Ratio & Basic Proportion: Eduqas GCSE Higher June 2022 Paper 1 Q8

Higher June 2022 Paper 1 Q8

EduqasHigherCurrent spec3 marksRatio & Basic Proportion

8. Vikram wanted to find out how many moths there were in a small woodland.

One night, Vikram captured a random sample of 12 moths and marked them.
He then released them back into the woodland.

The next night, Vikram captured a second random sample of 30 moths.
He found that 9 of the moths in the second sample had been marked.

Vikram estimated that there were 40 moths in the woodland.

(a) Show that Vikram’s estimate of the number of moths was correct. [2]

(b) Comment on how reliable Vikram’s estimate was likely to be. [1]

Mark scheme (a)

Scheme	Marks	Comments
(Proportion of marked moths in sample is) \(\dfrac{9}{12}\left(=\dfrac{3}{4}\right)\) oe, si or (Proportion of 2nd sample marked is) \(\dfrac{9}{30}\left(=\dfrac{3}{10}\right)\) oe, si	B1	Allow for e.g. ‘9 out of 12 (marked)’ or ‘9 (marked) out of 30’ allow for sight of e.g. \(\dfrac{12\times30}{9}\ (= 40)\)
Correct completion e.g. \(\dfrac{9}{30}=\dfrac{12}{40}\) (so 40 moths) OR \(\dfrac{9}{12}=\dfrac{30}{40}\) (so 40 moths) OR 75% (of population) is 30 (moths) so 100% (of population) is 30 + 10 = 40 (moths) oe	B1	Implies the first B1; Allow for showing ‘12 out of 40’ and ‘9 out of 30’ are both ‘3 out of 10’ or \(\dfrac{9}{12}=\dfrac{30}{x}\) and \(9x = 360,\ x = 40\) oe NB \(\dfrac{12\times30}{9}=\dfrac{360}{9}=40\) is B2

Mark scheme (b)

Scheme	Marks	Comments
Valid comment based on sample or population size e.g. ‘It may not be very reliable as he only captured 12 moths in his first sample.’ or ‘Some of the moths may have been eaten so the results may not be accurate.’	E1	Allow e.g. ‘Not reliable because the population would be bigger at different times of the year.’ Allow comments which refer to the experiment needing to be repeated E1 for e.g. ‘Somewhat reliable because it was done once and it could be different if repeated again’ or ‘Not reliable as he needs to do it more often.’ Must not contain contradictions/errors but may contain irrelevant statements E0 for e.g. ‘Not very reliable as there could have been more moths.’ or ‘Unlikely (to be reliable) because it has only been tested twice’ or ‘Not reliable because he could keep catching the same moths over and over.’
	(3)