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Five graded worksheets on completing the square for GCSE Higher, with full mark schemes. From the basic form through to solving, turning points and reasoning.

How the series builds:

  • Expressing in the form (x + a)² + b
  • The form a(x + p)² + q (non-monic, negative leading coefficient, fractional a)
  • Solving quadratics by completing the square (exact/surd roots)
  • Turning points, lines of symmetry, least/greatest values, and meeting the x-axis
  • Reasoning & proof (identities, always-positive arguments, discriminant reasoning)

Board-agnostic (AQA, Edexcel, OCR). Every question worked in the mark scheme. Print-and-go for lessons, homework, starters and revision.

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