Ratio & Basic Proportion: Eduqas GCSE Foundation November 2022 Paper 1 Q9

Foundation November 2022 Paper 1 Q9

9. Alan builds a model of a steam train.

The scale he uses is 1 cm represents 75 cm.

(a)

The width of a wheel on Alan’s model is 3 cm.

What is the width of a wheel on the steam train? [2]

(b)

The length of the whistle on the steam train is 375 millimetres.

What is the length of the whistle on Alan’s model train?
Give your answer in centimetres. [3]

(c)

Alan’s model train has 6 wheels.
Alan’s friend Mandy says,

“The steam train has 6 × 75 = 450 wheels.”

Explain why Mandy is not correct. [1]

Scheme	Marks	Comments
\(3 \times 75\)	M1
225 (cm) oe	A1	If units given, they must be correct. If no marks, award M1 for an unsupported 2.25.

Mark scheme (b)

Scheme	Marks	Comments
\(375 \div 75\)	M1
5 (mm)	A1
(\(5 \div 10\) =) 0.5 (cm)	B1	FT ‘their 5’ \(\div\) 10. Correct answer implies 3 marks.

Scheme	Marks	Comments
1cm ≡ 750mm	B1	Units may be implied in further working.
\(375 \div 750\)	M1	FT ‘their 750’.
0.5 (cm)	A1	FT

Mark scheme (c)

Scheme	Marks	Comments
Valid explanation explaining the scale factor can be used for finding lengths or that the number of wheels remains the same e.g. ‘Both the train and the model have 6 wheels’. ‘The ratio is only used for scaling lengths (not numbers of things).’	E1	Accept other correct statements e.g. ‘There will still be 6 wheels.’ Ignore superfluous statements. e.g. ‘It doesn’t make sense to multiply wheels by length of 75’.
	(6)