Edexcel A-Level Mathematics Revision
Explore Edexcel A-Level Mathematics revision topics. Check the official specification for complete requirements for your exam year and route.
Qualification code: 9MA0
Course details
Assessment The assessment includes Paper 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 · Pure Mathematics §1.1 Proof — disproof by counterexample
Open revision guidance
What to know
- A universal claim says a statement is true for every value in a stated set. One valid counterexample is enough to disprove it; several confirming examples are never enough to prove a universal claim.
What to do in an assessment
- Check the domain, choose a legal value that tests the claim, calculate accurately, and state explicitly why the result contradicts the claim. Do not present a value outside the stated domain.
In plain language
For example, the claim that n²+n+41 is prime for every integer n is false. At n=40, the expression is 1600+40+41=1681=41², which is composite. The single allowed value n=40 therefore disproves the “every integer” claim. Showing n=0, 1 and 2 all give primes would not establish that it always works.
Self-check
Does n²+n+41 always give a prime for integer n? Find one counterexample.
Show the answer
No. At n=40 it gives 1681=41², which is not prime.
Earlier topic checklist
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Mathematics topic list
This is a topic overview, not a complete specification checklist. Check the official course for all assessed content, options and your exam year.
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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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