Necessary and sufficient conditions
Free TMUA Paper 2 lesson. Problem-solving strategies, fully worked examples of the question types that keep coming up, common mistakes and a self-check.
What the lesson covers
- The patterns to expect
- What if, only if and iff really say
- Necessary and sufficient: sets, and two one-way tests
- Conditions on functions and shapes
- Numbers, lists and solutions
- Habits that win marks
- Self-check questions with answers (8)
Specification: 2.1 if-then, iff, converse, contrapositive, necessary, sufficient. Section numbers are Heurisco's own, following the headings of the published TMUA specification.
How to use it
- Read a section, then cover the worked example and try it yourself.
- Check the common mistakes list: these are the slips the real test is built to catch.
- Do the self-check without looking back. Mark it against the answers.
- Then practise the topic under time, with the matching practice set.
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