Intermediate November 2022 Unit 2 Q13
13. A, B and C are points on the circumference of a circle with centre O.
The length of BC is 10 cm.
The diameter of the circle is 18 cm.
Diagram not drawn to scale
Calculate the shaded area.
You must show all your working. [7]
| Scheme | Marks | Comments |
|---|---|---|
| (Length of AB) 182 = AB2 + 102 OR (AB2 =) 182 – 102 or equivalent | M1 | note: (AB2 =) 324 – 100 |
| (AB2 =) 224 | A1 | |
| (AB =) 14·9(66…) or 15 or 4√14 or √224 (cm) | A1 | FT √’their 224’ provided M1 gained for M1A0A1. Alternative method to find AB A correct and complete method that would lead to a correct answer (using trigonometric relationships). M2 (AB =) 14·9(66…) or 15 or 4√14 or √224 (cm) A1 |
| (Area of the circle =) π × 92 | M1 | |
| (Area of the triangle = ) ½ × 10 × 14·9(66…) or equivalent | M1 | Award M1 for sight of 75 or 20√14. FT ½ × 10 × ‘their AB’, provided not 18 or 10. Accept any valid method that leads to a correct answer. |
| 254.4(69…) (cm2) or 81π AND 74·8(33..) or 20√14 (cm2) | A1 | An answer between 254·3 and 254·51 (cm2). Allow 254. Allow 75. |
| (Area of the shaded region = 254.4(69) – 74·8(33..) =) 179 to 180 (cm2) | B1 | Allow rounded or truncated answers. FT ‘their area of a circle’ – ‘their triangle’ (not ‘their AB’) provided at least one area M1 awarded previously. |