Higher June 2019 Unit 1 Q4
4. The point \(P\) is such that:
- \(P\) lies on the perpendicular bisector of the line \(AB\),
- \(B\hat{A}P = 30^\circ\).
Using only a ruler and a pair of compasses, show one of the possible positions of \(P\).
All construction lines and arcs must be shown. [4]
| Scheme | Marks | Comments |
|---|---|---|
| Correct construction arcs must be seen for the first three B1 marks. | ||
| Correct construction method for perpendicular bisector with line drawn. | B1 | Two pairs of intersecting arcs (centres at A and B). |
| Correct construction method for 60° at point A. | B1 | Allow if drawn at point B. Allow B1 for correct method (tolerance will be penalised with final B0). |
| Correct construction method for bisecting an angle with line drawn. | B1 | FT ‘their angle of 60°’ drawn at point A or point B. |
| Point P clearly identified | B1 | C.A.O. within tolerance. Intersecting lines alone with no indication that this is point P is not sufficient for this B1. Do not penalise if both possible positions shown. Final B1 may be awarded after B0B0B0. |
4. Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| Correct construction arcs must be seen for the first three B1 marks | ||
| Correct construction method for 60° at point A (or B). | B1 | Allow B1 for correct method (tolerance will be penalised with final B0). |
| Correct construction method for bisecting the angle at A (or B) with line drawn. | B1 | |
| Repeating the above two stages at B (or A) | B1 | |
| Point P clearly identified | B1 | C.A.O. within tolerance. Intersecting lines alone with no indication that this is point P is not sufficient for this B1. Do not penalise if both possible positions shown. Final B1 may be awarded after B0B0B0. |