Higher June 2022 Paper 1 Q10
10 Use a ruler and compasses in this question.
\(ABCD\) represents a garden.
A tree is to be planted in the garden.
The tree will be in the region that is closer to \(AB\) than to \(BC\).
Label the region, R, where the tree could be planted.
Show all your construction lines. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| Pair of arcs, equal radii (\(\pm\) 2 mm), centre \(B\), intersecting \(AB\) and \(BC\) | M1 | oe eg single arc, centre \(B\), intersecting \(AB\) and \(BC\) or single arc, centre \(B\), radius \(BC\) (\(\pm\) 2 mm), intersecting \(AB\) |
| Pair of intersecting arcs, equal radii (\(\pm\) 2 mm), centres the intersections on \(AB\) and \(BC\) and angle bisector drawn from \(B\) at least to the intersection of their arcs | A1 | dashed line or condone solid line |
| Correct region R shown as the area between \(AB\) and a straight line from \(B\) to within 2 mm of \(AD\) | B1 | R may be labelled or shaded arcs not required for this mark only SC1 angle bisector for a different angle correctly constructed with arcs |
| Alternative method 2 | ||
| Concentric arcs from \(B\), each intersecting \(AB\) and \(BC\) | M1 | intersections with \(AB\) and \(BC\) must be seen, but full arcs are not necessary |
| Two lines from the \(AB\) intersection of one arc to the \(BC\) intersection of the other arc and angle bisector drawn from \(B\) at least to the intersection of their lines | A1 | dashed line or condone solid line |
| Correct region R shown as the area between \(AB\) and a straight line from \(B\) to within 2 mm of \(AD\) | B1 | R may be labelled or shaded arcs not required for this mark only SC1 angle bisector for a different angle correctly constructed with arcs |
Additional guidance
| Mark any correct construction, ignoring incorrect attempts | |
| Unless shaded incorrectly, ignore construction arcs or other lines in the region labelled | |
| Bisector drawn with no construction arcs, but region correctly identified | M0A0B1 |