Angles in Polygons: WJEC GCSE Higher June 2023 Unit 2 Q10

Higher June 2023 Unit 2 Q10

WJECHigherCurrent spec8 marksAngles in Polygons Circles & Sectors Similar Shapes

10. ABCDE is a regular pentagon with sides of length 11 cm.
CDE is a sector of a circle with centre D and radius 11 cm.
The two shapes are joined together, as shown below.

Regular pentagon ABCDE joined to a sector CDE with centre D; the sector's arc runs round the outside from C to E, so the sector angle at D is the reflex angle

Diagram not drawn to scale

(a) In this part of the question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

Calculate the length of the arc CE shown in the diagram.
You must show all your working. [4 + 2 OCW]

(b) In a shape similar to the one shown above, the regular pentagon has sides of length 671 cm.

Complete the following statement.

Total area of new shape = ………………………… × total area of original shape

You must show all your working. [2]

Mark scheme (a)

Scheme	Marks	Comments
(Reflex angle D = ) 180 + 360/5 OR 360 – 3×180/5	M1	Or any other complete method. May be seen in stages.
= 252(°)	A1	Award for sight of 252(°) if not contradicted by further incorrect work.
(Arc length CE = ) 252/360 × \(\pi\) × 2 ×11	M1	FT for M1 for ‘their derived angle’.
48·3(…) OR 48·4 OR 77π/5 OR \(15\tfrac{2}{5}\)π OR 15·4π(cm) o.e.	A1	ISW Accept 48(cm) from correct working. 12089/250 from using 3·14 Allow a FT for this mark provided the angle used is >180°. If no marks award SC1 for sight of 108(°) OR 72(°)
Organisation and Communication	OC1	For OC1, candidates will be expected to: present their response in a structured way explain to the reader what they are doing at each step of their response lay out their explanation and working in a way that is clear and logical write a conclusion that draws together their results and explains what their answer means
Accuracy of writing	W1	For W1, candidates will be expected to: show all their working make few, if any, errors in spelling, punctuation and grammar use correct mathematical form in their working use appropriate terminology, units, etc.

Mark scheme (b)

Scheme	Marks	Comments
\(\left(\frac{671}{11}\right)^2\) (= 450241/121 ) OR \(61^2\)	M1
= 3721	A1	Answer in the sentence takes precedence. If no marks, allow SC1 for 3721/25 OR \(148\frac{21}{25}\) OR 148·84 [from (671/55)²].