WISKUNDIGE GELETTERDHEID
GRAAD 12
NOG OEFENINGE

Koers, verhouding en eweredigheid.

MATHEMATICAL LITERACY
GRADE 12
MORE EXERCISES

Rate, ratio and proportion.

Vraag  / Question  1

Verdeel

1.1  R35 in die verhouding 3 : 4.
Antwoord  1.1

1.2  45 lekkers in die verhouding 2 : 3 : 4.
Antwoord  1.2

1.3  R34 500 in die verhouding 2 : 8 : 15.
[ Ant. 1.3 ]

Divide

1.1  R35 in the proportion 3 : 4.
Answer 1.1

1.2  45 sweets in the proportion 2 : 3 : 4.
Answer 1.2

1.3  R34 500 in the proporion 2 : 8 : 15.
[ Ans. 1.3 ]

Vraag  / Question  2

Vermeerder

2.1  'n lengte van 21,6 m in die
verhouding 4 : 7.             Antwoord  2.1

2.2  'n wins van R3 672 in die
verhouding 4 : 5.              Ant.  2.2

2.3  'n massa van 91,2 kg in die
verhouding 7 : 5.                        [ A 2.3 ]

Increase

2.1  a length of 21,6 m in the
proportion 4 : 7            Answer 2.1

2.2  a profit of R3 672 in the
proportion 4 : 5.            Ans. 2.2

2.3  a mass of 91,2 kg in the
proportion 7 : 5.                    [ A 2.3 ]

Vraag  / Question  3

Jan draf 5 km in 25 minute.

3.1  Hoe lank neem dit hom om 2 km
te draf?                                     [ A 3.1 ]

3.2  Hoe ver kan hy in 65 minute
draf?                                        [ A 3.2 ]

John jogs 5 km in 25 minutes.

3.1  How long does he take to jog
2 km?                                  [ A 3.1 ]

3.2  How far can he jog in 65
minutes?                              [ A 3.2 ]

Vraag  / Question  4

Marie verdien R30 per uur. Sy werk elke
weeksdag, Maandag tot Vrydag, vir 8
uur per dag.

4.1  Bereken haar weeklikse loon.
[ A 4.1 ]

4.2  Hoeveel uur moet sy werk om
R1 770 te verdien?                     [ A 4.2 ]

4.3  Sy het R870 verdien. Hoe lank
het sy gewerk?                         [ A 4.3 ]

Mary is paid R30 per hour. She works
every day from Monday to Friday, 8
hours per day.

4.1  Calculate her weekly wages.
[ A 4.1 ]

4.2  How many hours does she have to
work to earn R1 770?              [ A 4.2 ]

4.3  She earned R870. How many hours
did she work?                         [ A 4.3 ]

Vraag  / Question  5

'n Motor verbruik 47,32 liter petrol
om 613 km te ry.

5.1  Bereken die motor se brandstofverbruik
in km/liter en ook in liter/100 km.
[ A 5.1 ]

5.2  Hoe ver kan die motor ry as dit 21,4 ℓ
petrol teen dieselfde brandstofverbruik
verbruik?                                          [ A 5.2 ]

5.3  Hoeveel liter petrol sal die motor
verbruik om 430 km te ry?                [ A 5.3 ]

A motor car uses 47,32 litres of petrol to
travel 613 km.

5.1  Calculate the fuel consumption of the
car in km/litre (km/ℓ) and also in
litres/100 km (ℓ/100km).               [ 5.1 ]

5.2  How far can the car travel using
21,4 ℓ of petrol at the same fuel
consumption?                               [ A 5.2 ]

5.3  How many litres of petrol will the car
use to travel 430 km?                   [ A 5.3 ]

Vraag  / Question  6

'n Plan van 'n gebou is geteken op
'n skaal van 1 : 50.

6.1  Watter afstand in die gebou word
voorgestel deur 'n afstand van

6.1.1  2 cm op die plan?                 [ A 6.1.1 ]

6.1.2  35 mm op die plan?              [ A 6.1.2 ]

6.1.3  0,35 m on die plan?              [ A 6.1.3 ]

6.2  Watter afstand op die plan word
voorgestel deur 'n afstand
van . . .   in die gebou?

6.2.1  35,4 m                                     [ A 6.2.1 ]

6.2.2  0,4 m                                       [ A 6.2.2 ]

6.2.3  1,26 m                                     [ A 6.2.3 ]

A plan of a building is drawn to a scale
of 1 : 50.

6.1  What distance in the building is
represented by a distance of

6.1.1  2 cm on the plan?                 [ A 6.1.1 ]

6.1.2  35 mm on the plan?              [ A 6.1.2 ]

6.1.3  0,35 m on the plan?               [ A 6.1.3 ]

6.2  What distance on the plan is
represented by a distance
of    . . .   in the building?

6.2.1  35,4 m                                   [ A 6.2.1 ]

6.2.2  0,4 m                                     [ A 6.2.2 ]

6.2.3  1,26 m                                   [ A 6.2.3 ]

Vraag  / Question  7

Die digtheid van 'n stof word

gedefinieer deur:
massa
digtheid van stof   =   ───────
volume

7.1  Watter hoeveelheid is direk eweredig

aan massa? Verduidelik.            [ A 7.1 ]

7.2  Die massa van 1 liter water is 1 kg.

Bereken die digtheid van

water in g/cm3                         [ A 7.2 ]

7.3  Die digtheid van goud is 19,3 g/cm3

7.3.1  Bereken die massa van 6 cm3

goud.                                   [ A 7.3.1 ]

7.3.2  Bereken die volume van 413,02 g

goud.                                   [ A 7.3.2 ]

7.3.3  Daar word beweer dat 'n ring met

massa 41,2 g en 'n volume van 2,4 cm3

van suiwer goud gemaak is. Is die

bewering korrek? Verduidelik jou

antwoord.                             [ A 7.3.3 ]

7.4  Die massa van 'n blokkie lood is 24,97 g

en die volume van die blokkie is 2,2 cm3

7.4.1  Bereken die digtheid van lood.
[ A 7.4.1 ]

7.4.2  'n Tweede blokkie van lood het 'n

massa van 181,6 gram. Bereken die

volume van die blokkie.
[ A 7.4.2 ]

7.4.3  'n Kubus is van lood gemaak.

Die lengte van 'n sy is 2 cm. Bereken

die massa van die kubus.      [ A 7.4.3 ]

The density of a substance is defined

as:
mass
density of substance   =   ──────
volume

7.1  Which quantity is directly proportional

to mass? Explain.                     [ A 7.1 ]

7.2  The mass of 1 litre of water is 1 kg.

Calculate the density of water

in g/cm3                                 [ A 7.2 ]

7.3  The density of gold is 19,3 g/cm3

7.3.1  Calculate the mass of 6 cm3

gold.                                 [ A 7.3.1 ]

7.3.2  Calculate the volume of 413,02 g of

gold.                                  [ A 7.3.2 ]

7.3.3  It is claimed that a ring with a mass

of 41,2 g and a volume of 2,4 cm3 is

made from pure gold. Is the claim

correct? Explain your answer.

[ A 7.3.3 ]

7.4  The mass of a block of lead is

24,97 g and the volume of the

block is 2,2 cm3

7.4.1  Calculate the density of lead.

[ A 7.4.1 ]

7.4.2  A second lead block has a mass of

181,6 gram. Calculate the volume

of the block.                       [ A 7.4.2 ]

7.4.3  A cube is made of lead. The length of

a side is 2 cm. Calculate the mass

of the cube.                       [ A 7.4.3 ]

Vraag  / Question  8

'n Pakkie pieangs, met massa

1,34 kg, kos R26,91.

8.1   Bereken die prys van piesangs

per kilogram.                            [ A 8.1 ]

8.2   Wat sal 2,44 kg piesangs kos?

[ A 8.2 ]

8.3   'n Pakkie piesangs kos R8,63.

Wat is die massa van die pakkie?

[ A 8.3 ]

A packet of bananas, mass

1,34 kg, costs R26,91.

8.1   Calculate the price of the bananas

per kilogram.                        [ A 8.1 ]

8.2   What will 2,44 kg of bananas cost?

[ A 8.2 ]

8.3   A packet of bananas costs R8,63.

What is the mass of this packet?

[ A 8.3 ]

Vraag  / Question  9

Op 'n sekere dag is die prys van

Brent ruolie \$69,29 per vat en die

Rand-VSA dollar wisselkoers

\$1 = R14,12 .

9.1   Bereken die prys van 30 vate

in VSA dollar.                         [ A 9.1 ]

9.2   Veronderstel dat 1 vat 'n inhoud

van 75 lter het. Bereken die

prys, in Rand, van 1 liter ru-olie.

[ A 9.2 ]

On a certain day the price of Brent

crude oil is \$69,29 per barrel and the

Rand-USA dollar exchange rate

is \$1 = R14,12 .

9.1   Calculate the price of 30 barrels

in USA dollar.                         [ A 9.1 ]

9.2   Suppose that the capacity of 1 barrel

is 75 litres. Calculate the price,

in Rand, of 1 litre of crude oil.

[ A 9.2 ]

Vraag  / Question  10

As \$1 = R13,99 en £1 = R20,24,

bepaal, by benadring, hoeveel

dollar gelyk is aan £1           [ A 10. ]

If \$1 = R13,99 and £1 = R20,24,

determine approximately how many

dollars are equal to £1            [ A 10. ]

Vraag  / Question  11

'n Pakkie piesangs en 'n pakkie

tamaties het dieselfde massa.

Die waarde van die pakkie tamaties

is R40,00 en die van die piesangs

is R25,10. Die prys van die piesangs

is R20,08 per kilogram.

11.1   Bepaal die massa van die pakkie

piesangs.                            [ A 11.1 ]

11.2   Bereken die prys van 1 kg tamaties.

[ A 11.2 ]

A packet of bananas and a packet of

tomatoes have the same mass.

The value of the packet of tomatoes

is R40,00 and that of the bananas

is R25,10. The price of the bananas

is R20,08 per kilogram.

11.1   Betermine the mass of the packet

of bananas.                       [ A 11.1 ]

11.2   Calculate the price of 1 kg of

tomatoes.                          [ A 11.2 ]

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