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  • 7/31/2019 Soalan Math Pmr Kertas 2.Doc No Label

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    50/2

    Matematik

    Kertas 2

    Ogos

    2010

    13

    4jam

    SULIT 1 50/2

    PEPERIKSAAN PERCUBAAN PMR 2010

    Kertas soalan ini mengandungi 17 halaman bercetak

    [Lihat sebelah

    50/2 SULIT

    MATEMATIK

    Kertas 2

    Satu jam empat puluh lima minit

    JANGAN BUKA KERTAS SOALAN INI

    SEHINGGA DIBERITAHU

    1. Tuliskan nama dan tingkatan anda pada

    ruang yang disediakan

    2. Kertas soalan ini adalah dalam bahasa

    Inggeris

    3. Kertas soalan ini mengandungi 20 soalan.

    4. Jawab semua soalan.

    5. Jawapan hendaklah ditulis pada ruangyang disediakan dalam kertas soalan.

    Kertas soalan ini hendaklah diserahkan

    pada akhir peperiksaan.

    6. Tunjukkan langkah-langkah penting. Ini

    boleh membantu anda untuk mendapatkan

    markah.

    7. Rajah yang mengiringi soalan tidak

    dilukiskan mengikut skala kecuali dinyata.

    8. Markah yang diperuntukkan bagi setiap

    soalan ditunjukkan dalam kurungan.

    9. Anda tidak boleh menggunakankalkulator.

    Guru Pemeriksa

    SoalanMarkah

    Penuh

    Markah

    Diperoleh

    1 2

    2 2

    3 3

    4 3

    5 3

    6 3

    7 3

    8 3

    9 2

    10 3

    11 2

    12 3

    13 3

    14 3

    15 5

    16 3

    17 2

    18 5

    19 3

    20 4

    Jumlah

    Nama : ..

    Tingkatan : 3 ...

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    SULIT 2 50/2

    The following formulae may be helpful in answering the questions. The symbols given are the ones

    commonly used.

    RELATIONS

    1 m n m na a a + =

    2 m n m na a a =

    3 ( )m n mna a=

    4 Distance = 2 22 1 2 1( ) ( )x x y y +

    5 Midpoint

    ( , )x y = +

    2

    21 xx,

    +

    2

    21 yy

    6 Average speed =distance travelled

    time taken

    7sum of data

    Mean = number of data

    8 Pythagoras Theorem2 2 2c a b= +

    SHAPE AND SPACE

    1 Area of rectangle = length width

    2 Area of triangle =1

    base height2

    3 Area of parallelogram = base height

    4 Area of trapezium =1

    sum of parallel sides height2

    50/2 SULIT

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    SULIT 3 50/2

    5 Circumference of circle = 2d r =

    6 Area of circle = 2r

    7 Curved surface area of cylinder = 2 rh

    8 Surface area of sphere = 24 r

    9 Volume of right prism = cross sectional area length

    10 Volume of cuboid = length width height

    11 Volume of cylinder = 2r h

    12 Volume of cone =21

    3r h

    13 Volume of sphere =34

    3r

    14 Volume of right pyramid =1

    3base area height

    15 Sum of interior angles of a polygon = ( 2) 180n o

    16arc length angle subtended at centre

    circumference of circle 360=

    o

    17area of sector angle subtended at centre

    area of circle 360=

    o

    18 Scale factor, k=PA

    PA

    19 Area of image =2 area of objectk

    [Lihat sebelah

    50/2 SULIT

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    For

    ExaminersUse

    SULIT 4 50/2

    Answerall questions.

    1 Calculate the value of3 3 3

    116 8 4

    and express the answer as a fraction in its lowest term.

    [2 marks]

    Answer:

    2 Calculate the value of3

    5.48 ( 6)4 and express the answer as a decimal.

    [2 marks]

    Answer:

    50/2 SULIT

    2

    2

    2

    1

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    For

    ExaminersUse

    SULIT 5 50/2

    3 (a) Find the value of 3 0.343

    (b) Calculate the value of( )2

    3( 3) 169 +

    [3 marks]Answer:

    (a)

    (b)

    4 In Diagram 1,JKL andLMNare right angled triangles.

    Given that3

    cos5

    x = .

    Find (a) the length ofLM

    (b) tany

    [3 marks]

    Answer:

    (a)

    (b)

    [Lihat sebelah

    50/2 SULIT

    3

    3

    3

    4

    K

    J

    L M

    N

    25 cm

    15 cmx

    y

    10 cm

    DIAGRAM 1

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    For

    ExaminersUse

    SULIT 6 50/2

    5 InDiagram 2, triangleP is the image of the trianglePunder a transformation V.

    Describe in full the transformation V.

    [3 marks]

    Answer:

    6 (a) Diagram 3 in the answer space shows J is the image ofJ under a certain

    translation. State the translation.

    50/2 SULIT

    3

    5

    DIAGRAM 2

    0 2 4 6 8 10 12

    12

    10

    8

    6

    4

    2

    P

    P

    x

    y

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    For

    ExaminersUse

    SULIT 7 50/2

    (b) On the diagram in the answer space, draw the image of quadrilateralABCD under a

    90anticlockwise rotation about the point (4, 3).

    [3 marks]

    Answer :

    (a)

    (b)

    7 Express

    2 6

    4 12

    d d

    e de

    as a single fraction in its simplest form.

    [3 marks]

    [Lihat sebelah

    50/2 SULIT

    3

    6

    J

    J

    DIAGRAM 3

    0 2 4 6 8 10

    10

    8

    6

    4

    2

    x

    y

    C

    B

    A

    D

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    For

    ExaminersUse

    SULIT 8 50/2

    Answer :

    8 The data below shows part of the number of goals scored by the 32 teams in the first

    rounds of the World Cup 2006.

    1 2 0 3 0 2 1

    2 1 2 1 1 0 2

    0 3 1 2 3 3 3

    2 0 0 1 0 0 0

    2 0 1 3 1 1 1

    3 0 2 1 2 3 1

    (a) Using the above data, complete the tally chart in the answer space.

    (b) State the mode.

    [3 marks]Answer :

    (a) Score Tally Frequency

    0

    1

    2

    3

    (b)

    9 Simplify2(2 3) 3(3 4 )a a +

    [2 marks]

    Answer :

    50/2 SULIT

    3

    8

    3

    7

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    For

    ExaminersUse

    SULIT 10 50/2

    12 Simplify

    1 3

    4 22 2(4 )qp q p

    .

    [3 marks]

    Answer :

    13 Given that2

    2

    182

    F m

    T= . Express Tin terms ofF and m.

    [3 marks]

    Answer:

    50/2 SULIT

    3

    12

    2

    11

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    For

    ExaminersUse

    SULIT 11 50/2

    14 Solve each of the following equations.

    (a) 7 5 2u u+ =

    (b)3

    (4 8) 72

    w w + =

    [3 marks]

    Answer:

    (a)

    (b)

    15 Diagram 4 in the answer space shows a rhombus. S,Xand Yare three moving points in the

    diagram.

    (a) S is the point which moves such that its distance from point A and point Care the

    same. By using the letters in the diagram, state the locus ofS.

    (b) On the diagram, draw

    (i) the locus for the pointXthat is constantly 2 cm from the lineAC,

    [Lihat sebelah

    50/2 SULIT

    3

    13

    3

    14

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    For

    ExaminersUse

    SULIT 12 50/2

    (ii) the locus for the point Ythat is constantly 4 cm from the pointA

    (c) Hence, state the number of intersection points of the locus ofXand the locus ofY.

    [5 marks]

    Answer:

    (a)

    (b)

    `

    (c)

    16 Factorise completely :

    (a) 24 8m m n

    (b)2(3 ) 4 2y y y +

    [3 marks]

    Answer:

    (a)

    50/2 SULIT

    5

    15

    D

    C

    B

    A

    DIAGRAM 4

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    For

    ExaminersUse

    SULIT 13 50/2

    (b)

    17 Diagram 5 in the answer space shows polygonABCDEFG and straight linePQ drawn on

    a grid of equal squares.

    Starting from the line PQ, draw polygon PQRSTUV which is congruent to polygon

    ABCDEFG.

    [2 marks]

    Answer:

    18 Set squares and protractors are not allowed for this question.

    [Lihat sebelah

    50/2 SULIT

    3

    16

    2

    17

    P

    R

    Q

    DIAGRAM 6

    S

    60

    DIAGRAM 5

    BA

    C

    D

    E

    F

    G

    P

    Q

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    For

    ExaminersUse

    SULIT 14 50/2

    (a) Using only a ruler and a pair of compasses, construct quadrilateralPQRS as shown

    in Diagram 6 using the straight linesPSand SR provided in the answer space.

    (b) Based on the diagram constructed in (a), construct QT, angle bisector of the

    PQR such that point Tlies on the linePS. Measure the length QT.

    [5 marks]

    Answer:

    19 The pictograph below shows the number of cakes sold by a school canteen within a

    week.

    Monday

    Tuesday

    Wednesday

    Thursday

    Friday

    50/2 SULIT

    5

    18

    RS

    P

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    For

    ExaminersUse

    SULIT 15 50/2

    Key : represents 10 cakes

    Draw a line graph in the answer space to represent all the information in the pictograph

    above.

    [3 marks]

    Answer:

    20 Use the graph paper given to answer this problem.

    Table 1 shows the value of two variables,x andy of a function.

    x 4 3 2 1 0 1 2

    y 5 0 3 4 3 0 5

    By using a scale of 2 cm to 1 unit on thex-axis and 2 cm to 2 unit on they-axis, draw

    the graph of the function on the graph paper p