# Mathematics Grade 9 ANA Exemplars 2012 Memo (English)

> Grade 9 Mathematics memorandum from the ANA Exemplars 2012 (English), 33 pages. Read online or get the free PDF download, question paper linked when available.

- Page: https://www.hlayiso.com/library/english-grade-9-exemplar-memo/9b8e01f9-9735-4a08-b213-546851d5d9ca
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 9
- Language: English
- Document type: Memorandum
- Year: 2012
- Exam period: ANA Exemplars
- Curriculum: CAPS
- Pages: 33

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Mathematics · Grade 9 · ANA Exemplars · 2012 · English. Memorandum, 33 pages. Read online or download the PDF.

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ANNUAL NATIONAL ASSESSMENT

          GRADE 9

       MATHEMATICS

       MEMORANDUM

   SET 1: 2012 EXEMPLAR

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                            ANNUAL NATIONAL ASSESSMENT 2012

                                   GRADE 9 MATHEMATICS

                                   EXEMPLAR MEMORANDUM

REAL NUMBER SYSTEM

1.
     1.1.1   4   - rational                                               (1)

     1.1.2   √2 - irrational                                              (1)
     1.1.3   0,2- rational                                                (1)

     1.2
              NUMBERS          REAL        NON - REAL    UNDEFINED
                      0        √
                      7
                      7                                  √
                      0
                     √7        √

                  √−7                      √
                                                                         (4)

 1.3.1               7                                                    (1)
             0,7 =
                     10

 1.3.2                 13                                                 (1)
             0,13 =
                      100

 1.3.3                201     1                                           (1)
             2,01 =       =2
                      100    100

 1.4.1       2,5 × 10 × 7 = 1,75 × 10                                     (1)
 1.4.2       0,007                                                        (2)

                                                                     2

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1.4.3    1,12 × 10     × 3 × 10     = 3,36 × 10                                              (2)

1.5.1    1,6                                                                                 (1)
1.5.2    −√5                                                                                 (1)

1.6.1    0,152, 0,153, 0,154 anyone of the three                                             (1)
1.6.2    0,71; 0,72;        0,73;   0,74;   0,75;       0,76; 0,77 anyone of the seven       (1)

1.7.1    2 and 3                                                                             (2)
1.7.2    4 and 5                                                                             (2)
1.7.3    1 and 2                                                                             (2)
1.7.4    4 and 5                                                                             (2)
1.8
         NATURAL WHOLE                INTEGER RATIONAL IRRATIONAL REAL
         NUMBER         NUMBER
 7                                                  √                           √
 15
                                                                 √              √
    1
  2
    8

 0,081                                                           √              √

 2                                                               √              √

−√16                                  √             √                           √
0,528                                               √                           √
 2,6                                                √                           √
  6      √              √             √             √                           √
  2

                                                                                         3

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     1.9.1   0,6 < 0,625 < 0,75 < 0,8                                  (1)
     1.9.2   0,2 < 0, 2̇ 0̇ < 0, 2̇ < 0,24                             (1)
     1.9.3   √0,36 < √0,366 < 0, 6̇ < 0,69                             (1)
     1.9.4   −3      5     1 −2                                        (1)
                < − <− <
             2       6     6    3
     1.9.5   −0, 12 < −0,11 < ̇−0,1 < −0,01̇                           (1)

FINANCIAL MATHEMATICS

1.                                                                    (3)

     1.1     Selling price=22 × 1,50 = 33

             Profit= Selling price – cost price = 33 − 20 = 13

     1.2.1

        a)   18%        75 000 = 13 500                               (2)

        b)   Tax = 12 000 + 20%              ( 97 500 − 80 000)       (2)

                                             = 12 000 + 2 100

                                                 = 14 100

       c)    Tax= 20 000 + 25%                30 000                  (2)

                                                 = 27 500

      d)     Tax= 42 000 + 35%                80 000                  (2)

                                                 = 70 000

     1.2.2

Taxable income          R140 000                  R100 000        R230

                                                                  000

Tax                     R25 000                   R16 000         R45

                                                                  4

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                                                       500

1.3     Increase: 1 740 − 1500 = 240

        % increase =               × 100 = 16              (2)

1.4          = (1 +     )                                  (2)

        = 1500(1 + 2(0,11))

        = 1 830

        or
                            × ×
        SI=     =                  = 330

        Total amount =            1500 + 330 = 1 830

1.5.1   Investment = (1 + )                                (3)

                            11,5
        = 2 750 1 +
                            100

        = 5 891,92

1.5.2   Interest earned= 5 891,92 − 2 750 = 3 141,92       (1)

1.6.1        = (1 + )                                      (4)
                                      ×
                              12
        = 9500 1 +
                            100 × 4

        = 24 463,29

        Interest = 24 463,29 − 9 500

                                  = 14 963,29

                                                       5

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1.6.2    = (1 + )                            (4)
                                ×
                      8
        = 9500 1 +
                   100 × 2

        = 17 793,32

        Interest= 17 793,32 − 9 500

                             = 8293,32

1.6.3    = (1 + )                            (4)
                                    ×
                     6,5
        = 9500 1 +
                   100 × 12

        = 15 956,86

        Interest= 15 956,86 − 9 500

                             = 6456,86

1.6.4    = (1 + )                            (4)

                      7,25
        = 9500 1 +
                      100

        = 16630,37

        Interest= 16630,37 − 9 500

                             = 7130,37

                                         6

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RATIO AND PROPORTION

1                                                                   (3)
    1.1   Speed=       km/h = 300 km/h

    1.2                                                             (3)
           MINUTES 2            4          6       8     20
           COST        R1,60 R3,20         R4,80 R6,40 R16,00

    1.3                                                             (3)
            NO OF MEN               TIME
                   5                 45
                   9

                                45 × 5
                            =          = 25ℎ
                                  9
          OR
          Time taken by 5 men = 45ℎ
          Time taken by 1 man = (45 × 5)ℎ
                                      ×
          Time taken by 9 men =            = 25ℎ

    1.4                                                             (3)
                TIME         NO OF HOURS
                   8                  3
                   2
                                2 =8×3
                                     = 12
          OR
          In 8 hours no of workers needed = 3
          In 1 hour no of workers needed = 3 × 8
          In 2 hours no of workers needed = 3 × 8 ÷ 2
                                           = 12

                                                                7

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1.5                                                         (2)
           NO OF KG            COST IN R
               3                        24
               7

                                         7
                                         =
                                    24 3
                                       7 × 24
                                     =
                                         3
        Cost = R56
        OR
        Cost of 3 kg = 24
        Cost of 1 kg = 24 ÷ 3
        Cost of 7 kg = 8 × 7
                   = 56

1.6.1 Direct proportion                                     (1)
1.6.2                                =5                     (1)
1.6.3                         = 5(25) = 125                 (1)

1.7                  COST IN R                NO OF         (3)
                                             APRICOTS
                       5,60                      15
                       10,08

                               15        10,08
                                    =
                                          5,60
                                    10,08 × 15
                               =
                                       5,60
                                     = 27

                                                        8

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 1.8                     ,                                     (3)
       Cost per ℓ =          =     8,65

 1.9                                                           (3)
                     NO OF KG                  COST IN R
                       0,35                       25,10
                         1
                                                1
                                           =
                              25,10            0,35
                                            2510
                                       =
                                             35
                                   = 71,714 …
                                       ~ 71,71

1.10                                                           (3)
          NO OF KG            COST IN R
             12,5                      90
             17,2
                                           7,2
                                       =
                                 90        12,5
                                      7,2 × 90
                                 =
                                        12,5
       Cost= R51,84
1.11                                                           (3)
        Distance in km            No of ℓ
             130                       6,5
              80

                                            80
                                       =
                                 6,5       130
                                      80 × 6,5
                                 =
                                        130
                                       =4
       No of ℓ = 4

1.12                                                           (3)

                                                           9

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                No of ℓ          No of m
                   5                  40
                   1

                                          1
                                          =
                                     40 5
                                       1 × 40
                                     =
                                         5
                                     =8m

SPEED/TIME /DISTANCE

1.             × =
     1.1   120 × = 600
                   =      h

                   = 5h
                                                           (2)
           ∴time taken is 5 hours.
     1.2                              × =
                                     × 8 = 600
                                          600
                                      =          /ℎ
                                           8
                                      = 75      /ℎ
                                                           (2)

                                                      10

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2.                                    S (km/h)           T (h)      D (km)        (3)
            car                     100            x              1 0x
            air                     300            6-x            300(6-x)

                                 100 + 300(6 − ) = 1200
                                          100 + 180 = 1200
                                                 −200 = −600
                                                            =3
           Time by air = (6 − 3)ℎ
                                                           = 3ℎ
3.           = (120 × 1,5) km = 180 km                                            (3)
                       ,
                                km
                   ,
             =                        = 125 km/h
                           h
                  660
           z=         h = 3h
                  220
4.         d =s×t                                                                 (3)
            = (5 × 0,5) km
            = 2,5 km
           s × 0,25 = 2,5
                               2,5
                   s=
                               0,25
                   s = 10 km/h
     5.1   Average speed =                    km/h                                (3)

                                    = 7,5 km/h
     5.2   Distance = ×                                                           (1)
                       = (7,5 × 6) km
                       = 45 km
6.                s×t=d                                                           (3)
           (p + 20)t = q

                               t=         h

                                                                             11

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EXPONENTS

1.
      1.1   99 × 1001 = 99 × 1 = 99                                                                 (1)
      1.2                                                                                           (1)
                      ×                        =           =

      1.3        (    )                                                                             (2)
                                  =                =

      1.4   (8        )(−4                     )       −32                                          (3)
                                                   =
                     (2    )                            4
                                           = −8
     1.5    2        8                                                                              (3)
                 2
                 2            2
            =
                      2
                 2
            =
                 2
            =2
     1.6    15 . 3 . 25                                                                             (4)
             9 . 125
                 .    .           .
            =
                          .
            =

            =3
                 1
            =
                 3
     1.7                               5                               5       10              10   (3)
                (2                )×               = (2        )×          =        = 10   =

     1.8                                                           1                                (1)
            (        )(           )=                   =       =

     1.9                                                               1                            (2)
            (    .            .       )÷           =       ÷   =

 1.10       (3         ) (                 )       27          ×1                                   (3)
                                               =                       = 27         = 27
                     (   )

                                                                                                          12

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PATTERNS, FUNCTIONS AND ALGEBRA

1
    1.1   90 and 69                                                (2)
    1.2   36; 72; 108; 144; 180 ; 216                              (2)
    1.3   39; 48                                                   (2)
2
    2.1   Add 6.                                                   (1)
    2.2     =6 −3                                                  (1)
    2.3   6 − 3 = 45
                6 = 48
                   =8                                              (1)
          The 8th term = 45
    3.1            Number 1     2     3    4     5       6    7    (2)
                   of
                   panels
                   Number 2     3     4    5     6       7    8
                   of poles
                   Number 6     12    18   24    30      36   42
                   of slabs

    3.2     =      +1                                              (2)
    3.3     =6                                                     (2)
    3.4     (       ) = 10 + 1 = 11                                (2)
            (       ) = 6(10) = 60
4                                                                  (3)
           Input              Rule              Output
                   1             −2 + 3                  1
                   2                                  −1
                   3                                  −3
5
           Input              Rule              Output
                   −2            2    −1                 7

                                                                         13

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                     −1                                1
                      0                                −1
                      1                                1
                      2                                7    (5)

6
    6.1       = −2(0) + 6(0) − 8 = −8                       (1)
    6.2       = −2(−1) + 6(−1) − 8 = −2 − 6 − 8 = −16       (1)
    6.3       = −2        +6 −8
    6.4       = −2( + 2) + 6( + 2) − 8                      (4)
              = −2(       + 4 + 4) + 6 + 12 − 8
              = −2    −8 −8+6 +4
              = −2    −2 −4
7
    7.1       =3 =1                                         (1)
    7.2       = 3 = 27                                      (1)
    7.3                   1                                 (1)
              =3      =
                          9

PRODUCTS

1
    1.1   6 −3−5=6 −8                                       (2)
    1.2   5 −6 +3= − +3                                     (3)
    1.3   5 −6        + 3 = −6       +8                     (3)
    1.4        −9                                           (2)
    1.5   9     −4                                          (2)
    1.6   3(    + 2 − 3) = 3        +6 −9                   (3)
    1.7   −5(2        +       −   ) = −10   −5    +5        (3)
    1.8        − 8 + 16                                     (3)
    1.9   4     − 12 + 9                                    (3)

                                                                  14

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     1.10    3(16             − 24 + 9) = 48                  − 72 + 27                                (3)
     1.11            −5 +6−(               + 4 + 4) = −9 + 2                                           (5)
     1.12    3        − 6 − 12             + 12 − 5               + 10 = −14              + 6 + 10     (6)
     1.13                       2                                   1 2               2
             (9           − 1) − (         − 1) = 3               −   −          +
                                3                                   3 3               3
                                                          7         1
                                                  =               +                                    (6)
                                                          3         3
     1.14              1        1  1                                        1                 1   1
             4(           −
                          )−( +   + )=4                                    − −            −     −
                       16       2  16                                       4                 2   16
                           1   5
                     =3 −    −
                           2   16
                                                                                                       (6)

     1.15.                        1                           2        1
                              −        − (            −            +       )

                                                          1                               1
                                       =              −       −            +2         −

                                                  2                                                    (6)
                                   =2         −

FACTORS

1.
     1.1     4(2 + 3 )                                                                                 (2)
     1.2     −5(2 + 3 )                                                                                (2)
     1.3             +                                                                                 (1)
     1.4     4(6 − 3 + 4)                                                                              (2)
     1.5             ( − 1)                                                                            (2)
     1.6     −2 (1 +               )                                                                   (2)
     1.7     2 (4             − 5)                                                                     (2)
     1.8     6        (       −2       + 3)                                                            (2)
     1.9     4 (2             −3       − 5) = 4 (2                − 5)(        + 1)                    (2)
     1.10        ( − ) − ( − ) = ( − )(                                − )                             (3)
     1.11    ( − )(               −     ) = ( − )( − )( + )                                            (3)
     1.12        − )( + )                                                                              (2)
     1.13        (        −    ) = ( − )( + )                                                          (3)

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     1.14     (     +     )(      −   )=(     +   )( + )( − )   (3)
     1.15     (4     +      )(4       −   )                     (2)
     1.16     3(     −9        ) = 3( − 3 )( + 3 )              (3)
     1.17     1         1                                       (3)
                ( − 4) = ( − 2)( + 2)
              2         2
     1.18     1           1                                     (3)
                (4 − ) = (2 − )(2 + )
              8           8
              OR
              4     −          (2 − )(2 + )
                           =
                    8               8

2
      2.1     (97 − 3)(97 + 3) = (94)(100) = 9400               (2)
      2.2     (101 − 100)(101 + 100) = 1(201) = 201             (2)
      2.3     (55 − 25)(55 + 25) = (30)(80) = 2400              (2)
      2.4     (20,5 − 15,5)(20,5 + 15,5) = (5)(36) = 180        (2)

EQUATIONS

1.                                                              (2)
     1.1    6 = 24                                              (3)
               =4
     1.2     ( − 3) = 0
             = 0 or       =3                                    (2)
     1.3    2 + 4 = 9 − 12
                  7 = 16 or 16 = 7
                         16 16                                  (3)
                     =         =
                         7 7

     1.4    × 36:    9( − 5) − 4(3 − 4 ) = 468
                         9 − 45 − 12 + 16 = 468
                    25 = 525
             = 21                                               (4)

                                                                      16

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1.5   × 15: 45 + 3 + 195 = 5(2 + 1)
                      48 + 195 = 10 + 5
                            38 = −190
                                 = −5                         (4)
1.6   5 =5
      ∴       =4                                              (2)
1.7    2      =2
      ∴− =5                                                   (2)
               = −5
1.8   3       =3                                              (2)
      ∴       +1 =4
                   =3
2.1       +    +1+      + 2 = 78
                      3 + 3 = 78
                         3 = 75
                             = 25
      The numbers are 25; 26; 27                              (4)
2.2
                               AGE NOW       AGE IN 4 YEARS
       Ben                                             +4
       Patrick                        5          5 +4

      5 + 4 = 3( + 4)
      5 + 4 = 3 + 12
           2 =8
               =4
      Ben’s age is 4 years and Patrick’s is 20 years          (4)

2.3   Area = ×
      −12       +6      = −6     ×
                            −12 + 6
                        =
                               −6
                            −6   (2   − 1)
                        =
                                 −6

                                                                    17

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                              = (2    − 1)        (3)
     2.4        Area = ×
            2    − 8 = × ( + 2)
                         2     −8
                     =
                              +2
                         2(− 4)
                     =
                          +2
                       2( + 2)( − 2)
                     =
                             +2
                     = 2( − 2)                    (5)

     2.5            =2
                Area = ×       = 32
            2 ×     = 32
                2    = 32
                    = 16
                    = ±4
                    =4        (because   > 0)
            ∴   =4       and = 2(4) = 8           (4)

INEQUALITIES

1.
      1.1

                                                    (2)

     1.2

                                 •
                                                    (2)

                                                        18

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     1.3
                            •         ••                           (2)

     1.4

                                                                   (2)

    1.5

                            •••
                                                                   (2)

2
     2.1       <2
                                                                   (2)
     2.2   3≤       ≤ 7and        ∈
                                                                   (2)
     2.3   √3 ≤         < 2,1and      ∈
                                                                   (2)
     2.4   −3 ≤         ≤ 0 and       ∈    or −4 <   < 1 and   ∈   (2)
     2.5       < −2 or      ≥ 0 and           ∈
                                                                   (2)

ALGEBRAIC FRACTIONS

1.
     1.1   2                                                       (2)
     1.2       −                                                   (2)
     1.3   3            2                 6                        (5)
                    ×        ×        =

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1.4    ( − 4)     4       ( − 1) ( − 4)( − 1)              (5)
              ×         ×       =
        4         ( − )            ( − )
1.5          2                                             (1)
       +   =    =
      2 2     2
1.6   3(7 − 5) − 2(10 − 7) 21 − 15 − 20 + 14     −1        (3)
                           =                  =
                6                  6             6
1.7   5(6 − 10) + 6(3 − 5) − 180 30 + 50 + 18 − 30 − 180   (4)
                                =
                  30                        30
                        48 − 60
                      =
                           30
                        16(3 − 10)
                      =
                             30
                        8(3 − 10)
                      =
                            15

1.8   3( − 1) − ( + 2)( + 1) 3 − 3 − − 3 − 2               (4)
                            =
          ( − 1)( + 1)         ( − 1)( + 1)
                         − −5
                   =
                       ( − 1)( + 1)

                                                           20

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GRAPHS

1
    1.1

                      2
                      3

                                        (4)

                                        21

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     1.2

               y   23 x  1

                                3
                                2

                                             (4)

2.
     2.1   = −2 − 2                          (2)
     2.2   = −2 + 3                          (2)
     2.3       1                             (2)
           =     +1
               3

                                             22

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3.                                                                    (3)
                                        Y

                                        8
                                        7
                          x  3
                                        6

                                        5               y  x 1
                                        4

                                        3
                                                         3y  x  3
                                        2
                                   B
                                       1
                  A
                    
        -5   -4   -3 -2 -1 0            1   2   3   4      X

                      
                          C

4.   =2 +2                                                            (3)

                                                                            23

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SPACE AND SHAPE

1.
     1.1   A.Trapezium
           B. Octagon
           C. Triangle
           D. Rectangle
           E. Parallelogram                                      (5)
     1.2   A. cylinder                                           (4)
           B. rectangular-based pyramid
           C. cube
           D. triangular pyramid
     2.1                                                         (1)
     2.2   70° East of North or 20° North of East or 70° North   (2)

3.         In ∆        and ∆                                     (5)
                  =       = 90°(given)
                      is common
                         =                    (given)
             ∴∆          ≡∆                   (90°, ℎ   , )

4.                +      =      (Pyth)                           (5)
                  + (3) = (5)
                         = 25 − 9
                         = 16
                         = 4unit
                         =      −
                         = 4 − √7 unit
                         =        +      (Pyth)
                                             = 7 + 9 unit
                                             = 16unit
                         = 4 units

                                                                       24

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5.   2     +         = 180°                   (co-int< ;        ||   )                    (4)
         + 120° = 180°
         2 = 60°
      2 +           +        = 180°                   ( sum of <         of ∆)
     but       =        (<     opp equal sides)
           2 +2                = 180°
               60° + 2         = 180°
                         2     = 120°
                         ∴     = 60°
      2    +        +          = 180°(sum of <        of ∆)
     but        =                            (< oppequal sides)
           2        +2        = 180°
           120° + 2           = 180°
                        2     = 60°
                     ∴        = 30°
      2    +         +        = 180° ( suppl<      on a str line
     or            is a str. <)60° +      + 30° = 180°
                        2     = 180° − 90°
                              = 90°
6.          =                           (<     opp.             sides)
     40° +               +       = 180°                    ( sum of <      of ∆)          (6)

     2          = 180° − 40°
      2         = 140°
               = 70°
               =             = 70°     ( alt < ,      ||    )
            +               = 180°       (suppl<      on a str line or K           is a
     str. <)
                    = 180° − 70°
           2            = 110°

                                                                                                25

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7.
     7.1   In ∆          and ∆                                                              (4)
                    =                 ( common side )
                =                              (alt. < ,             ||       )
                =       ( alt. < ,        ||         )
           ∴∆           ≡∆                     (<, <, )
                                                         ∴       =
                                 =                           (            .       ∆)

     7.2   In ∆              and ∆                                                          (4)
                                 =                       (proved above)
                =       (alt. < ,         ||     )
                =                              ( alt. < ,        ||)
                        ∴∆           ≡∆          ( <, <, )
                    ∴        =                       =           (            .        ∆)

 7.3       The diagonals of a parallelogram bisect each other.                              (1)
8.              =        =       =    (prop. sides of similar quads)                        (6)

                    7
                =
           9        28
                             9×7
                         =       = 2,25
                              28
            6           7
                  =
                        28

                        6 × 28
                    =          = 24
                          7

                                                                                                  26

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9.          In ∆           and ∆                                   (6)
                =       (alt < ,     ||    )
                =       (alt < ,     ||    )
                =        (vert. opp< )
            ∆           ||| ∆                  (<, <, <)

            ∴        =          =   (prop. sides of similar ∆s)
                2   3
            ∴     =
                6
                    =9
                           ,
            and =

                    = 7,5
                    =       +
                    = 2,5 + 7,5 = 10

TRANSFORMATIONS

1.
     1.1   (−1; −4)                                                (1)
     1.2   (3; −6)                                                 (1)
     1.3   (−3; −4)                                                (1)
     1.4   (−4; 3)                                                 (1)
2.         Reflection about the X-axis                             (4)
3.         Vertical translation
     3.1   Reflection about the Y-axis                             (2)
     3.2   Reflection about the Y-axis and then reflection about
           the X-axis or reflection about the X-axis and then
           reflection about the Y-axis                             (4)
4.          ′(−6; 9) ; ′(3; 15) ; ′(15; −6)                        (3)

                                                                         27

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5.1

                                    (1)

5.2

                                     (1)

                                           28

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MEASUREMENT

1.
     1.1     Area of ∆        =    ℎ = × 3 × 4 cm = 6cm                 (2)

     1.2     Area of ∆        =    ℎ = × 6 × 4 cm = 12cm                (3)

     1.3     Area of ADEG= (         +       )   = (9 + 6)4 cm = 30cm   (3)

     1.4     Area of BDEG=        × ℎ = 6 × 4 cm = 24cm                 (3)

     1.5         =       +         (Pyth)
                                       = 3 + 4 cm
                                         = 9 + 16cm
                                            = 25cm
                                         ∴ BE = 5cm
     1.6.1   Perimeter of ∆        = (5 + 5 + 6)cm = 16cm               (2)
     1.6.2   Perimeter of ADEG = (9 + 5 + 6 + 4)cm = 24cm               (4)
2.               =       +                  (Pyth)
                                     = 49 + 120 unit
                                         = 169 unit
                                            = 13 units
             Area =

                                     1           13
                                   =( ×      ×      )unit
                                     2           2
                                          = 66,36 unit                  (3)

3.
     3.1     Total surface area= 2(8 × 12) + 2(12 × 18) + 2(8 × 18)cm
                                                     = 912cm            (6)
     3.2     Volume= ×        ×ℎ
                                         = (8 × 12 × 18)cm
                                         = 1728cm                       (3)

                                                                              29

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4.           Volume of cylinder=        ℎ
                                             22
                                               550 =
                                                × (5) × ℎ
                                              7
                                       550 × 7
                                   ℎ=
                                      22 × (5)
                                                                              (4)
                                             ℎ=7
5.           Volume = ×      ×ℎ
                               50 × 30 × ℎ = 24000
                                                   24000
                                         ℎ=(              )
                                                  50 × 30
                                                 ℎ = 16                       (3)

DATA HANDLING

1.
     1.1     20 30 30 40 50 50 60 70 70 70 70 80 80 90 100                    (1)
     1.2
     1.2.1   Median = 70                                                      (1)
     1.2.2   Mode = 70                                                        (1)
     1.2.3   Range = 100 − 20 = 80                                            (1)
     1.2.4   Mean =      = 60,67 to decimal places                            (2)

2.
     2.1     24 passengers                                                    (1)
     2.2        Range = 70 − 1 = 69                                           (1)
     2.3     Mean=       = 26,7 = 27                                          (3)

     2.4       AGES IN YEARS                    TALLY             FREQUENCY
                  (INTERVAL)                   MARKS
              1 - 13                   IIIIII                 7
              14 - 26                  III                    3
              27 - 39                  IIIIIII                8
              40 - 70                  IIIII                  6               (4)

                                                                                    30

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     2.5   27-39                                         (1)
     2.6   18 passengers                                 (1)
3.
     3.1   22                                            (1)
     3.2   range= 15 − 2 = 13                            (1)
     3.3     SHOE SIZES              TALLY   FREQUENCY
                (INTERVAL)           MARKS
            1-5              IIII            4
            6 - 10           IIIIIIIIII      12
            11 - 15          IIIII           6           (4)

4.
     4.1   18 babies                                     (2)
     4.2   15 babies                                     (1)
     4.3   11 – 15 months                                (1)

     5.1
           DIE               COIN            COMBINED
                                             OUTCOMES
           1                 H               1H
                             T               1T
           2                 H               2H
                             T               2T
           3                 H               3H
                             T               3T
           4                 H               4H
                             T               4T
           5                 H               5H
                             T               5T
           6                 H               6H
                             T               6T
                                                         (6)

                                                               31

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     5.2

                                               (2)

     5.3

     5.3.1                   1                 (1)
                             12
     5.3.2   3    1                            (1)
                =
             12 4
     6.1     1                                 (1)
             10
     6.2     1                                 (1)
             10
     6.3     2    1                            (1)
                =
             10 5
7.
     7.1     18 3                              (1)
               =
             30 5
     7.2     12 2                              (1)
               =
             30 5
8.
     8.1     3                                 (1)

                                                     32

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8.2.1   3                                     (1)
        10
8.2.2   2    1                                (1)
           =
        10 5
8.2.3    1                                    (1)
         10

                                  H

                          H
                                      T

                  H               H
                          T
                                      T
                                      H
                          H
                                          T
                      T
                                      H
                              T
                                          T

                                                    33

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