Session 8D
Final assessment
45-75 min - work through lesson notes, practice, and the MCQ check.
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Session tips
- Finish the MCQ before marking complete.
- Check the answer outlines after trying on paper.
- Mark complete to update your certificate progress.
Lesson notes
- In a final assessment, the most important skill is controlling the logical structure under time pressure. Start by identifying the type of statement: implication, universal, existence, equality. Then commit to a method and write in a disciplined format. For example, for divisibility: "Let k be an integer such that..." and for subsets: "Let x be an arbitrary element of..." Those openings are not filler, they are the correct logical entry points.
- If you get stuck, don't do random algebra. Return to definitions and the goal. Ask: what exactly do I need to show? Can I rewrite it in a more workable form? Many proofs fail because the writer never wrote the goal in an actionable form, like "show m divides (expression)" becoming "show expression = m*t for some integer t." That rewrite often creates the path forward. A strong beginner proof is not fancy. It is controlled, explicit, and logically complete.
Practice
- 1Prove: For all integers n, n^3 - n is divisible by 3.
- 2Prove: If A subseteq B then A \ C subseteq B \ C.
MCQ
A standard factorization for n^3 - n is:
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Week 8 - Session 8D