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Koleksi Soalan-Soalan
Percubaan add math SPM
        kertas 1


          Disusun:
http://kampungebuku.blogspot.com
Daftar Isi
Koleksi Soalan-Soalan Percubaan Add Math Kertas 1
  1.   Peperiksaan Percubaan Sekolah Berasrama Penuh ……1
  2.   Jawapan Peperiksaan Percubaan SBP…………………. 19
  3.   Peperiksaan Percubaan Negeri Perak………………….. 25
  4.   Jawapan Peperiksaan Percubaan Negeri Perak ……… 41
  5.   Peperiksaan Percubaan Negeri Selangor ……………... 46
  6.   Jawapan Peperiksaan Percubaan S’ngor ……………. 71
  7.   Peperiksaan Percubaan Negeri Terengganu…………. 74
  8.   Jawapan Peperiksaan Percubaan T’gganu …………... 98
Name : ………………..……………                                               Form : ………………………..……




                            BAHAGIAN PENGURUSAN SEKOLAH BERASRAMA PENUH
                                        DAN SEKOLAH KLUSTER
                                  KEMENTERIAN PELAJARAN MALAYSIA



 PEPERIKSAAN PERCUBAAN SELARAS SPM 2009                                                       3472 / 1
 ADDITIONAL MATHEMATICS
 Kertas 1
 Ogos 2009
 2 jam                                                                                        Dua jam


                                                                            Untuk Kegunaan Pemeriksa
       JANGAN BUKA KERTAS SOALAN INI
                                                                   Soalan           Markah          Markah
           SEHINGGA DIBERITAHU                                                      Penuh          Diperolehi
                                                                     1                 2
           1. Tulis nama dan tingkatan anda pada
                                                                     2                 4
              ruangan yang disediakan.
                                                                     3                 4
           2. Kertas soalan ini adalah dalam                         4                 3
              dwibahasa.                                             5                 2
                                                                     6                 3
           3. Soalan dalam bahasa Inggeris                           7                 3
              mendahului soalan yang sepadan                         8                 3
              dalam bahasa Melayu.                                   9                 4
                                                                    10                 3
           4. Calon dibenarkan menjawab                             11                 3
              keseluruhan atau sebahagian soalan                    12                 4
              sama ada dalam bahasa Inggeris atau                   13                 3
              bahasa Melayu.                                        14                 3
                                                                    15                 3
           5. Calon dikehendaki membaca                             16                 3
              maklumat di halaman belakang kertas                   17                 4
              soalan ini.                                           18                 4
                                                                    19                 3
                                                                    20                 3
                                                                    21                 3
                                                                    22                 3
                                                                    23                 3
                                                                    24                 3
                                                                    25                 4

                                                                    TOTAL              80


                          Kertas soalan ini mengandungi 18 halaman bercetak


  3472/1   2009 Hak Cipta SBP                                                       [Lihat sebelah
                                                                                           SULIT
 http://kampungebuku.blogspot.com                                                                  1
SULIT                                                        2                                                    3472/1

    The following formulae may be helpful in answering the questions. The symbols given are the ones
    commonly used.
                                                              ALGEBRA
                                2
                      −b ± b − 4ac                                                            log c b
        1        x=                                                    8        logab =
                           2a                                                                 log c a

        2     am × an = a m + n                                         9       Tn = a + (n-1)d

        3     am ÷ an = a m -       n
                                                                                        n
                                                                       10        Sn =     [2a + ( n − 1) d ]
                                                                                        2
        4     (am) n = a nm                                            11        Tn = ar n-1
        5     loga mn = log am + loga n                                         a(r n − 1) a (1 − r n )
                                                                       12 Sn =            =             , (r ≠ 1)
                      m                                                           r −1        1− r
        6     loga      = log am - loga n
                                                                                  a
                      n                                                13 S ∞ =        , r <1
        7     log a mn = n log a m                                              1− r


                                                              CALCULUS

                         dy   dv  du
    1        y = uv ,       =u +v                                     4 Area under a curve
                         dx   dx  dx                                             b


                       du     dv
                                                                           =     ∫ y dx        or
                     v     −u                                                    a
               u dy
    2        y= ,   = dx 2 dx ,                                                   b

               v dx       v                                                 =     ∫ x dy
                                                                                  a

             dy dy du                                                 5 Volume generated
    3          =  ×                                                               b
             dx du dx                                                          = ∫ π y 2 dx or
                                                                                  a
                                                                                  b
                                                                                          2
                                                                            =     ∫π x        dy
                                                                                  a



                                                       GEOMETRY


1 Distance =                ( x 2 − x1 ) 2 + ( y 2 − y1 ) 2       5     A point dividing a segment of a line
                                                                                ⎛ nx + mx2 ny1 + my 2 ⎞
                                                                       ( x,y) = ⎜ 1         ,          ⎟
2 Midpoint                                                                      ⎝ m+n          m+n ⎠
                        ⎛ x1 + x 2   y + y2 ⎞
        (x , y) = ⎜                , 1      ⎟
                        ⎝ 2            2 ⎠                        6 Area of triangle
                                                                   1
3           r = x2 + y2                                           = ( x1 y 2 + x 2 y 3 + x3 y11 ) − ( x 2 y1 + x3 y 2 + x1 y 3 )
                                                                   2
                  xi + yj
4           ˆ
            r=
                  x2 + y2


    3472/1              2009 Hak Cipta SBP                                                                     [ Lihat sebelah
                                                                                                                      SULIT
    http://kampungebuku.blogspot.com                                                                                         2
SULIT                                                             3                                            3472/1

                                                     STATISTIC


           1      x =
                          ∑x                                                               ∑ w1 I1
                                                                                 7    I=
                           N                                                               ∑ w1
                                                                                                 n!
                          ∑ fx                                                   8      Pr =
                                                                                      n

           2      x =                                                                        (n − r )!
                          ∑f                                                                       n!
                                                                                 9     n
                                                                                         Cr =
                                                                                              (n − r )!r!
           3 σ =
                           ∑ (x − x )   2

                                            =
                                                    ∑x   2

                                                             −x
                                                                 _2


                                   N                N                            10    P(A ∪ B) = P(A)+P(B)- P(A ∩ B)


           4      σ=
                           ∑ f ( x − x)     2

                                                =   ∑ fx     2
                                                                 −x
                                                                      2          11    P (X = r) = nCr p r q n − r , p + q = 1
                              ∑f                    ∑f
                                                                                 12    Mean µ = np
                            ⎡1     ⎤
                            ⎢2 N −F⎥
           5 m =          L+⎢      ⎥C                                            13    σ = npq
                            ⎢ fm ⎥
                            ⎢
                            ⎣      ⎥
                                   ⎦                                                      x−μ
                                                                                 14    z=
                                                                                           σ
                       Q1
           6     I=       ×100
                       Q0

                                                TRIGONOMETRY

 1 Arc length, s = r θ                                                    9 sin (A ± B) = sinA cosB ± cosA sinB

                                   1 2                                    10 cos (A ± B) = cosA cosB m sinA sinB
 2 Area of sector , L =              rθ
                                   2
 3 sin 2A + cos 2A = 1                                                                        tan A ± tan B
                                                                          11 tan (A ± B) =
                                                                                             1 m tan A tan B
 4 sec2A = 1 + tan2A
                                                                                 a     b     c
            2                  2                                          12        =     =
 5 cosec A = 1 + cot A                                                         sin A sin B sin C

 6 sin 2A = 2 sinA cosA
                                                                          13 a2 = b2 + c2 - 2bc cosA
                      2            2
 7 cos 2A = cos A – sin A
          = 2 cos2A - 1                                                                               1
          = 1 - 2 sin2A                                                   14 Area of triangle =         absin C
                                                                                                      2

                   2 tan A
8 tan 2A =
                 1 − tan 2 A




3472/1          2009 Hak Cipta SBP                                                                      [ Lihat sebelah
                                                                                                             SULIT
http://kampungebuku.blogspot.com                                                                                        3
SULIT                                                      4                                                            3472/1

                  THE UPPER TAIL PROBABILITY Q(z) FOR THE NORMAL DISTRIBUTION N(0,1)
                  KEBARANGKALIAN HUJUNG ATAS Q(z) BAGI TABURAN NORMAL N(0, 1)

                                                                                                                   1   2   3     4    5     6        7   8    9
 z       0            1        2         3           4       5         6              7         8         9
                                                                                                                                 Minus / Tolak
0.0   0.5000      0.4960    0.4920    0.4880    0.4840    0.4801    0.4761         0.4721    0.4681    0.4641      4   8   12    16   20    24   28      32   36
0.1   0.4602      0.4562    0.4522    0.4483    0.4443    0.4404    0.4364         0.4325    0.4286    0.4247      4   8   12    16   20    24   28      32   36
0.2   0.4207      0.4168    0.4129    0.4090    0.4052    0.4013    0.3974         0.3936    0.3897    0.3859      4   8   12    15   19    23   27      31   35
0.3   0.3821      0.3783    0.3745    0.3707    0.3669    0.3632    0.3594         0.3557    0.3520    0.3483      4   7   11    15   19    22   26      30   34
0.4   0.3446      0.3409    0.3372    0.3336    0.3300    0.3264    0.3228         0.3192    0.3156    0.3121      4   7   11    15   18    22   25      29   32
0.5   0.3085      0.3050    0.3015    0.2981    0.2946    0.2912    0.2877         0.2843    0.2810    0.2776      3   7   10    14   17    20   24      27   31
0.6   0.2743      0.2709    0.2676    0.2643    0.2611    0.2578    0.2546         0.2514    0.2483    0.2451      3   7   10    13   16    19   23      26   29
0.7   0.2420      0.2389    0.2358    0.2327    0.2296    0.2266    0.2236         0.2206    0.2177    0.2148      3   6   9     12   15    18   21      24   27
0.8   0.2119      0.2090    0.2061    0.2033    0.2005    0.1977    0.1949         0.1922    0.1894    0.1867      3   5   8     11   14    16   19      22   25
0.9   0.1841      0.1814    0.1788    0.1762    0.1736    0.1711    0.1685         0.1660    0.1635    0.1611      3   5   8     10   13    15   18      20   23
1.0   0.1587      0.1562    0.1539    0.1515    0.1492    0.1469    0.1446         0.1423    0.1401    0.1379      2   5   7     9    12    14   16      19   21
1.1   0.1357      0.1335    0.1314    0.1292    0.1271    0.1251    0.1230         0.1210    0.1190    0.1170      2   4   6     8    10    12   14      16   18
1.2   0.1151      0.1131    0.1112    0.1093    0.1075    0.1056    0.1038         0.1020    0.1003    0.0985      2   4   6     7    9     11   13      15   17
1.3   0.0968      0.0951    0.0934    0.0918    0.0901    0.0885    0.0869         0.0853    0.0838    0.0823      2   3   5     6    8     10   11      13   14
1.4   0.0808      0.0793    0.0778    0.0764    0.0749    0.0735    0.0721         0.0708    0.0694    0.0681      1   3   4     6    7     8    10      11   13
1.5   0.0668      0.0655    0.0643    0.0630    0.0618    0.0606    0.0594         0.0582    0.0571    0.0559      1   2   4     5    6     7        8   10   11
1.6   0.0548      0.0537    0.0526    0.0516    0.0505    0.0495    0.0485         0..0475   0.0465    0.0455      1   2   3     4    5     6        7   8    9
1.7   0.0446      0.0436    0.0427    0.0418    0.0409    0.0401    0.0392         0.0384    0.0375    0.0367      1   2   3     4    4     5        6   7    8
1.8   0.0359      0.0351    0.0344    0.0336    0.0329    0.0322    0.0314         0.0307    0.0301    0.0294      1   1   2     3    4     4        5   6    6
1.9   0.0287      0.0281    0.0274    0.0268    0.0262    0.0256    0.0250         0.0244    0.0239    0.0233      1   1   2     2    3     4        4   5    5
2.0   0.0228      0.0222    0.0217    0.0212    0.0207    0.0202    0.0197         0.0192    0.0188    0.0183      0   1   1     2    2     3        3   4    4
2.1   0.0179      0.0174    0.0170    0.0166    0.0162    0.0158    0.0154         0.0150    0.0146    0.0143      0   1   1     2    2     2        3   3    4
2.2   0.0139      0.0136    0.0132    0.0129    0.0125    0.0122    0.0119         0.0116    0.0113    0.0110      0   1   1     1    2     2        2   3    3
2.3   0.0107      0.0104    0.0102                                                                                 0   1   1     1    1     2        2   2    2
                                      0.00990   0.00964   0.00939   0.00914                                        3   5   8     10   13    15   18      20   23
                                                                                   0.00889   0.00866   0.00842     2   5   7     9    12    14   16      16   21
2.4   0.00820     0.00798   0.00776   0.00755   0.00734                                                            2   4   6     8    11    13   15      17   19
                                                          0.00714   0.00695        0.00676   0.00657   0.00639     2   4   6     7    9     11   13      15   17
2.5   0.00621     0.00604   0.00587   0.00570   0.00554   0.00539   0.00523        0.00508   0.00494   0.00480     2   3   5     6    8     9    11      12   14
2.6   0.00466     0.00453   0.00440   0.00427   0.00415   0.00402   0.00391        0.00379   0.00368   0.00357     1   2   3     5    6     7        9   9    10
2.7   0.00347     0.00336   0.00326   0.00317   0.00307   0.00298   0.00289        0.00280   0.00272   0.00264     1   2   3     4    5     6        7   8    9
2.8   0.00256     0.00248   0.00240   0.00233   0.00226   0.00219   0.00212        0.00205   0.00199   0.00193     1   1   2     3    4     4        5   6    6
2.9   0.00187     0.00181   0.00175   0.00169   0.00164   0.00159   0.00154        0.00149   0.00144   0.00139     0   1   1     2    2     3        3   4    4
3.0   0.00135     0.00131   0.00126   0.00122   0.00118   0.00114   0.00111        0.00107   0.00104   0.00100     0   1   1     2    2     2        3   3    4




                      1     ⎛ 1     ⎞                                      f (z)
       f ( z) =          exp⎜ − z 2 ⎟                                                                            Example / Contoh:
                      2π    ⎝ 2     ⎠                                                          Q(z)
                ∞                                                                                                If X ~ N(0, 1), then P(X > k) = Q(k)
      Q ( z ) = ∫ f ( z ) dz                                                                                     Jika X ~ N(0, 1), maka P(X > k) = Q(k)
                  k

                                                                       O                                          z



                                                                                                                               [Lihat sebelah
                  3472/1                                                                                                              SULIT
                  http://kampungebuku.blogspot.com                                                                                               4
For     SULIT                                                           5                                                        3472/1
examiner’s
 use only
                                                                     Answer all questions.

               1   Diagram1 shows a function that maps set A to set B.
                   Rajah 1 menunjukkan fungsi yang memeta set A ke set B.
                                                              x
                                                                       f           x−3

                                                         −2                            −5

                                                             4                          m

                                                             6                          3

                                                             Set A                Set B

                                                                           Diagram 1
                                                                            Rajah 1

                   It is given that the function that maps set A to set B is f : x → x − 3 .
                   Diberi bahawa fungsi yang memeta set A ke set B ialah f : x → x − 3 .

                   Find
                   Cari
                   (a) the value of m ,
                       nilai m ,
                                                −1
                   (b) the value of ff               (3) .
                                   −1
                       nilai ff         (3) .                                                                                       [2 marks]
                                                                                                                                  [ 2markah]

                                                                                            Answer/Jawapan : (a) ……………………..
   1
                                                                                                         (b).........................................
       2
                                                 4
           2       Given that g : x →              , x ≠ 0 and the composite function gf : x → x + 2 , find
                                                 x
                                            4
                    Diberi g : x →            , x ≠ 0 dan fungsi gubahan gf : x → x + 2 , cari
                                            x
                    (a) f (x ) ,
                    (b) the value of x when fg ( x ) = 6 .
                        nilai bagi x bila fg ( x ) = 6 .                                                                           [4 marks]
                                                                                                                                  [4 markah]



   2

                                                                                       Answer/Jawapan : (a) ………......……………..
       4
                                                                                                       (b) ......……………………..

                                                                                                                     [Lihat sebelah
           3472/1                                                                                                           SULIT
           http://kampungebuku.blogspot.com                                                                                                   5
For
SULIT                                                  6                                            3472/1       examiner’s
                                                                                                                  use only
                                               6 − 2x
3   Given that f : x → 8 − px and g −1 : x →          ,
                                                   5
                                          6 − 2x
     Diberi f : x → 8 − px dan g −1 : x →        ,
                                             5

     find
     cari

     (a)     g (x ) ,

    (b)     the value of p if g ( x − 2) = f ( x ) .
            nilai p jika g ( x − 2) = f ( x ) .
                                                                                                 [4 marks]
                                                                                                [4 markah]




                                                               Answer/Jawapan : (a) ………......……………..


                                                                                  (b) ......……………………..             3

.
                                                                                                                       4
                                       1                                 2
4   Given that x = 2 and x = −           are the roots of the equation 3x + bx + c = 0 , find the value of
                                       3
    b and the value of c .
                                   1                               2
    Diberi x = 2 dan x = −           ialah punca-punca persamaan 3x + bx + c = 0 , cari nilai b
                                   3
    dan nilai c .
                                                                                                   [3 marks]
                                                                                                 [3 markah]




                                                                                                                   4


                                                                                                                       3
                                                           Answer/ Jawapan : b = ………… c = ………………


                                                                                           [Lihat sebelah
3472/1                                                                                            SULIT
http://kampungebuku.blogspot.com                                                                             6
For     SULIT                                                 7                                              3472/1
examiner’s
 use only
           5   Find the range of values of x for x 2 + 20 < 9 x .
               Cari julat nilai x bagi x 2 + 20 < 9 x .
                                                                                                                 [2 marks]
                                                                                                               [2 markah]




   5
                                                                              Answer/Jawapan :........... ……..........

       2


           6   Given quadratic function f ( x ) = −[ ( x + 6 p ) 2 − 5 ] + q has a maximum point T ( −3n , 15n 2 ) .
               Diberi fungsi kuadratik f ( x ) = −[ ( x + 6 p ) 2 − 5 ] + q mempunyai titik maksimum. T ( −3n , 15n 2 ) .

               Express q in terms p.
               Nyatakan q dalam sebutan p.
                                                                                                                 [3 marks]
                                                                                                               [3 markah]




   6
                                                                         Answer /Jawapan:        ………………………...

       3                                                                  .


                                                 1
           7   Solve the equation 25 x + 2 =           .
                                               625 x
                                                       1
               Selesaikan persamaan 25 x + 2 =               .
                                                     625 x
                                                                                                         [3        marks]
                                                                                                               [3 markah]




   7


       3
                                                                       Answer / Jawapan: …………….…………

                                                                                                       [Lihat sebelah
           3472/1                                                                                             SULIT
           http://kampungebuku.blogspot.com                                                                              7
SULIT                                              8                                              3472/1
                                                                                                                 For
                                                                                                              examiner’s
                                                                                                               use only
8    Solve the equation log 3 x − log 3 ( x − 2) = −1 .
     Selesaikan persamaan log 3 x − log 3 ( x − 2) = −1 .
                                                                                                [3 marks]
                                                                                              [ 3 markah]




                                                                                                                 8

                                                          Answer/Jawapan : ……..……...……….....
                                                                                                                     3


9    Given log 5 2 = h and log 5 3 = k , express log12 90 in terms of h and k .
     Diberi log 5 2 = h dan log 5 3 = k , ungkapkan log12 90 dalam sebutan h dan k .

                                                                                                  [4 marks]
                                                                                               [4 markah]




                                                                                                                 9

                                                  Answer/ Jawapan : ……………...………................
                                                                                                                     4

10    It is given an arithmetic progression is 5 , 7 , 9 , ………., 87. Find the number of terms of this
      progression.
      Diberi bahawa suatu janjang aritmetik ialah 5 , 7 , 9 , ………., 87 . Cari ilangan sebutan
      dalam janjang itu..

                                                                                                 [3 marks]
                                                                                               [ 3 markah]




                                                                                                                10


                                                          Answer/Jawapan: …...…………..…....................            3

                                                                                         [Lihat sebelah
3472/1                                                                                          SULIT
http://kampungebuku.blogspot.com                                                                        8
SULIT                                               9                                       3472/1
   For
examiner’s
 use only                                                                       1 1  1
             11   It is given the first three terms of a geometric series are    +  + + ……….Find the sum to
                                                                                9 27 81
                   infinity of the series.
                                                                                          1 1  1
                  Diberi bahawa tiga sebutan pertama dalam siri geometri ialah             +  + + ……….Cari
                                                                                          9 27 81
                  hasiltambah hingga sebutan ketakterhinggaan siri itu..
                                                                                                         [3 marks]
                                                                                                        [3 markah]




    11
     1
                                                                           Answer/Jawapan: : ……………...……….....
         3

             12   The variables x and y are related by the equation y = px 2 + 2 x + 5q , where p and q are
                  constants.
                                                                              2
                  Diagram 12 shows a straight line graph ( y − 2 x ) against x .

                  Pembolehubah x dan y dihubungkan oleh persamaan y = px 2 + 2 x + 5q , dengan keadaan
                  p dan q ialah pemalar.
                                                                  2
                  Rajah 12 menunjukkan graph ( y − 2 x ) melawan x .
                                                              y − 2x
                                                                                  (4,3)



                                                            O                             x2



                                                         −5



                                                                 Diagram 12
                                                                     Rajah 12
                  Find the value of p and of q .
                  Cari nilai p dan nilai q .

                                                                                                          [4 marks]
   12                                                                                                  [ 4 markah]

         4

                                                                          Answer : p = ……….… q = ………………….

                                                                                                  [Lihat sebelah
             3472/1                                                                                      SULIT
             http://kampungebuku.blogspot.com                                                                   9
SULIT                                          10                                              3472/1

                                                                                                             For
                                                                y x                                       examiner’s
13   Diagram 13 shows a straight line PQ with the equation       − = 1.                                    use only
                                                                8 6
                                                                          y x
     Rajah 13 menunjukan garis lurus PQ yang mempunyai pesamaan            − = 1.
                                                                          8 6

                                       y


                                      P•


                              •
                              Q        O                    x

                                               Diagram 13
                                                Rajah 13
      Find the equation of the straight line which is perpendicular to PQ and passes through the
      point Q.
      Cari persamaan garislurus yang berserenjang dengan PQ dan melalui titik Q.
                                                                                             [ 3 marks]
                                                                                            [3 markah]




                                                                                                             13


                                                                                                                  3

                                                    Answer/      Jawapan : ……….…………………….



                                                                                      [Lihat sebelah
3472/1                                                                                       SULIT
http://kampungebuku.blogspot.com                                                                   10
For
examiner’s   SULIT                                                11                                         3472/1
 use only

             14 Diagram 14 shows A,B and C are three points on a straight line .

                 Rajah 14 menunjukkan A , B dan C merupakan tiga titik yang terletak di atas garis lurus.

                                   y
                                                                           • B( x , y )


                                                  • C (2,3)
                                       • A(0,2)




                                   O                                                      x


                                                         Diagram 14
                                                          Rajah 14

                    It is given that 5AC = AB . Find the coordinates of B.
                    Diberi 5AC = CB. Cari koordinat B.
                                                                                                              [ 3 marks]
                                                                                                            [ 3 markah]




  14

                                                                              Answer/Jawapan : ………..………..
       3
                           →                      →
             15 Given PQ = 3 x − 2 y and QR = (1 − h) x + 4 y . The points P , Q and R are collinear.
                                   ~ ~                        ~
                                                              ~
                        →                  →
                 Diberi PQ = 3 x − 2 y dan QR = (1 − h) x + 4 y . Titik-titik P , Q dan R adalah segaris.
                                   ~     ~                    ~        ~
                 Find the value of h .
                 Cari nilai h .

                                                                                                             [ 3 marks]
                                                                                                            [3 markah]




   15


        3
                                                                                   Answer/Jawapan :…………………..…..


                                                                                                  [Lihat sebelah
             3472/1                                                                                      SULIT
             http://kampungebuku.blogspot.com                                                                      11
SULIT                                            12                                         3472/1
                                                                                                        For
                                                                                                     examiner’s
                                                                                                      use only
16     Solution by graph is not accepted for this question.
       Penyelesaian secara graf tidak diterima bagi soalan ini.
                                                                  →        →
       Diagram 16 shows OABC is a parallelogram such that OA = 4i + 3j and OB = 11i + 5j,

       Rajah 16 menunjukan OABC ialah sebuah segiempat selari dengan keadaan
                          →                                                     OA = 4i + 3j
            →
       dan OB = 11i + 5j,

                           y
                                                  B


                                   C


                                             A


                           O                                          x
                                       Diagram 16
                                        Rajah 16

                                              →
     Find the unit vector in the direction of OC .
                                →
     Cari vektor unit pada arah OC .
                                                                                  [3 marks]
                                                                                [ 3 markah]




                                                                                                       16


                                                 Answer/Jawapan:…………………………..…                               3


                                                                                 [Lihat sebelah
3472/1                                                                                  SULIT
http://kampungebuku.blogspot.com                                                               12
SULIT                                            13                                                      3472/1


   For
examiner’s
 use only
           17    Solve the equation 3 cos 2 x + sin 2 x = 0 for    0o ≤ x ≤ 360o

                 Selesaikan persamaan 3 kos 2 x + sin 2 x = 0 bagi 0 o ≤ x ≤ 360 o
                                                                                                                  [4 marks]
                                                                                                                [4 markah]




  17

                                                                     Answer /Jawapan : ………..……….………
       4
           18      Diagram 18 shows a semicircle PQR with center O.
                   Rajah 18 menunjukkan sebuah semibulatan PQR berpusat O.


                                              Q



                                                             θ
                                       P                 O                 R
                                                  Diagram 18
                                                   Rajah 18

                 It is given that the arc length PQ is 6.5 cm and the radius of the semicircle is 5 cm.
                 Diberi bahawa panjang lengkuk PQ ialah 6.5 cm dan jejari semibulatan ialah 5 cm.
                 [ Use / Guna π = 3.142 ]

                 Find
                Cari
                (a) the value of θ in radian ,
                    nilai θ dalam radian,

                (b) area , in cm2 , of sector QOR.
                    luas , dalam cm 2, sektor QOR.                                                                  [4 marks]
                                                                                                                  [4 markah]


  18


       3                                                                Answer / Jawapan : (a) …..……..................

                                                                                            (b).................................

                                                                                                      [Lihat sebelah
           3472/1                                                                                            SULIT
           http://kampungebuku.blogspot.com                                                                                13
SULIT                                                14                                                        3472/1

                                                                                                                              For
                                                                                                                           examiner’s
19   Given that f ( x) = x 3 (5 − 3 x) 2 , find   f ' (2).                                                                  use only
     Diberi f ( x) = x 3 (5 − 3 x) 2 , cari   f ' (2).

                                                                                                             [3 marks]
                                                                                                           [ 3 markah]




                                                                                                                             19
                                                                                                                              0
                                                              Answer/Jawapan : .........................................          3


                                                                    2
20    Two variables P and x are related by the equation P = 3 x +     . Given x increases
                                                                    x
      at a constant rate of 4 units per second when x = 2, find the rate of change of P.
                                                                            2
      Dua pembolehubah P dan x dihubungkan dengan persamaan P = 3 x +         .
                                                                            x
      Diberi x bertambah dengan kadar malar 4 unit sesaat apabila x = 2, cari
      kadar perubahan bagi P.
                                                                           [3 marks]
                                                                         [3 markah]




                                                                                                                             20

                                                         Answer / Jawapan : …...…………..……..…...
                                                                                                                                  3

                                                                                                    [Lihat sebelah
3472/1                                                                                                     SULIT
http://kampungebuku.blogspot.com                                                                                      14
SULIT                                              15                                              3472/1




   For                                                                                     3
                                          h          dy
examiner’s
                 21   Given y =                3
                                                 and    = g (x) , find the value of h if ∫ [ g ( x) + 1]dx = 7.
 use only                            (2 x − 5)       dx                                  2


                                                                                           3
                                          h          dy
                       Diberi y =              3
                                                 dan    = g (x) , cari nilai bagi h jika ∫ [ g ( x) + 1]dx = 7.
                                     (2 x − 5)       dx                                  2


                                                                                                                    [3 marks]
                                                                                                                  [3 markah ]




    21

                                                                                   Answer/Jawapan: ..…………........……..
         3

                 22    The mean of a set of data 2m – 3 , 8 , m+1 is 7.
                       Min bagi set data 2m – 3 , 8 , m+1 ialah 7.

                       Find
                       Cari

                       (a) the value of m ,
                              nilai m,

                       (b) the new mean if each of the data multiflied by 3.
                           Cari min yang baru jika setiap data didarabkan dengan 3.
                                                                                                                     [3 marks]
                                                                                                                  [ 3 markah]




     22
                                                                     Answer /Jawapan (a)          ..…………........……........
             3
                                                                                                            [Lihat sebelah
                 3472/1                                                                                            SULIT
                 http://kampungebuku.blogspot.com                                                                        15
SULIT                                         16                                                         3472/1


                                                                        (b)..............................................      For
23    Bag A contains 1 green pen, 2 red pens and 3 blue pens. Bag B contains 2 black erasers                                examiner’s
      and 3 white erasers. Bag C contains 6 gift cards labeled 1, 2, 3, 4, 5 and 6. An item is                               use only
       picked randomly from each bag.
      Beg A mengandungi 1 pen hijau, 2 pen merah dan 3 pen biru. Beg B mengandungi 2
       pemadam hitam dan 3 pemadam putih. Beg C mengandungi 6 kad hadiah yang dilabel
      1, 2, 3, 4, 5 dan 6. Satu item diambil secara rawak daripada setiap beg.

     Find the probability of getting a blue pen, a black eraser and a gift card with a number
     less than 3.
     Cari kebarangkalian mendapat satu pen biru, satu pemadam hitam dan satu kad hadiah
     yang berlabel nombor kurang daripada 3.

                                                                                                      [3 marks]
                                                                                                    [3 markah]




                                                                                                                              23
                                                            Answer /Jawapan: ...…..……..……..…....
                                                                                                                                    3

                                                                  2
24     The probability that it will rain on a particular day is     .
                                                                  5
       If X is the number of rainy days in a week, find

                                                                                     2
      Kebarangkalian bahawa hujan akan turun pada sebarang hari ialah                  .
                                                                                     5
      Jika X ialah bilangan hari hujan turun dalam seminggu, cari

      (a)    the mean of the distribution of X,
             min bagi taburan X,

      (b)    the standard deviation of the distribution of X.
             sisihan piawai bagi taburan X.
                                                                                              [3 marks]
                                                                                           [ 3 markah]



                                                                                                                               24
                                                        Answer/ Jawapan: (a)………..……………..
                                                                                                                                    3
                                                                                           [Lihat sebelah
3472/1                                                                                            SULIT
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SULIT                                                    17                                       3472/1


   For                                                                                           (b) ………………….….
examiner’s
 use only     25 Diagram 25 shows a standardized normal distribution graph.
                 Rajah 25 menunjukkan satu graf taburan normal piawai.
                                                       f(z)


                                                                           0.7286




                                                                                      z
                                                -k     O          k
                                                     Diagram 25
                                                      Rajah 25

                The probability represented by the area of the shaded region is 0.7286.
                Kebarangkalian yang diwakili oleh luas kawasan berlorek ialah 0.7286.

                (a) Find the value of k,
                    Cari nilai k,

                (b) X is a continuous random variable which is normally distributed with a mean
                    of μ and a standard deviation of 8. Find the value of μ if X = 70 when the z-score is k.

                      X ialah pembolehubah rawak selanjar bertaburan secara normal dengan min μ
                      dan sisihan piawai 8. Cari nilai μ jika X = 70 apabila skor-z ialah k.
                                                                                                                     [4 marks]
                                                                                                                   [4 markah]




    25


         4
                                                                           Answer/Jawapan : (a)......……...…..……..…...


                                                                                          (b) ...…………..……..….




                                                                                                       [Lihat sebelah
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SULIT                                         18                                          3472/1


                                    END OF THE QUESTION PAPER
                                   INFORMATION FOR CANDIDATES
                                      MAKLUMAT UNTUK CALON


    1. This question paper consists of 25 questions
       Kertas soalan ini mengandungi 25 soalan

    2. Answer all questions.
       Jawab semua soalan

    3. Write your answers in the spaces provided in the question paper.
       Tulis jawapan anda dalam ruang yang disediakan dalam kertas soalan.

    4. Show your working. It may help you to get marks.
       Tunjukkan langkah-langkah penting dalam kerja mengira anda. Ini boleh membantu anda untuk
       mendapatkan markah.

    5. If you wish to change your answer, cross out the answer that you have done.
       Then write down the new answer.
       Sekiranya anda hendak menukar jawapan, batalkan jawapan yang telah dibuat.
       Kemudian tulis jawapan yang baru.

    6. The diagrams in the questions provided are not drawn to scale unless stated.
       Rajah yang mengiringi soalan tidak dilukis mengikut skala kecuali dinyatakan.

    7. The marks allocated for each question are shown in brackets.
       Markah yang diperuntukkan bagi setiap soalan ditunjukkan dalam kurungan.

    8. A list of formulae is provided on pages 3 to 5.
       Satu senarai rumus disediakan di halaman 3 hingga 5.

    9. A booklet of four-figure mathematical tables is provided.
       Sebuah buku sifir matematik empat angka disediakan.

    10. You may use a non-programmable scientific calculator.
        Anda dibenarkan menggunakan kalkulator saintifik yang tidak boleh diprogram.

    11. Hand in this question paper to the invigilator at the end of the examination.
        Serahkan kertas soalan ini kepada pengawas peperiksaan di akhir peperiksaan.




                                                                                   [Lihat sebelah
3472/1                                                                                    SULIT

http://kampungebuku.blogspot.com                                                              18
SULIT
     3472/1
     Additional
     Mathematics
     Kertas 1
     Peraturan
     Pemarkahan
     August
     2009

                             BAHAGIAN PENGURUSAN
                SEKOLAH BERASRAMA PENUH DAN SEKOLAH KLUSTER
                      KEMENTERIAN PELAJARAN MALAYSIA
                            PEPERIKSAAN PERCUBAAN
                         SIJIL PELAJARAN MALAYSIA 2009



                  PEPERIKSAAN PERCUBAAN SPM
                          TAHUN 2009



                              ADDITIONAL MATHEMATICS
                                         KERTAS 1

                                   PERATURAN PEMARKAHAN


                            UNTUK KEGUNAAN PEMERIKSA SAHAJA




http://kampungebuku.blogspot.com                              19
Question                           Working / Solution                    Marks   Total
      1 (a)        1                                                           1       2

       1 (b)       3                                                            1


       2 (a)                   4                                                2      4
                    f ( x) =      , x ≠ −2
                             x+2
                            4               4
                    g −1   = , x ≠ 0 or          =x+2                          B1
                            x             f ( x)

        2(b)        x = −3                                                      2
                       4                                                       B1
                    4
                      +2
                    x
        3(a)                   6 − 5x                                           2      4
                    g ( x) =
                                  2

                    6 − 2x
                            =y                                                 B1
                       5
                         5
         (b)       p=                                                           2
                         2
                   6 − 5( x − 2)
                                 = 8 − px                                      B1
                         2
          4        b = - 5 and c = - 2                                          3      3

                   b = - 5 or c = - 2                                          B2
                                                  5   2
                   ( x – 2) ( 3x + 1) = 0 OR x 2 − x − = 0
                                                  3   3                        B1

          5         4< x<5                                                             2
                                                                                2
                    ( x − 5)( x − 4) < 0 OR                            x
                                                   4           5
                                                                               B1
                                              Must indicate the range
                                              correctly by shading or other
                                              method

                     or
                                   4           5




http://kampungebuku.blogspot.com                                                              20
Question                               Working / Solution                Marks   Total
        6            q = 60 p − 5 2                                            3       3
                    q = 15( 2 p ) 2 − 5
                                                                               B2
                    − 6 p = −3n or 5 + q = 15n 2                               B1
          7           2                                                         3      3
                    −
                      3

                    2 ( x + 2) = − 4                                           B2

                                                                               B1
                    5 2 ( x + 2 ) or    5 −4 x OR 25 −2 x
          8          −1                                                         3      3
                       x          1
                                =
                     x−2 3                                                     B2
                          ⎛ x ⎞
                    log⎜            ⎟                                          B1
                          ⎝ x −2⎠

          9         2k + h + 1                                                  4      4
                     2h + k

                    2 log 5 3 + log 5 2 + log 5 5                              B3
                            2 log 5 2 + log 5 3

                    log 5 2 2 + log 5 2 + log 5 5 or log 5 2 2 + log 5 3 or    B2
                    log 12 3 + log 12 2 + log 12 5
                              2



                    log 5 90
                             or 2 log 5 3 or 2 log52
                    log 5 12                                                   B1

         10        n = 42                                                       3      3
                   5 + ( n − 1)( 2) = 87                                       B2
                   d=2
                                                                               B1
         11         1                                                           3      3
                    6
                        1
                        9
                                                                               B2
                       1
                    1−
                       3
                        1                                                      B1
                     r=
                        3




http://kampungebuku.blogspot.com                                                              21
Question                         Working / Solution    Marks   Total
       12          p = 2 and q = −1                           4      4
                   p = 2 or q = −1                           B3
                        3 − (−5)
                    p=            or 5q = −5                 B2
                          4−0                                B1
                   y − 2 x = px 2 + 5q
         13             3     9                               3      3
                   y = x−
                        4     2

                             3                               B2
                    y − 0 = − ( x + 6)
                             4
                                                        3
                   P ( 0,8) or Q (-6,0) or m ⊥ PQ = −        B1
                                                        4
         14        (10, 7)                                    3      3

                   x = 10 or y = 7                           B2
                   x+0          y+8
                         = 2 or       =3                     B1
                     5            5
         15        h=7                                        3      3
                                    1
                   4λ = −2 or 3 = − (1 − h)
                                    2                        B2

                    ⎛ 3 ⎞ ⎛1 − h ) ⎞
                    ⎜ ⎟ = λ⎜
                    ⎜ − 2⎟ ⎜ 4 ⎟   ⎟                         B1
                    ⎝ ⎠ ⎝          ⎠
         16         7 i+ 2 j                                  3      3
                      ~      ~
                      53
                    OC = 53                                  B2
                                                             B1
                    11 i + 5 j − 4 i − 3 j
                      ~      ~         ~    ~
         17        90 , 123.69 ,270 ,303.69o
                      o            o       o
                                                              4      4

                   90o, 270o or 123.69o, 303.69o             B3
                    cos x (3 cos x + 2 sin x) = 0            B2

                   3 cos 2x + 2 sin x cosx = 0               B1




http://kampungebuku.blogspot.com                                            22
Question                              Working / Solution              Marks   Total
      18 (a)        θ = 1.842                                                2      4
                    5α = 6.5                                                B1

         (b)        23.025                                                  2
                    1 2                                                     B1
                      (5) (1.842) * (candidate’s θ from a)
                    2


         19        60                                                        3      3

                    x 3 2(5 − 3 x )1 ( −3) + (5 − 3 x) 2 3 x 2              B2

                                                                            B1
                   2(5 − 3 x )( −3) or 3 x 2
         20        10                                                        3      3
                    ⎛      2 ⎞        ⎛      2         ⎞
                    ⎜ 3 − 2 ⎟ × 4 or ⎜ 3 − 2           ⎟× 4                 B2
                    ⎝     x ⎠         ⎝    2           ⎠
                   dp           2
                        = 3− 2                                              B1
                    dr         x
         21         h=3                                                      3      3

                         h              h
                                 –             =7
                    [2(3) − 5] 3
                                   [2(2) − 5]3                              B2

                                   3
                    ⎡           ⎤
                                    ( with the correct l imit ) or [x ]3
                           h                                                B1
                    ⎢          3⎥                                      2
                    ⎣ (2 x − 5) ⎦ 2
         22           a)     m=5                                             2      3

                           2m − 3 + 8 + m + 1                               B1
                                              =7
                                   3

                      b) 21                                                  1
         23          1                                                       3      3
                        or an equivalent single fraction
                    15

                    3 2 2
                     × ×                                                    B2
                    6 5 6

                    3   2   2
                      or or                                                 B1
                    6   5   6




http://kampungebuku.blogspot.com                                                           23
Question                        Working / Solution      Marks   Total
                    14                                        1       3
                       or 2.8
       24(a)         5

       24(b)       1.296                                       2

                       2 ⎛ 2⎞
                    7 × × ⎜1 − ⎟ or equivalent                B1
                       5 ⎝ 5⎠

       25 (a)      1.1                                         2      4
                   0.1357                                     B1

       25(b)       61.2                                        2

                    70 − μ                                    B1
                           = *1.1 (candidate’s k)
                      8




                                   “END OF MARKING SCHEME”




http://kampungebuku.blogspot.com                                             24
SULIT
    NAMA:.                                          NO. ANGKA GILIRAN:

                                            PEPERIKSAAN PERCUBAAN
                                                NEGERTPERAK


    SIJIL PELAJARAN MALAYSIA 2OO9                                                          3472t1
    ADDITIOIAL MATHEMATICS
    Kertas I
    Sept.
    2 jam                                                                                 Dua jam


                                            ADDITIONAL MATHEMATICS
                                                    Paper I

                                                   Two hours

               JANGAN BUKA KERTAS SOALAN                                     Markah     Markah
                                                                  Soalan
                 INI SEHIIGGA DIBERI-IATIU                                  Penuir    Diperolehi
                                                                    1              J
                                                                    2              2
    1.      Tuliskan nama dan nombor kad pengenalan
                                                                    3              a
                                                                                   J
            anda pada ruangan yang disediaknn.
                                                                    4              3
                                                                                   a
                                                                    J              J
   7       Kertas soalan ini adalah dalam dtyibahasa.
                                                                    6              3
                                                                    I          4
   3.      Soalan dalam bahasa Inggeris mendahului
                                                                   8           a
                                                                               J
           soalan yang sepadan dalam bahasa Malaysia.                          .|
                                                                   9           L


                                                                   10          5
           Calon dibenarkan menjawab keseluruhan atau
                                                                   11          J
           sebahagian soalan sama ada dalam bahase
                                                                   t2          3
           Inggeris atau bahasa Malaysia.
                                                                   13          a
                                                                               J

                                                                   t4          a
                                                                               J
           Calon dikehendaki membaca maklumat di
                                                                   15          a
                                                                               J
           halaman belakang kertas soalan ini.
                                                                   16          4
                                                                   t7          4
                                                                   18          4
                                                                   t9          2
                                                                   20          a
                                                                               J

                                                                   2l          4
                                                                  ))           a
                                                                               J

                                                                  23           4
                                                                  24           .+
                                                                  25           +
                                                                Jumlah        80
                              Kertas soalan ini mengandungi20 halaman bercet:,k.
3472/l
                                                                                       [Lihat sebelah
                                                                                              SULIT
         http://kampungebuku.blogspot.com                                                  25
SULIT                                                    6                                      3472/1
     For
  Examiner 3
                                                        Answerall questions.
     Use                                                Jawab semuasoalan.

                    Diagram shows psaph thefunction
                           1    the   of          f(x)=lz-zxl                  ror ttredomain_3<x<4.
                    RajahI menunjukkan bagifungsi "f(x) = - Zxl untukdomain-3 <
                                    graf                                    < x 4.
                                                         i3




                                                       Diagram I
                   State                                Rujah 1
                   Nyataknn

                   (a)   the value of i,
                         nilai h,

                  (b)     range of flx) correspondingto the given domain.
                         julat flx) berdasarknn domain yang diberi.

                                                                                              [3 marl<s)
                                                                                             13 markahl




                                                  Answer / Jawaoan : (a) h :

                                                                     (r)
3472/l
                                                                                               SULIT
               http://kampungebuku.blogspot.com                                                  26
SULIT                                                           7                                34721r
                                                                                                For
                                         U'                a
                                                            a
    Given the function g : x - +                If g(1) =:- , find the valueof 2             Examiner's
                                                                                    12marl<sl Use
                                        __3               z
                                                       ^
                                                       1
     Diberi fungsi s : x -+              Jika g( 1) = 1,        car i nilai ) ,    12markahl
                                 k                     z




                                        Answer I Jawapan : )" :


                                       -5
                      function-fg@)=3x2 and function 8(x) = 2- *2 ,
     Giventhe composite
     findl-4).                                                                      [3 ntarks]
    Diberifungsi gubahanf|(x) =3x2 -5 danfungsi g(x) = 2- x2, ceri A-4).
                                                                                   y3 markahl




    Write the quadraticequation 2x2 -4x=3x2 +7x-15 in generalform. Then, solve it by
    using formula. Give your answer correct to 3 decimal places.
                                                                          [3 marl<s]
    Tulis persqmadn kuadratik 2x2 -4x=3x2 +7x-75 dalam bentuk am. Seterusnya,
    selesaikan dengan menggunakan rumus. Berikan jawapan tepat kepada 3 tempat
    perpuluhan.
                                                                                   [3 markah]




                                              Answer I Jawapan
3472/l                                                                                 [Lihat sebeiah
                                                                                              SULIT
     http://kampungebuku.blogspot.com                                                      27
SULIT                                                      8                                          3472t1
   For
Examiner's         Find the rangeof valuesof a if 2x2 -.r-15>0.                                  [3 marks]
   Use
                   Cari julat nilai x, jika 2x2 - x - 15 > 0.                                   [3 markah]




                                                      Answer / Jawapan


                   Find the coordinates the maximum point cf the quadraticequation !=4x-r2
                                       of                                                         -9 by
                   using the method of completing the square.                                    [3 marks)
                  Cari koordinqt titik maksimum bagi persamaan kuadrctik !:4x       - 12 -9 dengan
                  menggttnakanknedahpen))empurnaan     kua,sadua.                               13 markohl




                                                      Answer I Jowapan :

                  It is given that Io g zs +2 l o g 5 Q 1, expr ess in ter m s q.
                                         p             =         p           of                 14marks)
                                    p+2log5Q=7, ungkapkan dolamsebutan
                  Diberi bahawa logzs                  p             q.                        [4 markah]




3472t1
                                                                                                     SULIT
             http://kampungebuku.blogspot.com                                                        28
SULIT                                                      9                                         3472t1
                                                                                                           For
)
                           8 x 2'-3                                                                     Examiner
                                                                                                               b
         Solvethe equation      -3
                                                       1
                                                                                         [3 marks]         Use
                             22n

                         r                             = t.
                 persamssn
         setesaiknn                                                                    [3 markah]
                                             :r'=lt
                                             L




                                                 Answer/iawapan:n:

         It is given that the first four terms of an arithmetic progressionare 3, -8, x and -30.
         Diberi buhswa empat sebutanpertama suatujanjang aritmetik ialah 3, -8, x dan -30.
         Find the value of x.                                                           [2 marks]
         Cari nilai x.                                                                 12markahl




                                                 Answer / Jawapan


    l0   The third term of a geometric progressionis 16 and its common ratio is '

         Find the sum to infinity of the progression.                                   13marksl
         Sebutan kztiga suatu janjang geometri ialah 16 dan nisbah sepunya ialah

         Cari hasil tambah hingga ketakterhinggaanjanjang itu.                         [3 markah]




                                                   Answer I Jawapan
    3472t1                                                                                  [Lihat sebelah
                                                                                                   SULIT
          http://kampungebuku.blogspot.com                                                         29
I   SULIT


         Solvethe equation
                                   8 x 2n-3
                                       22n
                                          -3        1.                                   [3 marksl
                                                                                                         3472t1
                                                                                                          For
                                                                                                       Examiner 3
                                                                                                          Use



                           8 x 2n-3
                  persamaan--Fr=3-
         Selesaikan                                      I
                                                         l   .
                                                                                        13 markahl




                                               Answerliowapan:n:

         It is given that the first four terms of an arithmetic progressionare 3, -8, x and-30.
         Diberi buhowa empat sebutan pertama suatu janjang aritmetik ialah 3, -8, x dan-30.
         Find the value of x.                                                            12marksl
         Cari nilai x.                                                                  12marknh)




                                               Answer/Jawaoan:x:


    10   The third term of a geometric progressionis 16 and its common ratio is '

         Find the sum to infinity of the progression.                                    [3 marks]
                                                                                    2
         Sebutan ketiga suatu janjang geometri ialah 16 dan nisbah sepunya ialah ; .
                                                                                  J

         Cari hasil tambah hingga ketakterhinggaanjanjang itu.                          13marknhl




                                                Answer I Jawapan
    3472t1                                                                                  [Lihat sebelah
                                                                                                   SULIT
          http://kampungebuku.blogspot.com                                                        30
SULIT                                               10                                        3472tr
  For       1l   The first four termsof an arithmeticprogression -7, -3, l, 5.
                                                               are
Examinerb
  Use
                 Empatsebutan    pertamasuatujanjang aritmetikadalah -7, -3, l, 5.
                 Find
                 Cari
                 (a) the fifth term of the progression,
                     sebutankelimajanjang itu,
                 (b) the sum of next 24 termsafter the fourth term.
                     hasil tambah24 sebutanberikutnyaselepas    sebutankeempat.
                                                                                         [3 marks]
                                                                                       [3 marlcah]




                                             AnswerlJawapan:(a)

                                                                  (D)

                 The points P(2a,a), Q(b,c) and R(2b,3c)areon a straightline.
                 p dividesPR in the ratio 3 : 4.
                 Titik-titikP(2a,a), Q(b,c) dan R(2b,3c)terletak
                                                               pada satugaris lurus.
                 Q membahagi dengannisbah 3 : 4.
                               PR
                 Express in termsof c.
                       6                                                                [3 marks]
                 Ungkapkan dalam sebutanc.
                           b                                                           13markahl




                                               Answer I Jawapan
3472/l
                                                                                         SULIT
         http://kampungebuku.blogspot.com                                                31
SULIT                                                      1l                               3412tr
                                                                                              For
 13      The variables and y arerelatedby the equation/=2x2 +4x3. A straightline graphis
                     x                                                                     Examiner b
                                                                                              Use
      obtainedby plotting {              against x, as shown in Diagram2.
                                  xo

      Pembolehubah x dan y dihubungkan
                                     oleh persamoan!=2x2 +4x3.Graf garis lurus

      diperolehdenganmemplotka" + mebwan x, sepertiditunjukkanpada Rajah 2.
                                x-




                                                 Diagram2
                                                  Rajah 2
      Find the value of m and n.
                                                                              13marlul
      Cari niloi m dan n.
                                                                             [3 markah)




3472/l                                                                           [Lihat sebelah
                                                                                        SULIT
      http://kampungebuku.blogspot.com                                               32
SULIT                                                  t2                                                  3472t1
    For
 Examiner b
               14 Diagram shows straightline pe with the equation-           -+
                                                                             x       v
                                                                                     ?= |
    Use
                         3     a

                    Rajah 3 menunjukkan                                                   x     y        r
                                      garis lurus Pe yang mempunyai
                                                                  persamaan                     - - =    I
                                                                                          3      4
                    The point P lies on x-axis and the point e lies on the y-axis.
                    Titik P terletakpada paksi-x dan titik e terletakpada paksi-y.




                                                 Diagram 3
                                                  Rajah 3
                   Find the equation of the straight line perpendicularto PQ and passing through the point p.

                                                                                                     [3 mark^s]
                   Carikan persamaan garis lurus yang berserenjongdengan PQ dan melalui titik p.
                                                                                                   13 markohl




                                                  Answer I Jawapan :
3472t1
                                                                                                        SULIT
              http://kampungebuku.blogspot.com                                                           33

                                                                                                                      I
,   SULIT                                                         13                                        347211

    15                                                                                                       For
                                                                                                           Examiner's
                                                                                                              Use
                                            a                       D
                                            Jh       A
                                             
                                                 
                                    B                        a




                                                     Diagram 4
                                                      Rajah 4

         Diagram4 shows vectors OA'=g, OB'=b. OC'and Cd on a grid of equal squares.
         Rajah4 menunjukknn
                          vehord=                        g, O?= b, O? aordi   di atassatqhgrid segiempat
         sama.

         Expressin terms oi q and b.
         Ungkapknndalam sebutan g dan 12.

               ---
         (a)    OC,




                                                                                              [3 marks]
                                                                                             13 markahl




    3472t1                                                                                        [Lihat sebelah
                                                                                                         SULIT
         http://kampungebuku.blogspot.com                                                            34
SULIT                                                                   t4                                     3472t1
   t - o r l 1 6 Diagram 5 shows a trapezium P?RS.
 Examiner I
        s
   (Jse I        Rajah 5 menunjukkansebuah trapezium PQRS,

          I
                                                              Diagram 5
                                                               Rajah5
                   G i v e nth a tth e ve cto V d =@+4) L+ 6 j undTR) =3m i+ 107.Find
                                              r

                  D i b e r ive kto rP Q=@+4 )t_ +6j dan SR' = 3m i+ 10 Car i
                                                                      j.

                  (a) the valueof rz,
                      nilai m,

                  (b) the magnitude ur"ro, V/.
                                   of
                                                             )
                          mognitud bagi vehor              PQ'.

                                                                                                             [4 marl<sl
                                                                                                           [4 markah]




                                                           Answer I Jawapan : (a)

                                                                                          (b)

                  S o l v et h e e q u a t i o n s e c ' x - 5 = t a n x f o r 0 o ( x < 3 6 0 . .
                                               3
                                                                                                            [4 marl<s]
                 S e l e s a i k np e r s a m c a n3 s e k 2 x - 5 = t a n x b a g i 0 o ( x < 3 6 0 o .
                                   n
                                                                                                           14 markahl




                                                                  Answer I Jawaoan :
3472/l
                                                                                                             SULIT
              http://kampungebuku.blogspot.com                                                                 35
SULIT                                                      15                                           3472tr
18   Diagram6 showstwo concentriccircles with centreO.                                                   For
                                                                                                       Examiner
                                                                                                              b
     Rajah 6 menunjukkan
                       dua bulatan denganO sebagai   pusatnya..                                           Use




                                        Diagram  6
                                         Rajah 6

     Given that OP : 6 cm, OQ : 3OB and ISOR= 50o. POR and SOQ are straight lines.
     Diberi bahawa OP : 6 cm, OQ : 3OB dan ISOR = 50o. POR dan SOQ adalah garis
     lurus.

     (a)   Find the value of 0, in radians.(Use z =3.142)
           Cari nilai 0, dalam radian, (Guna n =3.142)
     (b)   Calculatethe area of the shadedregion.
           Hitungkan luas kawasan berlorek.
                                                                                          14marksl
                                                                                         14markahl




                                        Answer/Jawapan:(a)e:




     The curve y= -f(x) is such that I x -2px-3,
                      '      d                              wherep is aconstant.

     The gradientof curve at x= 4 is -p.             Find the value ofp.                  [2 marl<sl
     Suatu lengkung y= f(x)     adalah dengan keadaan !=2pr-3,                     p ialah pemalar.
                                                             d-r
     Kecerunan lengkung itu di x = 4 ialah - p . Cari nilai p.                           12marknhl




                                        Answer I Jov,epan: p :.........
317211                                                                                       [Lihat sebelah
     http://kampungebuku.blogspot.com                                                            36 S U L I T
SULIT                                              t6                                           3472/l
     For
  Examiner
         b   20 The curve ! = -2x2 +24x+r has a maximumpoint at x = /
     Use                                                              ow h e r e r i s a c o n s t a n t .
                Find the value of r.
                                                                                               [3 marl<s]
                Lengkungr =   -2x2 +24x + r mempunyai
                                                    titik maksimumpada x = r, dengankeadaan
                r ialah pemalar Cari nilai r.
                                                                                             [3 markahl




                                             Answer/Jawapan:r=


                    that Il, sfrXr = 5, find
                Given

                Diberifl,sftPr =5 , cari

                        r-l
               (a)
                        J, sG)dx,

               (b)      [lr[rrra- rx]d-r
                                                                                             [4 marks)
                                                                                           [4 markah]




                                             Ansrver I Jawapan : (a)

                                                                 (b)
3472/1

          http://kampungebuku.blogspot.com                                                    SULIT
                                                                                               37
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Koleksi soalan addmath kertas1

  • 1. Koleksi Soalan-Soalan Percubaan add math SPM kertas 1 Disusun: http://kampungebuku.blogspot.com
  • 2. Daftar Isi Koleksi Soalan-Soalan Percubaan Add Math Kertas 1 1. Peperiksaan Percubaan Sekolah Berasrama Penuh ……1 2. Jawapan Peperiksaan Percubaan SBP…………………. 19 3. Peperiksaan Percubaan Negeri Perak………………….. 25 4. Jawapan Peperiksaan Percubaan Negeri Perak ……… 41 5. Peperiksaan Percubaan Negeri Selangor ……………... 46 6. Jawapan Peperiksaan Percubaan S’ngor ……………. 71 7. Peperiksaan Percubaan Negeri Terengganu…………. 74 8. Jawapan Peperiksaan Percubaan T’gganu …………... 98
  • 3. Name : ………………..…………… Form : ………………………..…… BAHAGIAN PENGURUSAN SEKOLAH BERASRAMA PENUH DAN SEKOLAH KLUSTER KEMENTERIAN PELAJARAN MALAYSIA PEPERIKSAAN PERCUBAAN SELARAS SPM 2009 3472 / 1 ADDITIONAL MATHEMATICS Kertas 1 Ogos 2009 2 jam Dua jam Untuk Kegunaan Pemeriksa JANGAN BUKA KERTAS SOALAN INI Soalan Markah Markah SEHINGGA DIBERITAHU Penuh Diperolehi 1 2 1. Tulis nama dan tingkatan anda pada 2 4 ruangan yang disediakan. 3 4 2. Kertas soalan ini adalah dalam 4 3 dwibahasa. 5 2 6 3 3. Soalan dalam bahasa Inggeris 7 3 mendahului soalan yang sepadan 8 3 dalam bahasa Melayu. 9 4 10 3 4. Calon dibenarkan menjawab 11 3 keseluruhan atau sebahagian soalan 12 4 sama ada dalam bahasa Inggeris atau 13 3 bahasa Melayu. 14 3 15 3 5. Calon dikehendaki membaca 16 3 maklumat di halaman belakang kertas 17 4 soalan ini. 18 4 19 3 20 3 21 3 22 3 23 3 24 3 25 4 TOTAL 80 Kertas soalan ini mengandungi 18 halaman bercetak 3472/1 2009 Hak Cipta SBP [Lihat sebelah SULIT http://kampungebuku.blogspot.com 1
  • 4. SULIT 2 3472/1 The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. ALGEBRA 2 −b ± b − 4ac log c b 1 x= 8 logab = 2a log c a 2 am × an = a m + n 9 Tn = a + (n-1)d 3 am ÷ an = a m - n n 10 Sn = [2a + ( n − 1) d ] 2 4 (am) n = a nm 11 Tn = ar n-1 5 loga mn = log am + loga n a(r n − 1) a (1 − r n ) 12 Sn = = , (r ≠ 1) m r −1 1− r 6 loga = log am - loga n a n 13 S ∞ = , r <1 7 log a mn = n log a m 1− r CALCULUS dy dv du 1 y = uv , =u +v 4 Area under a curve dx dx dx b du dv = ∫ y dx or v −u a u dy 2 y= , = dx 2 dx , b v dx v = ∫ x dy a dy dy du 5 Volume generated 3 = × b dx du dx = ∫ π y 2 dx or a b 2 = ∫π x dy a GEOMETRY 1 Distance = ( x 2 − x1 ) 2 + ( y 2 − y1 ) 2 5 A point dividing a segment of a line ⎛ nx + mx2 ny1 + my 2 ⎞ ( x,y) = ⎜ 1 , ⎟ 2 Midpoint ⎝ m+n m+n ⎠ ⎛ x1 + x 2 y + y2 ⎞ (x , y) = ⎜ , 1 ⎟ ⎝ 2 2 ⎠ 6 Area of triangle 1 3 r = x2 + y2 = ( x1 y 2 + x 2 y 3 + x3 y11 ) − ( x 2 y1 + x3 y 2 + x1 y 3 ) 2 xi + yj 4 ˆ r= x2 + y2 3472/1 2009 Hak Cipta SBP [ Lihat sebelah SULIT http://kampungebuku.blogspot.com 2
  • 5. SULIT 3 3472/1 STATISTIC 1 x = ∑x ∑ w1 I1 7 I= N ∑ w1 n! ∑ fx 8 Pr = n 2 x = (n − r )! ∑f n! 9 n Cr = (n − r )!r! 3 σ = ∑ (x − x ) 2 = ∑x 2 −x _2 N N 10 P(A ∪ B) = P(A)+P(B)- P(A ∩ B) 4 σ= ∑ f ( x − x) 2 = ∑ fx 2 −x 2 11 P (X = r) = nCr p r q n − r , p + q = 1 ∑f ∑f 12 Mean µ = np ⎡1 ⎤ ⎢2 N −F⎥ 5 m = L+⎢ ⎥C 13 σ = npq ⎢ fm ⎥ ⎢ ⎣ ⎥ ⎦ x−μ 14 z= σ Q1 6 I= ×100 Q0 TRIGONOMETRY 1 Arc length, s = r θ 9 sin (A ± B) = sinA cosB ± cosA sinB 1 2 10 cos (A ± B) = cosA cosB m sinA sinB 2 Area of sector , L = rθ 2 3 sin 2A + cos 2A = 1 tan A ± tan B 11 tan (A ± B) = 1 m tan A tan B 4 sec2A = 1 + tan2A a b c 2 2 12 = = 5 cosec A = 1 + cot A sin A sin B sin C 6 sin 2A = 2 sinA cosA 13 a2 = b2 + c2 - 2bc cosA 2 2 7 cos 2A = cos A – sin A = 2 cos2A - 1 1 = 1 - 2 sin2A 14 Area of triangle = absin C 2 2 tan A 8 tan 2A = 1 − tan 2 A 3472/1 2009 Hak Cipta SBP [ Lihat sebelah SULIT http://kampungebuku.blogspot.com 3
  • 6. SULIT 4 3472/1 THE UPPER TAIL PROBABILITY Q(z) FOR THE NORMAL DISTRIBUTION N(0,1) KEBARANGKALIAN HUJUNG ATAS Q(z) BAGI TABURAN NORMAL N(0, 1) 1 2 3 4 5 6 7 8 9 z 0 1 2 3 4 5 6 7 8 9 Minus / Tolak 0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641 4 8 12 16 20 24 28 32 36 0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247 4 8 12 16 20 24 28 32 36 0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859 4 8 12 15 19 23 27 31 35 0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483 4 7 11 15 19 22 26 30 34 0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121 4 7 11 15 18 22 25 29 32 0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776 3 7 10 14 17 20 24 27 31 0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451 3 7 10 13 16 19 23 26 29 0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148 3 6 9 12 15 18 21 24 27 0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867 3 5 8 11 14 16 19 22 25 0.9 0.1841 0.1814 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611 3 5 8 10 13 15 18 20 23 1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379 2 5 7 9 12 14 16 19 21 1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170 2 4 6 8 10 12 14 16 18 1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985 2 4 6 7 9 11 13 15 17 1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 2 3 5 6 8 10 11 13 14 1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0721 0.0708 0.0694 0.0681 1 3 4 6 7 8 10 11 13 1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559 1 2 4 5 6 7 8 10 11 1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0..0475 0.0465 0.0455 1 2 3 4 5 6 7 8 9 1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367 1 2 3 4 4 5 6 7 8 1.8 0.0359 0.0351 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294 1 1 2 3 4 4 5 6 6 1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233 1 1 2 2 3 4 4 5 5 2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 0 1 1 2 2 3 3 4 4 2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143 0 1 1 2 2 2 3 3 4 2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110 0 1 1 1 2 2 2 3 3 2.3 0.0107 0.0104 0.0102 0 1 1 1 1 2 2 2 2 0.00990 0.00964 0.00939 0.00914 3 5 8 10 13 15 18 20 23 0.00889 0.00866 0.00842 2 5 7 9 12 14 16 16 21 2.4 0.00820 0.00798 0.00776 0.00755 0.00734 2 4 6 8 11 13 15 17 19 0.00714 0.00695 0.00676 0.00657 0.00639 2 4 6 7 9 11 13 15 17 2.5 0.00621 0.00604 0.00587 0.00570 0.00554 0.00539 0.00523 0.00508 0.00494 0.00480 2 3 5 6 8 9 11 12 14 2.6 0.00466 0.00453 0.00440 0.00427 0.00415 0.00402 0.00391 0.00379 0.00368 0.00357 1 2 3 5 6 7 9 9 10 2.7 0.00347 0.00336 0.00326 0.00317 0.00307 0.00298 0.00289 0.00280 0.00272 0.00264 1 2 3 4 5 6 7 8 9 2.8 0.00256 0.00248 0.00240 0.00233 0.00226 0.00219 0.00212 0.00205 0.00199 0.00193 1 1 2 3 4 4 5 6 6 2.9 0.00187 0.00181 0.00175 0.00169 0.00164 0.00159 0.00154 0.00149 0.00144 0.00139 0 1 1 2 2 3 3 4 4 3.0 0.00135 0.00131 0.00126 0.00122 0.00118 0.00114 0.00111 0.00107 0.00104 0.00100 0 1 1 2 2 2 3 3 4 1 ⎛ 1 ⎞ f (z) f ( z) = exp⎜ − z 2 ⎟ Example / Contoh: 2π ⎝ 2 ⎠ Q(z) ∞ If X ~ N(0, 1), then P(X > k) = Q(k) Q ( z ) = ∫ f ( z ) dz Jika X ~ N(0, 1), maka P(X > k) = Q(k) k O z [Lihat sebelah 3472/1 SULIT http://kampungebuku.blogspot.com 4
  • 7. For SULIT 5 3472/1 examiner’s use only Answer all questions. 1 Diagram1 shows a function that maps set A to set B. Rajah 1 menunjukkan fungsi yang memeta set A ke set B. x f x−3 −2 −5 4 m 6 3 Set A Set B Diagram 1 Rajah 1 It is given that the function that maps set A to set B is f : x → x − 3 . Diberi bahawa fungsi yang memeta set A ke set B ialah f : x → x − 3 . Find Cari (a) the value of m , nilai m , −1 (b) the value of ff (3) . −1 nilai ff (3) . [2 marks] [ 2markah] Answer/Jawapan : (a) …………………….. 1 (b)......................................... 2 4 2 Given that g : x → , x ≠ 0 and the composite function gf : x → x + 2 , find x 4 Diberi g : x → , x ≠ 0 dan fungsi gubahan gf : x → x + 2 , cari x (a) f (x ) , (b) the value of x when fg ( x ) = 6 . nilai bagi x bila fg ( x ) = 6 . [4 marks] [4 markah] 2 Answer/Jawapan : (a) ………......…………….. 4 (b) ......…………………….. [Lihat sebelah 3472/1 SULIT http://kampungebuku.blogspot.com 5
  • 8. For SULIT 6 3472/1 examiner’s use only 6 − 2x 3 Given that f : x → 8 − px and g −1 : x → , 5 6 − 2x Diberi f : x → 8 − px dan g −1 : x → , 5 find cari (a) g (x ) , (b) the value of p if g ( x − 2) = f ( x ) . nilai p jika g ( x − 2) = f ( x ) . [4 marks] [4 markah] Answer/Jawapan : (a) ………......…………….. (b) ......…………………….. 3 . 4 1 2 4 Given that x = 2 and x = − are the roots of the equation 3x + bx + c = 0 , find the value of 3 b and the value of c . 1 2 Diberi x = 2 dan x = − ialah punca-punca persamaan 3x + bx + c = 0 , cari nilai b 3 dan nilai c . [3 marks] [3 markah] 4 3 Answer/ Jawapan : b = ………… c = ……………… [Lihat sebelah 3472/1 SULIT http://kampungebuku.blogspot.com 6
  • 9. For SULIT 7 3472/1 examiner’s use only 5 Find the range of values of x for x 2 + 20 < 9 x . Cari julat nilai x bagi x 2 + 20 < 9 x . [2 marks] [2 markah] 5 Answer/Jawapan :........... …….......... 2 6 Given quadratic function f ( x ) = −[ ( x + 6 p ) 2 − 5 ] + q has a maximum point T ( −3n , 15n 2 ) . Diberi fungsi kuadratik f ( x ) = −[ ( x + 6 p ) 2 − 5 ] + q mempunyai titik maksimum. T ( −3n , 15n 2 ) . Express q in terms p. Nyatakan q dalam sebutan p. [3 marks] [3 markah] 6 Answer /Jawapan: ………………………... 3 . 1 7 Solve the equation 25 x + 2 = . 625 x 1 Selesaikan persamaan 25 x + 2 = . 625 x [3 marks] [3 markah] 7 3 Answer / Jawapan: …………….………… [Lihat sebelah 3472/1 SULIT http://kampungebuku.blogspot.com 7
  • 10. SULIT 8 3472/1 For examiner’s use only 8 Solve the equation log 3 x − log 3 ( x − 2) = −1 . Selesaikan persamaan log 3 x − log 3 ( x − 2) = −1 . [3 marks] [ 3 markah] 8 Answer/Jawapan : ……..……...………..... 3 9 Given log 5 2 = h and log 5 3 = k , express log12 90 in terms of h and k . Diberi log 5 2 = h dan log 5 3 = k , ungkapkan log12 90 dalam sebutan h dan k . [4 marks] [4 markah] 9 Answer/ Jawapan : ……………...………................ 4 10 It is given an arithmetic progression is 5 , 7 , 9 , ………., 87. Find the number of terms of this progression. Diberi bahawa suatu janjang aritmetik ialah 5 , 7 , 9 , ………., 87 . Cari ilangan sebutan dalam janjang itu.. [3 marks] [ 3 markah] 10 Answer/Jawapan: …...…………..….................... 3 [Lihat sebelah 3472/1 SULIT http://kampungebuku.blogspot.com 8
  • 11. SULIT 9 3472/1 For examiner’s use only 1 1 1 11 It is given the first three terms of a geometric series are + + + ……….Find the sum to 9 27 81 infinity of the series. 1 1 1 Diberi bahawa tiga sebutan pertama dalam siri geometri ialah + + + ……….Cari 9 27 81 hasiltambah hingga sebutan ketakterhinggaan siri itu.. [3 marks] [3 markah] 11 1 Answer/Jawapan: : ……………...………..... 3 12 The variables x and y are related by the equation y = px 2 + 2 x + 5q , where p and q are constants. 2 Diagram 12 shows a straight line graph ( y − 2 x ) against x . Pembolehubah x dan y dihubungkan oleh persamaan y = px 2 + 2 x + 5q , dengan keadaan p dan q ialah pemalar. 2 Rajah 12 menunjukkan graph ( y − 2 x ) melawan x . y − 2x (4,3) O x2 −5 Diagram 12 Rajah 12 Find the value of p and of q . Cari nilai p dan nilai q . [4 marks] 12 [ 4 markah] 4 Answer : p = ……….… q = …………………. [Lihat sebelah 3472/1 SULIT http://kampungebuku.blogspot.com 9
  • 12. SULIT 10 3472/1 For y x examiner’s 13 Diagram 13 shows a straight line PQ with the equation − = 1. use only 8 6 y x Rajah 13 menunjukan garis lurus PQ yang mempunyai pesamaan − = 1. 8 6 y P• • Q O x Diagram 13 Rajah 13 Find the equation of the straight line which is perpendicular to PQ and passes through the point Q. Cari persamaan garislurus yang berserenjang dengan PQ dan melalui titik Q. [ 3 marks] [3 markah] 13 3 Answer/ Jawapan : ……….……………………. [Lihat sebelah 3472/1 SULIT http://kampungebuku.blogspot.com 10
  • 13. For examiner’s SULIT 11 3472/1 use only 14 Diagram 14 shows A,B and C are three points on a straight line . Rajah 14 menunjukkan A , B dan C merupakan tiga titik yang terletak di atas garis lurus. y • B( x , y ) • C (2,3) • A(0,2) O x Diagram 14 Rajah 14 It is given that 5AC = AB . Find the coordinates of B. Diberi 5AC = CB. Cari koordinat B. [ 3 marks] [ 3 markah] 14 Answer/Jawapan : ………..……….. 3 → → 15 Given PQ = 3 x − 2 y and QR = (1 − h) x + 4 y . The points P , Q and R are collinear. ~ ~ ~ ~ → → Diberi PQ = 3 x − 2 y dan QR = (1 − h) x + 4 y . Titik-titik P , Q dan R adalah segaris. ~ ~ ~ ~ Find the value of h . Cari nilai h . [ 3 marks] [3 markah] 15 3 Answer/Jawapan :…………………..….. [Lihat sebelah 3472/1 SULIT http://kampungebuku.blogspot.com 11
  • 14. SULIT 12 3472/1 For examiner’s use only 16 Solution by graph is not accepted for this question. Penyelesaian secara graf tidak diterima bagi soalan ini. → → Diagram 16 shows OABC is a parallelogram such that OA = 4i + 3j and OB = 11i + 5j, Rajah 16 menunjukan OABC ialah sebuah segiempat selari dengan keadaan → OA = 4i + 3j → dan OB = 11i + 5j, y B C A O x Diagram 16 Rajah 16 → Find the unit vector in the direction of OC . → Cari vektor unit pada arah OC . [3 marks] [ 3 markah] 16 Answer/Jawapan:…………………………..… 3 [Lihat sebelah 3472/1 SULIT http://kampungebuku.blogspot.com 12
  • 15. SULIT 13 3472/1 For examiner’s use only 17 Solve the equation 3 cos 2 x + sin 2 x = 0 for 0o ≤ x ≤ 360o Selesaikan persamaan 3 kos 2 x + sin 2 x = 0 bagi 0 o ≤ x ≤ 360 o [4 marks] [4 markah] 17 Answer /Jawapan : ………..……….……… 4 18 Diagram 18 shows a semicircle PQR with center O. Rajah 18 menunjukkan sebuah semibulatan PQR berpusat O. Q θ P O R Diagram 18 Rajah 18 It is given that the arc length PQ is 6.5 cm and the radius of the semicircle is 5 cm. Diberi bahawa panjang lengkuk PQ ialah 6.5 cm dan jejari semibulatan ialah 5 cm. [ Use / Guna π = 3.142 ] Find Cari (a) the value of θ in radian , nilai θ dalam radian, (b) area , in cm2 , of sector QOR. luas , dalam cm 2, sektor QOR. [4 marks] [4 markah] 18 3 Answer / Jawapan : (a) …..…….................. (b)................................. [Lihat sebelah 3472/1 SULIT http://kampungebuku.blogspot.com 13
  • 16. SULIT 14 3472/1 For examiner’s 19 Given that f ( x) = x 3 (5 − 3 x) 2 , find f ' (2). use only Diberi f ( x) = x 3 (5 − 3 x) 2 , cari f ' (2). [3 marks] [ 3 markah] 19 0 Answer/Jawapan : ......................................... 3 2 20 Two variables P and x are related by the equation P = 3 x + . Given x increases x at a constant rate of 4 units per second when x = 2, find the rate of change of P. 2 Dua pembolehubah P dan x dihubungkan dengan persamaan P = 3 x + . x Diberi x bertambah dengan kadar malar 4 unit sesaat apabila x = 2, cari kadar perubahan bagi P. [3 marks] [3 markah] 20 Answer / Jawapan : …...…………..……..…... 3 [Lihat sebelah 3472/1 SULIT http://kampungebuku.blogspot.com 14
  • 17. SULIT 15 3472/1 For 3 h dy examiner’s 21 Given y = 3 and = g (x) , find the value of h if ∫ [ g ( x) + 1]dx = 7. use only (2 x − 5) dx 2 3 h dy Diberi y = 3 dan = g (x) , cari nilai bagi h jika ∫ [ g ( x) + 1]dx = 7. (2 x − 5) dx 2 [3 marks] [3 markah ] 21 Answer/Jawapan: ..…………........…….. 3 22 The mean of a set of data 2m – 3 , 8 , m+1 is 7. Min bagi set data 2m – 3 , 8 , m+1 ialah 7. Find Cari (a) the value of m , nilai m, (b) the new mean if each of the data multiflied by 3. Cari min yang baru jika setiap data didarabkan dengan 3. [3 marks] [ 3 markah] 22 Answer /Jawapan (a) ..…………........……........ 3 [Lihat sebelah 3472/1 SULIT http://kampungebuku.blogspot.com 15
  • 18. SULIT 16 3472/1 (b).............................................. For 23 Bag A contains 1 green pen, 2 red pens and 3 blue pens. Bag B contains 2 black erasers examiner’s and 3 white erasers. Bag C contains 6 gift cards labeled 1, 2, 3, 4, 5 and 6. An item is use only picked randomly from each bag. Beg A mengandungi 1 pen hijau, 2 pen merah dan 3 pen biru. Beg B mengandungi 2 pemadam hitam dan 3 pemadam putih. Beg C mengandungi 6 kad hadiah yang dilabel 1, 2, 3, 4, 5 dan 6. Satu item diambil secara rawak daripada setiap beg. Find the probability of getting a blue pen, a black eraser and a gift card with a number less than 3. Cari kebarangkalian mendapat satu pen biru, satu pemadam hitam dan satu kad hadiah yang berlabel nombor kurang daripada 3. [3 marks] [3 markah] 23 Answer /Jawapan: ...…..……..……..….... 3 2 24 The probability that it will rain on a particular day is . 5 If X is the number of rainy days in a week, find 2 Kebarangkalian bahawa hujan akan turun pada sebarang hari ialah . 5 Jika X ialah bilangan hari hujan turun dalam seminggu, cari (a) the mean of the distribution of X, min bagi taburan X, (b) the standard deviation of the distribution of X. sisihan piawai bagi taburan X. [3 marks] [ 3 markah] 24 Answer/ Jawapan: (a)………..…………….. 3 [Lihat sebelah 3472/1 SULIT http://kampungebuku.blogspot.com 16
  • 19. SULIT 17 3472/1 For (b) ………………….…. examiner’s use only 25 Diagram 25 shows a standardized normal distribution graph. Rajah 25 menunjukkan satu graf taburan normal piawai. f(z) 0.7286 z -k O k Diagram 25 Rajah 25 The probability represented by the area of the shaded region is 0.7286. Kebarangkalian yang diwakili oleh luas kawasan berlorek ialah 0.7286. (a) Find the value of k, Cari nilai k, (b) X is a continuous random variable which is normally distributed with a mean of μ and a standard deviation of 8. Find the value of μ if X = 70 when the z-score is k. X ialah pembolehubah rawak selanjar bertaburan secara normal dengan min μ dan sisihan piawai 8. Cari nilai μ jika X = 70 apabila skor-z ialah k. [4 marks] [4 markah] 25 4 Answer/Jawapan : (a)......……...…..……..…... (b) ...…………..……..…. [Lihat sebelah 3472/1 SULIT http://kampungebuku.blogspot.com 17
  • 20. SULIT 18 3472/1 END OF THE QUESTION PAPER INFORMATION FOR CANDIDATES MAKLUMAT UNTUK CALON 1. This question paper consists of 25 questions Kertas soalan ini mengandungi 25 soalan 2. Answer all questions. Jawab semua soalan 3. Write your answers in the spaces provided in the question paper. Tulis jawapan anda dalam ruang yang disediakan dalam kertas soalan. 4. Show your working. It may help you to get marks. Tunjukkan langkah-langkah penting dalam kerja mengira anda. Ini boleh membantu anda untuk mendapatkan markah. 5. If you wish to change your answer, cross out the answer that you have done. Then write down the new answer. Sekiranya anda hendak menukar jawapan, batalkan jawapan yang telah dibuat. Kemudian tulis jawapan yang baru. 6. The diagrams in the questions provided are not drawn to scale unless stated. Rajah yang mengiringi soalan tidak dilukis mengikut skala kecuali dinyatakan. 7. The marks allocated for each question are shown in brackets. Markah yang diperuntukkan bagi setiap soalan ditunjukkan dalam kurungan. 8. A list of formulae is provided on pages 3 to 5. Satu senarai rumus disediakan di halaman 3 hingga 5. 9. A booklet of four-figure mathematical tables is provided. Sebuah buku sifir matematik empat angka disediakan. 10. You may use a non-programmable scientific calculator. Anda dibenarkan menggunakan kalkulator saintifik yang tidak boleh diprogram. 11. Hand in this question paper to the invigilator at the end of the examination. Serahkan kertas soalan ini kepada pengawas peperiksaan di akhir peperiksaan. [Lihat sebelah 3472/1 SULIT http://kampungebuku.blogspot.com 18
  • 21. SULIT 3472/1 Additional Mathematics Kertas 1 Peraturan Pemarkahan August 2009 BAHAGIAN PENGURUSAN SEKOLAH BERASRAMA PENUH DAN SEKOLAH KLUSTER KEMENTERIAN PELAJARAN MALAYSIA PEPERIKSAAN PERCUBAAN SIJIL PELAJARAN MALAYSIA 2009 PEPERIKSAAN PERCUBAAN SPM TAHUN 2009 ADDITIONAL MATHEMATICS KERTAS 1 PERATURAN PEMARKAHAN UNTUK KEGUNAAN PEMERIKSA SAHAJA http://kampungebuku.blogspot.com 19
  • 22. Question Working / Solution Marks Total 1 (a) 1 1 2 1 (b) 3 1 2 (a) 4 2 4 f ( x) = , x ≠ −2 x+2 4 4 g −1 = , x ≠ 0 or =x+2 B1 x f ( x) 2(b) x = −3 2 4 B1 4 +2 x 3(a) 6 − 5x 2 4 g ( x) = 2 6 − 2x =y B1 5 5 (b) p= 2 2 6 − 5( x − 2) = 8 − px B1 2 4 b = - 5 and c = - 2 3 3 b = - 5 or c = - 2 B2 5 2 ( x – 2) ( 3x + 1) = 0 OR x 2 − x − = 0 3 3 B1 5 4< x<5 2 2 ( x − 5)( x − 4) < 0 OR x 4 5 B1 Must indicate the range correctly by shading or other method or 4 5 http://kampungebuku.blogspot.com 20
  • 23. Question Working / Solution Marks Total 6 q = 60 p − 5 2 3 3 q = 15( 2 p ) 2 − 5 B2 − 6 p = −3n or 5 + q = 15n 2 B1 7 2 3 3 − 3 2 ( x + 2) = − 4 B2 B1 5 2 ( x + 2 ) or 5 −4 x OR 25 −2 x 8 −1 3 3 x 1 = x−2 3 B2 ⎛ x ⎞ log⎜ ⎟ B1 ⎝ x −2⎠ 9 2k + h + 1 4 4 2h + k 2 log 5 3 + log 5 2 + log 5 5 B3 2 log 5 2 + log 5 3 log 5 2 2 + log 5 2 + log 5 5 or log 5 2 2 + log 5 3 or B2 log 12 3 + log 12 2 + log 12 5 2 log 5 90 or 2 log 5 3 or 2 log52 log 5 12 B1 10 n = 42 3 3 5 + ( n − 1)( 2) = 87 B2 d=2 B1 11 1 3 3 6 1 9 B2 1 1− 3 1 B1 r= 3 http://kampungebuku.blogspot.com 21
  • 24. Question Working / Solution Marks Total 12 p = 2 and q = −1 4 4 p = 2 or q = −1 B3 3 − (−5) p= or 5q = −5 B2 4−0 B1 y − 2 x = px 2 + 5q 13 3 9 3 3 y = x− 4 2 3 B2 y − 0 = − ( x + 6) 4 3 P ( 0,8) or Q (-6,0) or m ⊥ PQ = − B1 4 14 (10, 7) 3 3 x = 10 or y = 7 B2 x+0 y+8 = 2 or =3 B1 5 5 15 h=7 3 3 1 4λ = −2 or 3 = − (1 − h) 2 B2 ⎛ 3 ⎞ ⎛1 − h ) ⎞ ⎜ ⎟ = λ⎜ ⎜ − 2⎟ ⎜ 4 ⎟ ⎟ B1 ⎝ ⎠ ⎝ ⎠ 16 7 i+ 2 j 3 3 ~ ~ 53 OC = 53 B2 B1 11 i + 5 j − 4 i − 3 j ~ ~ ~ ~ 17 90 , 123.69 ,270 ,303.69o o o o 4 4 90o, 270o or 123.69o, 303.69o B3 cos x (3 cos x + 2 sin x) = 0 B2 3 cos 2x + 2 sin x cosx = 0 B1 http://kampungebuku.blogspot.com 22
  • 25. Question Working / Solution Marks Total 18 (a) θ = 1.842 2 4 5α = 6.5 B1 (b) 23.025 2 1 2 B1 (5) (1.842) * (candidate’s θ from a) 2 19 60 3 3 x 3 2(5 − 3 x )1 ( −3) + (5 − 3 x) 2 3 x 2 B2 B1 2(5 − 3 x )( −3) or 3 x 2 20 10 3 3 ⎛ 2 ⎞ ⎛ 2 ⎞ ⎜ 3 − 2 ⎟ × 4 or ⎜ 3 − 2 ⎟× 4 B2 ⎝ x ⎠ ⎝ 2 ⎠ dp 2 = 3− 2 B1 dr x 21 h=3 3 3 h h – =7 [2(3) − 5] 3 [2(2) − 5]3 B2 3 ⎡ ⎤ ( with the correct l imit ) or [x ]3 h B1 ⎢ 3⎥ 2 ⎣ (2 x − 5) ⎦ 2 22 a) m=5 2 3 2m − 3 + 8 + m + 1 B1 =7 3 b) 21 1 23 1 3 3 or an equivalent single fraction 15 3 2 2 × × B2 6 5 6 3 2 2 or or B1 6 5 6 http://kampungebuku.blogspot.com 23
  • 26. Question Working / Solution Marks Total 14 1 3 or 2.8 24(a) 5 24(b) 1.296 2 2 ⎛ 2⎞ 7 × × ⎜1 − ⎟ or equivalent B1 5 ⎝ 5⎠ 25 (a) 1.1 2 4 0.1357 B1 25(b) 61.2 2 70 − μ B1 = *1.1 (candidate’s k) 8 “END OF MARKING SCHEME” http://kampungebuku.blogspot.com 24
  • 27. SULIT NAMA:. NO. ANGKA GILIRAN: PEPERIKSAAN PERCUBAAN NEGERTPERAK SIJIL PELAJARAN MALAYSIA 2OO9 3472t1 ADDITIOIAL MATHEMATICS Kertas I Sept. 2 jam Dua jam ADDITIONAL MATHEMATICS Paper I Two hours JANGAN BUKA KERTAS SOALAN Markah Markah Soalan INI SEHIIGGA DIBERI-IATIU Penuir Diperolehi 1 J 2 2 1. Tuliskan nama dan nombor kad pengenalan 3 a J anda pada ruangan yang disediaknn. 4 3 a J J 7 Kertas soalan ini adalah dalam dtyibahasa. 6 3 I 4 3. Soalan dalam bahasa Inggeris mendahului 8 a J soalan yang sepadan dalam bahasa Malaysia. .| 9 L 10 5 Calon dibenarkan menjawab keseluruhan atau 11 J sebahagian soalan sama ada dalam bahase t2 3 Inggeris atau bahasa Malaysia. 13 a J t4 a J Calon dikehendaki membaca maklumat di 15 a J halaman belakang kertas soalan ini. 16 4 t7 4 18 4 t9 2 20 a J 2l 4 )) a J 23 4 24 .+ 25 + Jumlah 80 Kertas soalan ini mengandungi20 halaman bercet:,k. 3472/l [Lihat sebelah SULIT http://kampungebuku.blogspot.com 25
  • 28. SULIT 6 3472/1 For Examiner 3 Answerall questions. Use Jawab semuasoalan. Diagram shows psaph thefunction 1 the of f(x)=lz-zxl ror ttredomain_3<x<4. RajahI menunjukkan bagifungsi "f(x) = - Zxl untukdomain-3 < graf < x 4. i3 Diagram I State Rujah 1 Nyataknn (a) the value of i, nilai h, (b) range of flx) correspondingto the given domain. julat flx) berdasarknn domain yang diberi. [3 marl<s) 13 markahl Answer / Jawaoan : (a) h : (r) 3472/l SULIT http://kampungebuku.blogspot.com 26
  • 29. SULIT 7 34721r For U' a a Given the function g : x - + If g(1) =:- , find the valueof 2 Examiner's 12marl<sl Use __3 z ^ 1 Diberi fungsi s : x -+ Jika g( 1) = 1, car i nilai ) , 12markahl k z Answer I Jawapan : )" : -5 function-fg@)=3x2 and function 8(x) = 2- *2 , Giventhe composite findl-4). [3 ntarks] Diberifungsi gubahanf|(x) =3x2 -5 danfungsi g(x) = 2- x2, ceri A-4). y3 markahl Write the quadraticequation 2x2 -4x=3x2 +7x-15 in generalform. Then, solve it by using formula. Give your answer correct to 3 decimal places. [3 marl<s] Tulis persqmadn kuadratik 2x2 -4x=3x2 +7x-75 dalam bentuk am. Seterusnya, selesaikan dengan menggunakan rumus. Berikan jawapan tepat kepada 3 tempat perpuluhan. [3 markah] Answer I Jawapan 3472/l [Lihat sebeiah SULIT http://kampungebuku.blogspot.com 27
  • 30. SULIT 8 3472t1 For Examiner's Find the rangeof valuesof a if 2x2 -.r-15>0. [3 marks] Use Cari julat nilai x, jika 2x2 - x - 15 > 0. [3 markah] Answer / Jawapan Find the coordinates the maximum point cf the quadraticequation !=4x-r2 of -9 by using the method of completing the square. [3 marks) Cari koordinqt titik maksimum bagi persamaan kuadrctik !:4x - 12 -9 dengan menggttnakanknedahpen))empurnaan kua,sadua. 13 markohl Answer I Jowapan : It is given that Io g zs +2 l o g 5 Q 1, expr ess in ter m s q. p = p of 14marks) p+2log5Q=7, ungkapkan dolamsebutan Diberi bahawa logzs p q. [4 markah] 3472t1 SULIT http://kampungebuku.blogspot.com 28
  • 31. SULIT 9 3472t1 For ) 8 x 2'-3 Examiner b Solvethe equation -3 1 [3 marks] Use 22n r = t. persamssn setesaiknn [3 markah] :r'=lt L Answer/iawapan:n: It is given that the first four terms of an arithmetic progressionare 3, -8, x and -30. Diberi buhswa empat sebutanpertama suatujanjang aritmetik ialah 3, -8, x dan -30. Find the value of x. [2 marks] Cari nilai x. 12markahl Answer / Jawapan l0 The third term of a geometric progressionis 16 and its common ratio is ' Find the sum to infinity of the progression. 13marksl Sebutan kztiga suatu janjang geometri ialah 16 dan nisbah sepunya ialah Cari hasil tambah hingga ketakterhinggaanjanjang itu. [3 markah] Answer I Jawapan 3472t1 [Lihat sebelah SULIT http://kampungebuku.blogspot.com 29
  • 32. I SULIT Solvethe equation 8 x 2n-3 22n -3 1. [3 marksl 3472t1 For Examiner 3 Use 8 x 2n-3 persamaan--Fr=3- Selesaikan I l . 13 markahl Answerliowapan:n: It is given that the first four terms of an arithmetic progressionare 3, -8, x and-30. Diberi buhowa empat sebutan pertama suatu janjang aritmetik ialah 3, -8, x dan-30. Find the value of x. 12marksl Cari nilai x. 12marknh) Answer/Jawaoan:x: 10 The third term of a geometric progressionis 16 and its common ratio is ' Find the sum to infinity of the progression. [3 marks] 2 Sebutan ketiga suatu janjang geometri ialah 16 dan nisbah sepunya ialah ; . J Cari hasil tambah hingga ketakterhinggaanjanjang itu. 13marknhl Answer I Jawapan 3472t1 [Lihat sebelah SULIT http://kampungebuku.blogspot.com 30
  • 33. SULIT 10 3472tr For 1l The first four termsof an arithmeticprogression -7, -3, l, 5. are Examinerb Use Empatsebutan pertamasuatujanjang aritmetikadalah -7, -3, l, 5. Find Cari (a) the fifth term of the progression, sebutankelimajanjang itu, (b) the sum of next 24 termsafter the fourth term. hasil tambah24 sebutanberikutnyaselepas sebutankeempat. [3 marks] [3 marlcah] AnswerlJawapan:(a) (D) The points P(2a,a), Q(b,c) and R(2b,3c)areon a straightline. p dividesPR in the ratio 3 : 4. Titik-titikP(2a,a), Q(b,c) dan R(2b,3c)terletak pada satugaris lurus. Q membahagi dengannisbah 3 : 4. PR Express in termsof c. 6 [3 marks] Ungkapkan dalam sebutanc. b 13markahl Answer I Jawapan 3472/l SULIT http://kampungebuku.blogspot.com 31
  • 34. SULIT 1l 3412tr For 13 The variables and y arerelatedby the equation/=2x2 +4x3. A straightline graphis x Examiner b Use obtainedby plotting { against x, as shown in Diagram2. xo Pembolehubah x dan y dihubungkan oleh persamoan!=2x2 +4x3.Graf garis lurus diperolehdenganmemplotka" + mebwan x, sepertiditunjukkanpada Rajah 2. x- Diagram2 Rajah 2 Find the value of m and n. 13marlul Cari niloi m dan n. [3 markah) 3472/l [Lihat sebelah SULIT http://kampungebuku.blogspot.com 32
  • 35. SULIT t2 3472t1 For Examiner b 14 Diagram shows straightline pe with the equation- -+ x v ?= | Use 3 a Rajah 3 menunjukkan x y r garis lurus Pe yang mempunyai persamaan - - = I 3 4 The point P lies on x-axis and the point e lies on the y-axis. Titik P terletakpada paksi-x dan titik e terletakpada paksi-y. Diagram 3 Rajah 3 Find the equation of the straight line perpendicularto PQ and passing through the point p. [3 mark^s] Carikan persamaan garis lurus yang berserenjongdengan PQ dan melalui titik p. 13 markohl Answer I Jawapan : 3472t1 SULIT http://kampungebuku.blogspot.com 33 I
  • 36. , SULIT 13 347211 15 For Examiner's Use a D Jh A B a Diagram 4 Rajah 4 Diagram4 shows vectors OA'=g, OB'=b. OC'and Cd on a grid of equal squares. Rajah4 menunjukknn vehord= g, O?= b, O? aordi di atassatqhgrid segiempat sama. Expressin terms oi q and b. Ungkapknndalam sebutan g dan 12. --- (a) OC, [3 marks] 13 markahl 3472t1 [Lihat sebelah SULIT http://kampungebuku.blogspot.com 34
  • 37. SULIT t4 3472t1 t - o r l 1 6 Diagram 5 shows a trapezium P?RS. Examiner I s (Jse I Rajah 5 menunjukkansebuah trapezium PQRS, I Diagram 5 Rajah5 G i v e nth a tth e ve cto V d =@+4) L+ 6 j undTR) =3m i+ 107.Find r D i b e r ive kto rP Q=@+4 )t_ +6j dan SR' = 3m i+ 10 Car i j. (a) the valueof rz, nilai m, (b) the magnitude ur"ro, V/. of ) mognitud bagi vehor PQ'. [4 marl<sl [4 markah] Answer I Jawapan : (a) (b) S o l v et h e e q u a t i o n s e c ' x - 5 = t a n x f o r 0 o ( x < 3 6 0 . . 3 [4 marl<s] S e l e s a i k np e r s a m c a n3 s e k 2 x - 5 = t a n x b a g i 0 o ( x < 3 6 0 o . n 14 markahl Answer I Jawaoan : 3472/l SULIT http://kampungebuku.blogspot.com 35
  • 38. SULIT 15 3472tr 18 Diagram6 showstwo concentriccircles with centreO. For Examiner b Rajah 6 menunjukkan dua bulatan denganO sebagai pusatnya.. Use Diagram 6 Rajah 6 Given that OP : 6 cm, OQ : 3OB and ISOR= 50o. POR and SOQ are straight lines. Diberi bahawa OP : 6 cm, OQ : 3OB dan ISOR = 50o. POR dan SOQ adalah garis lurus. (a) Find the value of 0, in radians.(Use z =3.142) Cari nilai 0, dalam radian, (Guna n =3.142) (b) Calculatethe area of the shadedregion. Hitungkan luas kawasan berlorek. 14marksl 14markahl Answer/Jawapan:(a)e: The curve y= -f(x) is such that I x -2px-3, ' d wherep is aconstant. The gradientof curve at x= 4 is -p. Find the value ofp. [2 marl<sl Suatu lengkung y= f(x) adalah dengan keadaan !=2pr-3, p ialah pemalar. d-r Kecerunan lengkung itu di x = 4 ialah - p . Cari nilai p. 12marknhl Answer I Jov,epan: p :......... 317211 [Lihat sebelah http://kampungebuku.blogspot.com 36 S U L I T
  • 39. SULIT t6 3472/l For Examiner b 20 The curve ! = -2x2 +24x+r has a maximumpoint at x = / Use ow h e r e r i s a c o n s t a n t . Find the value of r. [3 marl<s] Lengkungr = -2x2 +24x + r mempunyai titik maksimumpada x = r, dengankeadaan r ialah pemalar Cari nilai r. [3 markahl Answer/Jawapan:r= that Il, sfrXr = 5, find Given Diberifl,sftPr =5 , cari r-l (a) J, sG)dx, (b) [lr[rrra- rx]d-r [4 marks) [4 markah] Ansrver I Jawapan : (a) (b) 3472/1 http://kampungebuku.blogspot.com SULIT 37