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Map Reading, Scale and Interpretation

Geography · WAEC and JAMB · SS2 and SS3

Map work is the compulsory first question in WAEC Geography Paper 2, and it is the easiest full marks on the whole paper because the answers are measured, not remembered. Candidates who practise scale conversion, grid references, gradient and cross-sections for two weeks walk away with marks that essay candidates sweat for.

What you need to know

  • Scale is expressed in three ways: a statement (1 cm represents 0.5 km), a representative fraction or RF (1:50,000), and a linear or line scale drawn on the map. The linear scale is the only one that remains correct after a map is enlarged or reduced, because it grows or shrinks along with the map.
  • To turn an RF into a statement in kilometres, divide the denominator by 100,000, since 1 km = 100,000 cm. So 1:50,000 means 1 cm represents 0.5 km, and 1:100,000 means 1 cm represents 1 km. Most Nigerian topographical sheets you will meet in the exam are 1:50,000.
  • Measure a straight distance with a ruler. Measure a winding feature such as a road or river by laying a thread along it, or by pivoting the straight edge of a sheet of paper round each bend and marking off each segment, then straightening the thread or paper against the ruler.
  • Grid references are read eastings first, then northings: along the corridor, then up the stairs. A four-figure reference such as 3847 names a whole grid square; a six-figure reference such as 384476 fixes a point to the nearest 100 m on a 1:50,000 sheet because each grid square is divided mentally into tenths.
  • Bearings are measured clockwise from north and always written in three figures: 045 degrees, 135 degrees, 270 degrees. Place the protractor centre on the starting point with zero pointing to grid north, then read round clockwise to the target.
  • A back bearing is the bearing of the first point from the second. Add 180 degrees if the forward bearing is less than 180 degrees, and subtract 180 degrees if it is more. The bearing of B from A as 060 degrees gives the bearing of A from B as 240 degrees.
  • Contours are lines joining places of equal height above sea level, and the fixed difference between successive contours is the contour interval, usually 50 ft or 15 m on older Nigerian sheets. Contours packed close together mean a steep slope; contours far apart mean a gentle slope; evenly spaced contours mean a uniform slope.
  • Learn the signature of each relief feature: a conical hill is a set of small closed concentric rings; a ridge is a long narrow set of elongated contours; a spur shows contours bending outward towards the lower land; a valley shows contours bending as a V that points upstream, that is towards the higher land.
  • An escarpment or cuesta has contours crowded on one face and widely spaced on the other, a plateau is a broad flat top ringed by crowded contours, a col or saddle is the low gap between two hills, and a depression is marked by contours with short ticks pointing inward.
  • Gradient is vertical interval divided by horizontal equivalent, with both quantities converted to the same unit, and it is quoted as 1 in n. A gradient of 1 in 20 means the land rises 1 m for every 20 m travelled horizontally.
  • To draw a cross-section, lay the straight edge of a sheet of paper along the section line, tick off every point where a contour, river or road crosses it and write its height, then transfer the ticks to a base line, choose a vertical scale, plot the heights and join them with a smooth curve rather than straight jagged lines.
  • Vertical exaggeration is the vertical scale divided by the horizontal scale, and it is the reason your drawn profile looks more mountainous than the real land. Always state it when the question asks for it.
  • Intervisibility is tested by drawing the cross-section between the two points and ruling a straight line of sight from one to the other; if any land rises above that line, the two points are not intervisible.
  • Area of an irregular feature is found by counting complete grid squares, then adding half the number of incomplete squares. On a 1:50,000 sheet each grid square measures 1 km by 1 km, so each square counts as 1 square kilometre.

Key terms

Scale
The fixed ratio between a distance measured on a map and the corresponding distance on the ground.
Representative fraction
A scale written as a ratio or fraction in which both numbers are in the same unit, such as 1:50,000.
Contour
A line on a map joining all points of the same height above mean sea level.
Contour interval
The constant vertical difference in height between two successive contour lines on a map.
Gradient
The slope of the land, calculated as vertical interval divided by horizontal equivalent and expressed as 1 in n.
Bearing
The direction of one point from another measured in degrees clockwise from north and written in three figures.
Vertical exaggeration
The number of times the vertical scale of a cross-section is greater than the horizontal scale of the map.

Formulae

  • Distance in km per cm = RF denominator / 100,000
  • Ground distance = map distance x scale denominator
  • Gradient = vertical interval / horizontal equivalent (both in the same unit), expressed as 1 in n
  • Area = number of complete squares + (number of incomplete squares / 2)
  • On a 1:50,000 map, one grid square = 1 square kilometre
  • Vertical exaggeration = vertical scale / horizontal scale
  • Back bearing = forward bearing + 180 degrees (if forward bearing is less than 180 degrees), or forward bearing - 180 degrees (if it is more)

Worked examples

On a map of scale 1:50,000, the road from Ilaro to Owode measures 7.4 cm. Calculate the actual ground distance in kilometres.

  1. Convert the scale to a statement: 50,000 / 100,000 = 0.5, so 1 cm on the map represents 0.5 km on the ground.
  2. Multiply the measured map distance by the ground value of 1 cm: 7.4 x 0.5.
  3. 7.4 x 0.5 = 3.7

A trigonometrical station stands at 420 m and a river crossing 3 km away stands at 270 m. Calculate the gradient between them.

  1. Find the vertical interval: 420 m - 270 m = 150 m.
  2. Convert the horizontal equivalent to the same unit: 3 km = 3,000 m.
  3. Gradient = 150 / 3,000 = 1 / 20.

The mistake to avoid

Candidates lose the gradient mark by dividing 150 m by 3 km without first turning the 3 km into 3,000 m, and they lose grid reference marks by quoting the northing before the easting. Convert both heights and distances to metres before you divide, and say eastings first, northings second, out loud, every single time.

In the exam

Question 1 of Paper 2 is compulsory map work and it carries the heaviest single block of marks on the paper, so do it first while your hand is steady. Show every stage of your working, including the conversion line, because WAEC awards method marks even where the final figure is wrong. Always write the unit beside your answer, and for a cross-section always label the vertical axis with heights and state the vertical scale you used.