Higher November 2016 Unit 2 Q8
8. In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
Points \(A\), \(B\), \(C\) and \(D\) lie on the circumference of a circle, centre \(O\).
\(BD\) is a diameter of the circle.
The straight line \(BC\) = 4·7 cm and \(B\hat{A}C\) = 28°.
Diagram not drawn to scale
Write down the size of \(B\hat{D}C\).
Hence, calculate the length \(BD\).
You must show all your working. [5 + 2 OCW]
| Scheme | Marks | Comments |
|---|---|---|
| BDC = 28(°) | B1 | Angles may be shown on the diagram. Allow D = 28. |
| BCD = 90(°) | B1 | May be implied in later work. (Allow this B1 for any use of a right-angle triangle trigonometric relationship for triangle BCD) |
| BD = \(\dfrac{4{\cdot}7}{\text{Sin } 28}\) | M2 | This implies previous B mark. FT ‘their BDC’. M1 for \(\dfrac{4{\cdot}7}{\text{BD}}\) = sin 28. |
| BD = 10(·…)(cm) | A1 | |
| Organisation and Communication | OC1 | For OC1, candidates will be expected to:
|
| Accuracy of writing | W1 | For W1, candidates will be expected to:
|
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| COB = 56(°) | B1 | |
| OB = \(\dfrac{2{\cdot}35}{\sin 28}\) | M2 | (M1 for \(\dfrac{2{\cdot}35}{\text{OB}}\) =sin 28 ) |
| OB = 5(·…)(cm) | A1 | |
| BD = 10(·..)(cm) | A1 |