(a) The scale 1 cm represents 25 m can be written in the form \(1 : k\).
Find the value of \(k\). [1]
(b) The scale drawing represents a harbour.
A boat leaves the harbour from point C and sails on a path that is equidistant from BC and CD. The harbour rules do not allow boats to sail within 75 m of point E.
Find by construction whether the path of the boat will follow the harbour rules. Show all your construction lines. [5]
Mark scheme (a)
Answer
Marks
Part marks and guidance
2500
1
Ignore units
Mark scheme (b)
Answer
Marks
Part marks and guidance
Bisector of angle BCD accurate with pairs of correct arcs
M2
B1 for accurate bisector of angle BCD with no/incorrect arcs
Tol ± 2º use overlay Condone solid/broken lines bisector
Arc centre E radius 3 cm with length fit for purpose
M2
B1 for arc centre E
Tol ± 2 mm For B1 accept 5 correctly marked points in tolerance
No oe with correct constructions
B1
Dep on at least B1M2
Accept the boat will travel within 75 m
Notes
The drawing on this page is not printed at its original size, so measurements taken from it on screen will not match the 1 cm to 25 m scale.