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                   SPM Trial Examination 2011 Perak
                           Marking Scheme
                     Addition Mathematics Paper 1

No         Marking Scheme                                                      Total
                                                                               Mark
     1.    (a)      7                                                          1

           (b)      8                                                          1

           (c)      many to many                                               1
                    banyak dengan banyak

     2.     (a) 53                                                             1

            (b)     h  3 and k  22                                           3

                    B2:       h  3 or 9h  k  5 or g(x) = 3x2 - 22
                    B1:       h(3  x) 2  k

     3.                     x4                                                1
          (a)       g 1 ( x) 
                              7
                            x4
                    Accept:
                             7

          (b)       p  10
                                                                               2
                              p4
                    B1:            2 or 7(2)  4  p
                               7

     4.                   p  6                                               2

                   B1: (3) 2  5(3)  p  0 OR ( x  3)(x  2)  0
                       OR  3  h  5 and  3h   p

     5.                        1                                               3
                   3  x 
                               2

                 B2:                      1
                                                     ( indicated the correct
          region )          -3
                                          2



                  B1:       ( x  3)(2 x  1)


     6.            (a)    x2                                                  1
                  (b)     f ( x)  ( x  2) 2  16                             2

                                                                                       1
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                B1: b  2 or c  16
7.                       1
                  n                                           3
                         2
             B2: n  2  3n  4 or equivalent
             B1: 3n2  33n  34 or equivalent

8.
              x = 64                                            3
                              1

             B2: log 2 x  3 or log 4 x  3
                              2


                  log 2 x       log 4 x
             B1:
                  log 2 4
                            or log 4 2

9.               x = 40                                         2
                   x      x 8
                        
             B1: x  10     x

10.               1                                             1
       (a)             
                  3
       (b)      18                                             2
                   24
           B1:
                    1
               1  
                    3

11.
              n = 20                                            2
              B: 56 + ( n – 1 ) ( – 3 ) < 0


12.
             a = 7 and b = – 2                                  4

              B3: a = 7 or b = – 2 OR 1 = a – 2(3) or 5 = a –
      2(1)
                                                        5 1
              B2: 5  a  b(1) or 1  a  b(3) OR b 
                                                        1 3
              B1: log y  bx 2  a

13.
      (a) h  6                                                2
               40 h0
          B1:            or equivalent
               1 3 6  3

       (b)      2:3
                           n(1)  m(6)                          2
             B1: 3 
                              nm
                                                                    2
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14.           6,  6                                              3
                 p 12
           B2:     
                 3 p
                     12                                p
           B1: m1      or                      m2 
                      p                                3
15.   ( a)        k 6                                            2
              B1:            k  8  10
                                2       2


      (b)
                      1 *
                     10
                            
                          6i  8 j                               1
                      3 i+4j
                      5     5

16.   (a)      x  2y                                            1
              3    1
      (b)       x y                                              3
              4    2
                     1                     3
             B2: x  ( x  2 y ) or 2 y  ( x  2 y )
                     4                     4
                 1                  3
             B1 : ( x  2 y ) or  ( x  2 y )
                 4                  4

17.                                 1                             1
      (a)           sec  
                                    k
                            1 k 2
      (b)                                                        2
                             k
              B1:               1 k 2

18.   ( a)              5                                         1

      (b)      45.56                                              3
                  1              1
              B2: (13) 2 (1.19)  (10  12)5
                  2              2
                   1                  1
              B1 : (13) 2 (1.19) or     (10  12)5
                   2                  2

19.               24                                              3
              B2:  2(2)( 3)( 2 x  3) 4 (2)
              B1:  2(2 x  3) 21 (2)

20.                15                                             3
                   11
                   dx      5
              B2 :                               or equavalent
                   dt (4  3x  2 )

                                                                      3
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                    dy                 dy
             B1:        4  3x  2 or    5
                    dx                 dt

21.                   y = 3x2 – 4x  5                3
              B2:     2 = 3(1)2 – 4(1) + c
              B1:     y = 3x2 – 4x + c



22.    (a)           x = 42                          1
       (b)           x = 324
                          2
                                                      2


             B1:     5=
                              x    2

                                         72
                                6

23.   (a)          1716                               1

      (b)       1008                                  3
             B2 : 8C4 x 5C2 + 8C5 x 5C1 + 8C6 x 5C0
             B1: 8C4 x 5C2


24.   (a)           x=5                               2

                      12     6
             B1 :          
                     33  x 19

                  3                                   2
      (b)
                  38
                    5 18       25 20
             B1 :       or 1  
                   30 38       30 38

25.    (a)          0.1587                            2
                              103  95
             B1: P( Z                 )
                                 8
      (b)       0.6826                                2
              B1: P(1 < Z < 1)


                                          Total       80




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