GCSE Maths · Higher · Chapter 6: Angles · Lesson 3

Scale drawings and bearings

Grades 4–7About 50 minutesNo calculator36 marks

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NameClassDate

Do Now

Grades 4–6

The first question is what today's lesson needs. The others bring back earlier topics.

A1
Needed today
Write $2.5$ litres in cm $^{3}$ .
[1 mark]
Answer
A2
Last lesson
Find the interior angle of a regular 10-sided polygon.
[1 mark]
Answer
A3
From chapter 1
Write $84$ as a product of its prime factors.
[1 mark]
Answer
A4
From chapter 6
The angles of a triangle are $x$ , $2 x$ and $x + 4 0^{\circ}$ . Find $x$ .
[1 mark]
Answer

Grades 4–6

Your teacher works through each example with you. Then try the one beside it.

Example 1

A map has a scale of $1 : 80000$ . Two villages are $9.5$ cm apart on the map. How far apart are they really, in kilometres?

Hint

1

cm on the map is

80000

cm. There are

100000

cm in a kilometre.

B1
A map has a scale of $1 : 60000$ . Two farms are $7.5$ cm apart on the map. How far apart are they really, in kilometres?
[2 marks]
Answer

Example 2

The bearing of $B$ from $A$ is $23 7^{\circ}$ . Work out the bearing of $A$ from $B$ .

Hint The two bearings differ by

18 0^{\circ}

. Draw a north line at each point.

B2
The bearing of $Q$ from $P$ is $10 8^{\circ}$ . Work out the bearing of $P$ from $Q$ .
[2 marks]
Answer

Grades 5–6

C1
A map has a scale of $1$ cm to $5$ km. Two towns are $37$ km apart. How far apart are they on the map?
[2 marks]
Answer
C2
A road $12$ km long is $4.8$ cm long on a map. Write the scale of the map in the form $1 : n$ .
[2 marks]
Answer

C3
Write down the bearing of $Q$ from $P$ .
[2 marks]
Not drawn accurately
Answer
C4
From a tower $T$ , ship $A$ is on a bearing of $07 2^{\circ}$ and ship $B$ is on a bearing of $21 3^{\circ}$ . Work out the size of angle $A T B$ .
[2 marks]
Not drawn accurately
Answer
C5
A plan of a house has a scale of $1 : 50$ . A room is $4.2$ m long. How long is it on the plan, in centimetres?
[2 marks]
Answer

Grades 6–7

D1
A plan has a scale of $1 : 500$ . A lawn covers $3$ cm $^{2}$ on the plan. Jo says, "The real lawn is $1500$ cm $^{2}$ , because the scale multiplies by $500$ ."
Explain why Jo is wrong. Work out the real area of the lawn, in m $^{2}$ .
[3 marks]

D2
On a map with a scale of $1 : 400000$ , a lighthouse $L$ is $5.5$ cm from a harbour $H$ , on a bearing of $05 0^{\circ}$ . A rock $R$ is due east of $L$ . The bearing of $R$ from $H$ is $07 5^{\circ}$ .
Not drawn accurately
(a)
Work out the real distance from $H$ to $L$ , in kilometres.
[2 marks]
Answer
(b)
Work out the bearing of $H$ from $L$ .
[1 mark]
Answer
(c)
A boat leaves $H$ at 10:40 and sails straight to $L$ at $24$ km/h. At what time does it arrive?
[2 marks]
Answer $\dots\dots\dots\dots$
(d)
Work out the size of angle $H R L$ . You must show your working.
[3 marks]
Answer
Total for D2: 8 marks
D3
A ship sails $18$ km from port $P$ on a bearing of $14 0^{\circ}$ to a buoy $Q$ . It then sails $18$ km from $Q$ on a bearing of $23 0^{\circ}$ to a rock $R$ . Work out the bearing of $R$ from $P$ . You must show your working.
[4 marks]
Not drawn accurately
Answer

Grade 8 and beyond

No route is given. The hints are at the end of the sheet. Use one at a time.

Colour one circle on each line.

	Not yet	Nearly	Yes
I can use a map scale written as a ratio in both directions.
I can write a three-figure bearing and the bearing back again.
I can use north lines to find angles in a bearings problem.

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