Higher November 2024 Unit 2 Q6
6. Line \(AB\) is drawn below.
Point \(C\) lies below the line \(AB\).
The region in which point \(C\) is located is such that:
- \(A\hat{B}C \leqslant 30^\circ\)
- line \(BC \leqslant 5\) cm.
Use a ruler and a pair of compasses to construct suitable arcs and lines to show this region.
You must show your construction arcs.
Shade the region in which point \(C\) is located. [4]
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 |
|---|---|---|
| Allow a tolerance of ± 2° and ± 2 mm. The construction need not be below the line for the B2 and the first B1 (but the final B1 won’t be awarded). | ||
| Correct bisector of 60° | B2 | Allow at A or B. Correct construction arcs (initial and secondary) must be seen or an alternative valid method. The angle must be formed for the bisector and the line must reach the intersection of the arcs. Award B1 for one of the following:
|
| Arc of radius 5 cm, centre B. | B1 | For B1, the arc must be of sufficient length so as not to be considered a ‘point’ or a ‘notch’ i.e. for a sector of at least 10° at B. |
| Correct region identified. | B1 | For this B1, the region must be:
|