Higher June 2024 Paper 2R Q4

EdexcelHigherCurrent spec5 marksSets

4 \(\mathscr{E} = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}\)
\(A = \{\text{factors of } 6\}\)
\(B = \{\text{prime numbers}\}\)

(a) List the members of the set

(i) \(A \cup B\) (1)

(ii) \(A'\) (1)

Harpreet states that \(\;A \cap B = \varnothing\)

Harpreet is incorrect.

(b) Explain why. (1)

\(C\) is a set with 4 members such that

the set \(A \cap C\) has 2 members
the set \(B \cap C\) has 2 members

Set \(A \cap C\) and set \(B \cap C\) have no members in common.

Scheme	Marks
(i) Answer: 1, 2, 3, 5, 6, 7	B1
(ii) Answer: 4, 5, 7, 8, 9, 10	B1
	(2)

Mark scheme (b)

Scheme	Marks
eg 1. 2 (or 3 or 2 and 3) is in both sets oe 2. \(A\) and \(B\) have 2 (or 3 or 2 and 3) oe 3. 2 (or 3 or 2 and 3) is common oe 4. 2 (or 3 or 2 and 3) is in the intersection oe 5. \(A \cap B = \{2, 3\}\) oe or \(A \cap B = \{2\}\) oe or \(A \cap B = \{3\}\) oe 6. They share 2 (or 3 or 2 and 3) oe 7. As 2 and/or 3 are factors of 6 and also prime numbers oe Allow sector for set This is not an exhaustive list Answer: 2 (or 3 or 2 and 3) is a member of \(A\) and \(B\)	B1
	(1)

Scheme

Marks

eg
1. 2 (or 3 or 2 and 3) is in both sets oe
2. \(A\) and \(B\) have 2 (or 3 or 2 and 3) oe
3. 2 (or 3 or 2 and 3) is common oe
4. 2 (or 3 or 2 and 3) is in the intersection oe
5. \(A \cap B = \{2, 3\}\) oe or \(A \cap B = \{2\}\) oe or \(A \cap B = \{3\}\) oe
6. They share 2 (or 3 or 2 and 3) oe
7. As 2 and/or 3 are factors of 6 and also prime numbers oe

Allow sector for set
This is not an exhaustive list
Answer: 2 (or 3 or 2 and 3) is a member of \(A\) and \(B\)

(1)

Notes

B1: for identifying the element 2 or 3 or 2 and 3 with a correct explanation to show they know the meaning of intersection and empty set

If students mention a number that is common, it must be correct