The scale drawing shows the positions of a lighthouse (L), a port (P) and a harbour (H).
A boat (B) is at sea on a bearing of 135° from the lighthouse (L) and 064° from the port (P).
Mark the position of the boat on the drawing. [3]
On screen this diagram may not be shown at actual size. To measure it, use the question paper (PDF) printed at 100%.
Scale: 1 cm represents 10 km
(b)
(i)
In normal conditions, the boat uses 1 litre of fuel to travel 5 km.
Work out how many litres of fuel the boat will use to get to the harbour (H). The scale is 1 cm represents 10 km. [3]
(ii) State any assumption you have made in answering part (b)(i). How would your answer to part (b)(i) change if you did not make this assumption? [2]
Mark scheme (a)
Scheme
Marks
Comments
Indication of bearing 135° ± 2° from L
B1
Indication of bearing 064° ± 2° from P
B1
Position of the boat marked
B1
Position may be implied by intersection of straight lines for bearings
Mark scheme (b)
Scheme
Marks
Comments
(i) 6 × 10 ÷ 5
M2
Or equivalent full method
STRICT FT ‘their position of the boat’, so ‘their 6’ × 10 ÷ 5 Tolerance ± 2 mm
M1 for ‘their 6’ in cm × 10 or ‘their 6’ in mm × 10 ÷ 5
12 (litres)
A1
FT; must follow correct use of ‘their 6’ in cm
If there is no ‘position of the boat’ marked in (a) allow SC2 for ‘a number of litres’ correctly found from ‘a length in cm’ × 10 ÷ 5 or SC1 for ‘a length in cm’ × 10 ÷ 5
(ii) Valid assumption about the conditions or straight line of the journey e.g. ‘The conditions were normal so the boat travelled 5km per litre.’ or ‘The weather was normal.’ or ‘The sea was normal.’ or ‘The weather conditions were unusually good.’ or ‘The boat travelled in a straight line to H.’
E1
Valid impact based on their assumption e.g. ‘The boat would use more fuel.’ or ‘The boat would use less fuel.’ or ‘The amount of fuel used to travel 5 km would be different, so the total amount needed would be different.’
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