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Brainlag Learn / GCSE Maths

Proof and iteration

Algebraic proof and counterexamples, then finding roots that do not come out exactly: changes of sign and iteration. Higher tier.

Lessons

  1. Algebraic proofWrite whole numbers in general (n, 2n, 2n + 1), expand and simplify, and conclude for every case at once. 25 min, free, Higher tier
  2. CounterexamplesOne example is enough to show a statement is false. Decide whether statements are always, sometimes or never true. 20 min, free, Higher tier
  3. Roots by a change of signIf f(a) and f(b) have different signs, a continuous graph must cross the axis between them. Narrow the interval to find a root. 25 min, with the Graphing Calculator, Plus, Higher tier
  4. IterationRearrange an equation into x = g(x), then feed each answer back in until the values settle on a root. 25 min, with the Numerical methods simulation, Plus, Higher tier

Practise and test

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