Intermediate November 2022 Unit 1 Q22
22. \(P\), \(Q\) and \(R\) are points on the circumference of a circle with centre \(O\).
Diagram not drawn to scale
Calculate the value of \(x\).
You must state all the angle properties that you use.
You must show all your working. [4]
| Scheme | Marks | Comments |
|---|---|---|
| Check diagram for answers. | ||
| \(POQ\) = 180 – ( 2 × 38) | M1 | |
| 104 (°) | A1 | Award M1A1 for sight of 104. |
| \(x\) = 52(°) | B1 | FT ‘their 104’ ÷ 2. |
| For two valid angle properties appropriately stated with at least one circle property (e.g. two radii make an isosceles triangle AND angle subtended by an arc at the centre of a circle is twice the angle subtended at the circumference). | E1 | Award E1 for any one correct appropriate angle property AND any one appropriate correct circle property associated with correct workings. ISW any other incorrect properties. Allow
|
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| 22. Alternative method – angles in a semi-circle Extending the line (PO or QO) to create a right-angled triangle | S1 | Shown on diagram. |
| 180 – 90 – 38 | M1 | M1 implies S1. |
| \(x\) = 52(°) | A1 | |
| For two valid angle properties appropriately stated with at least one circle property (e.g. the angle subtended at the circumference by a semicircle is a right angle AND that angles in the same segment are equal) | E1 |
The alternative method is printed in italics in the original.