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Proof

Revise Proof in Algebra for GCSE Mathematics with 14 exam-style questions and 12 flashcards. This is a very high-frequency exam topic, so it is worth revising until the core ideas feel automatic.

Study this topic

1

Proving It's ALWAYS True

Introduction2

Key Representations

Key Facts3

Worked Example

Notes

Sample Flashcards

What is a counter-example in mathematics?
A single specific example that shows a statement is NOT always true. One counter-example is enough to disprove a conjecture.
What are the three steps in an algebraic proof?
1. State what your letters represent (e.g. let n be any integer) 2. Manipulate algebraically (expand, simplify, factorise) 3. Show the result matches the required form with a clear conclusion

Sample Questions

Which expression represents an even number for all integer values of n?

  • A. n + 2
  • B. 2n
  • C. 2n + 1
  • D. n²
1 markfoundation

Prove by exhaustion that when you divide any single-digit positive integer by 4, the remainder is always 0, 1, 2, or 3. Show your working by testing all possible cases.

2 markshigher

14

exam-style questions

12

revision flashcards

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