WJEC A-Level Mathematics Revision
Explore WJEC A-Level Mathematics revision topics. Check the official specification for complete requirements for your exam year and route.
Course details
Assessment The assessment includes Unit 1; see the official specification for the full structure.
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Reviewed course guidance
Revision points, with the explanation beside them
Open a point to read what to know, how to use it in an assessment, a plain-language explanation and a self-check. Answers stay hidden until you choose to reveal them.
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Topic group
Reviewed requirements
- Core
Scope: Core · §2.1 AS Unit 1 Pure Mathematics A, 2.1.1 Proof — disproof by counterexample
Open revision guidance
What to know
- A statement claiming something is true for every value can be disproved by one permitted value for which it fails. A few confirming examples do not prove a universal statement.
What to do in an assessment
- Check the stated domain, select a valid value, substitute carefully, and explain the contradiction. Keep the counterexample exact so it cannot be dismissed as a rounding or arithmetic error.
In plain language
Consider the claim that n²+n+41 is prime for every integer n. Choose n=40: 40²+40+41=1681, and 1681=41². Since this is composite, one counterexample is enough to show the claim is false. A proof by counterexample is different from testing several values that happen to work.
Self-check
Give a counterexample to “n²+n+41 is prime for every integer n.”
Show the answer
n=40 gives 1681=41², which is composite.
Earlier topic checklist
These earlier topic ticks are separate from the reviewed points above and do not count towards that progress.
Mathematics topic list
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These ticks keep your earlier topic checklist. They do not count towards the new reviewed requirements above. Its numbering may be internal; use the linked references above for the exact reviewed source requirements.
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This guide is also available in Welsh (Cymraeg): Welsh (Cymraeg) guide
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