FRQ — Sets and Functions

Long answer·Hard exam skill (4/5)·No calculatorNeeds mentor review

Difficulty guide

The label describes the problem, not your ability.

1/5 - Foundational

Warm-up setup; checks one basic idea.

2/5 - Routine exam skill

Normal syllabus skill; usually one main rule or interpretation.

3/5 - Standard multi-step

Exam-style problem with multiple steps or a common trap.

4/5 - Hard exam skill

High-end exam problem; combines methods carefully.

5/5 - Challenge

Stretch problem beyond normal exam pressure.

Question

A puzzle pairs two numbers from

A=\{1,2,3,4\}

when their ordered sum is

5.

Define

R=\{(x,y):x,y\in A

and

x+y=5\}.

Total: 4 marks

(a) Write all ordered pairs recorded by the puzzle. (2 marks)

(b) Find the set of possible first numbers. (1 mark)

Your response (optional — you can also work on paper)

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