Higher June 2022 Paper 5 Q9
9 The diagram shows the scale drawing of a sandpit, ABCD.
It also shows the arc of all points in the sandpit that are 80 cm from corner A.
Scale: 1 cm represents 20 cm
A game is played by throwing a ball into the sandpit.
Points may be scored when the ball lands in the sandpit.
- 1 point if the ball lands within 80 cm of corner A,
and - 1 point if the ball is closer to side AB than side AD,
and - 1 point if the ball is closer to corner A than corner B.
By completing the construction, find and shade the regions where 2 points can be scored.
Show all your construction lines. [6]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Accurate ruled angle bisector with two pairs of supporting arcs isw | B2 | B1 for accurate angle bisector at least 2 cm long with no/incorrect arcs isw | Use overlay as a guide, bisectors should lie within or on the lines For B2 allow use of the arc around A as one pair – at least 2 cm long for B2 Tolerance ±2° |
| Accurate ruled perpendicular bisector with two correct pairs of intersecting arcs isw | B2 | B1 for accurate perpendicular bisector at least 2 cm long with no/incorrect arcs isw | Tolerance ±2° and ±2 mm At least 2 cm long for B2 but must remain in tolerance if extended within shape for B1 and B2 |
| 2 correct regions shaded/clearly indicated with no extras | B2 dep | Dep on at least B1B1 B1dep for 1 correct region with no extras or 2 correct regions and one extra | B1dep on B1 for angle bisector for region bounded by angle bisector or dep on B1B1 for region bounded by both bisectors and arc See Appendix for solution |
Appendix: correct answer for Question 9
