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MATHEMATICAL LITERACY
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Antwoorde  / Answers  1

1.1  A = 3; B = ││││
C = ┼┼┼┼ en D = 1.
[ V 1.1 ]

1.2  Die data is diskreet. 'n Leerling
kan net 'n heelgetal punte hê
'n Leerling kan 3 punte hê, maar
nie 3,2 punte nie. Uitsondering
is waar punte uit bv. 10 gegee
word maar die oorspronklike punt
is uit bv, 100
[ V 1.2 ]

1.3  Die swakste punt is 1 en
die hoogste punt is 9.
[ V 1.3 ]

1.4  4 leerlinge het 2 punte.
[ V 1.4 ]

1.5  Die frekwensie van 6 punte is 2
[ V 1.5 ]

1.6  1, 3 en 5 punte het 'n
frekwensie van 3.
[ V 1.6 ]

1.7  Die laagste frekwensie is 1 en
dit is die frekwensie van 8 punte.
[ V 1.7 ]

1.8  Die hoogste frekwensie is 5 en
dit is die frekwensie van 7 punte.
[ V 1.8 ]

1.1  A = 3; B = ││││
C = ┼┼┼┼ and D = 1.
[ Q 1.1 ]

1.2  The data is discrete. A pupil can
only have a whole number of marks.
A Pupil can have 3 marks but not
3,2 marks. An exception is where
marks are allocated out of 10 but
the original mark is given out
of 100.
[ Q 1.2 ]

1.3  The lowest mark is 1 and the
best mark is 9.
[ Q 1.3 ]

1.4  4 pupils have 2 marks.
[ Q 1.4 ]

1.5  The frquency of 6 marks is 2.
[ Q 1.5 ]

1.6  1, 3 and 5 marks have a
frequency of 3.
[ Q 1.6 ]

1.7  The lowest frequency is 1 and
that is the frequency of 8 marks.
[ Q 1.7 ]

1.8  7 marks have the highest
frequency which is 5.
[ Q 1.8 ]

Antwoorde  / Answers  2

2.1  A = ┼┼┼┼  en B = 5
[ V 2.1 ]

2.2  Die data is diskreet. Die dobbelsteen
vertoon net heelgetalle.
[ V 2.2 ]

2.3  Die frekwensie van 1 = 3
[ V 2.3 ]

2.4  Die getal 3 het 'n frekwensie van 4
[ V 2.4 ]

2.5  Getal 2 verskyn die meeste omdat
sy frekwensie die hoogste is.
[ V 2.5 ]

2.6  Getal 5 verskyn die minste omdat
sy frekwensie die laagste is.
[ V 2.6 ]

2.1  A = ┼┼┼┼  and B = 5.
[ Q 2.1 ]

2.2  The data is discrete.
The die shows only whole numbers.
[ Q 2.2 ]

2.3  The frequency of 1 = 3.
[ Q 2.3 ]

2.4  The number 3 has a frequency of 4.
[ Q 2.4 ]

2.5  Number 2 appeared most because
it has the highest frequency.
[ Q 2.5 ]

2.6  Number 5 appeared least because
it has the lowest frequency.
[ Q 2.6 ]

Antwoorde  / Answers  3

 Massa / Mass Telling / Tally Frekwensie, f / Frequency, f 45 ─ 49 ┼┼┼┼  ┼┼┼┼  │ 11 50 ─ 54 ┼┼┼┼  │ 6 55 ─ 59 ││││ 4 60 ─ 64 ┼┼┼┼  │ 6 65 ─ 69 │││ 3 70 ─ 74 ┼┼┼┼ 5
Σf = 35

[ V 3.1 ]

3.2  Die 45 is die onderste of laagste
klasgrens en die 49 is die
boonste of hoogste klasgrens.
Enige massa tussen 45 en 49,
beide ingesluit, hoort in die klas.
[ V 3.2 ]

3.3  Die 11 is die frekwensie van
daardie klas, 45 - 49.
Dit beteken dat daar 11
massas groter as 44 en
kleiner as 50 is.
[ V 3.3 ]

3.4  Die laagste of onderste klasgrens
is 45 en die boonste of hoogste
klasgrens is 48.
[ V 3.4 ]

3.5  Frekwensie van klas 65 - 69 is 3.
[ V 3.5 ]

3.6  Frekwensie van klas 55 - 59 is 4.
[ V 3.6 ]

3.7  Die laagste frekwensie is 3
en klas 65 - 69 het daardie
frekwensie.
[ V 3.7 ]

3.8  Die hoogste frekwensie is 11
en klas 45 - 49 het daardie
frekwensie.
[ V 3.8 ]

3.9  Ja omdat die massa korrek tot
die naaste kilogram aangeteken
is sodat die data uit heelgetalle
bestaan. Geen massa van
bv. 46,345 kg, alhoewel moontlik,
is aangeteken nie.
[ V 3.9 ]

3.2  The 45 is the bottom or lower
boundary and the 49 is the
upper or higher boundary.
Any mass between 45 and 49,
both included, belongs to this class.
[ Q 3.2 ]

3.3  The 11 is the frequency of that
class, 45 - 49.That means that there
are 11 masses greater than 44 and
smaller than 50

[ Q 3.3 ]

3.4  Lower/bottom boundary 45 and
upper/higher 49.

[ Q 3.4 ]

3.5  Frequency of class 65 - 69 is 3.
[ Q 3.5 ]

3.6  Frequency of class 55 - 59 is 4.
[ Q 3.6 ]

3.7  The smallest frequency is 3 and
that is the frequency of class 65 - 69.

[ Q 3.7 ]

3.8  The highest frequency is 11 and
that is the frequency of class 45 - 49.

[ Q 3.8 ]

3.9  Yes because the mass is noted correct
to the nearest kilogram, the data
consists of whole numbers. No mass
of e.g. 46,345 kg is noted,
although it can exist.

[ Q 3.9 ]

Antwoorde  / Answers  4

4.1

 Hoogte / Height Telling / Tally Frekwensie, f / Frequency, f 1,0 ─ 1,9 ┼┼┼┼  ││ 7 2,0 ─ 2,9 ┼┼┼┼  ┼┼┼┼  │ 11 3,0 ─ 3,9 ┼┼┼┼  ┼┼┼┼  │││ 13 4,0 ─ 4,9 ┼┼┼┼  │ 6 5,0 ─ 5,9 │││ 3
Σf = 35

[ V / Q 4.1 ]

4.2  Klas 3,0 - 3,9 het die
meeste bome, 13
[ V 4.2 ]

4.3  7 + 11 = 18 bome is
korter as 2 m.
[ V 4.3 ]

4.4  6 + 3 = 9 bome is
langerer as 4 m.
[ V 4.4 ]

4.2  Class 3,0 - 3,9 has the most
trees, 13.
[ Q 4.2 ]

4.3  7 + 11 = 18 trees
are shorter than 2 m.
[ Q 4.3 ]

4.4  6 + 3 = 9 trees
are taller than 4 m.
[ Q 4.4 ]

Antwoorde  / Answers  5

5.1

 Lengte / Height Telling / Tally Frekwensie, f / Frequency, f 1,00 ─ 1,19 │││ 3 1,20 ─ 1,39 ┼┼┼┼  ││ 7 1,40 ─ 1,59 ┼┼┼┼  ┼┼┼┼ 10 1,60 ─ 1,79 ┼┼┼┼  ┼┼┼┼  ┼┼┼┼  │ 16 1,80 ─ 2,00 ││││ 4
Σf = 40

[ V / Q 5.1 ]

5.2  Kleinste lengte = 1,12 m en
grootste lengte = 1,84 m
[ V 5.2 ]

5.3  Klas 1,00 - 1,19 het die
laagste frekwensie, 3
[ V 5.3 ]

5.4  3 + 7 = 10 leerlinge is
korter as 1,40 m
[ V 5.4 ]

5.5  1,60 maar kortste leerling
in die klas, volgens die tabel,
is 1,62 m.
[ V 5.5 ]

5.6  20 leerlinge is langer as 1,59 m.

20            100
Persentasie  =  ───  X  ─────  %
40              1
=  50  %
[ V 5.6 ]

5.2  Smallest length = 1,12 m and
greatest length = 1,84 m..
[ Q 5.2 ]

5.3  Class 1,00 - 1,19 has the smallest
frequency, 3.
[ Q 5.3 ]

5.4  3 + 7 = 10 pupils
are shorter than 1,40 m.
[ Q 5.4 ]

5.5  1,60 but according to the
tabel the shortest pupil
is 1,62 m.
[ Q 5.5 ]

5.6  20 pupils are taller than 1,59 m.

20            100
Percentage  =  ───  X  ─────  %
40              1
=  50  %
[ Q 5.6 ]

Antwoorde  / Answers  6

6.1

 Punt / Mark Telling / Tally Frekwensie, f / Frequency, f 0 ─ 19 │││ 3 20 ─ 39 ┼┼┼┼  │ 6 40 ─ 59 ┼┼┼┼  ┼┼┼┼  ┼┼┼┼  │ 16 60 ─ 79 ┼┼┼┼  │││ 8 80 ─ 100 ││ 2
Σf = 35

[ V / Q 6.1 ]

6.2  Laagste punt = 12 en
hoogste punt = 96
[ V 6.2 ]

6.3  26 leerlinge het meer
as 39 punte.
[ V 6.3 ]

6.4  2 leerlinge het meer
as 79 punte.
[ V 6.4 ]

6.5  24 leerlinge se punte is groter
as 39 en kleiner as 80
24        100
Persentasie  =  ─── X ────  %
35          1
=  68,56  %
[ V 6.5 ]

6.6  omvang  =  maksimum  ─  minimum
=  96  ─  12
=  84
[ V 6.6 ]

6.2  Smallest mark = 12 and
highest mark = 96.
[ Q 6.2 ]

6.3  26 pupils have more than
39 marks.
[ Q 6.3 ]

6.4  2 pupils have more than
79 marks.
[ Q 6.4 ]

6.5  24 pupils have marks more than
39 and less than 80.
24          100
Percentage  =  ───  X  ────  %
35            1
=  68,56  %
[ Q 6.5 ]

6.6  range  =  maximum  ─  minimum
=  96  ─  12
=  84
[ Q 6.6 ]

Antwoorde  / Answers  7

Antwoorde  / Answers  8

Antwoorde  / Answers  9

Antwoorde  / Answers  10

10.1

 LMI / BMI Telling / Tally Frekwensie, f / Frequency, f x < 18,5 ││││ 4 18,5 < x < 25 ┼┼┼┼  ┼┼┼┼  ┼┼┼┼  ┼┼┼┼ 20 25 < x < 30 ┼┼┼┼  ┼┼┼┼ 10 x > 30 ││││ 4
Σf = 40

[ V / Q 10.1 ]

10.2  Laagste punt = 12 en
hoogste punt = 96
[ V 10.2 ]

10.2  Lowest mark = 12 and
highest mark = 96
[ V 10.2 ]

Antwoorde  / Answers  11

943,4 ????
11.1  Gemiddelde / Mean  =  ──────
40

=  23,6                                                            [ V / Q 11.1 ]

11.2

 LMI / BMI Telling / Tally Frekwensie, f / Frequency, f 17,0 ─ 18,5 ││││ 4 18,5 ─ 25,0 ┼┼┼┼  ┼┼┼┼  ┼┼┼┼  ┼┼┼┼ 20 25,0 ─ 30,0 ┼┼┼┼  ┼┼┼┼ 10 30,0 ─ 40,0 ││││ 4
Σf = 40

[ V / Q 11.2 ]

11.3  Die gemiddelde gewig val in
die normale gewig kategorie.
[ V 11.32 ]

11.4.1  6 leerlige is onder gewig.
6        100
Persentasie  =  ─── X ─── %
40          1
=  15 %
[ V 11.4.1 ]

11.4.2  20 leerlige is normale gewig.
20        100
Persentasie  =  ─── X ─── %
40          1
=  50 %
[ V 11.4.2 ]

11.4.3  10 leerlige is geset.
10        100
Persentasie  =  ─── X ─── %
40          1
=  25 %
[ V 11.4.3 ]

11.4.4  4 leerlige is geset.
4        100
Persentasie  =  ─── X ─── %
40          1
=  10 %
[ V 11.4.4 ]

11.3  The mean weight falls in the
normal weight category.
[ Q 11.3 ]

11.4.1  6 pupils are under weight.
6            100
Percentage  =  ───  X  ──── %
40             1
=  15 %
[ Q 11.4.1 ]

11.4.2  20 pupils have normal weight.
20          100
Percentage  =  ───  X  ──── %
40             1
=  50 %
[ Q 11.4.2 ]

11.4.3  10 pupils are obese.
10          100
Percentage  =  ───  X  ──── %
40             1
=  25 %
[ Q 11.4.3 ]

11.4.4  4 pupils are over weight.
4            100
Percentage  =  ───  X  ──── %
40             1
=  10 %
[ Q 11.4.4 ]

Antwoord  / Answer  12

12.1   12   13   18   23   29   32   34   37   38   42   43   45   45   47   52   54   54   54
56   56   57   58   58   59   59   61   62   63   63   64   67   74   78   86   96
[ V / Q 12.1 ]

12.2  kleinste / lowest  =  12  en / grootste / highest  =  96                                 [ V / Q 12.2 ]

12.3  omvang / range  =  grootste / highest  ─  kleinste / lowest
=  96  ─  12
=  84                                                                             [ V / Q 12.3 ]

som van al die punte / sum of all the marks
12.4  Rekenkundige gemiddelde / Mean  =  ─────────────────────────────
aantal puntee / number of marks

1789
=  ─────
35

=  51,114                                             [ V / Q 12.4 ]

12.5  Die mediaan is die waarde presies in die middel /
The median is the value exactly in the middle.

Die mediaan / The median  =  54                                                               [ V / Q 12.5 ]

12.6  Die modus is die waarde wat die meeste voorkom. /
The mode is the value that has the highest frequency / that appears most often.

Die modus  =  54  . . . kom die meeste, drie keer, voor  /
The mode  =  54  . . . appears most often, three times
[ V / Q 12.6 ]

Antwoord  / Answer  13

13.1   31   32   33   37   38   42   42   42   45   46   53   55   58   61   67           [ V / Q 13.1 ]

 13.2 Stingel / Stem Blare / Leaves 3 1   2   3   7   8 4 2   2   2   5   6 5 3   5   8 6 1   7

[ V / Q 13.2 ]

13.3  Minimum  =  31  ;   Maksimum / Maximum  =  67                                 [ V / Q 13.3 ]

13.4  Omvang / Range  =  Maksimum / Maximum  ─  Minimum
=  67  ─  31
=  36                                                                      [ V / Q 13.4 ]

som van al die punte / sum of all the marks
13.5  Rekenkundige gemiddelde / Mean  =  ─────────────────────────────
aantal punte / number of marks

682
=  ─────
15

=  45,467                                      [ V / Q 13.5 ]

13.6  Mediaan / Median  =  42                                                                    [ V / Q 13.6 ]

13.7  Modus / Mode  =  42                                                                         [ V / Q 13.7 ]

Antwoord  / Answer  14

14.1   43   46   47   49   51   53   53   53   55   55   55   55   55   57   59   60   66
66   70   78                                                                                       [ V / Q 14.1 ]

 14.2 Stingel / Stem Blare / Leaves 4 3   6   7   9 5 1   3   3   3   5   5   5   5   5   7   9 6 0   6   6 7 0   8
[ V / Q 14.2 ]

14.3  Minimum  =  43  ;   Maksimum / Maximum  =  78                                 [ V / Q 14.3 ]

14.4  Omvang / Range  =  Maksimum / Maximum  ─  Minimum
=  78  ─  43
=  35                                                                      [ V / Q 14.4 ]

som van al die punte / sum of all the marks
14.5  Rekenkundige gemiddelde / Mean  =  ─────────────────────────────
aantal punte / number of marks

1 126
=  ─────
20

=  5,300                                      [ V / Q 14.5 ]

14.6                                    55 + 55
Mediaan / Median  =  ───────
2

=  55                                                                     [ V / Q 14.6 ]

14.7  Modus / Mode  =  55                                                                          [ V / Q 14.7 ]

Antwoord  / Answer  15

15.1   5   6   9   12   12   14   14   14   14   16   17   17   25   25   27   30
[ V / Q 15.1 ]

15.2  Minimum  =  5  ;   Maksimum / Maximum  =  30                                 [ V / Q 15.2 ]

15.3  Omvang / Range  =  Maksimum / Maximum  ─  Minimum
=  30  ─  5
=  25                                                                      [ V / Q 15.3 ]

som van al die punte / sum of all the marks
15.4  Rekenkundige gemiddelde / Mean  =  ─────────────────────────────
aantal punte / number of marks

257
=  ─────
16

=  16,063                                      [ V / Q 15.4 ]

15.5                                    14 + 14
Mediaan / Median  =  ───────
2

=  14                                                                     [ V / Q 15.5 ]

15.6  Modus / Mode  =  14                                                                          [ V / Q 15.6 ]

Antwoord  / Answer  16

Omvang / Range  =  Maksimum / Maximum  ─  Minimum / Minimum
18  =  23  ─  a
a  =  23  ─  18
a  =  5

som van al die punte / sum of all the marks
Rekenkundige gemiddelde / Mean  =  ─────────────────────────────
aantal punte / number of marks

126
b  =  ─────
9

=  14

c  =  126  ─  (5   7   9   14   16   17   20   23)
=  15
a = 5 ;   b  =  14   en / and   c  =  15
[ V / Q 16 ]

Antwoord  / Answer  17

Omvang / Range  =  Maksimum / Maximum  ─  Minimum / Minimum
c  =  88  ─  35
=  53

som van al die punte / sum of all the marks
Rekenkundige gemiddelde / Mean  =  ─────────────────────────────
aantal punte / number of marks

880
d  =  ─────
16

=  55

49 + b
Mediaan / Median  =  ─────      . . .  ewe aantal waardes  /  even number of values
2

49 + b
50  =  ─────      . . .  ewe aantal waardes  /  even number of values
2

b  =  2 X 50  ─  49
=  51

a  =  880  ─  (35 + 36 + 38 + 39 + 43 + 45 + 49 + 51 + 53 + 55 + 61 + 68 + 73 + 79 + 87 + 88)
=  39
a = 39 ;   b  =  51 ;   c  =  53   en / and   d  =  55
[ V / Q 17 ]

Antwoord  / Answer  18

18.1  Gerangskik / Arranged   :    7    8    9    10    11    11    14          [ V / Q 18. ]

18.2  Minimum = 7 ;      Maksimum / Maximum =  14                           [ V / Q 18. ]

18.3  Omvang / Range  =  Maksimum / Maximum   ─   Minimum

=  14  ─  7

=  7                                                                 [ V / Q 18. ]

7 + 8 + 9 + 10 + 11 + 11 + 14             70
18.4  Gemiddelde / Mean  =  ───────────────────     =  ───
7                                       7

=  10                                                          [ V / Q 18. ]

18.5  Mediaan / Median  =  10  . . . middelste waarde  /  midmost value

[ V / Q 18. ]

18.6  Modus = 11  (2 waardes)    /  Mode   =  11     (2 values)             [ V / Q 18. ]

18.7  3 dae   /   3 days    gemiddelde / mean =  10                              [ V / Q 18. ]

18.8  1 dag   /   1 day    modus / mode =  11                                        [ V / Q 18. ]

18.9  3 dae   /   3 days    mediaan / median =  10                                [ V / Q 18. ]

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