Foundation November 2018 Paper 3 Q23

OCRFoundationCurrent spec7 marksRatio & Basic Proportion

23 This map shows part of a village.

Neil knows that Packer Street is 180 m long in real life.

(a) Neil measures the map.

He says

Packer Street is 3.5 cm long.
High Street is 11.2 cm long.

Therefore, I calculate that High Street is 576 m long in real life.

Use Neil’s figures to show that the answer to his calculation is correct. [3]

(b) Jodie measures the same map.

She says

I think Packer Street is longer than Neil’s measurement of 3.5 cm.
Therefore, High Street must be longer than 576 m in real life.

Is Jodie’s reasoning correct?
Show how you decide. [2]

Express the scale of this map in the form 1 : \(n\). [2]

Mark scheme (a)

Answer	Marks	Part marks and guidance
180 \(\div\) 3.5 \(\times\) 11.2 = 576 or 180 \(\div\) 3.5 = 51.4[…] and 576 \(\div\) 11.2 = 51.4[…] or 576 \(\div\) 180 = 3.2 and 11.2 \(\div\) 3.5 = 3.2	3	M2 for 180 \(\div\) 3.5 \(\times\) 11.2 or 180 \(\div\) 3.5 and 576 \(\div\) 11.2 or 576 \(\div\) 180 and 11.2 \(\div\) 3.5 or M1 for 180 \(\div\) 3.5 soi 51.4[…] or 576 \(\div\) 11.2 soi 51.4[…] or 576 \(\div\) 180 soi 3.2 or 11.2 \(\div\) 3.5 soi 3.2	For M marks allow figs used eg M2 for 18 \(\div\) 350 \(\times\) 112 If in two stages: For full marks, condone premature rounding if accurate and answer is stated as 576. e.g. 3 marks for 180 \(\div\) 3.5 = 51.4 and 51.4 \(\times\) 11.2 [= 575.68 or 575.7] = 576 (required) eg M2 for 180 \(\div\) 3.5 = 51.5 and 51.5 \(\times\) 11.2 = 576 Accept equivalent methods eg divisions inverted or correct use of lengths in other units.

Mark scheme (b)

Answer	Marks	Part marks and guidance
No oe and correct explanation	2	B1 for 180 \(\div\) \(k\) \(\times\) 11.2 where \(k \gt 3.5\) leading to answer \(\lt 576\) or [180 \(\div\) 3.5 =] 51.4… and 180 \(\div\) \(k\), \(k \gt 3.5\) leading to answer \(\lt 51.4(\ldots)\) or Each cm on the map will be worth fewer km in real life oe	For full marks, clear conclusion and an explanation earning B1 is needed [180 \(\div\) 3.5 =] may be referred to in (a)