Intermediate June 2018 Unit 1 Q17
17. The line AB is drawn below.
The point P lies above the line AB.
The region in which P is located is such that
- P is nearer to point A than to point B,
- \(B\hat{A}P \leqslant 60^\circ\),
- \(AP \geqslant 6\) cm.
Using a ruler and a pair of compasses, construct suitable lines and arcs to represent these conditions.
Construction arcs must be clearly shown.
Shade the region in which the point P is located. [5]
On screen this diagram may not be shown at actual size. To measure it, use the question paper (PDF) printed at 100%.
| Scheme | Marks | Comments |
|---|---|---|
| Correct construction of perpendicular bisector of line AB. | B2 | Allow ± 2° and ± 2 mm B1 for a perpendicular bisector with no arcs or only one pair of intersecting arcs (above or below) shown. B1 for two pairs of correct arcs, with no line or an incorrect line. |
| Correct construction of 60° at A. | B1 | Must show relevant arcs. |
| Arc of radius 6 cm, centre A. | B1 | Must be of sufficient length so as not to be considered a ‘point’ or a ‘notch’. |
| Correct region identified. | B1 | FT for similar viable region (a straight line intersecting AB, an angle at point A and an arc with centre A) even if no previous marks gained. |