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Nama Pelajar : …………………………………                Tingkatan 5 : …………………….
3472/1
Additional
Mathematics
Paper1
September 2010




         PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA
                     SEKOLAH MENENGAH
                  NEGERI KEDAH DARUL AMAN

                 PEPERIKSAAN PERCUBAAN SPM    2010

                      ADDITIONAL MATHEMATICS
                           MARKING SCHEME
                               Paper 1




                               .
SULIT                                          2                        3472/1

                       SPM Trial Examination 2010 Kedah Darul Aman
                                     Marking Scheme
                              Additional Mathematics Paper 1

Question                        Solution/ Marking Scheme            Answer             Marks
   1                                                           (a) 8                    1

                                                               (b) 0 ≤ f ( x) ≤ 8          1

    2                 2+n                                      (a) 13                      2
           (a) B1:        =5
                       3
                                                               (b) 3 x − 13                1
    3
           (a) B1: 4 g ( x) + 2 = 5 x − 2                            5x − 4
                                                               (a)                         2
                                                                       4

                     5(4 x + 2) − 4                                  1
           (b) B1:                  =4                         (b)                         2
                           4                                         2

    4
                            2
                 1    k
           B2: 2 −  =                                                    2               3
                 9    9
                                                                           9
                                  3                        k
           B1 : α + 2α = −              or     α × 2α =
                                  9                        9

    5
                                                                     (a) 3                 1

                                                                     (b) 11                1

                                                                     (c) -7                1

    6
           B2:
                                       6                                           6
                                                                     −2≤ x ≤
                       -2
                                       5                                                   3
                                                                                   5
           B1: (5 x − 6)( x + 2)

    7
           B2: x + 3 = −4(2 x + 3)
                                                                               5
                                                                      x= −                 3
           B1 : 2 x + 3 or 2 −4( 2 x + 3)                                      3



3472/1                   Additional Mathematics Paper 1
                                                                                   SULIT
SULIT                                         3                   3472/1

Question                   Solution/ Marking Scheme                Answer          Marks
   8           117  27 
                               2
           B2:    −                                                 4                3
                9  9 
               31 − 4
           B1:         or 3 or 133− 4 2 or 117
                 9
    9          1 5                                                    7
           B3: +                                                                       4
               3 6                                                    6
               log p p log q q          1        1
           B2:          +         or         +
               log p 2    log q 2    log p 2   log q 2

           B1: log 2 pq = log 2 p + log 2 q
   10                                                                 (a) -2           1

                           10
           (b) B2: S10 =      [2(−6) + 9(3)]                          (b) 75           3
                            2

                 B1: a = −6 and d = 3
   11      (a)    B2: r 3 = 27                                       (a) 3             3

                  B1: ar = 6        or    ar 4 = 162                 (b) 2             1

   12                      3
           B2: S ∞ =       8
                       1 − (− 1 )
                              2
                                                                      1
                                                                      4                3
                      1
           B1: r = −
                      2
   13            3 x + 11         8 + 3y
           B2 :           = 2 and        = 17                      ( −1, 20)           3
                     4               4

                3 x + 11        8 + 3y
           B1 :          = 2 or        = 17
                    4              4
   14      B2 : p = −1.2    or  q = 6.3                            p = -1.2
           B1 :                                                                        3
                                                                   q = 6.3
                  5.1 − 1.5
           p=               or 5.1 = q − 1.2 or 1.5 = q − 1.2(4)
                    1− 4

           B2: h=7 or k=8
                                                                     h=7
   15                                                                                  3
           B1: BA = hi − (k − 3) j                                   k=8




3472/1                   Additional Mathematics Paper 1
                                                                               SULIT
SULIT                                             4                         3472/1

 Question             Solution/ Marking Scheme                   Answer           Marks
   16

                   3   5h
            B2:      =
                   2 6h − 8                                          3                3

                    3     5h 
            B1:   = k 
                 2     6h − 8  or AB // AC
                                 
                                  

    17

            B2 : 75 0      or     195 0
                                                              75 0 ,1950              3

            B1 : x − 45 0 = 30 0         or 150 0


    18              1 2                  1 2
            B2 :      (3) (2)    =         (4) θ              1.125 rad               3
                    2                    2

                   1 2                     1 2
            B1:      (3) (2)      or         (4) θ
                   2                       2


    19                   1                                               1
            (a) B1: m = −                                  (a) y = −       x+8        2
                         2                                               2
                         1
            (b) B1: 0 = − x + 8                               (b) (16, 0)
                         2                                                            2


    20      B3: − 6(0 + 1)(4 − 0) + 2(4 − 0) 2
                                                                 8                    4
            B2: 2(2 x + 1)(4 − 3x)(−3) + 2(4 − 3 x)    2



            B1: 2(2 x + 1)(4 − 3x)(−3) or 2(4 − 3x) 2
    21
                   (2) 2 8(2) −1                                 x2 8
            B2 : 11 =    −       +c                         y=     + +5               3
                     2     −1                                    2 x
                x2            8 x −1
            B1:         or
                2              −1




3472/1                    Additional Mathematics Paper 1
                                                                                      SULIT
SULIT                                        5               3472/1

 Question                Solution/ Marking Scheme        Answer        Mark
   22
            B2 : δy = −24(2) −3 × p                        -3p          3


                   dy
            B1 :      = −24 x − 3 or δx = p
                   dx


    23
            B1: 10C3 (0.15) 3 (0.85) 7                    0.1298        2




    24                                                     (a) 35       1

            (b) B1: 7 C3 − 5C1 or 2 ×5 C 2 + 5C3
                                                          (b) 30        2

    25
                       100 − 92                           (a) 1.6       2
            (a) B1 :
                          5
                       88 − 92                           (b)0.7881      2
            (b) B1 :
                          5




                             END OF MARKING SCHEME




3472/1                  Additional Mathematics Paper 1
                                                                       SULIT

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Add Maths 1

  • 1. Nama Pelajar : ………………………………… Tingkatan 5 : ……………………. 3472/1 Additional Mathematics Paper1 September 2010 PERSIDANGAN KEBANGSAAN PENGETUA-PENGETUA SEKOLAH MENENGAH NEGERI KEDAH DARUL AMAN PEPERIKSAAN PERCUBAAN SPM 2010 ADDITIONAL MATHEMATICS MARKING SCHEME Paper 1 .
  • 2. SULIT 2 3472/1 SPM Trial Examination 2010 Kedah Darul Aman Marking Scheme Additional Mathematics Paper 1 Question Solution/ Marking Scheme Answer Marks 1 (a) 8 1 (b) 0 ≤ f ( x) ≤ 8 1 2 2+n (a) 13 2 (a) B1: =5 3 (b) 3 x − 13 1 3 (a) B1: 4 g ( x) + 2 = 5 x − 2 5x − 4 (a) 2 4 5(4 x + 2) − 4 1 (b) B1: =4 (b) 2 4 2 4 2  1 k B2: 2 −  = 2 3  9 9 9 3 k B1 : α + 2α = − or α × 2α = 9 9 5 (a) 3 1 (b) 11 1 (c) -7 1 6 B2: 6 6 −2≤ x ≤ -2 5 3 5 B1: (5 x − 6)( x + 2) 7 B2: x + 3 = −4(2 x + 3) 5 x= − 3 B1 : 2 x + 3 or 2 −4( 2 x + 3) 3 3472/1 Additional Mathematics Paper 1 SULIT
  • 3. SULIT 3 3472/1 Question Solution/ Marking Scheme Answer Marks 8 117  27  2 B2: −  4 3 9  9  31 − 4 B1: or 3 or 133− 4 2 or 117 9 9 1 5 7 B3: + 4 3 6 6 log p p log q q 1 1 B2: + or + log p 2 log q 2 log p 2 log q 2 B1: log 2 pq = log 2 p + log 2 q 10 (a) -2 1 10 (b) B2: S10 = [2(−6) + 9(3)] (b) 75 3 2 B1: a = −6 and d = 3 11 (a) B2: r 3 = 27 (a) 3 3 B1: ar = 6 or ar 4 = 162 (b) 2 1 12 3 B2: S ∞ = 8 1 − (− 1 ) 2 1 4 3 1 B1: r = − 2 13 3 x + 11 8 + 3y B2 : = 2 and = 17 ( −1, 20) 3 4 4 3 x + 11 8 + 3y B1 : = 2 or = 17 4 4 14 B2 : p = −1.2 or q = 6.3 p = -1.2 B1 : 3 q = 6.3 5.1 − 1.5 p= or 5.1 = q − 1.2 or 1.5 = q − 1.2(4) 1− 4 B2: h=7 or k=8 h=7 15 3 B1: BA = hi − (k − 3) j k=8 3472/1 Additional Mathematics Paper 1 SULIT
  • 4. SULIT 4 3472/1 Question Solution/ Marking Scheme Answer Marks 16 3 5h B2: = 2 6h − 8 3 3  3  5h  B1:   = k   2  6h − 8  or AB // AC      17 B2 : 75 0 or 195 0 75 0 ,1950 3 B1 : x − 45 0 = 30 0 or 150 0 18 1 2 1 2 B2 : (3) (2) = (4) θ 1.125 rad 3 2 2 1 2 1 2 B1: (3) (2) or (4) θ 2 2 19 1 1 (a) B1: m = − (a) y = − x+8 2 2 2 1 (b) B1: 0 = − x + 8 (b) (16, 0) 2 2 20 B3: − 6(0 + 1)(4 − 0) + 2(4 − 0) 2 8 4 B2: 2(2 x + 1)(4 − 3x)(−3) + 2(4 − 3 x) 2 B1: 2(2 x + 1)(4 − 3x)(−3) or 2(4 − 3x) 2 21 (2) 2 8(2) −1 x2 8 B2 : 11 = − +c y= + +5 3 2 −1 2 x x2 8 x −1 B1: or 2 −1 3472/1 Additional Mathematics Paper 1 SULIT
  • 5. SULIT 5 3472/1 Question Solution/ Marking Scheme Answer Mark 22 B2 : δy = −24(2) −3 × p -3p 3 dy B1 : = −24 x − 3 or δx = p dx 23 B1: 10C3 (0.15) 3 (0.85) 7 0.1298 2 24 (a) 35 1 (b) B1: 7 C3 − 5C1 or 2 ×5 C 2 + 5C3 (b) 30 2 25 100 − 92 (a) 1.6 2 (a) B1 : 5 88 − 92 (b)0.7881 2 (b) B1 : 5 END OF MARKING SCHEME 3472/1 Additional Mathematics Paper 1 SULIT