Higher June 2022 Unit 2 Q4
4. In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
In the diagram above, the area of triangle \(BCD\) is 60 cm2.
Calculate the length of \(CD\).
You must show all your working. [6 + 2 OCW]
From the formula list: In any triangle \(ABC\): Cosine rule \(a^2 = b^2 + c^2 - 2bc\cos A\)
| Scheme | Marks | Comments |
|---|---|---|
| (BC2 = ) 9·62 + 12·82 or equivalent | M1 | note: (BC2 =) 92·16 + 163·84 (ignore place values for M1) Award M1 for the correct values substituted into the Cosine rule. |
| (BC2 =) 256 or (BC =) √256 | A1 | |
| (BC =) 16 (cm) | A1 | Allow (BC =) ±16 (cm). FT from M1 for the correctly evaluated square root of 'their 256’ provided their answer > 12·8. |
| CD = 2 × 60 ÷ 16 or equivalent | M2 | FT ‘their derived BC’ OR ‘their stated 16’ (not derived) provided 12·8 < ‘their stated 16’ < 22·4. Award M1 for 60 = ½ × 16 × CD or equivalent. |
| (CD =) 7·5 (cm) | A1 | Allow M2A1 for a correct embedded answer BUT M2A0 if contradicted by CD ≠ 7·5 (cm). |
| Organisation and Communication. | OC1 | For OC1, candidates will be expected to:
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| Accuracy of writing. | W1 | For W1, candidates will be expected to:
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Alternative method:
| Scheme | Marks | Comments |
|---|---|---|
| Correct use of ‘two-step’ method | M2 | A partial trigonometric method is M0. |
| (BC =) 16 (cm) | A1 | |
| CD = 2 × 60 ÷ 16 or equivalent | M2 | FT ‘their derived BC’ OR ‘their stated 16’ (not derived) provided 12·8 < ‘their stated 16’ < 22·4. Award M1 for 60 = ½ × 16 × CD or equivalent. |
| (CD =) 7·5 (cm) | A1 | Allow M2A1 for a correct embedded answer BUT M2A0 if contradicted by CD ≠ 7·5 (cm). |