Scale Drawing and Navigation — National 5 Applications of Maths Practice Questions

1

A map has a scale of

\displaystyle 1 : 50000

.
Two points are

\displaystyle 4

cm apart on the map.
Calculate the actual distance between them in kilometres.

Video solution coming soon

2

A plan is drawn to a scale of

\displaystyle 1

cm :

\displaystyle 5

m.
A wall measures

\displaystyle 3.5

cm on the plan.
Calculate the actual length of the wall.

Video solution coming soon

3

A scale drawing uses

\displaystyle 1

cm to represent

\displaystyle 20

m.
A field measures

\displaystyle 240

m by

\displaystyle 160

m.
Calculate the dimensions of the field on the drawing.

Video solution coming soon

4

A ship sails from a harbour on a bearing of

\displaystyle 072^\circ

.
Calculate the bearing it must follow to return directly to the harbour.

Video solution coming soon

5

A walker sets off on a bearing of

\displaystyle 295^\circ

.
Calculate the bearing of the return journey.

Video solution coming soon

6

2018 P1 Q12

(3, 2)5 Marks

A helicopter flew from Aberdeen airport to transport workers to oil rig 1 and then continued on to oil rig 2.
It flew 82 km on a bearing of $\displaystyle 042^{\circ}$ to oil rig 1.
It then flew 46 km on a bearing of $\displaystyle 194^{\circ}$ to oil rig 2.

(a) Construct a scale drawing to illustrate this journey.
Use a scale of 1 cm : 10 km.

Starting point marked Airport with North line

The helicopter then returns to Aberdeen airport from oil rig 2.

(b) Use the scale drawing to determine the distance and bearing of the airport from oil rig 2.

7

2021 P2 Q8(b)

(3, 2)5 Marks

The local orienteering club set up a course at the event. Participants leave the start point and run on a bearing of $\displaystyle 055^\circ$ for 140 m to flag A. They then run on a bearing of $\displaystyle 170^\circ$ for 252 m to flag B.

(b) (i) Construct a scale drawing to illustrate the route. Use a scale of 1 cm: 40 m

(ii) The pupils then return to the start point. Use the scale drawing to determine the bearing and distance of the start point from flag B.

8

2024 P1 Q11

(3, 2)5 Marks

A helicopter was hired to drop passengers off at two separate locations.

It flew 60 km on a bearing of $\displaystyle 227^\circ$ to the first location.
It then flew 45 km on a bearing of $\displaystyle 152^\circ$ to the second location.

(a) Construct a scale drawing to illustrate this journey.
Use a scale of 1 cm : 10 km.

The helicopter then returns to the start from the second location.

(b) Use your scale drawing to determine the distance and bearing of the start from the second location.

9

2025 P2 Q8

3 Marks

The start of an orienteering course is being planned.
Competitors leave the start point and run on a bearing of 335° for 400 metres to checkpoint A.
From checkpoint A they then run on a bearing of 030° for 320 metres to checkpoint B.

Construct a scale drawing to illustrate this part of the course.
Use a scale of 1 cm = 100 m.