Scale and Generalisation Questions and Answers

Answer: A

Correct answer: a representative fraction

A representative fraction states the scale as a pure ratio, so it is independent of units - one of anything on the map is 50,000 of the same thing on the ground, whether inches, centimetres or paces. That unit independence is its advantage over a verbal scale, and unlike a bar scale it does not survive photocopying at a different size.

Answer: B

Photocopying or resizing a sheet changes every printed distance, so a stated ratio becomes wrong while a drawn bar shrinks or grows with the map and stays true. That is why bars are printed on maps intended to be reproduced.

Answer: C

One centimetre on the map stands for 50,000 centimetres on the ground. Dividing by 100 gives 500 metres, so a kilometre of ground occupies two centimetres of paper. Converting the ratio into ground units once, at the start, saves repeating the division for every measurement taken.

Answer: D

Six centimetres represents 6 times 25,000, which is 150,000 centimetres. Converting gives 1,500 metres, or 1.5 kilometres. Checking against the unit value confirms it: each centimetre is 250 metres at this scale, and six of those is indeed 1.5 kilometres of ground.

Answer: A

Four kilometres is 400,000 centimetres, and dividing by 100,000 gives 4 centimetres. At this scale one centimetre of map covers exactly one kilometre of ground, which makes the arithmetic quick to check and is why 1:100,000 is a convenient scale for regional sheets.

Answer: B

Area scales with the square of the linear ratio, so 10,000 squared gives 100 million. This is why a modest change in linear scale produces a very large change in the ground area a sheet can cover, and why halving the linear scale quadruples the area one sheet must hold.

Answer: C

Correct answer: 15,000 square metres

Convert each side to the ground first: \[ 2\ \mathrm{cm} \times 5000 = 10{,}000\ \mathrm{cm} = 100\ \mathrm{m}, \qquad 3\ \mathrm{cm} \times 5000 = 150\ \mathrm{m}, \] so the area is \( 100\times150 = 15{,}000\ \mathrm{m^2} \). Multiplying the map area of 6 cm² by 5000 once gives 600, which is the trap - area scales with the *square* of the linear factor, so the multiplier is \( 5000^2 \).

Answer: D

Correct answer: 1:1,000

The larger the scale, the smaller the denominator, because the fraction is genuinely a fraction: 1/1,000 is larger than 1/250,000. So 1:1,000 shows the most detail over the least ground, and 1:250,000 the least detail over the most. The wording is counter-intuitive precisely because a large-scale map covers a small area.

Answer: A

It is the other way round. A large scale means a large representative fraction, so a small area is shown at considerable detail. Small-scale maps cover wide areas with correspondingly less detail, and the wording trips people constantly.

Answer: B

Both statements are true and the reason explains the assertion directly: when one centimetre must stand for ten kilometres rather than 250 metres, most features cannot be drawn at a legible size and must be omitted or combined.