7 The scale diagram below shows towns, A, B and C. Line AB represents the road from A to B and line AC represents the road from A to C.
A shopping centre is to be built so that it is
nearer to the road from A to B than the road from A to C,
less than 14 km from town C.
(a) Using construction, shade the region where the shopping centre could be built. Show all your construction lines.[5]
(b) Explain why the region found in part (a) may not be an appropriate site for the shopping centre. [1]
Mark scheme (a)
Answer
Marks
Part marks and guidance
Accurate angle bisector with 2 pairs of correct arcs
2
B1 for correct bisector with no arcs or incorrect arcs
The bisector does not have to go through A but if extended it must go through A and it must lie within green lines in overlay. For 2 marks condone intersecting arcs of equal radius, one centre B and the other centre C for the construction with bisector drawn.
Arc centre C radius 7cm
2
B1 for arc centre C with incorrect radius
For arc, measure radius using ruler.
Correct region indicated
1Dep
Dependent on at least B1 for bisector and B2 for arc
tolerance ± 2 mm and ± 2° for both constructions
Mark scheme (b)
Answer
Marks
Part marks and guidance
accept any correct assumption e.g. Road[s] is not/are not straight, road AB is busier than road AC, land is not suitable for construction
1
If more than one choose the best one see list of exemplars
Appendix: exemplar responses for Q7(b)
Response
Mark
Road[s] are/are not straight
1
Land is not suitable for construction [ e.g. it may be a lake]
1
The land may flood
1
Site is too small for centre
1
Site is too steep for construction
1
Land lies in a AONB/National Park
1
Too far from the towns (A/B/C)
1
The roads may not be able to cope with the increased traffic
