Ratio & Basic Proportion: WJEC GCSE Higher June 2022 Unit 1 Q1

Higher June 2022 Unit 1 Q1

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

Diagram not drawn to scale

\(ABC\) is a straight road, where the ratio \(AB : BC = 3 : 4\).
\(AC = 56\) km.

Calculate the length of \(BC\).
Give your answer in miles.
You must show all your working. [4 + 2 OCW]

Length of \(BC\) = …………………… miles

Mark scheme

Scheme	Marks	Comments
(BC =) 56 (km) ÷ (3 + 4) × 4 or equivalent 32 (km)	M1 A1	M1 awarded for complete method.
(BC =) 32 (km) ÷ 8 × 5 or equivalent 20 (miles)	M1 A1	FT ‘their derived 32’ ÷ 8 × 5. If a candidate works with AB instead of BC, then treat as a misread -1 (from A mark). Example 1 56 (km) ÷ (3 + 4) × 3 = 24 (km) M1A1 (-1) 24 (km) ÷ 8 × 5 = 15 (miles) M1 A1 (Total = 3 marks) Example 2 e.g. 56 (km) ÷ (3 + 4) × 3 = 16 (km) M1A0 16 (km) ÷ 8 × 5 = 10 (miles) M1 A1 (-1) (Total = 2 marks)
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

Scheme	Marks	Comments
(AC =) 56 (km) ÷ 8 × 5 or equivalent 35 (miles)	M1 A1	M1 awarded for complete* method*
(BC =) 35 (miles) ÷ (3 + 4) × 4 or equivalent 20 (miles)	M1 A1	FT ‘their derived 35’ ÷ (3 + 4) × 4 If a candidate works with AB instead of BC, then treat as a misread -1 (from second A mark). 56 (km) ÷ 8 × 5 = 35 (miles) M1 A1 35 (miles) ÷ (3 + 4) × 3 = 15 (miles) M1A1(-1) (Total = 3 marks)