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  • 8/14/2019 MRSM Maths P2 2005

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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 :

    For

    Examiners

    Use

    Tutor Maths Mr Muruliwww.tutormuruli.blogspot.com

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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

    For

    Examiners

    Use

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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

    For

    Examiners

    Use

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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)

    For

    Examiners

    Use

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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)

    For

    Examiner

    Use

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    SULIT

    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)

    For

    Examiners

    Use

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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 = .

    For

    Examiners

    Use

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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]

    For

    Examiners

    Use

    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) .

    ..

    ..

    For

    Examiner

    Use

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    SULIT

    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

    For

    Examine

    Use

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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

    For

    Examiners

    Use

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    SULIT

    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

    For

    Examiners

    Use

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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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