Higher June 2023 Unit 1 Q10
10. \(XY\) is a tangent to a circle, centre \(O\), at the point \(A\).
\(A\hat{Y}O = 54^\circ\).
Diagram not drawn to scale
(a) What percentage of the whole circle is shaded?
You must show how you calculated your answer. [3]
You must show how you calculated your answer. [3]
(b) What tangent property of circles did you use in order to answer part (a)? [1]
| Scheme | Marks | Comments |
|---|---|---|
| (\(AOY\) =) 36(°) | B1 | Check diagram. |
| (% shaded =) \(\dfrac{36}{360}\) (× 100) or equivalent | M1 | FT ‘their derived or stated angle \(AOY\)’ provided not 54°. Award M0A0 for \(\dfrac{360(^\circ)}{36(^\circ)}\) = 10, but award M1A1 if a final answer of 10% is seen. |
| = 10(%) | A1 | If no marks awarded, award:
|
| Scheme | Marks | Comments |
|---|---|---|
| Statement explaining that, ‘The tangent at any point on a circle is perpendicular (or equivalent) to the radius at that point’. | E1 | Accept unambiguous similar wording. e.g. ‘Radius and tangent 90(°)’. Diameter could be used in place of radius. Must refer to tangent and radius by name (not simply \(AY\) and \(OA\) or description). |