Higher November 2024 Paper 2 Q21

EdexcelCurrent spec4 marksSets

21 The Venn diagram shows information about the numbers of items in set \(A\), set \(B\) and set \(C\), where \(x\) is an integer.

Venn diagram with three overlapping circles A, B and C in the universal set: A only 3x, A and B only x + 2, all three x, B only 4x, A and C only x + 7, B and C only 2x, C only 5x, outside all circles 3x + 2

Given that \(\mathrm{n}(A \cup B)' = 26\)

find \(\mathrm{n}(A' \cap C)\)

(4)

Mark scheme

Scheme	Marks
\(5x + 3x + 2 = 26\) oe	M1
\(x = 3\) Correct value of \(x\) scores M1A1 (unless from obvious incorrect working)	A1
7 × “3” oe eg “15” + “6” (where “15” is 5 × “3” and “6” is 2 × “3”)	M1ft
Correct answer scores full marks (unless from obvious incorrect working) Answer: 21	A1
	(4)
	(4 marks)

Notes

M1: a correct equation for \(x\)

M1ft: use of their positive value for \(x\) in \(7x\) (ie use of correct regions from Venn diagram for the set required)

[their value is their value given for \(x\) which must be clearly assigned as \(x\)]

A1: cao