2. Katie walks on a bearing of 120º. Students could experiment with reading their own directions of travel from compasses. Other practical work, like taking the bearing of a nearby landmark from the school field, or drawing and measuring bearings on local maps, could be used to develop students’ appreciation of the applications of this topic.

3. The ferry is called the Dublin Swift.

4. The ferry sails between Holyhead, in north Wales, and Dublin. A map of the British Isles would demonstrate the practicalities of this route. You could consider the reasons for the establishment of other well-known crossings, like Stranraer-Belfast, Dover-Calais, Harwich-Hook of Holland, Hull-Zeebrugge, and Portsmouth-Le Havre.

5. There are three different instruments displaying the ship’s course as a bearing: a traditional compass, a red digital compass, and the blue computer screen giving information about the ship’s status. Knowing the ship’s bearing at all times is vital. The magnetic compass is particularly important as a backup if there is an electronic or power failure.

6. Ben draws a north line at Holyhead, to allow him to measure the bearing to Dublin. Textbooks, examination questions and maps could be examined to establish the conventions for how to show north. What methods can students suggest for constructing a north line if the given direction of north does not lie on a grid line? You could emphasise the significance of the word from in deciding where to construct the north line and where to measure the bearing.

7. Ben finds that the bearing of Dublin from Holyhead is 275º. The ideal bearing of the course the ship aimed to follow was 269º (although this varied, as the captain explained, because of varying conditions throughout the crossing). The ship must keep within established shipping lanes; and this is the reason for the difference in values. Ben asks viewers to work out the bearing for the return crossing from Dublin to Holyhead.

8. Katie measures the angle anticlockwise. Her mistake is probably more likely when working with a standard 180º protractor. What calculation could she have done to find the correct bearing from her working? You could more fully cover protractor use and methods of measuring and drawing bearings here.

9. The plane follows a bearing of 063º on take-off. The term ‘three-figure bearing’ and the need to include zero could be discussed here. The compass in the flight simulator is marked every 30 degrees, with numerals for the first two figures of the bearing, and had a scale of 6 units between these points. The bearing Katie takes at the start of the flight is shown on the compass as just past the number 6 (so this compass does not use ‘06’).

10. Katie must turn to a bearing of 323º. The compass shows her course between the marks 33 and 30. The runway is 32, and, as Katie explains, these figures represent the first two figures of the required bearing. Viewers are asked to work out the return bearings if Katie wished to retrace her route. Students could discuss methods of working these out from the given diagram using their knowledge of angle properties.

Worksheet 2: Tick or Trash

Question 1

Student B is correct. Student A has shown the return journey correctly but has measured the angle C within the triangle ABC. Student A did not construct a north line at C, which would have assisted in the solution. You could discuss alternative ways of measuring the correct angle.

Question 2

Student A is correct. Student B has found the bearing of B from A. Student B has either placed the protractor on A or measured the angle from south at B and failed to add 180º. Students should be encouraged to consider which compass points the route from B to A lies between, and use these to check the solutions.

Worksheet 3: Exam Practise Questions (Edexcel)

This is a selection of past exam questions from Edexcel, targeted at the middle ability range. You can use the sequence as it stands or select individual questions to suit your needs.

Given below is the mark scheme for each question, which will help you to see how marks are allocated and what the examiner is especially looking out for. The mark schemes use the following abbreviations:
oe
or equivalent
cao
correct answer only
ft
follow-through marks
dep
dependent
indep
independent
M
method marks
A
accuracy marks
B
benefit-of-doubt mark
SC
special case

Question 1

(a) Cardiff (F)

(b) NE (F)

Question 2

Bearing of 157 degrees is drawn.

Question 3

(a) i) 5 cm

ii) ‘5’ x 20 = 100 km (E)

(b) i) 060º

ii) 180º + ‘60º’ = 240º (D)

Question 4

(a) 32² — 15²

root(799)

= 28.3 km

(b) cos W = ¹⁵/₃₂

W = 62.0

Bearing = 360 — ‘W’

= 298º

Notes:

(a) M1 for 32² — 15². M1 (dep) for root. A1 cao for 28.3 or better.

(b) M1 for cos W = ¹⁵/₃₂, sin W = ^‘a’/₃₂, etc. M1 (dep) for inv cos, inv sin etc. A1 cao for 62º or better. B1 ft on angle for bearing 360 — ‘W’.

SC: 306 ± 2º B1.

SC: finding angle at B and identified gets M1, M1 max.

Question 5

(a) root(440² + 440²) = 622 km

(b) Tan 20º = ^x/₄₄₀

x = 440 Tan 20º = 160

Distance = 440 + 160 = 600 km