Solaf 2011 Add Maths Set 1 Paper 1[Question Paper]

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    NAMA .

    TINGKATAN .

    JABATAN PELAJARAN PERAK

    JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

    Kertas soalan ini mengandungi 13 halaman bercetak.[Lihat halaman sebelah

    3472/1 2011 JPN PERAK SOLAF1 SULIT

    SOALAN LATIH TUBI BERFOKUS 1 3472 / 1ADDITIONAL MATHEMATICS

    Kertas 1

    April

    2 jam Dua jam

    Untuk Kegunaan Pemeriksa

    Kod Pemeriksa :

    SoalanMarkah

    Penuh

    Markah

    Diperoleh

    1 3

    2 3

    3 3

    4 3

    5 4

    6 3

    7 28 3

    9 3

    10 3

    11 4

    12 3

    13 4

    14 4

    15 3

    16 3

    17 418 3

    19 3

    20 3

    21 3

    22 3

    23 3

    24 3

    25 4

    Jumlah 80

    1. Kertas soalan ini mengandungi 25 soalan.

    2. Answer all questions.

    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 are not

    drawn to scale unless stated.

    7. The marks allocated for each question are

    shown in brackets.

    8. You may use a scientific calculator.

    SULIT

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    For

    Examiner,s

    Use

    SULIT 2 3472/1

    Answer all questions

    1 Diagram 1 shows an incomplete arrow diagram which represents the relationship

    between setXand set Y.

    State(a) the values ofp and q,

    (b) the type of the relation.

    [ 3 marks]

    Answer :

    (a)

    (b)

    2 Functionsfand g are such that f:x 2x5 and g :x 1hx.

    Given that g1(1 ) = 4,

    find

    (a) the value of h,

    (b) g(8).

    [ 3 marks]

    Answer :

    (a)

    (b)

    3472/1 2011 JPN PERAK SOLAF1 SULIT

    2

    1

    q

    p

    1

    X square of Y

    Diagram 1

    3

    1

    3

    2

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    SULIT 3 3472/1

    3 Functionsfand g are such that g :xx7 and gf:x 2x1.

    Find

    (a) gf(3),

    (b) f(2).[3 marks]

    Answer :

    (a)

    (b)

    For

    Examiner,s

    Use

    4 Diagram4 shows the graph of a quadratic functiony =f(x) with an axis of

    symmetryx = 1.

    (a) Find the value ofh.

    (b) Solvef(x) 0.

    [3 marks]

    Answer :(a)

    (b)

    Lihat Halaman Sebelah

    3472/1 2011 JPN PERAK SOLAF1 SULIT

    3

    3

    x

    y

    O

    y = f(x)

    Diagram 4

    2 h

    3

    4

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    For

    Examiner,s

    Use

    SULIT 4 3472/1

    5 Both the quadratic equations,px28x + 6 = 0 and 3x

    2+ 6xp + 1 = 0, wherep is a

    constant, have two different roots.

    Find the range of values ofp.

    [4 marks]

    Answer :

    6 Diagram 6 shows some information about the graph of the quadratic function

    y = ka(x + h )2, where a , h and kare constants.

    (a) State the values ofh and k.

    (b) Calculate the value ofa.

    [3 marks]

    Answer :

    (a)

    (b)

    3472/1 2011 JPN PERAK SOLAF1 SULIT

    4

    5

    y-intercept = 5

    Coordinates of maximum point = ( 1 , 7 )

    Diagram 6

    3

    6

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    SULIT 5 3472/1

    7 Given that 4x

    = N, express 8x

    in terms ofN.

    [2 marks]

    Answer :

    For

    Examiner,s

    Use

    8 Solve the equation:

    3x( 12 x

    ) = 3

    [3 marks]Answer :

    9 Simplify logb 8 log4b2

    log27 3.

    [3 marks]

    Answer :

    Lihat Halaman Sebelah

    3472/1 2011 JPN PERAK SOLAF1 SULIT

    2

    7

    3

    8

    3

    9

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    For

    Examiner,s

    Use

    SULIT 6 3472/1

    10 Solve the equation:

    log5 ( 4x1 ) = 1 + log5 ( 7x )

    [3 marks]

    Answer :

    11 It is given that a, 4, 11, b, . 46 is an arithmetic progression.

    Find

    (a) the value ofa and ofb,

    (b) the number of terms the progression has.

    [4 marks]

    Answer :

    (a)

    (b)

    3472/1 2011 JPN PERAK SOLAF1 SULIT

    3

    10

    4

    11

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    SULIT 7 3472/1

    12 In a geometric progression, the ratio of the fifth term to the second term is27

    1 .

    Given that the first term is 12, find

    (a) the common ratio,

    (b) the sum to infinity.[3 marks]

    Answer :

    For

    Examiner,s

    Use

    13 An arithmetic progression has 11 terms. The first term is7 and the sum of the

    last 7 terms is 441.

    Find

    (a) the common difference,

    (b) the middle term.

    [4 marks]Answer :

    (a)

    (b)

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    3472/1 2011 JPN PERAK SOLAF1 SULIT

    3

    12

    4

    13

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    For

    Examiner,s

    Use

    SULIT 8 3472/1

    14 The variablesx andy are related by the equationm

    y= nx

    2+ m, where m and n

    are constants and m < 0. A straight line graph is obtained by plottingy againstx2

    as shown in Diagram 14.

    Find the value ofm and ofn.

    [4 marks]

    Answer :

    15 The variablesx andy are related by the equationy = 10x3. When log10y is plotted

    against log10x, a straight line graph passing through the point ( 2 , k) is obtained.

    Find the value of k.

    [3 marks]

    Answer :

    3472/1 2011 JPN PERAK SOLAF1 SULIT

    4

    14

    3

    15

    9

    y

    x2

    O 6

    Diagram 14

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    SULIT 9 3472/1

    16 Point P moves such that it is equidistant fromR(1 , 3 ) and S( 2 , q ).

    It is given that the equation of the locus ofP is 6x + 4y = 19.

    (a) Express the coordinates of the midpoint ofRS in terms ofq.

    (b) Hence, find the value ofq.

    [3 marks]Answer :

    (a)

    (b)

    For

    Examiner,s

    Use

    17 Diagram 17 shows a straight line PQR with equationy = 2x + 3. Point P lies on the

    y-axis.

    Given that PQ : QR = 1 : 2, find

    (a) the value ofh,

    (b) the coordinates ofQ.

    [4 marks]Answer :

    (a)

    (b)

    Lihat Halaman Sebelah

    3472/1 2011 JPN PERAK SOLAF1 SULIT

    3

    16

    4

    17

    x

    y

    O

    R( h , 15)

    P Q

    Diagram 17

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    For

    Examiner,s

    Use

    SULIT 10 3472/1

    18 In Diagram 18,ABCis a sector of a circle with centreB andADB is a semicircle

    with diameterAB.

    Given that ABC

    = 2.5 radians, calculate the perimeter, in cm, of the shaded

    region. [3 marks]

    Answer :

    19 Diagram 19 shows a quadrant PQR with centreR and a sector QXYof a circlewith centre Q.

    Given that XQY

    =3

    radians, calculate the area, in cm2, of the shaded region.

    [3 marks]

    Answer :

    3472/1 2011 JPN PERAK SOLAF1 SULIT

    3

    18

    3

    19

    Diagram 18

    DC

    BA

    10 cm

    Q

    X

    RP

    Y

    Diagram 19

    6 cm

    2 cm

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    SULIT 11 3472/1

    20 Diagram 20 shows part of the graph ofy =f(x).

    [3 marks]

    Given that 2

    0123 dxxf )( , calculate the area of the shaded region PQR.

    Answer :

    For

    Examiner,s

    Use

    21 Given that 2

    12

    523 dxxfx )( , find the value

    2

    1dxxf )( .

    [3 marks]

    Answer :

    Lihat Halaman Sebelah

    3472/1 2011 JPN PERAK SOLAF1 SULIT

    3

    20

    3

    21

    x

    y

    O

    R( 2 , 7 )P

    Q

    Diagram 20

    y =f(x)

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    For

    Examiner,s

    Use

    SULIT 12 3472/1

    22 The area of a circle is increasing at a rate of 3 cm2

    s 1.

    Calculate the rate at which the radius of the circle is increasing at the instant its

    perimeter is 9 cm.

    [3 marks]

    Answer :

    23 Diagram 23 shows a graph with equationy =x312x + 8.

    Given that point P is the maximum point of the graph, find the coordinates ofP.

    [3 marks]

    Answer :

    3472/1 2011 JPN PERAK SOLAF1 SULIT

    3

    22

    3

    23

    x

    y

    O

    Diagram 23

    P

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    SULIT 13 3472/1

    24 The set of numbers 2, 7, 4, 11, 5, n has a mean of 6.

    Find

    (a) the value ofn,

    (b) the median.

    [3 marks]Answer :

    (a)

    (b)

    For

    Examiner,s

    Use

    25 Diagram 25 shows some information about a set of numbers.

    Given thatx2 = 8 and it is taken out from the set.

    Calculate the standard deviation of the remaining numbers in the set.

    [4 marks]

    Answer :

    END OF QUESTION PAPER3472/1 2011 JPN PERAK SOLAF1 SULIT

    3

    24

    4

    25

    Numbers : x1 ,x2 ,x3 ,x4 ,x5

    x= 28 , x2

    = 170

    Diagram 25