Higher November 2022 Unit 1 Q9
9. 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 |
|---|---|---|
| POQ = 180 – ( 2 × 38) | M1 | Check diagram for answers. |
| 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
|
9. Alternative method – angles in a semi-circle
| Scheme | Marks | Comments |
|---|---|---|
| Extending the line (PO or QO) to create a right-angle 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 |