WISKUNDIGE GELETTERDHEID
GRAAD 11
NOG OEFENINGE
  
Koers, verhouding en eweredigheid.
  
MATHEMATICAL LITERACY
GRADE 11
MORE EXERCISES
  
Rate, ratio and proportion.
  
        Skryf die volgende verhoudings in hulle
        eenvoudigste vorm :
        Write the following ratios in the simplest form:
        
  
                 38
        1.1  ───
                 57                                                   [ 1.1 ]
  
  
                 52
        1.3  ───
                 91                                                   [ 1.3 ]
  
  
                 247
        1.5  ───
                 437                                                 [ 1.5 ]
  
  
  
                 42
        1.2  ───
                105                                                   [ 1.2 ]
  
  
                 136
        1.4  ────
                 221                                                   [ 1.4 ]
  
  
                 316
        1.6  ────
                 553                                                   [ 1.6 ]
  
  
        Verdeel
        2.1  35 albasters onder Piet en Jan in die
                verhouding 3 : 4.                                      [ 2.1 ]
  
        2.2  R 1 378 tussen A en B in die
              verhouding 4 : 9.                                        [ 2.2 ]
  
        2.3  R18 214 tussen A, B en C in
                verhouding 7 : 5 : 2.                                 [ 2.3 ]
  
        2.4  R323,68 tussen C en D in die
                 verhouding 3 : 11.                                    [ 2.4 ]
  
        2.5  96 osse tussen P en Q in die
                verhouding 5 : 7.                                       [ 2.5 ]
  
        2.6  364 skape tussen R, S en T in die
                verhouding 7 : 4 : 2.                                  [ 2.6 ]
  
        Divide
        2.1  35 marbles between Peter and John in
               the ratio 3 : 4.                                     [ 2.1 ]
  
        2.2  R 1 378 between A and B in the
               ratio 4 : 9.                                            [ 2.2 ]
  
        2.3  R18 214 between A, B and C in
               the ratio 7 : 5 : 2.                                 [ 2.3 ]
  
        2.4  R323,68 between C and D in the
               ratio 3 : 11.                                          [ 2.4 ]
  
        2.5  96 oxen between P and Q in the
               ratio 5 : 7.                                            [ 2.5 ]
  
        2.6  364 sheep between R, S and T in
               the ratio 7 : 4 : 2.                                 [ 2.6 ]
  
          A, B en C koop 'n winkel. Hulle besluit om die wins
          in dieselfde verhouding te verdeel as die verhouding
          waarin hulle tot die aankoopprys bygedra het.
          A het R120 000, B het R100 000 en
          C het R60 000 bygedra.
  
        3.1  Skryf die verhouding van hulle bydraes
               in die eenvoudigste vorm.                     [ 3.1 ]
        3.2  Verdeel 'n wins van R48 601
                tussen hulle.                                           [ 3.2 ]
        3.3  C besluit om nog R5 000 tot die fonds
                by te dra.
        3.3.1  Skryf die nuwe verhouding van
                   hulle bydraes neer.                            [ 3.3.1 ]
        3.3.2  Die tweede jaar toon die winkel 'n
                   wins van R72 917,25.
                   Verdeel hierdie wins deur die
                   nuwe verhouding te gebruik.             [ 3.3.2 ]
  
  
          A, B and C buy a shop. They decide to divide
          the profit in the same ratio as the ratio in which
          they contributed to buy the shop.
          A contributed R120 000, B contributed
          R100 000 and C contributed R60 000.
  
        3.1  Write down the ratio of their contributions
               in its simplest form.                             [ 3.1 ]
        3.2  Divide a profit of R48 601
                between them.                                     [ 3.2 ]
        3.3  C decides to contribute another R5 000
                to the fund.
        3.3.1  Write down the new ratio of their
                   contributions.                                    [ 3.3.1 ]
        3.3.2  The second year the shop shows a
                   profit of R72 917,25.
                   Divide this profit by using the
                   new ratio.                                         [ 3.3.2 ]
  
  
        4.1  As 24 albasters tussen Jan en Martiens
                verdeel word, kry Jan 9 albasters.
                Bereken die verhouding waarin die
                albasters verdeel is.                               [ 4.1 ]
  
  
        4.2  'n Bedrag van R1 968 word tussen
                A, B en C verdeel. A kry R984,
                B kry R615 en C kry die res.
                Bereken die verhouding waarin die
                geld verdeel is.                                       [ 4.2 ]
  
  
        4.1  When 24 marbles are divided between John
                and Martin, John gets 9 marbles.
                Calculate the rate at which the
                marbles were divided.                          [ 4.1 ]
  
  
        4.2  An amount of R1 968 is divided amongst
                A, B and C. A receives R984,
                B receives R615 and C the rest.
                Calculate the rate at which the
                division was made.                                [ 4.2 ]
  
  
                Vermeerder
  
        5.1  82 kg in die verhouding 4 : 5.                    [ 5.1 ]
  
        5.2  R735 in die verhouding 5 : 9.                    [ 5.2 ]
  
        5.3  21,7 m in die verhouding 7 : 11.                [ 5.3 ]
  
        5.4  28,4 kg in die verhouding 4 : 3.                  [ 5.4 ]
  
        5.5  R324 in die verhouding 8 : 5.                     [ 5.5 ]
  
        5.6  34,2 liter in die verhouding 9 : 5.                [ 5.6 ]
  
        5.7  220 volt in die verhouding 55 : 3.               [ 5.7 ]
  
                Increase
  
        5.1  82 kg in the ratio 4 : 5.                    [ 5.1 ]
  
        5.2  R735 in the ratio 5 : 9.                    [ 5.2 ]
  
        5.3  21,7 m in the ratio 7 : 11.                [ 5.3 ]
  
        5.4  28,4 kg in the ratio4 : 3.                  [ 5.4 ]
  
        5.5  R324 in the ratio 8 : 5.                     [ 5.5 ]
  
        5.6  34,2 liter in the ratio 9 : 5.                [ 5.6 ]
  
        5.7  220 volt in the ratio 55 : 3.               [ 5.7 ]
  
                 Die verhouding van seuns tot dogters in
                 'n klas is 8 : 7. Daar is 45 leerlinge in
                 die klas. Hoeveel seuns en dogters
                 is daar in die klas?                                    [ 6. ]
  
  
                 The ratio of boys to girls in a class
                 is 8 : 7. There are 45 pupils in
                 the class. How mant boys and girls
                 are ther in the class?                                    [ 6. ]
  
  
                In 'n klas is daar 23 seuns en 22 dogters.
        7.1  Skryf die verhouding seuns : dogters in
               sy eenvoudigste vorm.                            [ 7.1 ]
        7.2  Drie seuns verlaat die skool en dus
               die klas en 4 dogters word tot die
               klas toegelaat.
               Skryf die nuwe verhouding
               seuns : dogters neer.                            [ 7.2 ]
        7.3  Die klas het nog steeds 23 seuns en
               22 dogters. Leerlinge verlaat die
               skool en word tot die klas toegelaat.
               Die totale aantal leerlinge in die klas
               is nou 44 en die verhouding s : d = 6 : 5.
               Bereken die aantal seuns en dogters
               in die klas en sê hoeveel seuns die
               klas verlaat het of toegelaat is tot
               die klas. Herhaal vir die dogters.          [ 7.3 ]
  
  
                A class contains 23 boys and 22 girls.
        7.1  Write the ratio boys : girls in its
               simplest form.                                       [ 7.1 ]
        7.2  Three boys leave school and thus
                the class and 4 girls are admitted to
                the class. Write down
                the new ratio boys : girls.                     [ 7.2 ]
        7.3  The class still contains 23 boys and
                22 girls. Pupils leave the school and
                are admitted to the school and this class.
                The total number of pupils in the
                class is now 44 and the ratio b : g = 6 : 5.
                Calculate the number of boys and
                girls in the class and then say how
                many boys left the class or were
                admitted to the class.
                Repeat for the girls.                            [ 7.3 ]
               'n Blik bevat rooi, groen en geel
               lekkers in die verhouding
               r : gr : ge = 3 : 4 : 5.
               Daar is 12 rooi lekkers in die blik.
               Bereken die aantal groen en
               geel lekkers asook die totale
               aantal lekkers in die blik.                            [ 8. ]
  
  
               A tin contains red, green and
               yellow sweets in the ratio
               r : g : y = 3 : 4 : 5.
               There are 12 red sweets in the tin.
               Calculate the number of green and
               yellow sweets and the total number
               of sweets in the tin.                            [ 8. ]
  
  
               'n Sak bevat 10 kg van 'n 3 : 2 : 1 (22)
               kunsmis.
        9.1  Verduidelik die betekenis van die
                verhouding en die syfer 22.                     [ 9.1 ]
        9.2  Bereken die massa van die
                voedingstowwe in die sak.                       [ 9.2 ]
        9.3  Bereken die massa N, massa P en
                die massa K in die sak.                            [ 9.3 ]
  
  
               A bag contains 10 kg of 3 : 2 : 1 (22)
               fertiliser.
        9.1  Explain the meaning of the ratio
                and the 22.                                       [ 9.1 ]
        9.2  Calculate the mass of nutrients
               in the bag.                                          [ 9.2 ]
        9.3  Calculate the mass of N of P and
                K in the bag.                                     [ 9.3 ]
  
  
        10.1  Bereken die volume verf benodig om
                  20,8 m2 te verf as 1 liter verf 'n oppervlakte
                  van 5,2 m2 bedek.                                [ 10.1 ]
  
        10.2  Bereken die oppervlakte wat deur
                  5,8 liter verf bedek word as 17,6 m2
                  bedek word deur 2,8 liter verf.            [ 10.2 ]
  
        10.3  'n Blik bevat 4,2 liter verf. 2,5 liter van
                  hierdie verf bedek 'n oppervlakte van
                  11,5 m2. Sal die verf in die blik genoeg
                  wees om 'n oppervlakte van 21,4 m2 te
                  bedek? Verduidelik.                             [ 10.3 ]
  
  
        10.1  Calculate the volume of paint needed
                  to cover 20,8 m2 if 1 litre of paint
                  covers an area of 5,2 m                [ 10.1 ]
  
        10.2  Calculate the area covered by
                  5,8 litres of paint if 17,6 m2 is
                  covered by 2,8 litres of paint.       [ 10.2 ]
  
        10.3  A tin contains 4,2 litres of paint.
                  2,5 litres of this paint covers an area
                   of 11,5 m2. Will the tin contain
                  enough paint to cover an area of
                  21,4 m2? Explain.                        [ 10.3 ]
  
  
        11.1  'n Motor gebruik 21,082 liter petrol om
                  'n afstand van 254 km te reis. Hoeveel
                  petrol sal die motor gebruik as dit 'n
                  afstand van 613 km ry?                       [ 11.1 ]
  
        11.2  Hoe ver sal die motor met 14,2 liter
                  petrol ry met dieselfde
                  brandstofverbruiik?                              [ 11.2 ]
  
  
        11.1  A car uses 21,082 litres of petrol
                  to travel 254 km. How much petrol
                  will the car use if it travels
                   613 km?                                      [ 11.1 ]
  
        11.2  How far will the car drive using
                  14,2 liter petrol at the same
                  petrol comsumption?                  [ 11.2 ]
  
  
                  'n Motor ry 253,5 km in 2 uur 36 minute.
        12.1  Toon aan dat 2 uur 36 minute gelyk
                  is aan 2,6 uur.                                        [ 12.1 ]
  
        12.2  Hoe ver sal die motor in
                  3 uur en 48 minute ry, as
                  dit teen dieselfde spoed ry?                 [ 12.2 ]
  
        12.3  Hoe lank sal dit neem om 415 km
                  teen dieselfde spoed af te lê?               [ 12.3 ]
  
  
                  A car travels 253,5 km in 2 hours 36 minutes.
        12.1  Show that 2 hours 36 minutes is equal to
                  2,6 hours.                                             [ 12.1 ]
  
        12.2  How far will the car travel in
                  3 hours and 48 minutes, if it travels at
                  the same speed?                                 [ 12.2 ]
  
        12.3  How long will it take to travel
                  415 km at the same speed?               [ 12.3 ]
  
  
                  Tien mans kan 'n sekere werk in 3 dae verrig.
        13.1  Hoe lank sal 6 mans neem om
                  dieselfde werk te verrig as hulle teen
                  dieselfde tempo werk?                       [ 13.1 ]
        13.2  Hoe lank sal 12 mans neem om
                  dieselfde werk te verrig as hulle
                  teen dieselfde tempo werk?               [ 13.2 ]
        13.3  Hoeveel mans is nodig om die
                  werk in 7 dae te voltooi?                     [ 13.3 ]
        13.4  Hoeveel mans is nodig om die
                  werk in 2 dae te voltooi?                     [ 13.4 ]
  
  
                  Ten men can finish a job in 3 days.
        13.1  How long will 6 men take to finish
                  the same job if they work at
                  the same rate?                                  [ 13.1 ]
        13.2  How long will 12 men take to finish
                  the same job if they work at
                  the same rate?                                   [ 13.2 ]
        13.3  How many men are needed to
                  finish the job in 7 days?                     [ 13.3 ]
        13.4  How many men are needed to
                  finish the job in 2 days?                     [ 13.4 ]
  
  
                  Twintig kinders kry elk 8 lekkers uit 'n bottel.
        14.1  Hoeveel lekkers sal elke kind kry
                  das daar 40 kinders is?                      [ 14.1 ]
        14.2  Hoeveel lekkers sal elke kind kry
                  as daar 8 kinders is?                          [ 14.2 ]
        14.3  Hoeveel kinders is daar as elke
                  kind 16 lekkers kry?                            [ 14.3 ]
        14.4  Hoeveel kinders is daar as elke
                  kind 4 lekkers kry?                               [ 14.4 ]
  
  
                  Twenty children each get 8 sweets from a bottle.
        14.1  How many sweets will each child
                  get if there are 40 children?              [ 14.1 ]
        14.2  How many sweets will each child
                  get if there are 8 children?                [ 14.2 ]
        14.3  How many children are there if
                  each child gets 16 sweets?              [ 14.3 ]
        14.4  How many children are there if
                  each child gets 4 sweets?                [ 14.4 ]
  
  
  
  
  
  
  
  
  
  
  
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