GCSE · Ratio

Scale drawings and map scales (1 cm represents…, 1 : n)Exam-style questions

Turn a length on a map or scale drawing into a real length and back again: use a scale written as "1 cm represents 5 km", as a scale bar or as a ratio 1 : n, change the units inside a ratio scale, write any scale in the form 1 : n, follow a route instead of a straight line, measure and draw to scale, and scale an area by the square of the scale.

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14 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4

1
A railway tunnel is $2.7$ km long.

The tunnel is shown on a map with a scale of $1 : 30\,000$

How long is the tunnel on the map?

Give your answer in centimetres.

(3 marks)
Level 3 · 3 marksTry it
2
A map uses the scale $2$ cm represents $7$ km.

Kofi saysThis scale is $1 : 3.5$ when it is written as a ratio.(a) Describe the error Kofi has made.

(1 mark)
(b) Write the scale of the map in the form $1 : n$ .

(2 marks)
Level 3 · 3 marksTry it
3
A rectangular field is $90$ m long and $60$ m wide.

A straight path crosses the field from one corner to the opposite corner.
(a) On plain or squared paper, make an accurate scale drawing of the field and the path.

Use a scale of $1$ cm represents $15$ m.

(2 marks)
(b) Use your scale drawing to find the real length of the path.

Give your answer in metres.

(2 marks)
Level 3 · 4 marksTry it
4
Here is a scale diagram showing two villages, $P$ $P$ and $Q$ $Q$ , on a centimetre grid.(Each square of the grid is $1$ $1$ cm by $1$ $1$ cm.)

Scale $1 : 80\,000$ $1 : 80000$
(a) Assume that the road from $P$ $P$ to $Q$ $Q$ is a straight line.

Work out the distance along the road from $P$ $P$ to $Q$ $Q$ .

Give your answer in kilometres.

(4 marks)
(b) In fact, the road from $P$ $P$ to $Q$ $Q$ bends around a hill.

What does this mean about the distance along the road from $P$ $P$ to $Q$ $Q$ ?

Tick one box.
- ☐ It is more than the answer to part (a)
- ☐ It is the same as the answer to part (a)
- ☐ It is less than the answer to part (a)
- ☐ It is impossible to tell
(1 mark)
Level 3 · 5 marksTry it
5
Lily wants to make a scale drawing of her bedroom on a sheet of paper.

The bedroom is a rectangle $4.8$ m long and $3.6$ m wide.

The sheet of paper is a rectangle $29.7$ cm long and $21$ cm wide.

Lily uses a scale of $1 : 20$

Will the scale drawing fit on the sheet of paper?

You must show how you get your answer.

(3 marks)
Level 3 · 3 marksTry it