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  • 7/31/2019 Additional Math Paper 1(Solaf)

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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

    April2 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 5 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

    Visit to download more maths paper

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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 set X and set Y.

    State(a) the values ofp and q,

    (b) the type of the relation.

    [ 3 marks]

    Answer :(a)

    (b)

    2 Functionsf and g are such that f: x 2x 5 and g : x 1 hx.

    Given that g 1

    ( 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 Functions f and g are such that g : x x 7 and gf: x 2x 1.

    Find

    (a) gf(3),

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

    Answer :

    (a)

    (b)

    ForExaminer,s

    Use

    4 Diagram 4 shows the graph of a quadratic function y = f(x) with an axis of

    symmetry x = 1.

    (a) Find the value ofh.

    (b) Solve f(x) 0.

    [3 marks]

    Answer :(a)

    (b)

    Lihat Halaman Sebelah3472/1 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, px2 8x + 6 = 0 and 3x2 + 6x p + 1 = 0, wherep is a

    constant, have two different roots.

    Find the range of values of p.

    [4 marks]

    Answer :

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

    y = k a( 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

    5

    y-intercept = 5

    Coordinates of maximum point = ( 1 , 7 )

    Diagram 6

    3

    6

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    For

    Examiner,s

    Use

    SULIT 6 3472/1

    10 Solve the equation:

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

    [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

    11

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    SULIT 7 3472/1

    12 In a geometric progression, the ratio of the fifth term to the second term is7

    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 is 7 and the sum of the

    last 7 terms is 441.

    Find(a) the common difference,

    (b) the middle term.

    [4 marks]Answer :

    (a)

    (b)

    Lihat Halaman Sebelah

    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 variables x and y are related by the equationy

    = nx2 + m, where m and n

    are constants and m < 0. A straight line graph is obtained by plotting y against x 2

    as shown in Diagram 14.

    Find the value of m and of n.

    [4 marks]

    Answer :

    15 The variables x and y are related by the equation y = 10x3. When log10 y is plotted

    against log10 x, 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

    14

    3

    15

    9

    y

    x 2

    O 6

    Diagram 14

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    SULIT 9 3472/1

    16 Point P moves such that it is equidistant from R( 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 Sebelah3472/1 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, ABC is a sector of a circle with centre B and ADB is a semicircle

    with diameter AB.

    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 cm 2, 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 of y = 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

    1

    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 cm 2 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 equation y =x3

    12 x + 8.

    Given that point P is the maximum point of the graph, find the coordinates of P.[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 that x2 = 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 , x 2 = 170

    Diagram 25

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    3472/2 JPN PERAK SOLAF 2011 / 1 ADD. MATHS PAPER 2 SULIT

    SULIT

    JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

    1. This question paper consists of three sections: Section A, Section B and Section C.

    2. Answer all questions in Section A, any four questions from Section B and any twoquestions from Section C.

    3. Show your working. It may help you to get marks.

    4. The diagrams provided in the questions are not drawn to scale unless stated otherwise.

    5. The marks allocated for each question and sub-part of a question are shown in

    brackets.

    6. You may use a scientific calculator.

    Kertas soalan ini mengandungi 10 halaman bercetak.[Lihat halaman sebelah

    SOALAN LATIH TUBI BERFOKUS 1 3472 /2ADDITIONAL MATHEMATICSKertas 2April

    12 jam Dua jam tiga puluh minit

    JABATAN PELAJARAN PERAK

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    3472/2 JPN PERAK SOLAF 2011 / 1 ADD. MATHS PAPER 2 SULIT

    SULIT 2 3472/2

    SECTION A

    [40 marks]

    Answer all questions.

    1 Solve the following simultaneous equations and give your answer correct to twodecimal places.

    y2 + 7x

    23)1( 2 yxy

    [5 marks]

    2 Diagram 2 shows the mapping of y onto x by the function bayyf : and the

    mapping of onto by the functionyb

    ayg

    2:

    ,2

    by .

    Find

    (a) the value ofa and b, [ 3 marks]

    (b) the function that mapped x onto y, [ 2 marks]

    (c) the function that mapped x onto z. [ 2 marks]

    3 Diagram 3 shows a pattern formed by joining the midpoints of the sides of each

    subsequent square beginning from the biggest square.

    (a) Show that the areas of the squares form a geometric progression.

    [3 marks](b) It is given thatx = 8.

    Find

    (i) the sum of the areas, in cm2, of all the squares in the pattern,

    (ii) the sum to infinity of the areas, in cm2, of the squares if the pattern

    continues in the manner described.[3 marks]

    zyx

    1

    3

    Diagram 2

    gf

    Diagram 3

    x cm

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    3472/2 JPN PERAK SOLAF 2011 / 1 ADD. MATHS PAPER 2 SULIT

    SULIT 3 3472/2

    4 (a) The gradient function of a curve is given by2x

    kx

    x

    dy . The curve has a

    turning point with coordinates ( 2 , 1 ).

    Find

    (i) the value of k,(ii) the equation of the curve.

    [4 marks]

    (b) Diagram 4 shows part of the curve 922 yx which intersects the -axis

    and the y - axis at point A and point B respectively.

    .

    The shaded region is revolved

    360 about the y - axis.

    Find the volume of the solid generated

    [4 marks]5 Table 5 shows the frequency distribution of the marks obtained by a group ofstudents.

    Table 5

    (a) Use graph paper to answer this part of the question.

    Using a scale of 2cm to 10 marks on the horizontal axis and 2cm to 2 students

    on the vertical axis, draw a histogram to represent the frequency distributionof the marks in Table 5.

    Hence, find the mode.

    [3 marks]

    (b) Calculate the standard deviation for the distribution of marks.[4 marks]

    [Lihat halaman sebelah

    Marks Number of students

    1 10 5

    11 20 8

    21 30 20

    31 40 10

    41 50 7

    Ox

    y

    A

    B

    Diagram 4

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    3472/2 JPN PERAK SOLAF 2011 / 1 ADD. MATHS PAPER 2 SULIT

    SULIT 4 3472/2

    6 Solution by scale drawing will not be accepted.

    Diagram 6 shows a straight line ACwhich intersects the y-axis at point B.

    The equation ofAC is 1523 xy .

    Find

    (a) the equation of the straight line which passes through point A andperpendicular to AC,

    [4 marks]

    (b) (i) the coordinates of B,

    (ii) the coordinates ofC, given AB : BC= 2 : 7.

    [3 marks]

    A( 3 , 7 )

    Ox

    y

    C

    B

    Diagram 6

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    3472/2 JPN PERAK SOLAF 2011 / 1 ADD. MATHS PAPER 2 SULIT

    SULIT 5 3472/2

    Section B

    [40 marks]Answer any four questions from this section.

    7 Use graph paper to answer this question.

    Table 7 shows some experimental values of two variables, x and y. It is known that xand y are related by the equation y =H kx where H and k are constants.

    Table 7(a) Plot log10 y againstx by using a scale of 2 cm to 1 unit on the x-axis and 2 cm

    to 0.2 unit on the log10 y - axis.

    Hence draw the line of best fit.[4 marks]

    (b) Use the graph in 7(a) to find the value of(i) H,

    (ii) k,

    (iii) x when y = 50.

    [6 marks]

    8 Diagram 8 shows a semicircle ABCwith centre O. It is given that AOB is 1.2 radians

    and the length of OA is 5 cm.

    Find,

    (a) BOCin radians,

    [1 mark]

    (b) the shortest distance, in cm,from the centre O to the straight line BC,[2 marks]

    (c) the perimeter, in cm, of the shaded region,

    [4 marks]

    (d) the area, in cm2, of the shaded region.

    [3 marks]

    (Use 142.3 )[Lihat halaman sebelah

    x 1 2 4 6 8 10

    y 6.92 9.80 19.40 37.40 74.00 144.40

    Diagram 8

    O

    A

    C

    B

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    3472/2 JPN PERAK SOLAF 2011 / 1 ADD. MATHS PAPER 2 SULIT

    SULIT 6 3472/2

    9 Diagram 9 shows a rhombus ABCD. Vertex B lies on the x-axis.

    (a) Find the equation of the perpendicular bisector of AC,

    [4 marks]

    (b) Calculate the area of. rhombus ABCD.[3 marks]

    (c) A point P moves such that its distances from points A and Care in the ratio2 : 1.

    Find the equation of the locus ofP.

    [3 marks]

    10 Diagram 10 shows part of the curve y =x2

    + 3 and straight line 2y + 3x = 20.

    (a) Show that k= 2.

    [2 marks]

    (b) Find the area of the shaded region.

    [4 marks]

    (c) Find the volume generated, in terms of, when the region bounded by the

    y - axis, the curvey =x2

    + 3 and the straight line 2y + 3x = 20 is revolvedthrough 3600 about the y - axis.

    [4 marks]

    B

    D

    A( 1 , 10 )

    C( 3 , 2 )

    O

    y

    x

    Diagram 9

    Diagram 10

    A( k , k+ 5 )

    xO

    y = x2

    + 3

    y

    2y + 3x = 20

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    3472/2 JPN PERAK SOLAF 2011 / 1 ADD. MATHS PAPER 2 SULIT

    SULIT 7 3472/2

    11 Diagram 11 shows the first few triangles of a series of triangles of equal heights

    drawn on a straight line AB. The length ofAB is 210 m .

    (a) Show that the lengths of the bases of the triangles form a geometric

    progression.

    Hence, state the common ratio.[2 marks]

    (b) Calculate the area of the 8th triangle.

    [3 marks]

    (c) Ifn triangles are drawn on the line AB, find the maximum value ofn.

    [5 marks]

    [Lihat halaman sebelah

    A B

    6 cm

    Diagram 11

    3 cm 6 cm 12 cm

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    3472/2 JPN PERAK SOLAF 2011 / 1 ADD. MATHS PAPER 2 SULIT

    SULIT 8 3472/2

    Section C

    [40 marks]Answer any two questions from this section.

    12 Diagram 12 shows a triangle ABCwhere ADB and AECare straight lines.

    .

    It is given that AD = 7.2 cm, AE= 4.6 cm, BC = 10.7 cm, DE= 6.3 cm and 46ACB

    (a) Calculate

    (i) BAC

    ,(ii) the length, in cm, ofAC.

    [4 marks]

    (b) Point A lies on ACsuch that AB = AB.

    (i) Sketch BCA ' ,

    (ii) Calculate the area, in cm2

    , of BCA' .

    [6 marks]

    Diagram 12

    B

    A

    C

    D

    E

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    3472/2 JPN PERAK SOLAF 2011 / 1 ADD. MATHS PAPER 2 SULIT

    SULIT 9 3472/2

    13 Table 13 shows the price indices and percentage usage of four ingredients, A, B, C

    and D, in the production of a type of chocolate cake.

    Ingredient Price index for the year 2009based on the year 2005

    Percentage usage

    A 125 25

    B y 30

    C 110 10

    D 140 x

    Table 13

    (a) Calculate

    (i) the price ofCin the year 2005 if the price in the year 2009 is

    RM 38.50,(ii) the price index ofD in the year 2009 based on the year 2002

    if its price index in the year 2005 based on the year 2002 is 125.

    [4 marks]

    (b) The composite index for the cost of chocolate cake production for the year2009 based on the year 2005 is 130.

    . Calculate

    (i) the price of a chocolate cake in the year 2009 if the corresponding

    price in the year 2005 is RM 45.00,

    (ii) the value ofx and of y.[6 marks]

    14 Diagram 14 shows a quadrilateral ABCD where ABC is acute.

    Calculate

    (a) (i) ABC,(ii) ADC,

    (iii) the area, in cm2, of quadrilateral ABCD.

    [ 7 marks]

    (b) A triangle ABC has the same measurements as those given for triangle ABC,

    that is, AC

    = 12.6 cm, C

    B

    = 8.7cm and C

    A

    B

    = 38.5

    obut is different in

    shape compared to triangle ABC.

    (i) Sketch the triangleAB

    C

    .

    (ii) Calculate the length, in cm, ofAB.

    [ 3 marks]

    C

    BA

    D

    Diagram 14

    8.7 cm

    5.2 cm

    9.6 cm12.6 cm

    38.5

    [Lihat halaman sebelah

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    3472/2 JPN PERAK SOLAF 2011 / 1 ADD. MATHS PAPER 2 SULIT

    SULIT 10 3472/2

    15 A particular kind of bread is made by using four ingredients, P, Q, R and S. Table 15

    shows the prices of the ingredients for the years 2005 and 2006.

    Ingredient Price per kilogram (RM)Year 2005 Year 2006

    P 5.00 w

    Q 2.50 4.00

    R x y

    S 4.00 4.00

    Table 15

    (a) The index number of ingredient P in the year 2006 based the year 2005 is 120.

    Calculate the value of w .

    [2 marks]

    (b) The index number of ingredient R in the year 2006 based on the year 2005 is125. The price per kilogram of ingredient R in the year 2006 is RM2.00 more

    than its corresponding price in the year 2005.

    Calculate the value of x and of .

    [3 marks]

    (c) The composite index for the cost of making the bread in the year 2006 based

    on the year 2005 is 126.25.

    Calculate

    (i) the price of the bread in the year 2005 if its corresponding price in the

    year 2006 is RM5.05.

    (ii) the value of if the quantities of ingredients P, Q, R and S are used in

    the ratio of 7 : 3 : m : 2 respectively.

    [5 marks]

    END OF QUESTION PAPER

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    JABATAN PELAJARAN PERAK

    DARUL RIDZUAN

    PAPER 1

    No. Important steps / Answers Marks

    1 (a) p = 4q = 1

    (b) many to one

    111

    2 (a) 1 h(4) = 1

    h =2

    1

    (b) 3

    1

    1

    1

    3 (a) 5(b) f(x) 7 = 2x 1

    2

    11

    1

    4(a) 1

    2

    2

    h

    4

    (b) 2 x 4

    1

    1

    1

    5 82

    4(p)(6) > 0 or 62

    4(3)( p + 1 ) > 0

    p 2

    2 < p