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Topic: Algebraic Proof (Higher - Unit 2)

Specification References: N5.9h

N5.9h Use algebra to support and construct arguments and simple proofs


Candidates should be able to:

  • use algebraic expressions to support an argument or verify a statement
  • construct rigorous proofs to validate a given result

Notes

Candidates should be familiar with the term ‘consecutive’ and understand that an even number can always be represented by 2n and an odd number can always be represented by 2n + 1

This reference includes all the requirements of N5.9 and some additional requirements for the Higher tier only.

At Higher tier, candidates will be expected to use skills of expanding and factorising when constructing a proof.

Examples

  1. w is an even number, explain why (w – 1)(w + 1) will always be odd.

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  1. Liz says that when m > 1, m2 + 2 is never a multiple of 3.
    Give a counter example to show that she is wrong.

  2. Alice says that the sum of three consecutive numbers will always be even.
    Explain why she is wrong.

  3. n is a positive integer.
    Prove that the product of three consecutive integers must always be a multiplier of 6.

  4. n is a positive integer.
      1. Explain why n(n + 1) must be an even number.
      2. Explain why 2n + 1 must be an odd number.

    2. Expand and simplify (2n + 1)2

    3. Prove that the square of any odd number is always 1 more than a multiple of 8.