spb maths p2 pmr 2009

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    1SULIT

    BAHAGIAN PENGURUSANSEKOLAH BERASRAMA PENUH& SEKOLAH KLUSTER

    KEMENTERIAN PELAJARAN MALAYSIA

    PEPERIKSAAN PERCUBAANPENILAIAN MENENGAH RENDAH 2009 50/2MATEMATIKKertas 2

    Ogos 2009

    14

    3 jam Satu jam empat puluh lima minit

    JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

    Kertas soalan ini mengandungi 17 halaman bercetak

    Untuk Kegunaan Pemeriksa

    Kod Pemeriksa:

    SoalanMarkahPenuh

    MarkahDiperoleh

    1 22 23 34 35 36 37 38 29 5

    10 511 212 2

    13 214 315 316 317 418 319 320 4

    Jumlah

    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 anda hendaklah ditulis pada ruang yangdisediakan dalam kertas soalan ini.

    6. Tunjukkan langkah-langkah penting dalam kerjamengira anda. Ini boleh membantu untuk mendapatkan markah.

    7. Jika anda hendak menukar jawapan, batalkan jawapan yang telah dibuat. Kemudian tulis jawapan yang baru.

    8. Rajah yang mengiringi soalan tidak dilukismengikut skala kecuali dinyatakan.

    9. Markah yang diperuntukkan bagi setiap soalanditunjukkan dalam kurungan.

    10. Penggunaan kalkulator tidak di- benarkan.

    11. Serahkan kertas soalan ini kepada pengawas peperiksaan pada akhir peperiksaan.

    Nama: Tingkatan:

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

    221 x x ,

    221 y y

    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

    5 Circumference of circle = 2d r

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    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 = 213

    r h

    13 Volume of sphere = 343

    r

    14 Volume of right pyramid =13

    base area height

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

    16arc length angle subtended at centre

    circumference of circle 360

    17area of sector angle subtended at centrearea of circle 360

    18 Scale factor, k =PAPA

    19 Area of image = 2 area of objectk

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    SULIT 50/2

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    Answer all questions

    1 Calculate the value of 48 3 117[2 marks ]

    Answer :

    2 Calculate the value of 2.052148.0

    [2 marks ]

    Answer :

    3 (a) Find the value of 169

    1

    (b) Calculate the value of 23 1008.0[3 marks ]

    Answer :

    (a)

    (b)

    1

    2

    For Examiners

    Use

    2

    2

    3

    3 www.tutormuruli.blogspot.com

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    4 (a) Expand

    k w43

    632

    (b) Simplify ( 2 x 3 )( 3 x + 2 ) x( 3x 3 )

    [3 marks ] Answer :

    (a)

    (b)

    5 Factorise completely

    (a) 5gh 10g2h2

    (b) p + pq 2 2q

    [3 marks ]

    Answer :

    (a)

    (b)

    5

    For Examine

    Use

    4

    3

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    For Examiners

    Use6 Express

    hhh

    22

    23 2

    as a single fraction in its simplest form.

    [3 marks ] Answer :

    7 Solve each of the following equations:

    (a) e = 7 e

    (b) 3( a + 3 ) = a 5[3 marks ]

    Answer :

    (a)

    (b)

    8 Givena

    cbb

    2. Express b in terms of a and c. [2 marks ]

    Answer:

    6

    3

    7

    3

    8

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    7F

    ExamU9 Diagram 9 shows a quadrilateral ABCD .

    [5 marks ]

    Using only a ruler and a pair of compasses, construct Diagram 1 beginning from thediagram provided in the answer space.

    Based on the diagram constructed, measure the length, in cm, of CD .

    Answer:

    CD = .

    9

    45o

    7 cm

    D

    A

    C

    120 o

    B

    Diagram 9

    AB

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    For Examiners

    Use

    10 Diagram 10 in the answer space shows a rectangle PQRS.

    K, L, M and N are midpoints of PQ, QR, RS and PS respectively. X, Y and Z are three

    moving points in the diagram.

    (a) X is the point which moves such that it is equidistant from PQ and SR. By using

    the letters in the diagram, state the locus of X.(b) On the diagram, draw

    (i) the locus of the point Y which moves such that its distance is constantly

    4 cm from point K .

    (ii) the locus of the point Z which moves such that it is equidistant from

    straight lines PQ and PS.

    (c) Hence mark with the symbol the intersections of the locus of Y and the

    locus of Z.

    [5 marks ] Answer :

    (a)

    (b) (i), (ii)

    10

    5

    Diagram 10

    Q

    O

    P

    N

    R

    L

    K

    S M

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    9 Fo Exami

    Us

    11 Diagram 11 in the answer space shows a quadrilateral R drawn on a square grid.

    Draw the image of the quadrilateral R under a translation .3

    5

    [2 marks ]

    11

    Diagram 11

    R

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    10For

    ExaminersUse 12 Diagram 12 in the answer space shows two triangles drawn on a grid of equal squares.

    S is the image of S under an enlargement.

    Diagram 12

    [2 marks ]State(a) the centre of the enlargement.(b) the scale factor of the enlargement.

    Answer :

    (a)

    (b)

    12

    2

    S

    S

    6420

    2

    108

    4

    -2

    -2

    x

    10

    8

    6

    y

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    11For

    ExamineUse13 . Diagram 13 shows a polygon.

    Diagram 13

    On the grid in the answer space, redraw the polygon using the scale 1 : 400. The

    grid has equal squares with side of 1 cm.[2 marks ]

    Answer :

    13

    2

    32 m

    28 m

    24 m

    12 m

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    12For

    ExaminersUse

    14 . Find the value of 21

    21

    205

    [3 marks ]

    Answer :

    15 Given that 3 x = 3327 x

    Calculate the value of x [3 marks ]

    Answer :

    16 Given 3 > 2 p and 432

    p

    Solve the simultaneous linear inequalities above and represent the common values of p

    which satisfy both the inequalities on a number line.

    [3 marks ]

    Answer :

    14

    3

    15

    3

    16

    3

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    13 For Examine

    Use

    17 Table 17 shows the sale of books at Kedai Buku Utara over 5 months.

    On Diagram 17 in the answer space, complete the scale and draw a line graph torepresent all the information in Table 17.

    [4 marks ]

    Answer :

    Jan Feb Mar Apr May

    Month Jan Feb Mar Apr May

    Number of books sold 800 2 400 2 600 2 200 3 000

    17

    3000

    Number of books sold

    MonthDiagram 17

    Table 17

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    14For

    ExaminersUse 18 In Diagram 18, PQR and RST are right-angled triangles.

    [3 marks ]

    Given that cos xo =53

    and RT =23

    PR .

    (a) Find the length, in cm, of ST .

    (b) Tan yo.

    Answer :

    (a)

    (b)

    18

    3

    yo

    xo

    10 cm

    RP

    Q

    S

    T

    Diagram 18

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    15For

    ExaminerUse19 Diagram 19 is a pie chart which shows the sale of 4 types of cars in a month. Given

    that the number of car C sold is twice the number of car B.

    Diagram 19

    (a) State the value of angle D

    (b) By using the data from the pie chart, complete Table 19.

    [3 marks ]

    Answer :

    (a)

    (b)

    Table 19

    Type of car A B C

    Number of cars sold 60

    19

    3

    75o

    B

    C

    30o

    D

    A

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    16For

    ExaminersUse

    20 Use the graph paper provided to answer this question .

    Table 20 shows the values of two variables, x and y of a function.

    x 3 2 1 0 1 2

    y 7 0 5 8 9 8

    Table 20

    (a ) By using the scale of 1 cm to 1 unit on the y-axis, complete and label the y-axis.

    (b) Based on Table 20, plot the points on the graph paper.

    (c) Hence, draw the graph of the function.

    [4 marks ]

    20

    4

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