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Nama: Kelas:
[Lihat sebelah
1449/2 2005 Hak Cipta Bahagian Pendidikan & Latihan (Menengah) MARA SULIT
MAKTAB RENDAH SAINS MARA
PEPERIKSAAN PERCUBAAN
SIJIL PELAJARAN MALAYSIA 2005
MATEMATIK
Kertas 2
Dua jam tiga puluh minit
Bahagian SoalanMarkah
Penuh
Markah
Diperoleh
1 4
2 4
3 3
4 4
5 46 5
7 6
8 5
9 5
10 6
A
11 6
12 12
13 12
14 1215 12
B
16 12
JANGAN BUKA KERTAS SOALAN
INI SEHINGGA DIBERITAHU
1. Tuliskan nama dan kelas anda padaruang yang disediakan.
2. Kertas soalan ini adalah dalamdwibahasa.
3. Soalan dalam bahasa Melayumendahului soalan dalam bahasa
Inggeris.
4. Calon dibenarkan menjawabkeseluruhan atau sebahagian soalan
sama ada dalam bahasa Melayu atau
bahasa Inggeris.
5. Calon dikehendaki membaca maklumatdi halaman 2 atau halaman 3.
Jumlah
Kertas soalan ini mengandungi 47 halaman bercetak dan 1 halaman tidak bercetak
SULIT
1449/2
Matematik
Kertas 2
September
2005
2 jam
1
4
4
9
2
1449/2
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INFORMATION FOR CANDIDATES
1. This question paper consists of two sections : Section A and Section B.Answerall questions in Section Aandfourquestions inSection B.
2.
Write your answers clearly in the spaces provided in the question paper.
3. Show your working. It may help you to get marks.4. If you wish to change your answer, neatly cross out the answer that you have
done. Then write down the new answer.
5. The diagrams in the questions provided are not drawn to scale unless stated.6. The marks allocated for each question and sub-part of a question are shown in
brackets.
7. A list of formulae is provided on pages 4 to 7.8. A booklet of four-figure mathematical tables is provided.9. You may use a non-programmable scientific calculator.10. This question paper must be handed in at the end of the examination.
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The following formulae may be helpful in answering the questions. The symbols given are
the ones commonly used.
RELATIONS
1 ama n = a m + n
2 am a n = a m n
3 (a m)n = a mn
4 A1
=
ac
bd
bcad
1
5 P(A) =)(
)(
Sn
An
6 P(A' ) = 1 P(A)
7 Distance = 2122
12 )()( yyxx +
8 Midpoint
(x ,y ) =
++
2,
2
2121 yyxx
9 Average speed =takentime
travelleddistance
10 Mean =dataofnumber
dataofsum
11 Mean =sfrequencieofsum
)frequencymarkclass(ofSum
12 Pythagoras Theorem
c2
= a2
+ b2
13 m =12
12
xx
yy
14 m = intercept
intercept
x
y
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SHAPE 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 = r2h
8 Volume of cone =3
1r2h
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
12circleofncecircumfere
lengtharc=
o360
centreatsubtendedangle
13circleofarea
sectorofarea=
o360
centreatsubtendedangle
14 Scale factor , k = PA
PA '
15 Area of image = k2 area of object
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Section A
[52 marks]
Answerallquestions in this section.
1 Solve the equation 2(x + 1)(x 3) = 24 11x. [4 marks]
Answer:
2 Calculate the value ofm and ofn that satisfy the following simultaneous linear
equations :
2m
2
n= 2 and 6m + n = 16 [4 marks]
Answer :
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3 (a) In the Venn diagram provided below, shade the area to represent
P ' (QR).
(b) Define the set that represent the shaded area below.
[3 marks]
Answer :
(a)
(b)
P
Q
R
For
Examiners
Use
XY
Z
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4 Diagram 1 shows a cuboid with a square baseABCD. Given thatEM= 2cm.
Calculate the angle between the planeABMand planeABCD.
[4 marks]Answer :
For
Examiner
Use
B
C
G
A
HE
D
F
M
8cm
6cm
DIAGRAM 1
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5 In Diagram 2, PS and OR are parallel lines such that PS = 2 OR.
Error!
(a) State the value ofh.
(b) Find the equation of PS.
(c) Hence, state they-intercept of line PS.[4 marks]
Answer :
(a)
(b)
(c)
R(3, 4)
S(h,8)
P (9, 0) O
DIAGRAM 2
y
x
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6 Diagram 3 shows a solid formed by combining a right prism with a halfcylinder on the rectangular planeBGHC.
DIAGRAM 3
Given thatBF = CE = 10 cm , FG = EH= 8 cm andBC= 13cm.Calculate the volume, in cm
3, of the solid.
[Use =7
22] [5 marks]
Answer :
AG B
CH
E
FD
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7 Diagram 4 shows the sectorOAB and 3 semicircles with equal radii. Given that
OA = 28 cm and AOB = 72o.
DIAGRAM 4Using =
7
22,calculate
(a) the perimeter, in cm, of the whole diagram,(b) the area, in cm
2, of the shaded region.
[6 marks]
Answer :
(a)
(b)
For
Examine
Use
72o
O
C
B
AD
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8 (a) Using the object and feature below, write a true statement using the
quantifiers all or some.
Object: Even number.
Feature: Divisible by 5 and 3.
(b) State the converse of the implication below and determine its truth.
If a triangle PQR is an isosceles triangle, then triangle PQR has two
interior angles with the same size.
(c) Complete the following premise:
Premise 1: ______________________________________
Premise 2: Determinant of matrix P is zero.
Conclusion: Matrix P does not have an inverse.
[5 marks]
Answer :
(a)
(b)
(c)
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9 MRSM Putrajaya decided to send 2 uniform bodies, Scouts and Red Crescent as
a relief group to help the Tsunami victims at two of the affected areas.
Table 1 shows the probability of each uniform body being sent to the Tsunami
affected areas.
Tsunami Affected AreaUniform Bodies Kota Kuala
Muda
Banda
Acheh
Scouts5
1
Red Crescent3
2
TABLE 1
Calculate the probability that:
(a) the Scouts are sent to Banda Aceh,(b) the Scouts are sent to Kota Kuala Muda and the Red Crescent to Banda Aceh,(c) both groups are sent to the same place.
[5 marks]Answer :
(a)
(b)
(c)
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10 Diagram 5 shows the speed-time graph of a particle for a period of 24 seconds.
Error!
(a) State the length of time, in seconds, that particle moves with uniform speed,
(b) Calculate the value of u, in m/s, if the total distance traveled in the last 12seconds is 264 m,
(c) Calculate the average speed, in m/s, in 24 seconds.[ 6 marks ]
Answer :
(a)
(b)
(c)
For
Examiner
Use
Speed
(m/s)
Time (s)
32
u
6
12 20 240
DIAGRAM 5
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11 Given that P is a 22 matrix, where P
43
65=
10
01.
(a) Find the matrix P.
(b) Hence, by the use of matrices, calculate the value ofm and ofn that satisfy
the following simultaneous linear equations.
2m 3n = 8
62
5
2
3=+ nm
[ 6 marks ]
Answer :
(a)
(b)
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Bahagian B
[48 marks]
Answerfour questions from this section.
12 (a) Table 2 shows the values ofx andy which satisfy the equationy =x
6+ 3.
Complete the following table.
x 4 3 2 1 1 2 3 4
y 1.5 1 3 9 6 4.5
TABLE 2[2 marks]
(b) For this part of the question, use the graph paper on page 31. You may use a
flexible curve.
By using a scale of 2 cm to 1 unit on both thex-axis and y-axis, draw the
graph of y =x
6+ 3 for 4 x 4. [4 marks]
(c) From your graph, find
(i) the value ofy whenx = 2.3(ii) the value ofx wheny = 1
[2 marks]
(d) Draw a suitable straight line on your graph to find the values ofx whichsatisfies the equation 2x
2 3x 6 = 0 for 4 x 4.
State the values ofx.
[4 marks]
Answer :
(a) Refer to Table 2(b) Refer to graph on page 31(c) (i) y = .
(ii) x = .
(d) x = .
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Graph for Question 12
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13 Diagram 6 shows trapeziums ABCD, PQRS, PJKS and NMLS, drawn on a
Cartesian plane.
(a) Transformation T is a translation
4
2and transformation U is a
reflection about the linex = 10.
State the coordinates of the image of point A under each of the following
transformation:
(i) Translation T,(ii) Combined transformations UT.
[3 marks]
(b) PQRS is the image ofABCD under the transformation V. Describe in full, the
transformation V. [3 marks]
(c) (i) MLSNis the image ofQRSP under the combined transformations WZ.
Describe in full, the transformationZand the transformation W.
[4 marks]
(ii) Given the shaded region MLKJPN is 255cm2, calculate the area,
in cm2, of trapezium SKJP. [2 marks]
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DIAGRAM 6
2 4 6 8 10 12 14 16 18 20 22 24 260
2
4
6
8
10
12
14
16
18
20
D C
B
A
R
Q
P
S
J
K
N
M
L
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Answer :
(a) (i)
(ii)
(b) ..
..
..
(c) (i) ..
..
..
(ii) .
..
..
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14 Table 3 shows the distribution of donation collected from 200 staff of a company
for the children Education fund.
TABLE 3
(a) State the modal class. [1 mark]
(b) Based on the information in Table 3, complete Table 4 in the answer space
provided.
[3 marks]
(c) For this part of the question, use the graph paper provided on page 41.
You may use a flexible curve.
By using a scale of 2 cm to RM5 on thex-axis and 2 cm to 20 staff on they-axis , draw an ogive based on the data.
[4 marks]
(d) From the ogive in (c), find
(i) inter quartile range,(ii) percentage of staff who donated more than RM 25.00.
[4 marks]
Donation (RM) Frequency
2 6 10
7 11 16
12 16 48
17 21 91
22 26 23
27 31 8
32 36 4
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Answer:
14 (a) Modal class = .
(b)
TABLE 4
(c) Refer graph on page 41.
(d) (i) Inter quartile range
(ii) Percentage of staff who donated more than RM 25.00
Donation
(RM)Frequency
Upper class
boundaries
Cumulative
frequency
0 1.5
2 6 10
7 11 16
12 16 48
17 21 91
22 26 23
27 31 8
32 36 4
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Graph for Question 14
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15 Diagram 7 shows two solids which are joined at the planeADEF. The solidADNM
is a pyramid with an isosceles triangle base and o90=ADM .The solid
ABCDEFGHis a cuboid. A right prism PQRLKJwith a semicircular cross section
of radius 2 cm is removed from the cuboid.
DIAGRAM 7
Draw in full size,
(a) the plan,
[4 marks]
(b) the elevation on vertical plane parallel to lineAB as viewed fromX,
[4 marks]
(c) the elevation on vertical plane parallel to lineBCas viewed from Y.[4 marks]
N
D C
BA
F
E H
G
P
Q
R
J
K
LM
1 cm 1 cm
5 cm
6 cm
4 cm
3 cm
X
Y
5 cm
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16 P( 45oS, 70
oW), Q andR are three points on the surface of the earth. Q is situated
to the north ofP such that the angle subtended at the center of the earth by P and Qis 105
o. QR is the diameter of the parallel of latitude.
(a) State the latitude ofQ, [2 marks]
(b) Find the position ofR, [3 marks]
(c) Calculate the shortest distance, in nautical miles, from P toR measured along
the surface of the earth, [3 marks]
(d) An aeroplane took off from P and flew due north to Q with a speed of 600knots. From Q, the aeroplane flew due east with a speed of 540 knots toR.
Calculate the total time taken for the flight. [4 marks]
Answer:
(a)..
(b)
(c)
(d)
END OF QUESTION PAPER
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