Solved: Consider the following sets:The universal set U consists of all positive... [IB Mathematics Applications & Interpretation (Math AI)]

Question

SLPaper 1

Consider the following sets:

The universal set $U$ consists of all positive integers less than 15;
$A$ is the set of all numbers which are multiples of 3;
$B$ is the set of all even numbers.

Write down the elements that belong to $A \cap B$ .

[3]

Verified

Solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

$A$ = {3, 6, 9, 12} AND $B$ = {2, 4, 6, 8, 10, 12, 14} (M1)

Note: Award (M1) for listing all elements of sets $A$ and $B$ . May be seen in part (b). Condone the inclusion of 15 in set $A$ when awarding the (M1).

6, 12 (A1)(A1) (C3)

Note: Award (A1) for each correct element. Award (A1)(A0) if one additional value seen. Award (A0)(A0) if two or more additional values are seen.

[3 marks]

Write down the elements that belong to $A \cap B$ .

[2]

Verified

Solution

3, 9 (A1)(ft)(A1)(ft) (C2)

Note: Follow through from part (a) but only if their $A$ and $B$ are explicitly listed.
Award (A1)(ft) for each correct element. Award (A1)(A0) if one additional value seen. Award (A0)(A0) if two or more additional values are seen.

[2 marks]

Write down $n\left( {A \cap B$ .

[1]

Verified

Solution

2 (A1)(ft) (C1)

Note: Follow through from part (b)(i).

[1 mark]

Consider the following sets:The universal set U consists of all positive integers less than 15; A is the set of all numbers which are multiples of 3; B is the set of all even numbers.

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