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
Two students discuss the expression . Student A says it is rational because it is a sum of two similar-looking square roots. Student B says it is irrational but gives no proof.
Total: 4 marks
(a) Simplify . (1 mark)
(b) Decide whether Student A's conclusion is correct. (1 mark)
(c) Give a proof-level reason for the classification. (2 marks)
Something wrong with this item?