WISKUNDIGE GELETTERDHEID
GRAAD 11
NOG OEFENINGE
  
Kaarte en reise : antwoorde
  
MATHEMATICAL LITERACY
GRADE 11
MORE EXERCISES
  
Maps and trips : answers
  
  
Antwoorde / Answers  1  
  
    
        1.1   Ry vanaf Upington na Keimoes, draai
  
                af na Kenhardt en draai links af na
  
                Verneukpan by die afdraai gemerk P.
  
                                                                 [ V/Q 1. ]
    
        1.2   14,1 cm : 141 km
  
                14,1 cm : 141 X 1000 X 100 cm
  
                                   141 X 1000 X 100
                     1 cm : ─────────────  cm
                                               14,1
  
                          1 : 1 000 000
                                                                 [ V/Q 1.2 ]
    
        1.3   300 myl = 300 X 1,60934 km
  
                              = 482,802 km.
  
                300 mph = 483 km/h
                                                                 [ V/Q 1.3 ]
    
        1.4.1  
                                      afstand
                   spoed  =  ───────
                                         tyd
  
                   spoed X tyd  =  afstand
  
                                 afstand
                   tyd  =  ───────
                                 spoed
  
                                   1
                   tyd  =  ─────   uur
                                 300
  
                                      1
                          =  ─────  X 60 X 60  sekonde
                                    300
  
                          =  12  sekonde
                                                             [ V/Q 1.4.1 ]
    
        1.4.2  
                                      afstand
                   spoed  =  ───────
                                         tyd
  
                                     1 km
                   spoed  =  ─────
                                     12 s
  
                                               1 km
                   spoed  =  ────────────
                                     12 ÷ (60 X 60)  h
  
                               =  300  km/h
                                                             [ V/Q 1.4.2 ]
    
        1.5.1   Suid Oos.                       [ V/Q 1.5.1 ]
  
    
        1.5.2   Skaal : 1 : 1 000 000
  
                         1 cm : 1 000 000 cm
  
                     158 cm : 1 000 000 X 158 cm
  
                     158 ÷ 10 cm : 15 800 000 cm
  
                     158 cm : 15 800 000 ÷
  
                                                 (100 X 1000) km
  
                     158 cm : 158 km
  
                     Pofadder is 158 km van Verneukpan.
  
                                                             [ V/Q 1.5.2 ]
  
    
        1.5.3   Tyd = 09:05 ─ 08:15
  
                            = 50 minute
  
                            = 50 ÷ 60 h
  
                            = 0,833 h
  
                                                             [ V/Q 1.5.3 ]
    
        1.5.4  
                                      afstand
                   spoed  =  ───────
                                         tyd
  
                                      158 km
                   spoed  =  ───────
                                         0,833 h
  
                               =  189,608 km/h
                                                           [ V/Q 1.5.4 ]
    
        1.1   Drive from Upington to Keimoes, turn
  
                off to Kenhardt and turn left to
  
                Verneukpan at the turn-off marked P.
  
                                                                 [ A 1.1 ]
    
        1.2   14,1 cm : 141 km
  
                14,1 cm : 141 X 1000 X 100 cm
  
                                   141 X 1000 X 100
                     1 cm : ─────────────  cm
                                               14,1
  
                          1 : 1 000 000
                                                                 [ V/Q 1.2 ]
    
        1.3   300 miles  =  300 X 1,60934  km
  
                                  =  482,802  km
  
                                  =  483  km
                                                                 [ V/Q 1.3 ]
    
        1.4.1  
                                      distance
                   speed  =  ───────
                                         time
  
                   speed X time  =  distance
  
                                   distance
                   time  =  ───────
                                    speed
  
                                      1
                   time  =  ─────   hours
                                    300
  
                                      1
                            =  ─────  X 60 X 60  seconds
                                    300
  
                            =  12  seconds
                                                             [ V/Q 1.4.1 ]
    
        1.4.2  
                                      distance
                   speed  =  ───────
                                         time
  
                                     1 km
                   speed  =  ─────
                                     12 s
  
                                               1 km
                   speed  =  ────────────
                                     12 ÷ (60 X 60)  h
  
                               =  300  km/h
                                                             [ V/Q 1.4.2 ]
    
        1.5.1   South East.                       [ V/Q 1.5.1 ]
  
    
        1.5.2   Scale : 1 : 1 000 000
  
                         1 cm : 1 000 000 cm
  
                     158 cm : 1 000 000 X 158 cm
  
                     158 ÷ 10 cm : 15 800 000 cm
  
                     158 cm : 15 800 000 ÷
  
                                                 (100 X 1000) km
  
                     158 cm : 158 km
  
                     Pofadder is 158 km from Verneukpan.
  
                                                             [ V/Q 1.5.2 ]
  
    
        1.5.3   Time = 09:05 ─ 08:15
  
                            = 50 minutes
  
                            = 50 ÷ 60 h
  
                            = 0,833 h
  
                                                             [ V/Q 1.5.3 ]
    
        1.5.4  
                                      distance
                   speed  =  ───────
                                         time
  
                                      158 km
                   speed  =  ───────
                                         0,833 h
  
                               =  189,608 km/h
                                                           [ V/Q 1.5.4 ]
  
Antwoorde / Answers  2  
  
    
        2.1   Ry vanaf Die Dam op die R43 na
  
                Gansbaai, volg die R326 na Stanford
  
                en die aansluiting met die R316.
  
                Draai links op die R316 en ry
  
                na Caledon.
  
                OF
  
                Ry vanaf Die Dam op die R43 na
  
                Gansbaai, volg die R326 na Stanford
  
                draai op die R43 en ry na die
  
                aansluiting met die N2. Draai regs
  
                op die N2 en ry na Caledon.
  
                                                                 [ V/Q 2. ]
    
        2.2   Afstand = 26 + 32 km = 58 km
  
                                                                 [ V/Q 2. ]
    
        2.3   5 cm : 58 km
  
                5 cm : 58 X 1000 X 100 cm
  
                                   58 X 1000 X 100
                     1 cm : ─────────────  cm
                                               5
  
                          1 : 1 160 000
                                                                 [ V/Q 2. ]
    
        2.4   Scale : 1 : 1 160 000
  
                   1 160 000 cm : 1 cm (werklik : kaart)
  
                                          1
                         1 cm : ─────── cm
                                     1 160 000
  
                                          1
             2 200 000 cm : ─────── X 2 200 000 cm
                                       1 160 000
  
                     2 200 000 cm : 1,897 cm
  
                     Afstand op kaart is 1,897 cm.
  
                                                                 [ V/Q 2. ]
    
        2.5   Noord-Wes
  
                                                                 [ V/Q 2. ]
    
        2.6.1   380 km                                  [ V/Q 2. ]
  
    
        2.6.2   44 km                                    [ V/Q 2. ]
  
    
        2.1   Drive from Die Dam on the R43 to
  
                Gansbaai, follow the R326 to Stanford
  
                and to the intersection with the R316.
  
                Turn left onto the R316 and drive
  
                to Caledon.
  
                OR
  
                Drive from Die Dam on the R43 to
  
                Gansbaai, follow the R326 to Stanford,
  
                turn onto the R43 and drive to the
  
                intersection with the N2. Turn right
  
                onto the N2 and drive to Caledon.
  
                                                                 [ V/Q 2. ]
    
        2.2   Distance = 26 + 32 km = 58 km
  
                                                                 [ V/Q 2. ]
    
        2.3   5 cm : 58 km
  
                5 cm : 58 X 1000 X 100 cm
  
                                   58 X 1000 X 100
                     1 cm : ─────────────  cm
                                               5
  
                          1 : 1 160 000
                                                                 [ V/Q 2. ]
    
        2.4   Scale : 1 : 1 160 000
  
                   1 160 000 cm : 1 cm (real : map)
  
                                          1
                         1 cm : ─────── cm
                                     1 160 000
  
                                          1
             2 200 000 cm : ─────── X 2 200 000 cm
                                       1 160 000
  
                     2 200 000 cm : 1,897 cm
  
                     Distance on the map is 1,897 cm.
  
                                                                 [ V/Q 2. ]
    
        2.5   North West
  
                                                                 [ V/Q 2. ]
    
        2.6.1   380 km                                  [ V/Q 2. ]
  
    
        2.6.2   44 km                                    [ V/Q 2. ]
  
  
Antwoorde / Answers  3  
  
    
        3.1   Ry vanaf Carnarvon na Britstown oor
  
                De Aar na Hanover, Draai links en ry
  
                na Colesberg oor Waterkloof en
  
                Trompsburg na Bloemfontein.
  
                OF
  
                Ry vanaf Carnarvon na Britstown oor
  
                De Aar. Draai links en ry na
  
                Petrusville oor Koffiefontein
  
                na Bloemfontein.
                                                                 [ V/Q 3.1 ]
    
        3.2   1,1 cm : 55 km
  
                1 cm : 55 ÷ 1,1 = 50 km
  
                1 cm : 50 X 1 000 X 100 cm
  
                1 cm : 5 000 000  cm
  
                Skaal 1  : 5 000 000
  
                                                                 [ V/Q 3.2 ]
    
        3.3   Skaal : 1 : 5 000 000
  
                         2,6 : 5 000 000 X 2,6 cm
  
                         2,6 : 13 000 000 cm
  
            Afstand = 13 000 000 ÷ (1 00 X 1 000) km
  
                Afstand = 130 km
  
                                                                 [ V/Q 3.3 ]
    
        3.4   Noord Wes                               [ V/Q 3.4 ]
  
    
        3.5   Staaf-skaal                               [ V/Q 3.5 ]
  
    
        3.1   Drive from Carnarvon to Britstown via
  
                De Aar to Hanover. Turn left and drive
  
                to Colesberg via Waterkloof and
  
                Trompsburg to Bloemfontein.
  
                OR
  
                Drive from Carnarvon via Britstown to
  
                De Aar. Turn left and drive via
  
                Petrusville and Koffiefontein
  
                to Bloemfontein.
                                                                 [ V/Q 3.1 ]
    
        3.2   1,1 cm : 55 km
  
                1 cm : 55 ÷ 1,1 = 50 km
  
                1 cm : 50 X 1 000 X 100 cm
  
                1 cm : 5 000 000  cm
  
                Scale 1  : 5 000 000
  
                                                                 [ V/Q 3.2 ]
    
        3.3   Scale : 1 : 5 000 000
  
                         2,6 : 5 000 000 X 2,6 cm
  
                         2,6 : 13 000 000 cm
  
            Distance = 13 000 000 ÷ (1 00 X 1 000) km
  
                Distance = 130 km
  
                                                                 [ V/Q 3.3 ]
    
        3.4   North West                               [ V/Q 3.4 ]
  
    
        3.5   Bar scale                                  [ V/Q 3.5 ]
  
  
Antwoorde / Answers  4  
  
    
        4.1   Van Cork ry op die N20 oor Mullow
  
                en Rockhill om die N21 naby Limerick
  
                to ontmoet. Volg die N21 na Limerick.
  
                Ry dan met die N18 oor Ennis en Gort
  
                om die N6 naby Galway te ontmoet.
  
                Volg die N6 om die N17 naby Galway
  
                te ontmoet. Volg die N17 oor Tuam,
  
                Ballindine en Charlestown
  
                na Ballysadare.
  
                OF
  
                Van Cork volg die N25 om die N8
  
                te ontmoet. Volg die N8 oor Rathcormack,
  
                Mitchelstown, Caher, Cashel en
  
                Johnstone na Portlaoise. Draai op
  
                die N7 en volg dit so ver as die snyding
  
                met die M4. Volg die M4 om die N4 te
  
                ont,oet. Volg die N4 oor Longford,
  
                Carrick of Shannon en Boyle
  
                na Ballysadare.
  
                                                                 [ V/Q 4.1 ]
    
        4.2   Suid Wes                                 [ V/Q 4.2 ]
  
    
        4.3   0,67 duim : 25 myl
  
                1 duim : 25 X 63360  duim
  
                1 duim : 1 584 000  duim
  
                Scale 1  : 1 584 000
  
                                                                 [ V/Q 4.3 ]
    
        4.4   Scale : 1 584 000 : 1
  
                                           1 X 42 X 63 360
                 42 X 63 360  :  ─────────── duim
                                                1 584 000
  
                          42 myl  :  1,68  duim
  
                 Die afstand op die kaart is 1,68 duim
  
                                                                 [ V/Q 4.4 ]
    
          4.5   1 myl = 1,60934 km
  
                25 myl = 25 X 1,60934 km
  
                25 myl = 40,234 km
  
                                                                 [ V/Q 4.5 ]
    
          4.6   Staafskaal.                             [ V/Q 4.5 ]
  
    
        4.1   From Cork drive on the N20 via Mullow
  
                and Rockhill to intersect the N21 near
  
                Limerick. Follow the N21 to Limerick.
  
                Then drive on the N18via Ennis and
  
                Gort to intersect the N6 near Galway.
  
                Follow the N6 to meet the N17 near
  
                Galway. Follow the N17 via Tuam,
  
                Ballindine and Charlestown
  
                to Ballysadare.
  
                OR
  
                From Cork follow the N25 to intersect
  
                the N8. Follow the N8 via Rathcormack,
  
                Mitchelstown, Caher, Cashel and
  
                Johnstone to Portlaoise. Turn onto
  
                the N7 and follow it as far as the intersect
  
                with the M4. Follow the M4 to reach the N4.
  
                Follow the N4 via Longford,
  
                Carrick of Shannon and Boyle to
  
                Ballysadare.
  
                                                                 [ V/Q 4.1 ]
    
        4.2   South West                              [ V/Q 4.2 ]
  
    
        4.3   0,67 inches : 25 miles
  
                1 inch : 25 X 63360   inches
  
                1 inch : 1 584 000  inches
  
                Scale 1  : 1 584 000
  
                                                                 [ V/Q 4.3 ]
    
        4.4   Scale : 1 584 000 : 1
  
                                           1 X 42 X 63 360
                 42 X 63 360  :  ─────────── inches
                                                1 584 000
  
                       42 miles  :  1,68  inches
  
                 The distance on the map is 1,68 inches
  
                                                                 [ V/Q 4.4 ]
    
        4.5   1 mile = 1,60934 km
  
                25 miles = 25 X 1,60934 km
  
                25 miles = 40,234 km
  
                                                                 [ V/Q 4.5 ]
    
          4.6   Bar scale.                               [ V/Q 4.5 ]
  
  
Antwoorde / Answers  5  
  
    
        5.1   Rit duur = 07:15 − 05:30
  
                             = 1h45 min
  
                A = 1h 45min                           [ V/Q 5.1 ]
  
                Rit duur = 3h35m − 2h55m
  
                             = 40 min
  
                Vertrek om = 15:15 + 40 min
  
                                  = 15:15
  
                B = 15:15                              [ V/Q 5.1 ]
  
    
        5.2   Voor 07:15 ─ die bus vertrek om 07:15
  
                                                              [ V/Q 5.2 ]
  
    
        5.3   Prys = $23,50
  
                Prys van 2 kaartjies = 2 X $23,50
  
                                                = $47,00
  
                                                              [ V/Q 5.3 ]
  
    
        5.4   $47,00 = R 47,00 X 14,85
  
                            = R 697,95
  
                                                              [ V/Q 5.4 ]
  
    
        5.5   Duur = 18:50 − 07:15 
  
                         = 11h35m
  
                                                              [ V/Q 5.5 ]
  
    
        5.6   11h35m = 11 + (35 ÷ 60) h = 11,583 h
  
                              = 11,583 h
  
                                 afstand
                spoed = ───────
                                    tyd
  
                                   880
                spoed = ──────  km/h
                                11,583
  
                          = 75,973  km/h
  
                                                              [ V/Q 5.6 ]
  
    
        5.7   $16,23  =  R259,25
  
                                       259,25
                       $1  =  R  ──────
                                        16,23
  
                       $1  =  R 15,9735  
  
                                                              [ V/Q 5.7 ]
  
    
        5.8.1   100 mph  =  100  X  1,60934  km/h
  
                       =  160,934  km/h
                                                              [ V/Q 5.8.1 ]
  
    
        5.8.2   Duur  =  18:50 − 16:25
  
                             =  2h25m
  
                                                              [ V/Q 5.8.2 ]
  
    
        5.8.3   2h25m = 2 + (25 ÷ 60) h
  
                               = 2,417 h
  
                                afstand
                spoed = ───────
                                   tyd
  
                                  263
                spoed = ──────  km/h
                                2,417
  
                          = 108,813  km/h
  
                                                              [ V/Q 5.8.3 ]
  
    
        5.1   Duration = 07:15 − 05:30
  
                               = 1h45 min
  
                A = 1h 45min                           [ V/Q 5.1 ]
  
                Duration = 3h35m − 2h55m
  
                               = 40 min
  
                Departs at = 15:15 + 40 min
  
                                  = 15:15
  
                B = 15:15                              [ V/Q 5.1 ]
  
    
        5.2   Before 07:15 ─ the bus departs at 07:15
  
                                                              [ V/Q 5.2 ]
  
    
        5.3   Price = $23,50
  
                Price of 2 tickets = 2 X $23,50
  
                                           = $47,00
  
                                                              [ V/Q 5.3 ]
  
    
        5.4   $47,00 = R 47,00 X 14,85
  
                            = R 697,95
  
                                                              [ V/Q 5.4 ]
  
    
        5.5   Duration = 18:50 − 07:15 
  
                            = 11h35m
  
                                                              [ V/Q 5.5 ]
  
    
        5.6   11h35m = 11 + (35 ÷ 60) h = 11,583 h
  
                              = 11,583 h
  
                                distance
                speed = ───────
                                   time
  
                                   880
                speed = ──────  km/h
                                11,583
  
                          = 75,973  km/h
  
                                                              [ V/Q 5.6 ]
  
    
        5.7   $16,23  =  R259,25
  
                                       259,25
                       $1  =  R  ──────
                                        16,23
  
                       $1  =  R 15,9735  
  
                                                              [ V/Q 5.7 ]
  
    
        5.8.1   100 mph  =  100  X  1,60934  km/h
  
                       =  160,934  km/h
                                                              [ V/Q 5.8.1 ]
  
    
        5.8.2   Duration  =  18:50 − 16:25
  
                                   =  2h25m
  
                                                              [ V/Q 5.8.2 ]
  
    
        5.8.3   2h25m = 2 + (25 ÷ 60) h
  
                               = 2,417 h
  
                                distance
                speed = ───────
                                   time
  
                                  263
                speed = ──────  km/h
                                2,417
  
                          = 108,813  km/h
  
                                                              [ V/Q 5.8.3 ]