WISKUNDIGE GELETTERDHEID
GRAAD 12
NOG OEFENINGE
  
Koers, verhouding en eweredigheid.
  
MATHEMATICAL LITERACY
GRADE 12
MORE EXERCISES
  
Rate, ratio and proportion.
  
  
  
Vraag 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
  
  
  
  
Vraag 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 ]
  
  
  
  
Vraag 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 ]
  
  
  
  
Vraag 4.

  
               Marie verdien R30 per uur. Sy werk elke
  
               weeksdag, Maandag tot Vrydag, vir 8 uur
  
               per dag.
  
        4.1  Bereken haar weeklikse loon.
  
        4.2  Hoeveel uur moet sy werk om
  
               R1 770 te verdien?
  
        4.3  Sy het R870 verdien. Hoe lank het
  
               sy gewerk?
  
  
Antwoord  4.

  
  
  
Vraag 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 ]
  
  
  
  
Vraag 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?
  
        6.1.2  35 mm op die plan?
  
        6.1.3  0,35 m on die plan?                   [ 6.1 ]

  
        6.2  Watter afstand op die plan word voorgestel
  
               deur 'n afstand van . . .   in die gebou?
  
        6.2.1  35,4 m
  
        6.2.2  0,4 m
  
        6.2.3  1,26 m                                       [ 6.2 ]
  
  
  
  
Vraag 7.

  
                 Die digtheid van 'n stof word gedefinieer deur:
  
                                                           massa
                     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.
  
        7.3.2  Bereken die volume van 413,02 g goud.
  
        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 ]
  
  
        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.
  
        7.4.2  'n Tweede blokkie van lood het 'n
  
                  massa van 181,6 gram. Bereken die
  
                  volume van die blokkie.
  
        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 ]
  
  
  
  
Question 1.

  
                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
  
  
  
  
Question 2.

  
                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 ]
  
  
  
  
Question 3.

  
                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 ]
  
  
  
  
  
  
  
  
Question 4.

  
                Mary is paid R30 per hour. She works every day
  
                from Monday to Friday, 8 hours per day.
  
        4.1  Calculate her weekly wages.
  
        4.2  How many hours does she have to work to
  
               earn R1 770?
  
        4.3  She earned R870. How many hours
  
               did she workS?
  
  
  
Answer  4.

  
  
  
  
Question 5.

  
                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 ]
  
  
  
  
Question 6.

  
                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?
  
        6.1.2  35 mm on the plan?
  
        6.1.3  0,35 m on the plan?                              [ 6.1 ]
  
  
        6.2  What distance on the plan is represented by a
  
               distance of    . . .   in the building?
  
        6.2.1  35,4 m
  
        6.2.2  0,4 m
  
        6.2.3  1,26 m                                                   [ 6.2 ]
  
  
  
  
Question 7.

  
                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.
  
        7.3.2  Calculate the volume of 413,02 g of gold.
  
        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 ]
  
  
  
  
        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.
  
        7.4.2  A second lead block has a mass of 181,6 gram.
  
                  Calculate the volume of the block.
  
        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 ]