Higher June 2023 Unit 1 Q5
5. In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
The shape below consists of a semicircle attached to one side of a right-angled triangle.
\(A\hat{B}C = 90^\circ\), \(AB = 8\) cm, \(BC = 6\) cm.
\(BC\) is the diameter of the semicircle.
Diagram not drawn to scale
Calculate the perimeter of the shape.
Use \(\pi = 3{\cdot}14\).
You must show all your working. [5 + 2 OCW]
| Scheme | Marks | Comments |
|---|---|---|
| (\(AC^2\) =) \(8^2 + 6^2\) (\(AC\) =) \(\sqrt{8^2 + 6^2}\) or equivalent (\(AC\) =) 10 (cm) | M1 m1 A1 | Check diagram. Note: (\(AC^2\) =) 64 + 36 FT from \(\sqrt{\text{‘their }8^2\text{’} + \text{‘their }6^2\text{’}}\) CAO. Final answer of AC = 100 is M1m0A0. |
(Curved length =)
| B1 | Do not ignore subsequent working e.g. 3 × 3·14 = 9·42, then 9·42 × 2 or 9·42 ÷ 2 would gain B0. |
| (Perimeter of shape = 8 + 10 + 9·42 = ) 27·42(cm) | A1 | Allow 27·4(cm). Award A0 for 18 + 3\(\pi\). FT ‘their \(AC\)’ only if M1 gained. FT ‘their curved length’ only if B0 awarded and for one of the following:
M1m1A1 awarded for 10 (cm), B1 for 3 × 3·14 = 9 (cm) A0 for 8 + 10 + 9 = 27 (cm) as B1 previously awarded. Note, if a final answer of:
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| 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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