Add Maths (Q) 2011 by speedracerijok

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									SULIT
          NAMA           ……………………………………………………………………….

          TINGKATAN ………………………………………….


                                    JABATAN PELAJARAN PERAK


SOALAN LATIH TUBI BERFOKUS 1                                                        3472 / 1
ADDITIONAL MATHEMATICS
Kertas 1
April
2 jam                                                                                 Dua jam


            JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU
                                                               Untuk Kegunaan Pemeriksa
1.      Kertas soalan ini mengandungi 25 soalan.           Kod Pemeriksa :
                                                                         Markah   Markah
2.      Answer all questions.                                Soalan
                                                                          Penuh  Diperoleh
                                                                1           3
3.      Write your answers in the spaces provided               2           3
        in the question paper.                                  3           3
                                                                4           3
4.      Show your working. It may help you to
                                                                5           4
        get marks.
                                                                6           3
                                                                7           2
5.      If you wish to change your answer, cross
                                                                8           3
        out the answer that you have done. Then
        write down the new answer.                              9           3
                                                               10           3
6.      The diagrams in the questions are not                  11           4
        drawn to scale unless stated.                          12           3
                                                               13           4
7.      The marks allocated for each question are              14           4
        shown in brackets.                                     15           3
                                                               16           3
8.      You may use a scientific calculator.                   17           4
                                                               18           3
                                                               19           3
                                                               20           3
                                                               21           3
                                                               22           3
                                                               23           3
                                                               24           3
                                                               25           4
                                                             Jumlah        80
                          Kertas soalan ini mengandungi 13 halaman bercetak.
                                                                          [Lihat halaman sebelah
3472/1 2011 JPN PERAK SOLAF 1                                                            SULIT
   For       SULIT                                            2                           3472/1
Examiner,s
   Use
                                                     Answer all questions

             1   Diagram 1 shows an incomplete arrow diagram which represents the relationship
                 between set X and set Y.

                                                X        square of          Y

                                                2●
                                                                        ●   p
                                                1●
                                                                        ● 1
                                                q●

                                                         Diagram 1
                 State
                 (a) the values of p and q,
                 (b) the type of the relation.
                                                                                       [ 3 marks]
                 Answer :
                 (a)
   1
                 (b)
       3

             2   Functions f 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)



   2

       3




             3472/1    2011 JPN PERAK SOLAF 1                                            SULIT
SULIT                                           3                                  3472/1       For
                                                                                             Examiner,s
                                                                                                Use
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)




                                                                                                  3

                                                                                                      3

4   Diagram 4 shows the graph of a quadratic function y = f(x) with an axis of
    symmetry x = 1.
                                   y

                                                    y = f(x)

                                                               x
                                    –2 O        h


                                       Diagram 4

    (a)      Find the value of h.
    (b)      Solve f(x) ≤ 0.
                                                                                 [3 marks]
    Answer :
    (a)


    (b)
                                                                                                  4

                                                                                                      3



                                                                   Lihat Halaman Sebelah
3472/1    2011 JPN PERAK SOLAF 1                                                 SULIT
   For       SULIT                                          4                                 3472/1
Examiner,s
   Use
             5   Both the quadratic equations, px2 – 8x + 6 = 0 and 3x2 + 6x – p + 1 = 0, where p is a
                 constant, have two different roots.
                 Find the range of values of p.
                                                                                            [4 marks]
                 Answer :




   5

       4

             6   Diagram 6 shows some information about the graph of the quadratic function
                 y = k – a( x + h ) 2, where a , h and k are constants.

                                                    y-intercept = 5
                                        Coordinates of maximum point = ( 1 , 7 )

                                                     Diagram 6
                 (a)     State the values of h and k.
                 (b)     Calculate the value of a.
                                                                                            [3 marks]
                 Answer :
                 (a)


                 (b)




   6

       3




             3472/1    2011 JPN PERAK SOLAF 1                                                 SULIT
SULIT                                                 5                  3472/1      For
                                                                                  Examiner,s
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7   Given that 4x = N, express 8x in terms of N.
                                                                      [2 marks]
    Answer :




                                                                                       7

                                                                                           2

8   Solve the equation:
                                  3– x ( 12 x ) = 3
                                                                      [3 marks]
    Answer :




                                                                                       8

                                                                                           3

9   Simplify logb 8 × log4 b 2 ÷ log27 3.
                                                                      [3 marks]
    Answer :




                                                                                       9

                                                                                           3



                                                          Lihat Halaman Sebelah
3472/1   2011 JPN PERAK SOLAF 1                                         SULIT
   For       SULIT                                               6                       3472/1
Examiner,s
   Use
             10    Solve the equation:
                                                 log5 ( 4x – 1 ) = 1 + log5 ( 7 – x )
                                                                                        [3 marks]
                  Answer :




   10

        3

             11 It is given that a, 4, 11, b, ……………………. 46 is an arithmetic progression.
                Find
                (a) the value of a and of b,
                (b) the number of terms the progression has.
                                                                                  [4 marks]
                 Answer :
                 (a)




                  (b)




   11

        4




             3472/1     2011 JPN PERAK SOLAF 1                                           SULIT
SULIT                                            7                                     3472/1      For
                                                                                                Examiner,s
                                                                                                   Use
                                                                                       1
12   In a geometric progression, the ratio of the fifth term to the second term is       .
                                                                                       27
     Given that the first term is 12, find
     (a) the common ratio,
     (b) the sum to infinity.
                                                                                 [3 marks]
     Answer :




                                                                                                   12

                                                                                                         3

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)                                                                                           13

                                                                                                         4



                                                                 Lihat Halaman Sebelah
3472/1     2011 JPN PERAK SOLAF 1                                              SULIT
   For       SULIT                                       8                                       3472/1
Examiner,s
   Use
                                                                     y
             14    The variables x and y are related by the equation    = nx2 + m, where m and n
                                                                     m
                  are constants and m < 0. A straight line graph is obtained by plotting y against x 2
                  as shown in Diagram 14.
                                        y
                                               9




                                                                       x2
                                               O           6
                                                    Diagram 14
                  Find the value of m and of n.
                                                                                              [4 marks]
                  Answer :




   14

        4

             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 :




   15

        3




             3472/1   2011 JPN PERAK SOLAF 1                                                     SULIT
SULIT                                            9                                   3472/1       For
                                                                                               Examiner,s
                                                                                                  Use
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 of P is 6x + 4y = 19.
     (a) Express the coordinates of the midpoint of RS in terms of q.
     (b) Hence, find the value of q.
                                                                                   [3 marks]
     Answer :
     (a)



     (b)




                                                                                                  16

                                                                                                        3

17   Diagram 17 shows a straight line PQR with equation y = 2x + 3. Point P lies on the
     y-axis.
                                y
                                                       ● R( h , 15)
                                           ●

                                  P●       Q

                                                               x
                                  O
                                            Diagram 17
     Given that PQ : QR = 1 : 2, find
     (a) the value of h,
     (b) the coordinates of Q.
                                                                                   [4 marks]
     Answer :
     (a)



                                                                                                  17

     (b)                                                                                                4



                                                                   Lihat Halaman Sebelah
3472/1   2011 JPN PERAK SOLAF 1                                                  SULIT
   For       SULIT                                           10                                      3472/1
Examiner,s
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             18   In Diagram 18, ABC is a sector of a circle with centre B and ADB is a semicircle
                  with diameter AB.


                                                        D                  C

                                                                      10 cm
                                               A       B
                                                 Diagram 18
                   Given that  ABC = 2.5 radians, calculate the perimeter, in cm, of the shaded
                   region.
                                                                                           [3 marks]
                   Answer :




   18

        3

             19   Diagram 19 shows a quadrant PQR with centre R and a sector QXY of a circle
                  with centre Q.                       Q

                                                                  6 cm
                                                        X
                                                                  Y
                                                                  2 cm
                                               P                  R
                                                   Diagram 19
                                               
                  Given that  XQY =             radians, calculate the area, in cm 2, of the shaded region.
                                               3
                                                                                                    [3 marks]
                  Answer :



   19

        3




             3472/1   2011 JPN PERAK SOLAF 1                                                         SULIT
SULIT                                             11                                   3472/1       For
                                                                                                 Examiner,s
                                                                                                    Use
20 Diagram 20 shows part of the graph of y = f(x).
                                    y
                                    P               ●   R( 2 , 7 )

                                                               y = f(x)
                                    Q

                                    O                            x
                                           Diagram 20                               [3 marks]
     Given that    2
                  0   3 f ( x) dx  12 , calculate the area of the shaded region PQR.
     Answer :




                                                                                                    20

                                                                                                          3

                                               5
21   Given that  1 3x  2  f ( x) dx 
                  2
                                                 , find the value  21 f ( x) dx .
                                                                    
                                               2
                                                                                     [3 marks]
     Answer :




                                                                                                    21

                                                                                                          3



                                                                      Lihat Halaman Sebelah
3472/1   2011 JPN PERAK SOLAF 1                                                     SULIT
   For       SULIT                                       12                                       3472/1
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             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 :




   22

        3

             23   Diagram 23 shows a graph with equation y = x 3 – 12 x + 8.
                                              y
                                                 P
                                                ●




                                                                           x
                                                    O


                                              Diagram 23
                  Given that point P is the maximum point of the graph, find the coordinates of P.
                                                                                           [3 marks]
                  Answer :




   23

        3




             3472/1   2011 JPN PERAK SOLAF 1                                                      SULIT
SULIT                                                  13                      3472/1       For
                                                                                         Examiner,s
                                                                                            Use
24 The set of numbers 2, 7, 4, 11, 5, n has a mean of 6.
   Find
   (a)   the value of n,
   (b)   the median.
                                                                             [3 marks]
     Answer :
     (a)




     (b)                                                                                    24

                                                                                                  3

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

                                    Numbers : x1 , x2 , x3 , x4 , x5

                                       ∑ x = 28 , ∑x 2 = 170

                                             Diagram 25
     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 :




                                                                                            25

                                                                                                  4




                                     END OF QUESTION PAPER
3472/1     2011 JPN PERAK SOLAF 1                                             SULIT

								
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