WISKUNDE
GRAAD 12
NOG OEFENINGE
Kaarte : antwoorde
MATHEMATICS
GRADE 12
MORE EXERCISES
Maps : answers
1.1 v = l X b X h
= 800 X 750 X 500 mm
3
800 750 500
= ─── X ─── X ─── cm
3 | verander mm na cm / change m to cm
10 10 10
= 300 000 cm
3
= 300 ℓ | 1 000 cm
3 = 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 ]
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 ]
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 ]