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.                        [ 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.                    [ 2.3 ]
  
  
  
Vraag  / Question  3  
  
                 Jan draf 5 km in 25 minute.
  
        3.1  Hoe lank neem dit hom om 2 km
               te draf?                                     [ 3.1 ]
  
        3.2  Hoe ver kan hy in 65 minute
               draf?                                        [ 3.2 ]
  
  
                John jogs 5 km in 25 minutes.
  
        3.1  How long does he take to jog
               2 km?                                  [ 3.1 ]
  
        3.2  How far can he jog in 65
               minutes?                              [ 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.       [ 4.1 ]
  
        4.2  Hoeveel uur moet sy werk om
               R1 770 te verdien?                     [ 4.2 ]
  
        4.3  Sy het R870 verdien. Hoe lank
                het sy gewerk?                         [ 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.     [ 4.1 ]
  
        4.2  How many hours does she have to
               work to earn R1 770?              [ 4.2 ]
  
        4.3  She earned R870. How many hours
               did she work?                         [ 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.    [ 5.1 ]
  
  
        5.2  Hoe ver kan die motor ry as dit 21,4 l??
               petrol teen dieselfde brandstofverbruik
               verbruik?                                          [ 5.2 ]
  
        5.3  Hoeveel liter petrol sal die motor verbruik
               om 430 km te ry?                            [ 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?                               [ 5.2 ]
  
        5.3  How many litres of petrol will the car
               use to travel 430 km?                   [ 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?                   [ 6.1.1 ]
  
        6.1.2  35 mm op die plan?                [ 6.1.2 ]
  
        6.1.3  0,35 m on die plan?                [ 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                                     [ 6.2.1 ]
  
        6.2.2  0,4 m                                       [ 6.2.2 ]
  
        6.2.3  1,26 m                                     [ 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?                 [ 6.1.1 ]
  
        6.1.2  35 mm on the plan?              [ 6.1.2 ]
  
        6.1.3  0,35 m on the plan?               [ 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                                        [ 6.2.1 ]
  
        6.2.2  0,4 m                                          [ 6.2.2 ]
  
        6.2.3  1,26 m                                        [ 6.2.3 ]
  
  
  
Vraag  / Question  7  
  
                 Die digtheid van 'n stof word gedefinieer
  
                                                             massa
                 deur: digtheid van stof   =   ───────
                                                             volume
  
        7.1  Watter hoeveelheid is direk eweredig
  
               aan massa? Verduidelik.            [ 7.1 ]
  
  
        7.2  Die massa van 1 liter water is 1 kg.
  
               Bereken die digtheid van
  
               water in g/cm3                         [ 7.2 ]
     
        7.3  Die digtheid van goud is 19,3 g/cm3
  
        7.3.1  Bereken die massa van 6 cm3
  
                  goud.                                   [ 7.3.1 ]
  
  
        7.3.2  Bereken die volume van 413,02 g
  
                  goud.                                   [ 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.                             [ 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.
                                                               [ 7.4.1 ]
  
  
        7.4.2  'n Tweede blokkie van lood het 'n
  
                  massa van 181,6 gram. Bereken die
  
                  volume van die blokkie.
                                                           [ 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.      [ 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.                     [ 7.1 ]
  
  
        7.2  The mass of 1 litre of water is 1 kg.
  
               Calculate the density of water
  
                in g/cm3                                 [ 7.2 ]
  
        7.3  The density of gold is 19,3 g/cm3
  
        7.3.1  Calculate the mass of 6 cm3
  
                 gold.                                 [ 7.3.1 ]
  
  
        7.3.2  Calculate the volume of 413,02 g of
  
                 gold.                                  [ 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.
  
                                                          [ 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.
  
                                                           [ 7.4.1 ]
  
        7.4.2  A second lead block has a mass of
  
                  181,6 gram. Calculate the volume
  
                  of the block.                       [ 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.                       [ 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.                            [ 8.1 ]
  
  
        8.2   Wat sal 2,44 kg piesangs kos?
  
                                                              [ 8.2 ]
  
  
        8.3   'n Pakkie piesangs kos R8,63.
  
                Wat is die massa van die pakkie?
  
                                                              [ 8.3 ]
  
  
                 A packet of bananas, mass
  
                 1,34 kg, costs R26,91.
  
        8.1   Calculate the price of the bananas
  
                 per kilogram.                        [ 8.1 ]
  
  
        8.2   What will 2,44 kg of bananas cost?
  
                                                           [ 8.2 ]
  
  
        8.3   A packet of bananas costs R8,63.
  
                What is the mass of this packet?
  
                                                           [ 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.                         [ 9.1 ]
  
        9.2   Veronderstel dat 1 vat 'n inhoud
  
                van 75 lter het. Bereken die
  
                prys, in Rand, van 1 liter ru-olie.
  
                                                            [ 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.                         [ 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.
  
                                                            [ 9.2 ]
  
  
Vraag  / Question  10  
  
                 As $1 = R13,99 en £1 = R20,24,
  
                 bepaal, by benadring, hoeveel
  
                 dollar gelyk is aan £1           [ 10. ]
  
                 If $1 = R13,99 and £1 = R20,24,
  
                 determine approximately how many
  
                 dollars are equal to £1            [ 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.                            [ 11.1 ]
  
        11.2   Bereken die prys van 1 kg tamaties.
  
                                                            [ 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.                       [ 11.1 ]
  
        11.2   Calculate the price of 1 kg of
  
                 tomatoes.                          [ 11.2 ]