Fractions: Eduqas GCSE Foundation June 2018 Paper 1 Q15

Foundation June 2018 Paper 1 Q15

EduqasFoundationCurrent spec5 marksFractions

15.

(a)

One day, \(\dfrac{5}{7}\) of the pupils in Year 10 at North High School went on a school trip.

There were 46 pupils in Year 10 who did not go on the trip.

How many pupils are there in Year 10 at North High School? [2]

(b)

Alex and Mary go to North High School.

Alex walks \(\dfrac{5}{8}\) of a mile to school. His friend Mary walks \(\dfrac{7}{10}\) of a mile to school.
Mary says,

‘I walk exactly \(\dfrac{3}{40}\) of a mile more than Alex does to school.’

Is Mary correct?
Show calculations to support your decision. [3]

Scheme	Marks	Comments
\(\dfrac{46}{2} \times 7\) or equivalent	M1	May be in steps.
161 (pupils)	A1

Mark scheme (b)

Scheme	Marks	Comments
A correct sum or difference e.g. \(\dfrac{5}{8} + \dfrac{3}{40}\) or \(\dfrac{7}{10} - \dfrac{3}{40}\) or \(\dfrac{7}{10} - \dfrac{5}{8}\) or equivalent	B1	May be earned later.
Sight of two fractions with a common denominator equivalent to any two of \(\dfrac{5}{8}, \dfrac{7}{10}, \dfrac{3}{40}\)	B1	e.g \(\dfrac{25}{40}, \dfrac{28}{40}\) or \(\dfrac{50}{80}, \dfrac{56}{80}\); May be in a sum or difference e.g. \(\dfrac{25}{40} + \dfrac{3}{40}\) or \(\dfrac{28}{40} - \dfrac{3}{40}\) or \(\dfrac{28}{40} - \dfrac{25}{40}\) Allow any correct common denominator; may imply previous B1
Yes with a correctly evaluated sum or difference appropriately simplified or Yes following sight of \(\dfrac{25}{40}, \dfrac{28}{40}\) or a pair of equivalent fractions	E1	From a sum or difference, e.g. \(\left(\dfrac{25}{40} + \dfrac{3}{40} = \right)\dfrac{28}{40} = \dfrac{7}{10}\) or \(\left(\dfrac{28}{40} - \dfrac{3}{40} = \right)\dfrac{25}{40} = \dfrac{5}{8}\) or \(\left(\dfrac{56}{80} - \dfrac{50}{80} = \right)\dfrac{6}{80} = \dfrac{3}{40}\) if no sum or difference stated then maximum 2 marks (B0 B1 E1)
	(5)

Alternative method: (or equivalent in percentages)