WISKUNDE
GRAAD 12
NOG OEFENINGE
  
Kaarte : antwoorde
  
MATHEMATICS
GRADE 12
MORE EXERCISES
  
Maps : answers
  
  
Antwoorde / Answers  1  
  
      1.1  v = l X b X h
               =  800  X  750  X  500  mm3
  
                     800       750       500
               =  ───  X  ───  X  ───  cm3    |  verander mm na cm / change m to cm
                     10         10         10
  
               =  300 000  cm3
  
               =  300  ℓ    |  1 000 cm3  = 1 ℓ                                                                       [ V/Q 1. ]
  
  
      1.2        403 km gebruik / uses  165,23 ℓ diesel
  
                                                       165,23
                    1 km gebruik / uses  ──────  ℓ diesel
                                                         403
  
                                                       165,23
                100 km gebruik / uses  ──────  X  100  ℓ diesel
                                                         403
  
                                               d.i. / i.e.  41
  
                   Brandstof-verbruik / Fuel consumption is  41 ℓ / 100 km                             [ V/Q 1.2 ]
  
  
      1.3    d  =  875 − ( 403 + 73 ) km
  
                   =  399 km                                                                                               [ V/Q 1.3 ]
  
  
      1.4.1    Afstand / Distance  =  875 + 417 + 176 + 280  km
  
                                                  =  1 748 km                                                          [ V/Q 1.4.1 ]
  
  
      1.4.2    100 km benodig 41  ℓ  diesel    /    100 km uses  41  ℓ  diesel
  
                                               41                                                 41
                      1 km benodig  ────  ℓ  diesel    /        1 km uses  ────  ℓ  diesel
                                              100                                               100
  
                                             41                                                         41
              1 748 km benodig ──── X 1 748 ℓ diesel  /  1 748 km uses ──── X 1 748 ℓ diesel
                                           100                                                        100
  
                                      d.i.  716,68 ℓ                                             i.e.  716,68 ℓ
  
                        Die bestuurder is dus verkeerd  /  The driver is thus mistaken.
  
                                                                                                                               [ V/Q 1.4.2 ]
  
  
      1.5    P  :  Afstand / Distance ADEG  =  280  +  176  +  339  =  795  km
  
                      s = v X t | Gebruik formule om tyd te bereken / Use formula to calculate time
  
                               795 km  =  70 km/h  X  t  uur / hours
  
                                 795             70
                               ────    =  ────  X  t
                                  70             70
  
                      11,35714286  =  1  X  t
  
                      t  =  11  uur / hours  + 0,3571486 X 60  minute / minutes
  
                         =  11  uur / hours  + 21,4  minute / minutes
  
                     P neem 11 uur en 21 minute om die reis te voltooi  /  
  
                     P completes the journey in 11 hours and 21 minutes.
  
                Q  :  Afstand / Distance ABCDEG  =  116  +  132  +  238  +  176  +  339  =  1 001  km
  
                      s = v X t | Gebruik formule om tyd te bereken / Use formula to calculate time
  
                             1 001 km  =  85 km/h  X  t  uur / hours
  
                                1 001           85
                               ────    =  ────  X  t
                                  85             85
  
                      11,77647059  =  1  X  t
  
                      t  =  11  uur / hours  + 0,77647059 X 60  minute / minutes
  
                         =  11  uur / hours  + 46,58  minute / minutes
  
                     Q neem 11 uur en 47 minute om die reis te voltooi  /  
  
                     Q completes the journey in 11 hours and 47 minutes.
  
                     P bereik G dus eerste / P is the first to arrive at G.                                   [ V/Q 1.5 ]
  
  
      1.6.1     Lengte van / Length of  GF = 3,3 cm  en afstand / and distance  GF = 330 km
  
                   Dus / Thus   3,3 cm  stel voor / represents  330 km
  
                  3,3 cm : 330 x 1000 x 100 cm   | km na / to cm
  
                                 330 X 1 000 X 100
                    1 cm :  ─────────────  cm
                                            3,3
  
                    1 cm :  10 000 000  cm
  
                    Skaal / Scale  1  :  10 000 000                                                              [ V/Q 1.6.1 ]
  
  
      1.6.2     Skaal / Scale   1 : 10 000 000  :  
  
                   Dus / Thus   10 000 000 cm werklik / real    stel voor / represents  1 cm
  
                   Dus / Thus   100 000 m werklik / real    stel voor / represents  1 cm
  
                   Dus / Thus   100 km werklik / real    stel voor / represents  1 cm
  
                                                                                                              1
                   Dus / Thus   240 km werklik / real    stel voor / represents  ────  X  240   cm
                                                                                                            100
  
                                                                                                   d.i. / i.e.  2,40
                   Dus / Thus   lyn / line  CD  =  2,40 cm                                                     [ V/Q 1.6.2 ]
  
  
                   OF / OR
  
                   240 km  =  240 X 1 000 X 100  cm   =  24 000 000  cm
  
                   Skaal / Scale   1 : 10 000 000  of / or   10 000 000  :  1
  
                                                                                                       24 000 000
                                                                                24 000 000  :  ────────
                                                                                                       10 000 000
  
                                                                                24 000 000  :  2,4
  
                   Dus / Thus   lyn / line  CD  =  2,40 cm                                                    [ V/Q 1.6.2 ]
  
  
      1.7.1     Rigting / Direction  suid-wes /  south west                                               [ V/Q 1.7.1 ]
  
  
      1.7.2     Nee, D is wes van E    /  No,  D lies to the west of E                                [ V/Q 1.7.2 ]
  
  
  
Antwoorde / Answers  2  
  
      2.1  Totale afstand = 106 km       [ V/Q 2.1 ]
  

      2.2   Aantal waterpunte = 13       [ V/Q 2.2 ]
  

      2.3   Langste afstand tussen water punte
              is 12 km                           [ V/Q 2.3 ]
  

      2.4   5 of minder = 4                 [ V/Q 2.4 ]
  
      2.1  Total distance = 106 km     [ V/Q 2.1 ]
  

      2.2   Number of waterpoints = 13
                                                     [ V/Q 2.2 ]

      2.3   Greatest distance between waterpoints
              is 12 km                          [ V/Q 2.3 ]
  

      2.4   5 or less = 4                     [ V/Q 2.4 ]
  
                                                15
      2.5  3 uur 15 minute = 3 + ─── uur = 3 + 0,25 uur = 3,25 uur
                                                60
  
                                                     15
             3 hours 15 minutes = 3 + ─── hours = 3 + 0,25 hours = 3,25 hours                                                      60
  
             afstand / distance  =  spoed / speed  X  tyd / time
  
             d  =  s  X  t    :   106 km  =  s km/h  X  3,25  h
  
                                                         106
                                               s  =  ──────      =  32,615
                                                         3,25
  
             Gemiddelde spoed / Average speed  =  32,615  km/h                                     [ V/Q 2.5 ]
  
      
      2.6  Afstand na waterpunt 10  /   Distance to water point 10  =  88  km
  
             Gebruik / Use  d = s X t  :   88 = 12 X t
  
                                                                 88
                                                         t =  ───    =  7,33
                                                                 12
  
             7,33 uur / hours  =  7  +  0,33 X 60  minute / minutes
  
                                      =  7  +  20  minute / minutes
  
             Jy kom om 08:00 + 07:20 = 15:20 by waterpunt 10 aan. Jy is dus nog betyds.
  
             You arrive at water point at 08:00 + 07:20 = 15:20. You are thus in time.
  
                                                                                                                                 [ V/Q 2.6 ]
  
      
      2.7  Algemene rigting van waterpunt 4 na waterpunt 5 is suid-oos.  /  
  
             Generel diredtion from waterpoint 4 t0 waterpoint 5 is south east.                   [ V/Q 2.7 ]
  
  
  
Antwoorde / Answers  3  
  
      3.1  Korrek  /  Correct                                                                                           [ V/Q 3.1 ]
  
  
      3.2  Roete vanaf Bloemfontein na Molteno  /   Route from Bloemfontein na Molteno
  
            Roete / Route  ABDFG   =  127 + 80 + 132 + 58 = 397 km
  
            Roete / Route  ACEFG   =  133 + 108 + 52 + 58 = 351 km
  
            Roete / Route  ACEMG   =  133 + 108 + 84 + 38 = 363 km
  
            Die kortste afstand is vanaf Bloemfontein na Smithfield na Aliwal Noord na
  
            Burgersdorp na Molteno en dit is 351 km.
  
            The shortest distance is from Bloemfontein to Smithfield to Aliwal Noord to
  
            Burgersdorp to Molteno and that is 351 km.                                                    [ V/Q 3.2 ]
  
  
      3.3  Afstand / Distance  Tarkastad na / to Cradock = 78 km.
  
                                 52
            Tyd / Time = ───  =  0,8667  uur / hours
                                 60
  
            Gebruik / Use  :  d = s X t   : 78 = s X 0,8667
  
                                                                   78
                                                         s = ──────    =    90
                                                                0,8667
    
            Hulle spoed is 90 km/h  /  Their speed = 90 km/h                                               [ V/Q 3.3 ]
  
  
      3.4.1  Afstand / Distance  Molteno na / to Cradock = 249 km.
  
               Gebruik / Use  :  d = s X t   : 249 = 110 X t
  
                                                                     249
                                                               t = ───  =  2,264   uur / hours
                                                                     110
  
                                                               0,2636 h = 0,2636 X 60 min = 15,8 min = 16 min
  
              Tyd by Cradock  /  Time of arrival at Cradock  =  09:00 + 02:16    =  11:16       [ V/Q 3.4.1 ]
  
  
      3.4.2   Stop in Queenstown  =  11:45  -  11:16    =  0:29  =  29 minute / minutes      [ V/Q 3.4.2 ]
  
  
      3.4.3   Reistyd / Travel time  =  11:45 - 09:00  =  2:45    =  2 h + 45 min
  
                                                                                      45
                                                                     45 min  =  ───  h  =  0,75 h
                                                                                      60
                Totale reistyd  /  Travel time  =  2,75 h
  
                Gebruik / Use  :  d = s X t   : 249 = s X 2,75
  
                                                                     249
                                                               s = ───  =  90,55 km/h
                                                                     2,45
  
                Gemiddelde spoed / Average speed  =  90,55  km/h                                   [ V/Q 3.4.3 ]
  
  
      3.5.1   Skaal 1 : 2 500 000 beteken dat 1 eenheid op die kaart verteenwoordig
  
                                               2 500 000 werklike eenhede.
  
                Scale 1 : 2 500 000 means that 1 unit on the map represents
  
                                               2 500 000 real units.
                                                                                                                               [ V/Q 3.5.1 ]
  
  
      3.5.2   Alex is reg want Bloemfontein is amper reg Noord van Port Elizabeth MAAR
  
                hy is ook verkeerd - Zander moet amper reg noord vlieg om by Bloemfontein te
  
                kom. As hy amper reg suid vlieg is hy op pad Ant-Artika toe.                       [ V/Q 3.5.2 ]
  
                Alex is correct because Bloemfontein is about due north of Port Elizabeth BUT
  
                he is also wrong - Zander has to fly about due north to reach Bloemfontein.
  
                If he flies about due south, he is heading for Ant-Artica.                             [ V/Q 3.5.2 ]
  
  
      3.5.3      Afstand op kaart / Distance on map    Werklike afstand / Real distance
  
                                          1 cm                                                2 500 000 cm
  
                                      19,4 cm                                           19,4 X 2 500 000 cm
  
                                                                              d.i. / i.e.   48 500 000 cm
  
                                                                              d.i. / i.e.   48 500 000 ÷ (100 X 1 000)  km
  
                                                                              d.i. / i.e.   485 km
  
               Afstand / Distance  =  485 km                                                                    [ V/Q 3.5.3 ]
  
  
      3.5.4      160 knope / knots  =  160 X 1,852  km/h
  
                                                =  296,32  km/h                                                        [ V/Q 3.5.4 ]
  
  
      3.5.5  Gebruik / Use  :  d = s X t   : 485 = 296,32 X t
  
                                                                         485
                                                               t = ──────  =  1,636744 h
                                                                      296,32
  
                0,636744 h  =  1 h + 0,636744 X 60 min
  
                                  =  1 h + 38,2 min    =  1 h + 39 min
  
                Verwagte aankomtyd / Expected time of arrival  =  08:30 + 01:39    =  10:09
  
                                                                                                                                [ V/Q 3.5.5 ]