WISKUNDIGE GELETTERDHEID
GRAAD 11
NOG OEFENINGE
Kaarte en reise : antwoorde
MATHEMATICAL LITERACY
GRADE 11
MORE EXERCISES
Maps and trips : answers
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 ]
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. ]
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 ]
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 ]
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 ]