Foundation November 2017 Paper 1 Q20
20 Four points A, B, C and D are shown on the scale diagram below.
(a) On the diagram, construct and mark the two points that are
- the same distance from A and B
and
- 15 m from C.
Show all your construction lines. [5]
(b) The points A, B, C and D represent the four corners of Monty’s garden.
His garden is bounded by four straight fences A to B, B to C, C to D and D to A.
His garden is bounded by four straight fences A to B, B to C, C to D and D to A.
Monty wants to plant a tree in his garden at a place that satisfies the two conditions in part (a).
Explain why there is only one position where Monty can plant his tree. [1]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Accurate perpendicular bisector from at least AB passing within 3 cm of C with two pairs of correct arcs | 2 | B1 for accurate perpendicular bisector | Tolerance \(\pm\) 2 mm |
| Arc centre C, at least from BC to CD with radius 3 cm | 2 | B1 for any arc centre C | |
| Two correct points marked intersecting the line and the arc | 1 | Dep on B1 (bisector) and B2 (arc) scored above | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| One of the points is not in his garden or only one is in his garden | 1 | Accept any correct reason e.g. one point is behind the CD fence | |
Appendix
Exemplar responses for Q20(b)
| Response | Mark |
|---|---|
| One does not lie inside his garden | 1 |
| One is outside of the fence | 1 |
| Only one lies in his garden | 1 |