runner on the vertical axis, draw a frequency polygon for the data.
[5marks]
F
Exam
U
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1449/2 Form Four22
For
Examiners
Use
Answer:
(a)
Age (years) Midpoint Frequency
11 15
TABLE 1
(b) i)
ii)
(c) Refer graph on page 23.
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1449/2 Form Four
[T
23MOZ@C
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1449/2 Form Four24
For
Examiners
Use
16. The data in Diagram 12 shows the marks obtained by 40 pupils in a quiz.
67 76 91 79 81 82 87 71
79 82 88 83 72 84 71 89
80 86 70 86 62 83 83 80
75 84 84 77 84 86 85 76
80 75 95 77 73 86 77 68
DIAGRAM 12
(a) Using the data in Diagram 12, and a class interval of 5, complete Table 2 in
the answer space.
[6 marks]
(b) For this part of the question, use the graph paper provided on page 26.
By using a scale of 2 cm to 5 marks on the x-axis and 2 cm to 5 pupils on the
y-axis, draw an ogive based on the data.
[5 marks]
(c) From your ogive in (b), find the third quartile.
[1 mark]
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1449/2 Form Four
[T
25
Answer:
a)
Marks Frequency Cumulative Frequency Upper Boundary
61 65
TABLE 2
b) Refer graph on page 26
c)
Fo
Exam
Us
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1449/2 Form Four
[T
27
INFORMATION FOR CANDIDATES
1. This question paper consists of two sections: Section A and Section B.
2. Answer all questions in Section A and four questions from Section B.
3. Write your answers in the spaces provided in the question paper.
4. Show your working. It may help you to get marks.
5. If you wish to change your answer, cross out the answer that you have done. Then
write down the new answer.
6. The diagrams in the questions provided are not drawn to scale unless stated.
7. The marks allocated for each question and sub-part of a question are shown inbrackets.
8. A list of formulae is provided on page 2 to 3.
9. A booklet of four-figure mathematical tables is provided.
10. You may use a non-programmable scientific calculator.
11. Hand in this question paper to the invigilator at the end of the examination.
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Mathematics Form 4 Final year 2008
Section A[ 52 marks ]
No Marking Scheme Marks
1
a)
b)
P1
P2 3
2 a) FSQ
Tan22 86
5
'3426/57.26
b) FSQ
Tan4
12
'3471/57.71
P1
K2
N1
P1
K2
N1
4
4
312
2
7
2
7
7
22
2
1
627
27
722
31
21
5.269/2
1269
62
7
2
7
7
22
3
1
2
112
2
7
2
7
7
22
2
1
K1
K1
K1
N1 4
L
K
M
L
K
M
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No Marking Scheme Marks
4
1,6
1
0116
0156 2
x
xx
xx K1
K1
N1,N1 4
5
3
1,2
0132
0253 2
p
pp
pp K1
K1
N1,N1 4
6
2,3
6020
48183
mn
n
nm K1
K1
N1, N1 4
7
8,3
5117
24163
kh
h
hk K1
K1N1, N1 4
8 a) 77
222
360
6021
7
222
360
450
0
0
0
OR
83.65/6
565
777
222
360
601421
7
222
360
4521
0
0
0
0
b) 22 77
22
360
6021
7
22
360
45
OR
42.174@12
5174
772
17
7
22
360
6021
7
22
360
45 220
0
K1
K1
N1
K1
K1
N1 6
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No Marking Scheme Marks
9 a) Implication 1 : If m 6, then m 6 0Implication 2 : If m 6 0, then m 6
b) If x is a factor of 10, then x is a factor of 5False
c) ,2 2 nn .......,4,3,2,1n
P1
P1
P1P1
P1
P1 6
10 a) 304
012
ORPQ mm
153
15336
xy
cORc
b) 15y
K1
K1
N1
N1 4
11 a)2
1
33
03
PQm
62
1
6)0(2
16
2
1
xy
cORc
mm RSPQ
K1, N1
K1
K1
N1 5
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Section B
[48 marks]
No Marking Scheme Marks
12 a)i
ii.
b)i.
3
4m
83
4
)9(3
44
xy
c
ii. 83
40 x
6x
c) VWU
Tan12
5
'3722/62.22
P1
P2
K1
K1
N1
K1
N1
P1
K2
N1 12
P Q
R
P Q
R
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No Marking Scheme Marks
13 a) i) a) Non-statement
b) Statement
ii) andiii) all factors of 15 are factors of 30
iv) a )
(b) i) 147
222
360
600
0
OR 77
222
360
300
0
147
222
360
600
0
+ 77
222
360
300
0
+14+7+7
3
146 OR 46.34
ii) 14147
22
360
600
0
OR 777
22
360
300
14147
22
360
600
0
+ 777
22
360
300
= 89.832
cm or 6
589
P1
P1
P1P1
P1P1
K1
K1
N1
K1
K1
N1 12
14
5,1
051
056)( 2
m
mm
mma
2
3
62
206)(
e
d
d
edb
cm
cmw
wc
6292298
292727
22
2
187
87)(
22
K1N1
N1,N1
K1
K1
N1
N1
K1
K1, K1
N112
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No Marking Scheme Marks
15 (a)
Age(years) Midpoint Frequency
11 - 15 13 6
16 20 18 8
21 25 23 10
26 30 28 13
31 35 33 7
36 40 38 6
All values in Column 1 correct
All values in Column 2 correctAll values in Column 3 correct
(b)
5.25
50
1275
50
)6(38)7(33)13(28)10(23)8(18)6(13
(c) Refer to the graph
Axes drawn in the correct direction , uniform scale for 438 xand 130 y .
Horizontal axis labeled using midpoint / upper boundary / classinterval
6 points plotted correctly
(8,0) and (43,0).Straight line passing 8 point.
P1
P1
P2
K2
N1
K1
P1
P1
P1P1
12
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No Marking Scheme Marks
16 Marks Frequency Cumulative
frequency
Upper
boundary
I
55 60
II
0
III
0
IV
60.561 65 1 1 65.5
66 70 3 4 70.5
71 75 6 10 75.5
76 80 10 20 80.5
81 85 11 31 85.5
86 90 7 38 90.5
91 - 95 2 40 95.5
All values in Column ( I ) correct
All values in Column ( II ) correct excluding Row I correct.All values in Column ( III ) correct
All values in Column ( IV ) correct
(b) x-axis and y-axis are drawn with the right direction and in
uniform scale from 60.5 5.95 x , 110 y
All eight points* plotted correctly.
Note : Seven or six points* plotted correctly. 1 P1(60.5, 0) plotted or passed through
All the right eight points plotted correctly and ogive is drawn
smoothly passing through all the points.
(c) 85 0.5
P1
P2P2
P1
K1
K2
K1
N1
N1
12
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8 13 18 23 28 330
2
4
6
8
10
12
14
Graph is not drawn to scale.
38
43
Frequency
Mid-po
Graph for Question 15.
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655605 705 755 805 855 905
0
5
10
15
20
25
30
35
40
Graph is not drawn to scale.
Graph for Question 16.
95.5
Cumulative
Frequency
UpperBoundar
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SULIT 1449/1
1449/1
Matematik
Kertas1
Peraturan
Pemarkahan
Oktober
2008
SEKTOR SEKOLAH BERASRAMA PENUH
BAHAGIAN SEKOLAH
KEMENTERIAN PELAJARAN MALAYSIA
PERATURAN PEMARKAHANPEPERIKSAAN AKHIR TAHUN TAHUN 2008
TINGKATAN 4
MATEMATIK
KERTAS 1 & 2
1449/1/2
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QUESTION ANSWER QUESTION ANSWER
1 D 21 C
2 C 22 B
3 C 23 D
4 D 24 A
5 A 25 B
6 A 26 B
7 C 27 A
8 D 28 D
9 C 29 D
10 C 30 D
11 A 31 B
12 C 32 B
13 A 33 D
14 B 34 C
15 B 35 D
16 C 36 A
17 B 37 B
18 A 38 A
19 A 39 A
20 B 40 C
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1449/2 Form Four
[T
1
NAMA : ___________________________________
TINGKATAN : _____________________________
BAHAGIAN PENGURUSAN
SEKOLAH BERASRAMA PENUH / KLUSTERBAHAGIAN SEKOLAH
KEMENTERIAN PELAJARAN MALAYSIA
PEPERIKSAAN AKHIR TAHUN SELARAS SBP 2008 1449/2TINGKATAN EMPAT
MATHEMATICS
Kertas 2
Oktober
2 jam Dua jam tiga puluh minit
MATEMATIK
Kertas 2
Dua jam tiga puluh minit
Pemeriksa
Bahagian SoalanMarkah
Penuh
Markah
Diperoleh
A
1 3
2 8
JANGAN BUKA KERTAS SOALAN INI
SEHINGGA 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 4
6 4
7 4
8 6
9 6
10 4
11 5
B
12 12
13 12
14 12
15 12
16 12
Jumlah
Kertas soalan ini mengandungi 23 halaman bercetak dan 1 halaman tidak bercetak1449/2 2008 Hak Cipta Sektor SBP [Lihat sebelah
SULIT
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1449/2 Form Four2
MATHEMATICAL FORMULAE
The following formulae may be helpful in answering the questions. The symbols given are the
ones commonly used.
RELATIONS
1 am an = am + n 12 Pythagoras Theorem
c2
= a2
+ b2
2 am an = am n 13
12
12
xx
yym
3 (am
)n
= am n
14
intercept
intercept
x
ym
4
ac
bd
bcadA
11
5
)(
)()(
Sn
AnAP
6 )(1)'( APAP
7 Distance =2
12
2
12 )()( yyxx
8Midpoint,
2,
2),( 2121
yyxxyx
9
takentime
travelleddistancespeedAverage
10
dataofnumber
dataofsumMean
11
sfrequencieofsum
frequency)marks(classofsumMean
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1449/2 Form Four
[T
3
SHAPES AND SPACE
1heightsidesparallelofsum
2
1trapeziumofArea
2 Circumference of circle = d= 2 r
3 Area of circle = r2
4 Curved surface area of cylinder = 2 r h
5 Surface area of sphere = 4 r2
6 Volume of right prism = cross sectional area length
7 Volume of cylinder = r2
h
8Volume of cone hr
2
3
1
9Volume of sphere
3
3
4r
10Volume of right pyramid heightareabase
3
1
11 Sum of interior angles of polygon = (n 2)180
12o360
centreatsubtendedangle
circleofncecircumfere
lengtharc
13o360
centreatsubtendedangle
circleofarea
sectorofarea
14
PA
PA'k,factorScale
15 Area of image = k2 area of object
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1449/2 Form Four4
For
Examiners
Use
Section A
[52 marks]
Answerall questions in this section.
1 The Venn diagram in the answer space shows sets K, L and Msuch that the
universal set, = K L M.
On the diagrams in the answer space, shade
(a) L M ,
(b) ( K M) L.
[3 marks]
Answer:
(a)
(b)
L
KM
L
KM
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1449/2 Form Four
[T
5
2(a) Diagram 1 shows a right prism. The base GMND is a horizontal rectangle.
Right angled triangle MFG is the uniform cross-section of the prism.
S is the midpoint of ND.
DIAGRAM 1
Identify and calculate the angle between the line FS and the base GMND.
[4 marks]
Answer:
F
Exam
U
E
G
D
M
S
F
N
5 cm
16 cm6 cm
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1449/2 Form Four6
For
Examiners
e 2(b) Diagram 2 shows a right prism with a horizontal rectangular base JKLM .
The isosceles triangle KLHis the uniform cross-section of the prism.
N is the midpoint ofKL.
DIAGRAM 2
Identify and calculate the angle between the plane KLG and the plane KLH.
[4 marks]
Answer:
J
K L
H
G
N
M
6 cm
5 cm
12 cm
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1449/2 Form Four
[T
7
3 Diagram 3 shows a solid, formed by joining a half cylinder to a half cone.
The height of the cone is 6 cm.
By using7
22 , calculate the volume, in cm3 , of the combined solid.
[4 marks]
Answer:
F
Exam
U
7 cm
12 cm
DIAGRAM 3
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1449/2 Form Four8
For
Examiners
Use
4 Using factorisation, solve the quadratic equation 3x (2x 1) + 8x = 1.
[4 marks]
Answer:
5 Using factorisation, solve the quadratic equation pp
5
23 2.
[4 marks]
Answer:
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1449/2 Form Four
[T
9
6 Calculate the value ofm and ofn that satisfy the following simultaneous
linear equations:
1223
166
nm
nm
[4 marks]
Answer:
Fo
Exami
Us
7 Calculate the value ofh and ofkthat satisfy the following simultaneous
linear equations:
273
644
3
hk
hk
[4 marks]
Answer:
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1449/2 Form Four10
For
Examiners
Use 8 Diagram 4 shows two sectors OPQ and ORS, both with centre O.
It is given that POQ = 60.
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)
T
Q 14 cm
7 cm
R
S
O
PDIAGRAM 4
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1449/2 Form Four
[T
11
9(a) Write down two implications based on the following statement:
m > 6 if and only if m 6 > 0
(b) State the converse of the following statement and hence determine whether the
converse is true or false.
Ifx is a factor of 5, then x is a factor of 10.
(c) Make a general conclusion by induction for the sequence of numbers
1 , 6 , 15 , 28, . . . which follows the following pattern.
1 = 2 ( 1 )2 1
6 = 2 ( 2 )2 2
15 = 2 ( 3 )2 3
28 = 2 ( 4 )2 4
=
[6 marks]
Answer:
(a) Implication 1:
Implication 2:
(b)
...
(c) ...
Fo
Exami
Us
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1449/2 Form Four12
For
Examiners
Use 10 In Diagram 5 , OPQR is a parallelogram and O is the origin.
Find
(a) the equation of the straight line PQ,
(b) y intercept of the straight line PQ.
[4 marks]
Answer:
(a)
(b)
x
R ( 4 ,12)
DIAGRAM 5
y
P ( 3 , 6 )
O
Q
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1449/2 Form Four
[T
13
11 In Diagram 6 , O is the origin. KL, PQ and RS are straight lines.
PQ is parallel to RS.
The equation of the straight line KL is 62 xy .
Find
(a) the gradient of the straight line PQ,
(b) the equation of the straight line RS.
[5 marks]
Answer:
(a)
(b)
Fo
Exami
Us
xO
K
R
S
L
DIAGRAM 6
y
P
Q (3, 3)
3
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1449/2 Form Four14
For
Examiners
Use
Section B
[48 marks]
Answer any four questions from this section.
12(a) The Venn diagram in the answer space shows the universal set , sets P, Q
and R. On the diagram in the answer space, shade the region for
(i) P Q ,
(ii) ( P Q ) R.
[3 marks]
Answer:
(i)
(ii)
P
Q
R
P
Q
R
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1449/2 Form Four
[T
15
12(b) In Diagram 7 , O is the origin. Straight line NR is parallel to straight line OQ .
Find
(i) the equation of the straight line RN,
(ii) the x intercept of the straight line RN.
[5 marks]
Answer:
(i)
(ii)
Fo
Exam
Us
y
x
R
N( 4,9 )
Q (3, 4)
O
DIAGRAM 7
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1449/2 Form Four16
For
Examiners
Use
12(c) Diagram 8 shows a right prism. The base PQRS is a horizontal rectangle.
Trapezium PQGF is the uniform cross-section of the prism.
U, V, and Ware midpoints ofPS, FEand QR respectively.
DIAGRAM 8
Identify and calculate the angle between the plane QRVand the base PQRS.
[4 marks]
Answer:
E
P
G
H
Q
R
F
V
U
S
W8 cm
12 cm
5 cm
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1449/2 Form Four
[T
17
13(a) (i) State whether the following sentences is a statement or
non-statement.
(a) 2x + 5y 6
(b) 4 is a prime number.
(ii) Combine the two statements below to form a false statement.
Statement 1 : 3 13 = 39
Statement 2 : 39 is a prime number.
(iii) Write down Premise 1 to complete the following argument:
Premise 1 :
Premise 2 : 3 is a factor of 15
Conclusion : 3 is a factor of 30
(iv) Fill in the blanks with < or > to form
(a) a true statement,
6 3
(b) a false statement.
8 24
[6 marks]
Answer:
(i)(a) _________________________________
(b) _________________________________
(ii) ______________________________________________________
(iii) Premise 1 :______________________________________________
(iv) (a) 6 3
(b) 8 24
F
Exam
U
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1449/2 Form Four18
For
Examiners
Use
13(b) In Diagram 9, ORSTis a quadrant and KL is an arc of another circle both
with centre O. ORKand OSL are straight lines.
DIAGRAM 9
OR = RK= 7 cm.
Using7
22 , calculate
(i) the perimeter, in cm, of the whole diagram,
(ii) the area, in cm 2 , of the shaded region.
. [6 marks]
Answer:
(i)
(ii)
60
R
S
T
L
K
O
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1449/2 Form Four
[T
19
14(a) Using factorisation, solve the quadratic equation mm
6
52.
[4 marks]
Answer:
14(b) Calculate the value ofdand ofe that satisfy the following simultaneous linear
equations:
144
102
13
ed
ed
[4 marks]
Answer:
F
Exam
U
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1449/2 Form Four20
For
Examiners
Use
14(c) Diagram 10 shows a solid cuboid. A semi cylinder is taken out of the solid.
The volume of the remaining solid is 292 cm3
.
Calculate the width, in cm, of the remaining solid.
(Use =7
22)
[4 marks]
Answer:
2 cm
2 cm
8 cm
7 cm
DIAGRAM 10
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1449/2 Form Four22
For
Examiners
Use
Answer:
(a)
Age (years) Midpoint Frequency
11 15
TABLE 1
(b) i)
ii)
(c) Refer graph on page 23.
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1449/2 Form Four
[T
23
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1449/2 Form Four24
For
Examiners
Use
16. The data in Diagram 12 shows the marks obtained by 40 pupils in a quiz.
67 76 91 79 81 82 87 71
79 82 88 83 72 84 71 89
80 86 70 86 62 83 83 80
75 84 84 77 84 86 85 76
80 75 95 77 73 86 77 68
DIAGRAM 12
(a) Using the data in Diagram 12, and a class interval of 5, complete Table 2 in
the answer space.
[6 marks]
(b) For this part of the question, use the graph paper provided on page 26.
By using a scale of 2 cm to 5 marks on the x-axis and 2 cm to 5 pupils on the
y-axis, draw an ogive based on the data.
[5 marks]
(c) From your ogive in (b), find the third quartile.
[1 mark]
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1449/2 Form Four
[T
25
Answer:
a)
Marks Frequency Cumulative Frequency Upper Boundary
61 65
TABLE 2
b) Refer graph on page 26
c)
Fo
Exam
Us
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1449/2 Form Four26
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1449/2 Form Four
[T
27
INFORMATION FOR CANDIDATES
1. This question paper consists of two sections: Section A and Section B.
2. Answer all questions in Section A and four questions from Section B.
3. Write your answers in the spaces provided in the question paper.
4. Show your working. It may help you to get marks.
5. If you wish to change your answer, cross out the answer that you have done. Then
write down the new answer.
6. The diagrams in the questions provided are not drawn to scale unless stated.
7. The marks allocated for each question and sub-part of a question are shown inbrackets.
8. A list of formulae is provided on page 2 to 3.
9. A booklet of four-figure mathematical tables is provided.
10. You may use a non-programmable scientific calculator.
11. Hand in this question paper to the invigilator at the end of the examination.
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Mathematics Form 4 Final year 2008
Section A[ 52 marks ]
No Marking Scheme Marks
1
a)
b)
P1
P2 3
2 a) FSQ
Tan22 86
5
'3426/57.26
b) FSQ
Tan4
12
'3471/57.71
P1
K2
N1
P1
K2
N1
4
4
312
2
7
2
7
7
22
2
1
627
27
722
31
21
5.269/2
1269
62
7
2
7
7
22
3
1
2
112
2
7
2
7
7
22
2
1
K1
K1
K1
N1 4
L
K
M
L
K
M
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No Marking Scheme Marks
4
1,6
1
0116
0156 2
x
xx
xx K1
K1
N1,N1 4
5
3
1,2
0132
0253 2
p
pp
pp K1
K1
N1,N1 4
6
2,3
6020
48183
mn
n
nm K1
K1
N1, N1 4
7
8,3
5117
24163
kh
h
hk K1
K1N1, N1 4
8 a) 77
222
360
6021
7
222
360
450
0
0
0
OR
83.65/6
565
777
222
360
601421
7
222
360
4521
0
0
0
0
b) 22 77
22
360
6021
7
22
360
45
OR
42.174@12
5174
772
17
7
22
360
6021
7
22
360
45 220
0
K1
K1
N1
K1
K1
N1 6
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No Marking Scheme Marks
9 a) Implication 1 : If m 6, then m 6 0Implication 2 : If m 6 0, then m 6
b) If x is a factor of 10, then x is a factor of 5False
c) ,2 2 nn .......,4,3,2,1n
P1
P1
P1P1
P1
P1 6
10 a) 304
012
ORPQ mm
153
15336
xy
cORc
b) 15y
K1
K1
N1
N1 4
11 a)2
1
33
03
PQm
62
1
6)0(2
16
2
1
xy
cORc
mm RSPQ
K1, N1
K1
K1
N1 5
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Section B
[48 marks]
No Marking Scheme Marks
12 a)i
ii.
b)i.
3
4m
83
4
)9(3
44
xy
c
ii. 83
40 x
6x
c) VWU
Tan12
5
'3722/62.22
P1
P2
K1
K1
N1
K1
N1
P1
K2
N1 12
P Q
R
P Q
R
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No Marking Scheme Marks
13 a) i) a) Non-statement
b) Statement
ii) andiii) all factors of 15 are factors of 30
iv) a )
(b) i) 147
222
360
600
0
OR 77
222
360
300
0
147
222
360
600
0
+ 77
222
360
300
0
+14+7+7
3
146 OR 46.34
ii) 14147
22
360
600
0
OR 777
22
360
300
14147
22
360
600
0
+ 777
22
360
300
= 89.832
cm or 6
589
P1
P1
P1P1
P1P1
K1
K1
N1
K1
K1
N1 12
14
5,1
051
056)( 2
m
mm
mma
2
3
62
206)(
e
d
d
edb
cm
cmw
wc
6292298
292727
22
2
187
87)(
22
K1N1
N1,N1
K1
K1
N1
N1
K1
K1, K1
N112
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No Marking Scheme Marks
15 (a)
Age(years) Midpoint Frequency
11 - 15 13 6
16 20 18 8
21 25 23 10
26 30 28 13
31 35 33 7
36 40 38 6
All values in Column 1 correct
All values in Column 2 correctAll values in Column 3 correct
(b)
5.25
50
1275
50
)6(38)7(33)13(28)10(23)8(18)6(13
(c) Refer to the graph
Axes drawn in the correct direction , uniform scale for 438 xand 130 y .
Horizontal axis labeled using midpoint / upper boundary / classinterval
6 points plotted correctly
(8,0) and (43,0).Straight line passing 8 point.
P1
P1
P2
K2
N1
K1
P1
P1
P1P1
12
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No Marking Scheme Marks
16 Marks Frequency Cumulative
frequency
Upper
boundary
I
55 60
II
0
III
0
IV
60.561 65 1 1 65.5
66 70 3 4 70.5
71 75 6 10 75.5
76 80 10 20 80.5
81 85 11 31 85.5
86 90 7 38 90.5
91 - 95 2 40 95.5
All values in Column ( I ) correct
All values in Column ( II ) correct excluding Row I correct.All values in Column ( III ) correct
All values in Column ( IV ) correct
(b) x-axis and y-axis are drawn with the right direction and in
uniform scale from 60.5 5.95 x , 110 y
All eight points* plotted correctly.
Note : Seven or six points* plotted correctly. 1 P1(60.5, 0) plotted or passed through
All the right eight points plotted correctly and ogive is drawn
smoothly passing through all the points.
(c) 85 0.5
P1
P2P2
P1
K1
K2
K1
N1
N1
12
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8 13 18 23 28 330
2
4
6
8
10
12
14
Graph is not drawn to scale.
38
43
Frequency
Mid-po
Graph for Question 15.
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15
20
25
30
35
40
Graph is not drawn to scale.
Graph for Question 16.
Cumulative
Frequency