GCSE Mathematics (9-1)

15.5 Algebraic proof — Practise with help

Work each problem before revealing support.

Warm-up: remember

Answer these from memory. Do not look back at the section.

  1. Write an expression for an even number.
  2. Simplify 2n+3n2n+3n.
Check the warm-up
  1. 2n2n, where nn is a whole number.
  2. 5n5n.

If an answer differs, revisit Section 8.1 for algebraic notation and Section 8.2 for collecting like terms.

Practise with help

1. Prove that the sum of two consecutive integers is odd.

Hint

Represent the integers as nn and n+1n+1.

First step

Their sum is n+(n+1)n+(n+1). Collect the terms.

Full working

n+(n+1)=2n+1n+(n+1)=2n+1. This is odd because it is twice an integer plus one.

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