Grade 11 · Algebra · 77 pages · PDF

Completing the Square

Clear, exam-focused notes on completing the square, solving quadratics and deriving the quadratic formula, with fully worked examples.

A complete 14-page IGCSE guide to completing the square. It starts with perfect square identities, then teaches the method step by step, first when the coefficient of x² is 1 and then when it isn’t, including negative leading coefficients. Later sections use the completed square form to solve quadratic equations in surd form and decide how many real solutions an equation has. It also derives the quadratic formula. Every method comes with fully worked examples and an expand-to-check step. It ends with a summary, a quick-reference exam strategy and exam tips.

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• Cheatsheet · 1 page

  Cheatsheet

  The whole topic on a page or two, for the night before.

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• Worksheet · 32 pages

  Worksheet

  Practice questions in the order the notes teach them.

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• Main Notes · 15 pages

  Main Notes

  The full notes: one idea per page, a worked example beside every rule.

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• Solutions · 29 pages

  Solutions

  Every worksheet question worked in full.

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Topics covered

• Perfect square identities
• Completing the square when the coefficient of x² is 1
• Completing the square with fractions
• Completing the square when the coefficient of x² is not 1
• Negative leading coefficients
• Solving quadratic equations by completing the square
• Answers in surd form
• Number of real solutions
• Deriving the quadratic formula
• The discriminant
• Summary and exam tips

Format

Print-ready PDF

Items

4

Delivery

By email