# Mathematics Grade 9 ANA Exemplars 2012 Memo (Afrikaans)

> Grade 9 Mathematics memorandum from the ANA Exemplars 2012 (Afrikaans), 34 pages. Read online or download the free PDF.

- Page: https://www.hlayiso.com/library/afrikaans-grade-9-exemplar-memo/2cd2ba81-56c5-4845-bd96-691cb1835ca7
- Updated: 2026-09-27
- Subject: Mathematics
- Grade: Grade 9
- Language: Afrikaans
- Document type: Memorandum
- Year: 2012
- Exam period: ANA Exemplars
- Curriculum: CAPS
- Pages: 34

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## About this document

Mathematics · Grade 9 · ANA Exemplars · 2012 · Afrikaans. Memorandum, 34 pages. Read online or download the PDF.

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JAARLIKSE NASIONALE ASSESSERING

            GRAAD 9

           WISKUNDE

         MEMORANDUM

    STEL 1: 2012 VOORBEELD

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                      JAARLIKSE NASIONALE ASSESSERING 2012

                      GRAAD 9 WISKUNDE MEMORANDUM

REËLE GETALLESTELSEL

1.1.1   4   - rasionaal                                      (1)

1.1.2   √2 - irrasionaal                                     (1)
1.1.3   0,2- rasionaal                                       (1)

1.2
         GETAL             RËEL     NIE -      ONGEDEFI
                                    REËEL      NIEERD
                 0         √
                 7
                 7                             √
                 0
                √7         √

             √−7                    √

                                                             (4)

1.3
1.3.1                                                        (1)
        0,7 =

1.3.2                                                        (1)
        0,13 =

1.3.3                                                        (1)
        2,01 =       =2

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

                                                                   2

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1.4.2    0,007                                                                     (2)
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
1.6.1    0,152, 0,153, 0,154 enige een van die drie                                (1)
1.6.2    0,71; 0,72;     0,73;    0,74;       0,75;   0,76;   0,77 enige een
         van die sewe                                                              (1)

1.7.1    2 en 3                                                                    (2)
1.7.2    4 en 5                                                                    (2)
1.7.3    1 en 2                                                                    (2)
1.7.4    4 en 5                                                                    (2)

         NATUURLI        TELGETAL         HEELGE      RASIONA      IRRASIO     REËLE
         KE GETAL                         TAL         LE GETAL NALE            GETAL
                                                                   GETAL
 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       < − <− <                       (1)

1.9.5   −0, 12 < −0,11 < ̇−0,1 < −0,01̇    (1)

                                                 4

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FINANSIëLE WISKUNDE

1.1.       Verkoopsprys = 22 × 1,50 = 33                            (3)
           Wins = Verkoopsprys - kosprys = 33 − 20 = 13

1.2.1
a)         18%           75 000 = 13 500                            (2)
b)         Belasting = 12 000 + 20%        ( 97 500 − 80 000)
                     = 12 000 + 2 100
                     = 14 100                                       (2)

c)         Belasting = 20 000 + 25%         30 000
                     = 27 500                                       (2)

d)         Belasting = 42 000 + 35%         80 000                  (2)
                     = 70 000

1.2.2
Belasbare                 R140 000           R100 000    R230 000
inkomste
Belasting                 R25 000            R16 000     R45 500

1.3        Vermeerdering : 1 740 − 1500 = 240                        (2)

           % vermeerdering =          × 100 = 16

1.4             = (1 +    )
                = 1500(1 + 2(0,11))
                 = 1 830
           of

                                                                           5

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                          × ×
        ER =      =                     = 330

                                                      (2)
        Totale bedrag =         1500 + 330 = 1 830

1.5.1   Belegging = (1 + )
                                             ,
                  = 2 750 1 +

                      = 5 891,92
                                                      (3)

1.5.2   Rente verdien = 5 891,92 − 2 750 = 3 141,92   (1)
1.6
1.6.1    = (1 + )
                                         ×
          = 9500 1 +            ×

          = 24 463,29
        Rente =       24 463,29 − 9 500
                                                      (4)
               = 14 963,29
1.6.2    = (1 + )
                                        ×
         = 9500 1 +             ×

         = 17 793,32
        Rente = 17 793,32 − 9 500
                                                      (4)
               = 8293,32

1.6.3    = (1 + )
                                    ,        ×
          = 9500 1 +                ×

           = 15 956,86
        Rente = 15 956,86 − 9 500
               = 6456,86
                                                      (4)
1.6.4    = (1 + )
                            ,
          = 9500 1 +

           = 16630,37

                                                            6

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      Rente = 16630,37 − 9 500
                = 7130,37                                                    (4)

VERHOUDING EN KOERS

1.1   Spoed =               = 300   /ℎ                                         (3)

1.2                                                                            (3)
       Minute           2       4            6           8           20
       Koste            R1,60   R3,20            4,80        6,40   R16,00

1.3
       Aantal mans                   Tyd
                    5                   45
                    9

                ×
           =            = 25ℎ

      of
      Tyd geneem deur 5 mans = 45ℎ
      Tyd geneem deur 1 man = (45 × 5)ℎ
                                                  ×
      Tyd geneem deur 9 mans =                          = 25ℎ                  (3)
1.4                                                                            (3)
              Tyd           Aantal ure
               8                3
               2
      2 =8×3
         = 12
      of
      In 8 ure aantal werkers = 3
      In 1 uur aantal werkers = 3 × 8
      In 2 ure aantal werkers = 3 × 8 ÷ 2
                            = 12

                                                                                     7

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1.5                                                    (2)
          AANTAL kg                      KOSTE in R
              3                             24
              7

              =
                              ×
             =
        Koste = 56

        of
        Koste van 3                = 24
        Koste van 1                = 24 ÷ 3
        Koste van 7                = 8×7
                                  = 56

1.6.1   Direk eweredig.                                (1)
1.6.2    =5                                            (1)
1.6.3    = 5(25) = 125                                 (1)
1.7
          KOSTE in R                     AANTAL
                                         APPELKOSE
              5,60                           15
              10,08

                      ,
          =       ,
                  ,           ×
         =                                             (3)
                          ,
         = 27

1.8                                  ,                 (3)
        Koste per =                       =   8,65

1.9
          AANTAL kg                       KOSTE in R
             0,35                           25,10
              1
            = ,
          ,
             =
             = 71,714 …                                (3)
        Koste ~ 71,71

                                                             8

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1.10
               Aantal kg     Koste in R
                 12,5           90
                 17,2
                   ,
                = ,
                      , ×
                =        ,
       Koste= R51,84                         (3)
1.11    Afstand in            Aantal
                    130         6,5
                    80

           =
       ,
                × ,
           =

           =4
       Aantal         =4                     (3)
1.12
               AANTAL        AANTAL
                    5           40
                    1

           =
                ×
           =                                 (3)
           =8

                                                   9

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SPOED/TYD/AFSTAND

1.1         × =
      120 × = 600
                  =      ℎ

                  =5ℎ
                                                          (2)
      ∴ tyd is 5 ure.
1.2        × =
       × 8 = 600
             =          km/h.

             = 75 km/h.
                                                          (2)
      ∴ Spoed is 75 km/h.

2.                        S (km/h)     T (h)   A (km)
       Kar                100          x       100x
       Vliegtuig          300          6-x     300(6-x)

         100 + 300(6 − ) = 1200
       100 + 1800 − 300 = 1200
                             −200 = −600
                                  =3

      Tyd geneem deur vliegtuig = (6 − 3)ℎ
                                     = 3ℎ                 (3)

3.     = (120 × 1,5) km = 180 km
                  ,
        =               km/h = 125 km/h
              ,

       =              ℎ = 3ℎ

                                                          (3)

                                                                10

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4.                      S (km/h)     T (h)   A (km)
      Stap                      5    0,5         2,5
      Fiets                          0,25      0,25
       = ×
       = (5 × 0,5) km
       = 2,5 km
       × 0,25 = 2,5
                    ,
              = ,
                                                       (3)
              = 10 km/h
5.1   Gemiddelde spoed =            km/h
                                                       (3)
                          = 7,5 km/h

5.2   Afstand = ×
              = (7,5 × 6) km
              = 45 km
                                                       (1)

6         × =                                          (3)
      ( + 20) =

              t=            ℎ

                                                             11

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EKSPONENTE

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

1.3                                                                                        (2)
                                   =                    =

1.4                                                 =
               (                           )
                                                                                           (3)
                                                    = −8
1.5

       =

       =

       =2                                                                                  (3)

1.6            .                   .
                           .
                       .       .               .
       =
                               .
       =

           =3
                                                                                           (4)
           =

1.7    (2                          )×                   = (2        )×       =   = 10

                                                                                      10
                                                                                  =        (3)

1.8    (               )(                  ) =                  =        =                 (1)

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

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

                                                                                                 12

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PATRONE, FUNKSIES EN ALGEBRA

1.
1.1   90 en 69                                                        (2)
1.2   36; 72; 108 ; 144; 180 ; 216                                    (2)
1.3   39; 48                                                          (2)
1.2
2.1   Tel 6 by.                                                       (1)
2.2     =6 −3                                                         (1)

2.3   6 − 3 = 45                                                      (1)
          6 = 48
               =8
               = 45

3.1                                                                   (2)
               Aantal      1   2      3      4    5    6       7
               panele
               Aantal      2   3      4      5    6    7       8
               pale
               Aantal      6   12     18     24   30   36      42
               plate
3.2     =      +1                                                     (2)
3.3     =6                                                            (2)
3.4      (        ) = 10 + 1 = 11                                     (2)
         (          ) = 6 × 10 = 60

4.             INVOER                 REËL             UITVOER
                1               −2 + 3                     1
                2                                       −1          (3)

                3                                       −3

                                                                          13

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5.
      INPUT                   REËL        UITVOER
              −2                            7
              −1                            1
              0           2    −1          −1
              1                             1
              2                             7
                                                    (5)
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                             (1)
6.4    = −2( + 2) + 6( + 2) − 8
      = −2(   + 4 + 4) + 6 + 12 − 8
      = −2    −8 −8+6 +4
      = −2    −2 −4                                 (4)
7.
7.1     =3 =1                                       (1)
7.2    = 3 = 27                                     (1)
7.3    =3     =                                     (1)

                                                      14

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PRODUKTE

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

1.13       (9    − 1) − (           − 1)

       =3        − −            +
                                                                     (6)
       =         +

1.14   4(       −    )−(        +     +        )

       =4        − −        −        −

       =3        −      −                                            (6)

1.15                −       − (            −       +        )

       =             − −              +2           −

       =2        −                                                   (6)

                                                                           15

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FAKTORE

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)
1.14   (        +       )(         −        )=(      +   )( + )( − )    (3)
1.15   (4           +        )(4        −        )                      (2)
1.16   3(           −9        ) = 3( + 3 )( − 3 )                       (3)
1.17       (        − 4) = ( − 2)( + 2)                                 (3)

1.18       (4       −         ) = (2 − )(2 + )                          (3)

       of
                         (         )(        )
                     =

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)

                                                                              16

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VERGELYKINGS

1.
1.1    6 = 24                                    (2)
               =4
1.2        ( − 3) = 0                            (3)
           = 0 of     =3
1.3    22 + 4 = 9 − 12
               7 = 16 of 16 = 7                  (2)

                 =            =

1.4    × 36: 9( − 5) − 4(3 − 4 ) = 468
                    9 − 45 − 12 + 16 = 468
                                      25 = 525   (3)
                                         = 21
1.5    × 15: 45 + 3 + 195 = 5(2 + 1)
                         48 + 195 = 10 + 5
                               38 = −190
                                  = −5           (4)

1.6    5 =5
       ∴       =4

                                                 (4)
1.7    2       =2
       ∴− =5                                     (2)
                = −5
1. 8       3        =3
       ∴       +1 =4                             (2)
                    =3
2.1        +    +1+        + 2 = 78              (2)
                         3 + 3 = 78
                            3 = 75
                               = 25

                                                       17

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      Die getalle is 25; 26; 27

2.2
                                 OUDERDOM           OUDERDOM
                                                    OOR 4 JAAR
       Ben                                               +4
       Patrick                               5         5 +4      (4)
      5 + 4 = 3( + 4)
      5 + 4 = 3 + 12
          2 =8
             =4
      Ben is 4 jaar oud en Patrick is 20 jaar oud.
2.3   Oppervlakte = ×
      −12      +6        = −6            ×

                         =
                                     (          )
                         =

                         = (2            − 1)

                                                                 (4)
2.4   Oppervlakte = ×
      2    − 8 = × ( + 2)

                 =
                     (       )
                 =
                     (    )(     )
                 =                                               (3)

                 = 2( − 2)
2.5       =2
          Oppervlakte = ×                 = 32
      2 ×      = 32

                                                                       18

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          2    = 32
              = 16
              = ±4
              =4       (want   > 0)
      ∴   =4       en = 2(4) = 8             (5)

ONGELYKHEDE

1.
1.1

                                            (2)

1.2
                       •                    (2)

1.3                                         (2)
                   •       •   •

1.4
                                            (2)

                                                   19

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1.5

                             •                       •         •                (2)

2.

                                                                                (2)
2.1    < 2 en                    ∈

                                                                                (2)

2.2   3≤        ≤ 7 en               ∈                                          (2)

2.3   √3 ≤          < 2,1 en                 ∈                                  (2)

2.4   −3 ≤          ≤ 0 en               ∈           of −4 <       < 1 en   ∈   (2)
2.5    < −2 of               ≥0              ∈                                  (2)

ALGEBRA ̈ ESE BREUKE

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

1.4     (       )                                (       )                      (5)
                    ×                    ×
                             (       )
            (       )(           )
       =        (        )

1.5        + =               =                                                  (1)

                                                                                      20

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1.6   (           )        (            )                                  (3)

      =

      =

1.7   (               )        (        )                                  (4)

      =

      =
              (                )
      =
          (                )
      =

1.8   (       ) (                  )(       )                              (4)
                                                =
          (           )(            )                (        )(       )

                                                =(       )(        )

                                                                                 21

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GRAFIEKE

1.
1.1

                      2
                      3

                                         (4)

                                         22

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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)

                                         23

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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)

                                                                            24

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RUIMTE EN VORM

1.1
      A. Trapesium
      B. Oktogoon/agthoek
      C. Driehoek
      D. Reghoek
      E. Parallellogram                                        (5)
1.2   A. Silinder
      B. Reghoekige-basis piramide
      C. Kubus
      D. Driehoekige piramide                                  (4)
2.1                                                            (1)
2.2   70° Oos van Noord of 20° Noord van Oos of 70° Noord      (2)
3.    In ∆        en ∆
                    =             = 90°     ( gegee)
                  is gemeenskaplik
                  =                         (gegee)
        ∴∆            ≡∆                  ( 90°,       ,   )   (5)

4.           +          =                   (Pyth)
             + (3) = (5)
             = 25 − 9                 ℎ
             = 16             ℎ
             =4e          ℎ                                    (5)
             =        −
         = 4 − √7
             =          +                 (Pyth)
             =7+9                 ℎ
             = 16         ℎ
             =4           ℎ

                                                                     25

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5.             +       = 180°                              (ko-binne <    , KL||NM)
          + 120° = 180°
                        = 60°
      +        +        = 180°                          (som van<        van ∆)
     Maar               =                             (<    teenoor gelyke sye
     van ∆)
              +2        = 180°
      60° + 2               = 180°
                    2        = 120°
                   ∴         = 60°
          +     +           = 180°                    (som van<       van ∆)
     maar                    =                        (<    teenoor gelyke sye
     van ∆)
               +2           = 180°
      120° + 2               = 180°
                        2       = 60°
                    ∴           = 30°
          +        +         = 180°                   (Suppl.<
                                                                             <)
     60° +          + 30° = 180°
                                   = 180° − 90° = 90°                                 (4)
6.                                 =
     (<       teenoor gelyke sye)
     40° +              +          = 180°                   (som van<       van ∆)
                            2      = 180° − 40°
                            2      = 140°
                                     = 70°
                                   =          = 70°         (verw < ,       ||    )
                        +            = 180°
     (Suppl.<                                                    <)
                                     = 180° − 70°
                                                                                      (6)
                                        = 110°

                                                                                            26

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7.1   In ∆           en ∆                                                           (4)
                     =                           (gemeenskaplike sy)
                     =                         (verw. < ,          ||           )
                     =                      (verw. < ,       ||         )
        ∴∆               ≡∆                      (<, <, )
             ∴           =       =            (ooreenk sye van
      kongruente ∆ )

7.2   In ∆           en ∆                                                           (4)
                     =                          (bewys)
                     =                         (verw < ,          ||        )
                     =                      (verw. < ,      ||         )
        ∴∆               ≡∆                     (<, <, )
             ∴           =       =           (ooreenk sye van kongruente
      ∆ )

7.3   Die hoeklyne van ‘n parallelogram halveer mekaar                              (1)
8.      =            =       =       (ewer. sye van gelykvormige                    (6)

      vierhoeke)
        =
                 ×
            =        = 2,25

         =

                 ×
             =           = 24

                                                                                    (6)

9.    In ∆           en ∆
                         =                  (verw <         ||         )
                         =                  (verw < ,       ||         )

                                                                                          27

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                       =                      ( regoorstaande < )
             ∆       ||| ∆                    (<, <, <)                     (5)

         ∴       =     =         ∆       (ewer. sye van gelykvormige ∆ )

         ∴ =

                       =9
                             ,
                       =

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

TRANSFORMASIES

1.                                                                         (1)
1.1   (−1; −4)                                                             (1)
1.2   (3; −6)                                                              (1)
1.3   (−3; −4)                                                             (1)
1.4   (−4; 3)                                                              (4)
2.    Refleksie in die Y-as
      Vertikale translasie                                                 (2)
3.1   Refleksie in die Y-as.

                                                                           (4)
3.2   Refleksie in die Y-as en dan refleksie in die X-as of                (3)
      refleksie in die X-as en dan refleksie in die Y-as .

4.     ′(−6; 9) ; ′(3; 15) ; ′(15; −6)                                     (1)

5.1

                                                                                  28

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                                                          (1)

5.2

                                                          (1)

METING

1.
1.1      Oppervlakte van ∆   =   ℎ = × 3 × 4 cm = 6 cm    (2)

1.2      Oppervlakte van ∆   =   ℎ = × 6 × 4 cm = 12 cm   (3)

1.3      Oppervlakte van ABEG = (    +    )               (3)

                                                                29

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                                        = (9 + 6)4 cm

                                        = 30 cm

1.4     Oppervlakte van BDEG=                   × ℎ = 6 × 4 = 24 cm   (3)
1.5         =       +                   (Pyth.)
             = 3 + 4 cm
             = 9 + 16 cm
             = 25 cm
        ∴    = 5 cm
1.6.1   Omtrek van ∆            = (5 + 5 + 6) cm = 16 cm              (2)
1.6.2   Omtrek van ADEG = (9 + 5 + 6 + 4) cm = 24 cm                  (4)
2.          =       +                       (Pyth)
             = 49 + 120             ℎ
             = 169          ℎ
             = 13       ℎ
        Area =

              =( ×       ×          )       ℎ

             = 66,36            ℎ                                     (3)

3.1     Totale buite-oppervlakte
             = 2(8 × 12) + 2(12 × 18) + 2(8 × 18) cm = 912 cm         (6)
3.2     Volume= ×        ×ℎ
                = (8 × 12 × 18) cm
                 = 1728 cm                                            (3)
4.      Volume van silinder =               ℎ
                        550 =           × (5) × ℎ
                                        ×
                            ℎ=              cm
                                    ×( )

                            ℎ = 7cm                                   (4)
5.      Volume= ×        ×ℎ
        50 × 30 × ℎ = 24000 cm

                                                                            30

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                   ℎ=             cm
                         ×

                   ℎ = 16 cm
                                                        (3)

DATAHANTERING

1.
1.1     20 30 30 40 50 50 60 70 70 70 70 80 80 90 100   (1)
1.2
1.2.1   Mediaan = 70                                    (1)
1.2.2   Modus = 70                                      (1)
1.2.3   Omvang = 100 − 20 = 80                          (1)
1.2.4   Gemiddeld =     = 60,67 tot 2 desimale plekke   (2)

2.
2.1     24 passasiers                                   (1)
2.2     Omvang= 70 − 1 = 69                             (1)
2.3     Gemiddeld =     = 26,7 = 27                     (3)

2.4
         OUDERDOM        TELMERKIES        FREKWENSIE
         IN JARE
         1 - 13          |||| ||           7
         14 - 26         |||               3
         27 - 39         |||| |||          8
         40 - 70         |||| |            6            (4)

2.4.1   27-39                                           (1)

                                                              31

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2.4.2   18 passasiers                                          (1)
3.
3.1     22                                                     (1)
3.2     Omvang= 15 − 2 = 13                                    (1)
3.3      SKOENGROOTTES TELMERKIES                 FREKWENSIE
         1-5                  ||||                4
         6 - 10               |||| |||| ||        12
         11 - 15              |||| |              6            (4)

4.
4.1     18 babas                                               (2)
4.2     15 babas                                               (1)
4.3     11-15 maande                                           (1)
5.                                                             (2)
5.1
        DOBBLESTEEN MUNTSTUK                 UITKOMSTE
        1               K                    1K
                        S                    1S
        2               K                    2K
                        S                    2S
        3               K                    3K
                        S                    3S
        4               K                    4K
                        S                    4S
        5               K                    5K
                        S                    5S
        6               K                    6K
                        S                    6S

                                                               (6)

                                                                     32

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5.2

                   1            K
                                S
                   2            K
                                S
                   3            K
                                S
                   4            K
                                S
                   5            K
                                S
                   6            K
                                S             (2)

5.3.1

                                              (1)
5.3.2       =                                 (1)

6                                             (1)
6.1                                           (1)

6.2                                           (1)

6.3         =

7.                                            (1)
7.1         =                                 (1)

7.2         =

8.                                            (1)
8.1     3

                                              (1)
8.2.1                                         (1)

                                                    33

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8.2.2   =                                      (1)

8.2.3                                          (1)

                                               (1)

9.                                 K

                           K
                                       S

                   K               K
                           S
                                       S
                           K           K

                                           S
                       S
                                       K
                               S
                                           S   (4)

                                                     34

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