Higher January 2021 Paper 2 Q16

EdexcelHigherCurrent spec6 marksSets

16 Some students were asked the following question.

“Which of the subjects Russian (\(R\)), French (\(F\)) and German (\(G\)) do you study?”

Of these students

4 study all three of Russian, French and German
10 study Russian and French
13 study French and German
6 study Russian and German
24 study German
11 study none of the three subjects
the number who study Russian only is twice the number who study French only.

Let \(x\) be the number of students who study French only.

(a) Show all this information on the Venn diagram, giving the number of students in each appropriate subset, in terms of \(x\) where necessary.

Venn diagram with three overlapping circles R, F and G inside a universal set rectangle; x is written in the F only region

(3)

Given that the number of students who were asked the question was 80

(b) work out the number of these students that study Russian. (3)

Scheme	Marks
	B3
	(3)

Mark scheme (b)

Scheme	Marks
\(2x + 6 + x + 2 + 4 + 9 + 9 + 11 = 80\) (80 – 6 – 2 – 4 – 9 – 9 – 11 ) ÷ 3	M1ft
\(x = 13\)	A1
Correct answer scores full marks (unless from obvious incorrect working) Answer: 38	B1
	(3)
	(6 marks)

Notes

M1ft: ft their Venn diagram
A correct equation to find \(x\) or subtracting all numerical values from 80 and dividing by 3 or other fully correct method to find \(x\) with all sections completed

A1: correct value for \(x\)

B1: their \(2x + 12\)