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(MAPWORK)
The content and skills of this section are mostly tested in Geography Paper 2.
Most of this paper requires learners to apply skills.
It covers LO1, 2 and 3.
It is important that a learner must have a proper calculator and mathematical
Instruments.
Calculating distance on a map
distance on a map is calculated between two points
e.g. between school and museum
1:50 000
A
4cm
the two points are joined with a line as in the case of A above.
then measure the length of line A using a ruler with clear cm or mm units.
write down the reading you got after measuring line A, e.g. 4cm.
check the scale of the map on which the school and the museum are depicted, e.g.
1:50 000
then multiply the distance between the school and the museum by the scale on the
map, e.g.
4 cm x 50 000
= 200 000 cm
the answer above needs to be converted to the units of distance i.e. kilometres (km).
we use the following scale for conversion
km hdammdmcm mm10 0000We have used centimetres to measure line A, therefore, we must convert centimetres
to kilometres. This you achieve by placing 1under the kilometre box on the scale and
placing zeros as you move towards the right until you reach centimetres. According
to the conversion scale above, 1km is equal 100 000cm. Then to convert your
centimetres to kilometres you will have to divide the 200 000cm by 100 000,e.g.
200 000
100 000
= 2 km
This means that the distance between the school and the museum is 4cm on the map
but in reality is 2km.
If a learner has used millimetres to measure the distance between the school and the
museum, line A could have measured 40mm. Using the conversion scale, the learner
will place 1 under the kilometre box and placing zeros until reaching the millimetre
box as in the case below.
kmhdammdmcmmm10 00000
This means that for one to convert the millimetres to kilometres, he will divide
millimetres by 1000 000.
e.g. 40mm x 50 000
= 2 000 000
1 000 000
= 2 km
note that the same distance on a map measured in different units (whether cm or
mm) will give the same answer when converted to the same unit (e.g. km).
Summary
To calculate distance on a map you must do the following:
*measure distance between two points on a map in cm or mm
*Multiply this by the scale of the map and divide by 100 000 if you used
centimetres or by 1000 000 if you used millimetres to get kilometres.
*Another way of converting cm distance of 1 : 50 000 map into km is to
multiply by 0,5 (e.g. 4 cm x 0,5 = 2km)
*Should the distance be required in metres, then you will divide centimetres
by 100 or millimetres by 1000 according to the following tables.
kmhdammdmcmmm100
1m = 100 cm
or
kmhdammdmcmmm1000 1m = 1000mm
*sometimes distance can be calculated along a winding river or path, this you
do by using a piece of a string placed along the winding object and thereafter
stretch it along the units of your ruler to determine the length and then
calculate as shown in the previous steps.
Direction on a map
There are four main cardinal points north, south, east and west. There are other directions that lie between them and are known as intermediate points.
How to find direction between two points on a map: (e.g. from church to taxi rank)
first determine True North from the church because it is your point of departure
then join the church and the taxi rank as in the diagram above.
the direction of the taxi rank from the church is North East (NE)
True Bearing
True Bearing is an angle that is measured in a clockwise direction from True North. It is measured in degrees using a protractor. On a topographical map true bearing can be determined from any two points (one of these two points will be used as a point of reference to determine the bearing of the other).
Determining true bearing of the taxi rank from the church:
first determine True North from the church as your point of departure.
then join the church and the taxi rank as in the diagram above.
place your protractor in such a way that its centre corresponds with the centre of
where the line from TN and taxi rank meet.
take the reading of the outside number on the protractor that corresponds with the
black line towards the taxi rank, in this case it will be 90o.
therefore the true bearing of the taxi rank from the church is 90o.
Magnetic Bearing
Magnetic Bearing = True Bearing + Magnetic Declination
for example, if true bearing is 60o and the magnetic declination is 24o 16'. The
magnetic bearing will be 84o 16' (remember degrees add to degrees and not to
minutes).
Magnetic Declination
Magnetic declination is the angle between true north and magnetic north.
The angle is always to the west of True North in South Africa.
when asked to calculate the magnetic declination, look for more information around
the topographic map where you see the sign similar to the one above.
Example:
Use the information above to calculate the magnetic declination for 1992.
Step 1
the MD (22o. 5) above does not have minutes( ' ) but only degrees (o)
to get minutes multiply 22o (5x6) = 22o 30'
Step 2
get the difference in years
1992 1982 = 10 years
multiply the difference in years by mean annual change (2' east)
10 x 2' east = 20' east
this means that the magnetic declination will move towards the east by 20' and thus
become smaller or decrease.
Step 3
note that if the magnetic declination is to the east it becomes smaller and has to be
subtracted but if west it becomes bigger and has to be added.
22o 30' west
" 20' east
= 22o 10' west of TN
note that the magnetic declination decreased from 22o 30 in 1982 to 22o 10 in 1992
due to the fact that the mean annual change was to the east.
Useful Hints:
1o (degree) = 60' (minutes)
Minutes greater than sixty should be converted to degrees
e.g.13o 65' should be converted to 14o 05'
13o. 3 (always multiply number after a comma by 6) 13o (3x6)= 13o 18'
If mean annual change is east you subtract the total change and if west you add the
total change.
TASK
Use the diagram below to:
1. Find the direction of the following points (MR, YE, BT, CG, BO, PM, PR, WZ,
VX, YW).
2. Calculate distance between the following points (KL, PS, OC and UW).
4. Determine the true bearing of B from R, U from E, W from Y.
3. Calculate the magnetic declination for 2004, if in 1998 it was 25o. 4 and the mean
annual change is 3' west.
ANSWERS
1. Direction:
MR south
YE north east
BT south south west
CG south
BO north north east
PM east
PR south east
WZ west
VX north
YW north west
2. Distance:
KL: 6,3 cm x 50 000
= 315 000
100 000
= 3,15 km
PS: 9,4 cm x 50 000
= 470 000
100 000
= 4,7 km
OC: 4 cm x 50 000
= 200 000
100 000
= 2 km
UW: 5 cm x 50 000
= 250 000
100 000
= 2,5 km
3. Bearing:
B from R (90o)
U from E (131o)
W from Y (318o)
4. Magnetic declination:
2004 1998 = 6 years
3' west x 6 = 18' west (to add)
25o (4x6) = 250 24' west
25o 24'
+ 18'
25o 42' west of TN
Area
Learners can be requested to calculate area of a specific land use on a map.
The formula for area is Length x Breadth (A = L x B).
Area can be measured in square metres (m2) or square kilometres (km2).
Example:(use the following diagram to calculate area in km2 )
Step 1
Multiply the length by the scale of the map
= 7 cm x 50 000
= 350 000
100 000
= 3,5 km
Step 2
Multiply the breadth by the scale of the map
= 2cm x 50 000
= 100 000
100 000
= 1km
Step 3
Multiply the length by breadth as in the formula
A = L x B
= 3.5 km x 1 km
= 3.5 km2
NB: Follow the same steps when calculating area in m2.
Gradient
Gradient is the steepness or the slope of the ground
It is calculated between two points of different heights on a map.
These points might be a trig beacon ("202, spot height (" 242) or a
contour line ( 1020 ) and their heights are in metres.
The formula for gradient is G = Vertical Interval(VI)
Horizontal Equivalent (HE)
VI is the difference in height between two points. To get the VI you subtract the bigger height from the smaller height.
HE is the distance in metres between the two points. To get HE you calculate the
same way you work out distance on a map.
Example
Calculate the gradient between spot height (" 301) and trig beacon ("201). The map distance between these two points is 6cm and the map scale is 1:50 000.
Step 1
Minus the bigger height from the smaller height to get Vertical Interval
VI = 301m 201m
= 100m
Step 2
Calculate distance in metres to get Horizontal Equivalent
HE = 6 cm x 50 000
= 300 000
100
= 3000m
Step 3
Bring down the formula for gradient to replace values above:
G = VI
HE
= 100m 1
3000m simplify this fraction by 100 to get 30
= 1 : 30 (expressed as a ratio)
TASK
If the scale of the map is 1: 50 000, calculate the following:
Area (km2) with the length of 10 cm and the breadth of 6 cm.
Gradient between spot height 294 and trig beacon 334 with a map distance of 4 cm.
ANSWERS
A = L x B
L = 10 x 50 000 B = 6cm x 50 000
= 500 000 = 300 000
100 000 100 000
= 5 km = 3 km
A = 5 km x 3 km
= 15 km2
G = VI
HE
VI = 334 m 294 m HE = 4cm x 50 000
= 40 m = 200 000
100
= 2000 m
G = 40
2000 simplify the fraction by 40
= 1 : 50
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