Case study·Standard multi-step (3/5)·No calculator
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 rectangular art card has sides and . A student wants to know whether the diagonal length can be written exactly as a rational number.
Total: 4 marks
(a) Find the diagonal length in simplest radical form. (2 marks)
(b) State whether the exact diagonal is rational or irrational. (1 mark)
(c) Explain why a decimal approximation does not replace the exact value. (1 mark)
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