60-second revision
- 1 km = 1,000 m = 100,000 cm. A scale of 1 : 100,000 means 1 cm on the map = 1 km on the ground.
- Map distance × scale value = actual distance; keep units consistent.
- Standard maps have north at the top: up = north, right = east, down = south, left = west.
- Closely spaced contours = steep slope; widely spaced = gentle slope.
- Percentage change = (new − old) / old × 100 — always divide by the old value.
- Pie chart: angle = percentage × 3.6; percentage = angle / 3.6.
- Average = total / number of items.
Map scales
A map scale links map distance to ground distance. It can be a statement (1 cm represents 5 km), a representative fraction (1 : 500,000) or a drawn line scale. A representative fraction has the same unit on both sides, so 1 : 500,000 means 1 cm on the map is 500,000 cm, which is 5 km, on the ground.
| Scale | Meaning | Map 3 cm = ground |
|---|---|---|
| 1 cm = 5 km | statement | 15 km |
| 1 : 100,000 | 1 cm = 1 km | 3 km |
| 1 : 250,000 | 1 cm = 2.5 km | 7.5 km |
| 1 : 25,000 | 1 cm = 250 m | 750 m |
Directions on a map
Unless an arrow shows otherwise, north is at the top. The four cardinal directions sit at 90° to each other and the four intermediate directions lie between them: north-east (up-right), south-east (down-right), south-west (down-left) and north-west (up-left). Direction is always stated "from" the reference point: if A is up-right of B, A is north-east of B and B is south-west of A.
Contour lines
Contour lines join points of equal height above sea level. Their spacing shows slope: closely packed contours mean a steep slope, widely spaced ones a gentle slope, and contours forming closed loops with rising values towards the centre mark a hill. On Survey of India topographic sheets contours are printed in brown and water features in blue.
Reading tables and bar graphs
First read the title, units and scale. Then answer only what is asked. For change questions, decide whether the question wants absolute change (subtract) or percentage change (subtract, divide by the earlier value, multiply by 100).
Worked example: production 250 (Year 1), 300 (Year 2), 270 (Year 3). Year 2 rise = 50/250 = 20%. Year 3 fall = 30/300 = 10%. Note that a 20% rise followed by a 10% fall does not bring you back to the start.
Line graphs
A line graph shows change over time. The steeper the segment, the faster the change. To compare rates, compute the change for each interval (equal intervals make comparison direct). A downward segment is a decrease, not a "small increase".
Pie charts
| Percentage | Angle |
|---|---|
| 10% | 36° |
| 20% | 72° |
| 25% | 90° |
| 30% | 108° |
| 50% | 180° |
Worked example: a budget of Rs 60,000 shown in a pie chart with rent at 72°. 72/360 = 1/5, so rent = Rs 12,000. Equivalently 72° = 20%.
Shortcuts for data questions
- Ratio of two values: simplify early — 450 : 600 is 3 : 4.
- Percentage of a total: 135 out of 900 is 135/900 = 15%.
- Highest percentage rise is not always the highest absolute rise — compute both when the bases differ.
- Pie chart in degrees: compare angles directly; 54° versus 36° means the first is 1.5 times the second.
- If a value doubles, the rise is 100%; if it halves, the fall is 50%.
Averages and totals
Average = total / count. If the average of 6 days is 40, the total is 240. If one more day with 54 is added, the new average is (240 + 54) / 7 = 42. Quick checks like this help with "which day was above average" questions too.
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