(a) Construct the perpendicular from the point P to the line AB.[2]
(b) The diagram shows a field LMN.
A tree is to be planted in the field so that it is
the same distance from the fences MN and ML
and
the same distance from corner M as from corner N.
Show, by construction, whether this can be done or cannot be done.
This …………… be done. [5]
Mark scheme (a)
Answer
Marks
Part marks and guidance
Ruled line through P and perpendicular to AB constructed with correct arcs (one pair intersecting AB)
2
B1 for correct arcs (one pair intersecting AB) only but no line or correct ruled line but no, or incomplete, construction arcs
Condone dotted lines Set protractor to 90° and check 88° to 92° at AB Correct construction arcs as shown (may be two pairs of arcs used to draw line through P) Ignore other arcs if correct arcs clearly used to construct line Condone perpendicular extending beyond AB but must pass through P and reach AB (no daylight) Alternative arcs (eg a kite construction) One centred on A length AP and one centred on B length BP meeting below AB (may also pass through P). Candidates may use points on AB other than A and B for this construction. In such cases check radii of arcs using on-line ruler to judge
See appendix for exemplars
Appendix: Question 7(a)
The overlay only shows one solution.
Response
Comment
Mark
A
This is the a correct alternative method for arcs centred on A and B
Use overlay to see arcs lie within circles
(We can also check using on-line ruler)
Candidates may use points on AB other than A and B for this construction. In such cases check radii of arcs using on-line ruler to judge.
Scores 2
B
This is the main method not the alternative. Arc from P intersects AB at A and another point. Red arc from A intersects the arc from that other point.
Scores 2
C
Looks similar to Exemplar B but shows why the overlay must be used with caution.
Overlay shows red arc is centred at A.
The other arc is centred elsewhere on the line AB, but there is no evidence of where it is centred. This is checked by eye.
This is a valid alternative method.
Scores 2
D
Only one correct (pair of) arcs (One arc centred on P and cutting AB twice) and inaccurate line.
0 marks
E
No valid sets of arcs nor a correct line
0 marks
Mark scheme (b)
Answer
Marks
Part marks and guidance
accurate and correct ruled angle bisector of angle M with supporting arcs and accurate and correct ruled perpendicular bisector of MN with supporting arcs and ‘cannot’ with full evidence
5
B2 for accurate and correct ruled angle bisector of angle M with supporting arcs or B1 for accurate and correct ruled angle bisector of angle M
B2 for accurate and correct ruled perpendicular bisector of MN with supporting arcs or B1 for accurate and correct ruled perpendicular bisector of MN
B1 dep for correct decision (No) with full evidence dep on at least B1 B1
tolerance on angles ± 2° and on radius of arcs ± 2mm
For 5 marks the diagram must be fully correct with no extra constructions and lines touching the opposite sides of the triangle.
Bisectors to be at least 2 cm long
full evidence means two correct ruled lines within tolerance
