IGCSE Geography · Area 3 · Geographical Skills

Maps, graphs and cartographic skills

Skills questions come up on every paper, and most of the marks lost here are method marks: a grid reference read the wrong way round, a distance left in centimetres, a bearing measured from the wrong north, or a graph chosen that cannot show the pattern. This page covers the cartographic skills - locating places, scale and distance, direction and bearings, relief and cross-sections, and the types of map you may be given - and the graphical skills of choosing, drawing and interpreting graphs, charts and diagrams.

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Syllabus coverage

  • Select, construct and interpret maps using direction, scale, symbols, a key and other information
  • Extract, interpret, analyse and evaluate information presented on maps
  • Use co-ordinates, latitude and longitude, and four and six figure grid references
  • Give directions using the 16-point compass and bearings from grid north
  • Measure and estimate distances and area
  • Use and interpret gradient, contour lines and spot heights, and calculate differences in height
  • Use atlas maps, base maps, choropleth maps, desire line maps, distribution maps, flow line maps, isoline maps, maps of different scales including 1:50 000 and 1:25 000, route maps, sphere of influence maps, sketch maps and thematic maps
  • Select, present, construct and communicate data through appropriate graphs, charts and diagrams, using relevant scales and annotations
  • Extract, interpret, analyse and evaluate information presented on graphs, charts and diagrams
  • Identify and evaluate variations, trends and patterns from data provided
  • Use bar graphs (horizontal, vertical and divided), climate graphs, cross-sections, dispersion graphs, doughnut graphs, flow diagrams, histograms with equal class interval, kite graphs, line graphs, pictograms, pie charts, population pyramids, proportional symbols, radial graphs, rose charts, scatter graphs including a best fit line, systems diagrams, triangular graphs and venn diagrams

Part of the IGCSE Geography syllabus 0460.

Maps: what you are asked to doA four-figure reference locates a square; a six-figure reference locates a point inside it.Always give the eastings before the northings, and measure bearings clockwise from north.Reading a map: the four things you are asked to do424344181716six-figure reference: 4 3 2 1 7 2eastings first, then northingsGrid referencesfour figures locate a square, six locate a pointScale and distancemeasure with a ruler, then convert using the scale barDirection and bearingbearings are measured clockwise from north, in three digitsRelief and contoursclose contours mean steep ground; V shapes point upstreamCross-sectionstransfer the heights where the line crosses each contour
Cartographic skills on one map extract: eastings and northings for grid references, the scale bar for measuring distance, a protractor for bearings from grid north, and contour lines and spot heights for describing relief and calculating gradient.

Reading a map: the key, north, and knowing what type of map you have been given

Every map question begins with the same three moves: read the key, find north, and read the scale. The key, or legend, is the only place some of the information exists, so a symbol you have not checked cannot be interpreted. North is drawn at the top of the map unless the map says otherwise, and the scale bar tells you what a centimetre on the map represents on the ground.

Maps are built to show one kind of information, so recognising the type tells you what the map can and cannot tell you. A question may ask you to interpret a map, to choose a suitable type for a set of data, or to suggest an improvement to one. The syllabus names the types below, and you should be able to say what each is for and one weakness of it.

Type of mapWhat it showsWatch out for
Atlas mapA small-scale map of a large area - a country, a continent or the world - used to locate places and describe broad patternsDetail is generalised; you cannot read individual streets or fields
Base mapAn outline map showing only the basic features, such as the coastline and boundaries, on which you add your own dataNothing is on it until you plot it, so the key you draw must be complete
Choropleth mapAreas shaded or coloured in bands, one shade for each range of values, such as population density by districtIt suggests the change happens exactly at the boundary and hides variation inside each area
Desire line mapStraight lines drawn from where people live to where they travel, the line thickness showing the number of peopleLines cross and can be hard to read where the movement is heavy
Distribution mapWhere something is found, shown by dots, shading or symbolsA dot may stand for one item or for many, so check the key before comparing
Flow line mapLines of varying width with arrows showing movement between places, such as migration, trade or trafficThe width must be proportional to the flow, not chosen to look neat
Isoline mapLines joining places of equal value - contours for height, isobars for pressure, isohyets for rainfall, isotherms for temperatureThe lines are drawn from limited data, so the values between them are estimates
Route mapA journey or a proposed route, with the features that affect itOften simplified and not to scale, so it cannot be measured like a topographic map
Sphere of influence mapThe area served by a settlement, shop or service, with the boundary drawn from survey dataThe boundary is a zone, not a line; a few people travel from beyond it
Sketch mapA simplified hand-drawn map showing only the features that matter for the taskIt is not to scale, so it must be labelled clearly and never used for measuring
Thematic mapA map about one theme, such as land use, climate or healthThe theme is selective: other information that may explain the pattern is left out
Maps of different scalesThe same area at 1:50 000 and at 1:25 000, or a small-scale map of the whole countryThe larger scale map (1:25 000) shows more detail over a smaller area; the smaller scale map (1:50 000) covers twice the ground for the same sheet size
Check the key before you interpret anything. A symbol or shade you have not looked up is a guess, and guesses do not score.

Locating places: four and six figure grid references, co-ordinates, latitude and longitude

A map grid is numbered from the bottom left. The eastings are the vertical lines, numbered from left to right along the bottom of the map, and the northings are the horizontal lines, numbered from bottom to top up the side. Every grid reference is given eastings first, then northings - along the corridor and up the stairs. Get that order wrong and the point lands somewhere else entirely.

A four-figure grid reference names a whole square. Find the easting to the left of the point and the northing below it, and give the two figures together, such as 4318. On a map where the grid squares are 1 km across, that locates the place to the nearest kilometre, which is accurate enough to say which square a village or a wood is in.

A six-figure grid reference locates a point inside the square. Divide each side of the square into ten equal parts, by eye or with the edge of your ruler marked in tenths. Count the tenths across from the easting first, then the tenths up from the northing, and give three figures for each, such as 435 187. Each tenth is a tenth of a kilometre, so a six-figure reference locates a point to the nearest 100 m. A point that falls exactly on a line is written with a zero in that position.

Latitude and longitude locate places on atlas and world maps where there is no numbered grid. Latitude is the distance north or south of the Equator, measured from 0 degrees at the Equator to 90 degrees at each pole. Longitude is the distance east or west of the Greenwich meridian, measured from 0 degrees to 180 degrees. Both are given in degrees, minutes and seconds with a direction letter, for example 51 degrees 30 minutes north, so a pair of them fixes a position anywhere on the globe. Co-ordinates is the general word for any pair of numbers that fixes a position, whether that is a grid reference, a latitude and longitude, or a reading from two axes on a graph.

  • Eastings first, then northings: along the corridor, then up the stairs.
  • Four figures locate the square; six figures locate the point inside it, to the nearest tenth of a grid square.
  • Latitude: north or south of the Equator, 0 to 90 degrees. Longitude: east or west of Greenwich, 0 to 180 degrees.
Write the reference with a space in the middle, such as 435 187. It shows the examiner that you have given three figures for each direction and not mixed the two up.

Scale: measuring distance and estimating area

Scale is the link between the map and the ground. A scale of 1:50 000 means that one unit on the map represents 50 000 of the same units on the ground, so 1 cm on the map is 50 000 cm, which is 500 m, or 0.5 km, in reality. A scale of 1:25 000 means 1 cm on the map is 25 000 cm, which is 250 m. A 1:25 000 map is described as a larger scale map than a 1:50 000 map, because each centimetre covers a smaller area of ground and shows more detail; the 1:50 000 sheet covers twice as much ground for the same size of paper, with less detail. A line scale drawn along the bottom of the map can be used directly: place the edge of a piece of paper against it and mark off the kilometres.

For a straight-line distance, lay a ruler between the two points, read the length in centimetres, and multiply by the scale. On a 1:50 000 map, 4 cm represents 4 x 50 000 = 200 000 cm = 2 000 m = 2 km. Always finish the conversion in metres or kilometres; a distance left in centimetres is not a real-world distance.

For a curved distance along a road, a river or a coastline, a ruler is useless because it measures the shortcut. Lay the edge of a strip of paper along the route, marking the start and then turning the paper at each bend and marking the new position, or lay a piece of string along the route and pinch it at the end. Straighten the paper or the string against the ruler and convert the total length with the scale.

Area can be estimated in two ways. For a regular shape, measure the length and the width, convert both to real distances, and multiply them. For an irregular shape, such as a lake or a wood, trace the outline onto squared paper and count the squares: count the whole squares first, then add the part squares together to make whole ones, and multiply the total by the real area of one square, worked out from the scale. If a map's grid squares are 2 cm across and the scale is 1:50 000, then each grid square represents 1 km by 1 km, which is 1 km squared, and counting grid squares is the quickest estimate of all.

Convert every distance out of centimetres before you write it down. 250 000 cm is not an answer; 2.5 km is.

Direction: the 16-point compass and bearings from grid north

Direction on a map is given from north. The 16-point compass divides the full circle into sixteen directions, each 22.5 degrees apart, which is precise enough for a description of direction on a map: from the church, the wood lies to the north-east. Use the compass points when a question asks for a direction, and give the nearest one rather than a vague 'up and to the right'.

A bearing is more precise. It is measured in degrees clockwise from north, and it is always written as three figures, so due north is 000 degrees, due east is 090 degrees, due south is 180 degrees and due west is 270 degrees. A bearing of 45 degrees would be written 045. On a map, bearings are measured from grid north, which is the direction in which the northings run, not from true north or magnetic north, so the north line you draw must be parallel to the vertical grid lines.

To measure a bearing between two points: draw a straight line joining them; draw a north line through the starting point, parallel to the northings; place the centre of the protractor on the starting point with the 0 degree mark on the north line; and read the angle clockwise round to the line joining the points. If the line points to the left of north, read the scale the other way round and subtract from 360, so a line 30 degrees anticlockwise of north is a bearing of 330 degrees.

The back bearing, the bearing from the second point back to the first, is always 180 degrees different. If the bearing from A to B is less than 180 degrees, add 180; if it is more, subtract 180. A bearing of 060 degrees from A to B means a bearing of 240 degrees from B to A.

Compass directionBearing
North000 degrees
North-north-east022.5 degrees
North-east045 degrees
East-north-east067.5 degrees
East090 degrees
East-south-east112.5 degrees
South-east135 degrees
South-south-east157.5 degrees
South180 degrees
South-south-west202.5 degrees
South-west225 degrees
West-south-west247.5 degrees
West270 degrees
West-north-west292.5 degrees
North-west315 degrees
North-north-west337.5 degrees
Bearings are always three figures, measured clockwise from grid north. A bearing of 30 degrees is written 030; a line pointing to the left of north is read anticlockwise from 360.

Relief: contour lines, spot heights, gradient and cross-sections

Contour lines join points of equal height above sea level, and the vertical interval is the height difference between one contour and the next, which is always stated in the map key. Because contours never cross and never touch, the pattern they make is a picture of the shape of the land. Where contours are close together the ground rises quickly, so the slope is steep; where they are far apart the ground rises slowly, so the slope is gentle. A spot height is a dot with its exact height beside it, and a triangulation point is marked with a triangle and a height; these give precise figures where the contours alone can only bracket the height.

Learn the shapes. Contours that form a V pointing up a valley show a river valley, and the stream itself is drawn in the bottom of the V. A V pointing down the slope, with ground falling away on both sides, is a spur. Closed circles getting smaller and higher inwards mark a hill or a peak, and closed circles getting lower inwards, often drawn with hachures, mark a hollow or depression. A wide gap between contours on either side of a line of close contours is a plateau or a flat-topped ridge.

The difference in height between two points is found by subtracting the lower height from the higher one, taking care with spot heights that are not exactly on a contour. The gradient of a slope compares the vertical rise with the horizontal distance, so gradient = difference in height / horizontal distance. The two measurements must be in the same units before you divide. A slope that falls 60 m over a horizontal distance of 1.5 km has a gradient of 60 / 1500 = 1 / 25, which is written as a gradient of 1 in 25, as a ratio 1:25, or as a percentage, 60 / 1500 x 100 = 4%. A larger second number, such as 1 in 50, means a gentler slope; a smaller one, such as 1 in 5, means a steeper slope.

A cross-section shows the profile of the land along a chosen line across the map, and it is the clearest way to show relief in an answer. To draw one: place the straight edge of a piece of paper along the line of the section on the map; mark on the paper every point where a contour crosses the line, and write the height of each; draw a base line on graph paper the same length as the section; choose a vertical scale that fits the page and mark the contour heights up the vertical axis, labelling each with its height in metres; transfer the marks from the paper to the base line and plot each one at its correct height; join the points with a smooth line; and label the axes, the highest and lowest points and any named features such as a river, road or settlement. A cross-section is usually drawn with the vertical scale exaggerated, so the slopes look steeper than they really are - say so if the question asks you to interpret one.

Close contours mean steep, not flat. Then use the vertical interval to work out how much height the slope actually gains.

Choosing a graph, chart or diagram for the data you have

The choice of graph is decided by the data, not by what looks attractive. Ask what you are trying to show: the parts of a whole, a comparison between places, a change over time, a relationship between two variables, or the spread of one variable. Then pick the form built for that job. A graph that cannot show the pattern the data contain will lose the marks for interpretation as well as for presentation.

Two pairs are easy to confuse. A bar graph has a gap between the bars because each bar is a separate category, such as the population of each of five towns. A histogram has bars that touch, because the data are continuous and divided into equal class intervals, such as the number of houses in each price band. A pie chart shows the parts of a single whole at one moment, so it cannot show change over time; a line graph is the right choice for change over time. Every graph needs a title, both axes labelled with their units, and a key where symbols or colours are used.

Whichever form you choose, the scale on the axes must suit the data and the graph must be annotated so it tells the story by itself. Mark the highest and lowest values, name the places, and add short notes pointing to the important features rather than leaving the examiner to work out what the graph shows. For a pie chart, the angle of each sector is the percentage multiplied by 3.6, because a full circle is 360 degrees. For proportional symbols, the area of the symbol must be proportional to the value, not the radius; a circle drawn with twice the radius has four times the area, which exaggerates the difference.

Graph, chart or diagramWhat it isBest used for
Vertical bar graphBars of equal width standing on a base line, with a gap between the categoriesComparing a total between places or categories, such as rainfall for each month
Horizontal bar graphThe same, with the bars lying on their sideComparing categories with long names, or ranking places from largest to smallest
Divided bar graphOne bar for each place, divided into segmentsShowing the parts that make up a total, such as the sources of a country's energy
Climate graphBars for average monthly rainfall, with a line for average monthly temperature on a second axisShowing the climate of a station and identifying its climate type
Cross-sectionA line drawn to show the shape of the land along a chosen line across a mapShowing relief and slope, such as the profile of a valley or a beach
Dispersion graphThe individual values of a data set plotted as dots above or below a line showing the meanShowing the spread of values around the mean and comparing how variable two sites are
Doughnut graphA pie chart with a hole in the middleShowing parts of a whole, or progress towards a target
Flow diagramBoxes or lines joined by arrowsShowing movement or a sequence of stages, such as a process or a route
HistogramBars drawn with equal class intervals that touch each other, because the data are continuousShowing the frequency distribution of one continuous variable, such as prices in bands
Kite graphA line drawn along an axis, with bars that widen where a value is high and pinch to a point where it is zeroShowing how several species change along a transect
Line graphPoints joined by a line, or a smooth line drawn through themShowing continuous change, especially over time
PictogramRepeated symbols, each standing for a fixed numberSimple comparison for a general audience; less precise than a bar graph
Pie chartA circle divided into sectors, each sector's angle proportional to its share of the totalShowing the proportions of a whole, such as land use or employment structure
Population pyramidPaired horizontal bars, males on one side and females on the other, divided into age groupsShowing the age and sex structure of a population
Proportional symbolsSymbols whose size represents a value, usually circles on a mapComparing totals at different places; the area of the symbol must be proportional to the value
Radial graphValues plotted along spokes radiating from a central point and then joined upComparing several variables at a few sites, such as the characteristics of two settlements
Rose chartSpokes drawn to scale in different directions from a centreShowing how often something comes from each direction, such as wind direction or where visitors have travelled from
Scatter graphOne dot for each site, plotted against two variables, with a line of best fitShowing the relationship between two sets of data, such as pebble size and distance from the sea
Systems diagramBoxes for stores joined by arrows for flows, with feedback loopsShowing how a system works, such as a drainage basin or the carbon cycle
Triangular graphA triangle with three axes, each reading from 0 to 100 per centShowing the proportions of three components that together make up 100 per cent
Venn diagramOverlapping circlesShowing what two or three sets of data have in common and what is unique to each
Parts of a whole -> pie or doughnut chart. Change over time -> line graph. Relationship between two variables -> scatter graph. Name the form and justify it in terms of the data.

Reading and evaluating graphs: trends, variations, anomalies and weaknesses

Reading a graph is a sequence, and each step earns marks. First describe the overall trend, such as 'the population rose steadily between the two dates'. Then quote the evidence - the highest and lowest values, with figures and units, and the named places they belong to. Then describe the rate of change, because 'it rose quickly and then levelled off' is a different answer from 'it rose'. Only then explain the pattern using geography, and always check the graph for anomalies, the points that do not fit, which are worth mentioning rather than ignoring.

On a scatter graph, each dot is one site, with one variable on each axis. If the dots run from bottom left to top right the relationship is positive, so as one value rises so does the other; if they run from top left to bottom right it is negative. A line of best fit is drawn by eye through the middle of the points, with roughly equal numbers above and below it, and its steepness shows how strong the relationship is. Dots far from the line are anomalies and may have a real cause worth explaining. Correlation is not the same as cause: two variables can move together because a third factor drives both.

A line of best fit lets you predict. Interpolation means reading a value from inside the range of the data you have, which is reasonably reliable. Extrapolation means extending the line beyond the data, which is a guess: a trend that has been rising for ten years need not keep rising for the next ten.

Graphs can be used to mislead, and the syllabus asks you to identify the weaknesses in a statistical presentation. Watch for axes that do not start at zero or that use a broken scale, which makes a small change look dramatic; unequal class intervals in a histogram, which makes the tallest bar meaningless; missing units or no title; a pie chart with too many small slices to compare; three-dimensional pie charts, where the slices nearest the viewer look larger than they are; proportional symbols scaled by radius rather than area; a line graph with no scale on the vertical axis; and data drawn from a small sample or from one unrepresentative place but described as if it applied everywhere.

  • Describe the trend, quote the highest and lowest values with figures and units, describe the rate of change, then explain the pattern geographically.
  • Positive relationship: both variables rise together. Negative relationship: one rises as the other falls. No clear pattern: no relationship.
  • Interpolation, inside the data range, is reliable; extrapolation, beyond it, is a prediction and may be wrong.
  • Misleaders: a broken or non-zero axis, unequal class intervals, symbols scaled by radius, missing units, too many pie slices, a sample too small to generalise from.
A graph answer is not finished until you have quoted a figure from it. 'The rainfall increases inland' scores nothing; 'rainfall rises from 800 mm on the coast to 1 400 mm at the highest station inland' does.

Key terms you must be able to define

Scale
The relationship between a distance on a map and the same distance on the ground, written as a ratio such as 1:50 000, meaning that 1 unit on the map represents 50 000 of the same units on the ground.
Grid reference
A pair of numbers that locates a place on a map, given with the easting first and the northing second; four figures locate a whole grid square and six figures locate a point inside it.
Easting
A vertical grid line on a map, numbered from left to right along the bottom of the map, so the easting is the first half of any grid reference.
Northing
A horizontal grid line on a map, numbered from bottom to top up the side of the map, so the northing is the second half of any grid reference.
Latitude
The angular distance of a place north or south of the Equator, measured from 0 degrees at the Equator to 90 degrees at the poles.
Longitude
The angular distance of a place east or west of the Greenwich meridian, measured from 0 degrees to 180 degrees.
Bearing
The direction of one place from another, measured in degrees clockwise from grid north and always written as three figures, so due east is 090 degrees.
Grid north
The direction in which the northings of a map grid run; bearings on a map are measured from grid north, not from true north or magnetic north.
Contour line
A line on a map joining points of equal height above sea level; the closer the lines, the steeper the slope, and the height difference between one contour and the next is the vertical interval.
Spot height
A dot on a map with the exact height of that point printed beside it, used to give a precise height where the contour lines can only bracket the value.
Gradient
The steepness of a slope, calculated as the difference in height divided by the horizontal distance, and expressed as a ratio such as 1:25, as 1 in 25, or as a percentage.
Cross-section
A drawing showing the profile of the land along a line across a map, with height plotted on the vertical axis against distance on the horizontal axis.
Choropleth map
A map on which areas are shaded or coloured in bands, one shade for each range of values, such as population density by administrative district.
Isoline map
A map on which lines join places of equal value, for example contours for height, isobars for air pressure, isohyets for rainfall and isotherms for temperature.
Flow line map
A map on which lines of varying width, usually with arrows, show the volume and direction of movement between places, such as migration or traffic flows.
Desire line map
A map on which straight lines are drawn from where people live to where they travel, with the thickness of each line showing how many people make that journey.
Sphere of influence map
A map showing the area from which a settlement, shop or service draws its customers or users, with the boundary drawn from survey data.
Sketch map
A simplified hand-drawn map showing only the features that matter for a particular task, which is not drawn to scale and must be labelled clearly.
Thematic map
A map that shows information about one chosen theme, such as land use, climate or health, rather than the general topography of the area.
Base map
An outline map showing only basic features such as the coastline and boundaries, on which the student plots their own data to make a finished map.
Dispersion graph
A graph on which the individual values of a data set are plotted as dots above and below a line showing the mean, so that the spread of the data and any outliers are visible.
Scatter graph
A graph on which one dot represents one site, plotted against two variables, so that the relationship between the two sets of data can be seen.
Line of best fit
A straight or curved line drawn by eye through the middle of the points on a scatter graph, with roughly equal numbers of points above and below it, showing the trend of the relationship.
Triangular graph
A graph in the shape of a triangle with three axes, each reading from 0 to 100 per cent, used to show three components that together make up 100 per cent.
Proportional symbols
Symbols, usually circles on a map, drawn so that the area of the symbol is proportional to the value it represents.
Population pyramid
A graph of paired horizontal bars, males on one side and females on the other, divided into age groups, showing the age and sex structure of a population.
Kite graph
A graph drawn along an axis with bars that widen where a value is high and pinch to a point where it is zero, used to show how several species change along a transect.
Rose chart
A chart on which spokes are drawn to scale in different directions from a centre, used to show how often something comes from each direction, such as wind direction.
Radial graph
A graph on which values are plotted along spokes radiating from a central point and then joined up, used to compare several variables at a few sites.
Systems diagram
A diagram using boxes for stores and arrows for flows, often with feedback loops, to show how a system such as a drainage basin or the carbon cycle works.
Venn diagram
A diagram of overlapping circles, used to show what two or three sets of data have in common and what belongs to only one of them.
Histogram
A graph of continuous data divided into equal class intervals, drawn with bars that touch because there are no gaps between the classes.
Climate graph
A graph combining bars for average monthly rainfall with a line for average monthly temperature on a second vertical axis, used to describe the climate of a station.
Doughnut graph
A pie chart with a hole in the middle, used to show the proportions of a whole or progress towards a target.
Pictogram
A graph on which repeated symbols each stand for a fixed number of items, used for simple comparison but less precise than a bar graph.

Applied to real places

Geography marks sit in the named example and the detail around it. These show the shape of a strong answer - the place, the process, and the link between them - then you write your own using the case studies your teacher set.

Measuring a distance along a road on a 1:50 000 map

Choose the two points named in the question, lay a strip of paper along the road with its edge on the route, and mark the start. Turn the paper at each bend, marking the position each time, until you reach the end. Straighten the paper against the ruler and read the total length. If it comes to 6 cm, the real distance is 6 x 50 000 = 300 000 cm = 3 000 m = 3 km. A ruler laid straight between the two points would have given a shorter answer, because a road that bends is longer than the straight line joining its ends.

Describing the site of a settlement from a 1:25 000 map extract

A site description answers the question 'why is the settlement here?' using the map as evidence. Give the grid reference first, then work through relief, drainage, aspect and routeways: the village lies at 482 176, on the gentle lower slopes of a valley side where the contours are widely spaced, beside a river crossing where two roads meet. Add one comparison with a second settlement on the same extract, and one sentence on what the map cannot tell you, such as why the settlement has grown since the map was surveyed. Each statement must be tied to something on the map - a contour pattern, a spot height, a symbol or a grid reference - or it is only an assumption.

Plotting your own fieldwork data on a scatter graph

Suppose you measured the long axis of ten pebbles at each of several points down a beach and recorded the distance of each point from the high-water mark. Put distance along the beach on the horizontal axis and pebble size on the vertical axis, one dot for each point, then draw a line of best fit by eye. If the dots slope upwards to the right, pebble size increases with distance down the beach. Read off the highest and lowest values, name any point that sits well away from the line and suggest why - a sea wall, a stream outlet or a place where material was dumped - and then say how confident you are: ten points on one day at one beach support a pattern for that beach, not for every beach.

Showing three components of a total on a triangular graph

A triangular graph is the right choice when three values add up to 100 per cent, such as the share of a settlement's employment in primary, secondary and tertiary work, or the proportions of sand, silt and clay in a soil sample. Each of the three axes runs from 0 to 100 per cent, and the value for one component is read along the line parallel to the axis opposite it. Plot one point per site, and the position of the point inside the triangle shows the mix at once: points clustered in one corner have a similar economy, and points moving towards the tertiary corner across a series of settlements suggest a shift in the type of work available.

Comparing two places with climate graphs

A climate graph puts average monthly rainfall as bars and average monthly temperature as a line, with the two axes drawn so that the temperature line and the rainfall bars can be read together. To interpret one, describe the pattern rather than listing twelve numbers: state the wettest and driest months and their values, the highest and lowest temperatures, and the temperature range. Then explain what the shape means in terms of the geography of the place - the total rainfall, its seasonality, and whether the temperature range is large or small. Comparing two climate graphs is easier when you use the same scale for both, which is why an answer that re-draws one graph with a different scale has broken the comparison.

Drawing a cross-section across a river valley

Take the line of the section across the valley as given on the map, mark on the edge of a piece of paper every contour that crosses the line and its height, and draw a base line on graph paper of the same length. Mark a vertical scale that fits the page, plot each contour height at its correct distance along the base line, and join the points with a smooth line. Then label the axes with their units, mark the highest and lowest points, and label the river, any road and any settlement. Finally note that the vertical scale is exaggerated relative to the horizontal, so the valley sides look steeper on the section than they are on the ground - a point worth making when you interpret one.

Flashcards

Click a card to flip it. Mark honestly — the tracker uses this.

Q1In which order are the two halves of a grid reference given?
Eastings first, then northings - along the corridor and up the stairs. The easting is read from the vertical lines numbered along the bottom of the map, and the northing from the horizontal lines numbered up the side.
Q2What is the difference between a four-figure and a six-figure grid reference?
A four-figure reference names a whole grid square, to the nearest kilometre on a map with 1 km squares. A six-figure reference divides each side of the square into ten parts and locates a point inside it, to the nearest 100 m.
Q3On a 1:50 000 map, what real distance does 1 cm represent?
1 cm on the map represents 50 000 cm on the ground, which is 500 m, or 0.5 km. On a 1:25 000 map, 1 cm represents 250 m.
Q4Which is the larger scale map, 1:50 000 or 1:25 000, and what does that mean?
1:25 000 is the larger scale map, because each centimetre covers less ground and shows more detail. A 1:50 000 sheet covers twice as much ground for the same size of paper, with less detail.
Q5How do you measure the distance along a winding road on a map?
Lay the edge of a strip of paper along the road, turning it and marking the position at each bend, or lay a piece of string along the route. Straighten the paper or string against a ruler, read the length in centimetres, then convert it with the scale.
Q6How is a bearing measured and written?
Measure the angle clockwise from grid north - a north line drawn parallel to the northings - and write it as three figures, for example 045 degrees. The back bearing is 180 degrees different: add 180 if the forward bearing is under 180, subtract if it is over.
Q7What do close contour lines show, and what is the vertical interval?
Close contour lines show a steep slope; widely spaced lines show a gentle slope. The vertical interval is the height difference between one contour and the next, and it is stated in the map key.
Q8How is gradient calculated and expressed?
Gradient = difference in height / horizontal distance, with both measurements in the same units. Express it as a ratio such as 1:25, as 1 in 25, or as a percentage. A larger second number means a gentler slope.
Q9What are the steps in drawing a cross-section from a map?
Mark each contour crossing on the edge of a piece of paper with its height; draw a base line the same length as the section; mark a vertical scale and label the heights; plot each point at its height and distance; join them with a smooth line; then label the axes, the highest and lowest points and any named features.
Q10When should you use a bar graph and when a histogram?
A bar graph has gaps between the bars and is used for separate categories, such as the population of each of five towns. A histogram has bars that touch, because the data are continuous and divided into equal class intervals, such as prices in bands.
Q11What is a line of best fit, and what is the difference between interpolation and extrapolation?
A line of best fit is drawn by eye through the middle of the points on a scatter graph, with roughly equal numbers above and below it. Interpolation reads a value from inside the range of the data and is reliable; extrapolation extends the line beyond the data and is only a prediction.
Q12Give three ways a graph can be drawn so that it misleads the reader.
A vertical axis that does not start at zero or uses a broken scale, which exaggerates a small change; unequal class intervals in a histogram, which makes the tallest bar meaningless; and proportional symbols scaled by radius rather than area, so that a circle with twice the radius looks four times as large.
0 of 12 marked as known

Exam-style questions

8 questions, 25 marks. Write your answer, then reveal the mark scheme and tick each point you actually made. Answering honestly here is what makes the rest of the site useful.

StateAO11 mark
State the rule you follow when reading a four-figure grid reference.

Mark scheme — tick each point you actually made

Examiner tip: One mark, so give one complete rule. Naming the lines without saying which comes first does not score, because the order is the whole point.
CalculateAO22 marks
A map has a scale of 1:50 000. (a) Calculate the real distance represented by 4 cm on the map, giving your answer in kilometres. (b) A second map has a scale of 1:25 000 and the straight-line distance between two points on it is 6 cm. Calculate the real distance in kilometres.

Mark scheme — tick each point you actually made

Examiner tip: Show the multiplication and then the conversion, and finish in kilometres. An answer left in centimetres, or with the conversion done by the wrong power of ten, loses the mark.
DescribeAO23 marks
Describe how you would measure the distance along a winding road between two settlements on a 1:50 000 map.

Mark scheme — tick each point you actually made

Examiner tip: The method marks are for following the route and for the conversion. A ruler laid between the two settlements measures the shortcut, not the road, and the answer will be too short.
ExplainAO23 marks
Explain how contour lines and spot heights can be used to describe the relief of an area, and how the steepness of a slope is shown on a map.

Mark scheme — tick each point you actually made

Examiner tip: Three marks, three ideas: what contours show, what spot heights add, and how spacing shows steepness. Add the vertical interval from the key if the question gives you one.
CalculateAO23 marks
A hillside falls from a height of 160 m above sea level to a height of 100 m over a horizontal distance of 1.5 km. Calculate the gradient of the hillside as a ratio and as a percentage, and state what the ratio tells you about the slope.

Mark scheme — tick each point you actually made

Examiner tip: Convert both measurements to the same units before dividing - this is where most marks are lost. Give the answer as a ratio and as a percentage if both are asked for, and say what the ratio means.
ExplainAO24 marks
Explain two ways in which a choropleth map of population density by district could give a misleading impression of the distribution of population.

Mark scheme — tick each point you actually made

Any 4 of these score full marks. The examiner only needs 4 distinct points - pick the ones you actually made.
Examiner tip: Two ways are needed, so give two developed points rather than four short ones. The mark is for the limitation of the method, not for describing what a choropleth map is.
SuggestAO24 marks
A student has measured the size of beach material at ten points down a beach and the distance of each point from the high-water mark. Suggest a suitable graph for these data and explain how it would be constructed and used to show the relationship between the two measurements.

Mark scheme — tick each point you actually made

Examiner tip: Name the graph, then give the axes, the line of best fit and what it is used for. Marks are lost by describing a bar graph or by forgetting to say which variable goes on which axis.
EvaluateAO35 marks
A student investigating a river drew a line graph of discharge against distance downstream, using data collected at six sites on one day. The vertical axis started at 40 cubic metres per second rather than zero. Evaluate the presentation of the data and the conclusion the student can draw.

Mark scheme — tick each point you actually made

Any 5 of these score full marks. The examiner only needs 5 distinct points - pick the ones you actually made.
Examiner tip: An evaluate answer needs the good points, the faults and a judgement. Work through the choice of graph, the scale on the axes, the sample size and timing, and what else should have been measured, then finish with a sentence on how far the conclusion can be trusted.

Exam technique for this topic

  • Give the units every time. Distances in metres or kilometres, heights in metres, and gradient as a ratio such as 1 in 25 or as a percentage - never as a number on its own.
  • For a six-figure grid reference, split the square into ten equal parts by eye and estimate the tenths. A point that sits exactly on a grid line is written with a zero in that position, and the easting always comes first.
  • Measure along the route, not across it. Use a strip of paper or a piece of string for a road, a river or a coastline, and turn the paper at each bend.
  • Name the graph you have chosen and justify it in terms of the data - parts of a whole, comparison between places, change over time, or the relationship between two variables - then give the axes and their units.
  • When you describe a pattern, quote the evidence: give the highest and lowest values with their figures and units, or the grid references and named places, and only then explain the pattern using geographical ideas.

Why students lose marks here

A student wroteA student wrote: 'Grid reference 762 431 means I measure 762 up the map and then 431 across it.'
Why it loses marksGrid references are always read eastings first, then northings - along the corridor and up the stairs. Reading the pair the other way round puts the point in a completely different square, so the answer scores nothing even though the numbers were copied correctly from the map.
The answer that scoresThe first three figures are the easting, read from the vertical lines numbered along the bottom of the map, and the last three are the northing, read from the horizontal lines numbered up the side. Measure to the right first, then up, and check that the point you have found lies inside the square you identified.
A student wroteA student wrote: 'The distance on the map is 5 cm and the scale is 1:50 000, so the real distance is 5 x 50 000 = 250 000 km.'
Why it loses marksThe multiplication was right but the units were wrong. Multiplying centimetres on the map by the scale gives centimetres on the ground, not kilometres, and a distance of 250 000 km would be most of the way round the world.
The answer that scoresConvert the answer out of centimetres in two steps: divide by 100 to get metres, then by 1 000 to get kilometres. So 5 x 50 000 = 250 000 cm = 2 500 m = 2.5 km. On a 1:50 000 map, 1 cm on the map represents 0.5 km on the ground, which is a useful shortcut to remember.
A student wroteA student wrote: 'The bearing from the car park to the church is 070 degrees, so the bearing from the church back to the car park is also 070 degrees.'
Why it loses marksThe bearing from A to B and the bearing from B to A are measured from different points, and the two lines point in opposite directions. The back bearing is always 180 degrees different from the forward bearing.
The answer that scoresIf the forward bearing is less than 180 degrees, add 180 to get the back bearing: 070 + 180 = 250 degrees. If it is more than 180 degrees, subtract 180. Both bearings must be measured clockwise from grid north, that is from a line drawn parallel to the northings.
A student wroteA student wrote: 'The contours are very close together along this valley side, so the land there is almost flat.'
Why it loses marksIt is the opposite. Close contour lines mean that the height changes quickly over a short horizontal distance, which is a steep slope. Flat or gently sloping ground is shown by contours that are far apart.
The answer that scoresUse the vertical interval from the map key to work out the height gain. If the contours are 10 m apart and six of them are crossed in 200 m of horizontal distance, the slope rises 60 m over 200 m, a gradient of 60 / 200, or 1 in 3.3. Widely spaced contours on the valley floor show where the land is nearly level.
A student wroteA student wrote: 'I have shown how the population of the town changed between 1990 and 2020 using a pie chart, with one slice for each year.'
Why it loses marksA pie chart shows the parts of a single whole at one moment in time. Slicing it by year gives a set of percentages that cannot be compared, because there is no common total, and the change over the period - which is what the question asked about - cannot be seen at all.
The answer that scoresChange over time needs a graph with time on the horizontal axis: a line graph, or a vertical bar graph with one bar for each year or each census. Reserve the pie chart for the parts of one total, such as the proportion of the town's workers in each employment sector in a single year, and if you want to show how that proportion changed, draw two pie charts side by side or use a divided bar graph.

Where this fits in IGCSE Geography

This page is one topic of Cambridge IGCSE Geography 0460. IGCSE Geography is the course home: every area and every topic in Cambridge's own order, the papers you sit and what each one tests, and the exam-practice tools. The full topic list, with each topic linked to its revision page, is on the IGCSE Geography syllabus page.