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Constructing and solving quadratic equations

Algebra · Grade 4–6

Strand: Algebra Substrand: Solving quadratic equations Sparx code: U150 Sparx levels: 4, 5 Tier: Higher Only

Key steps (method)

  • Rearrange into the form ax² + bx + c = 0.
  • Choose a method: factorise (if possible), complete the square, or use the quadratic formula.
  • Solve for x, giving both solutions if there are two.
  • If using the quadratic formula, substitute carefully and simplify.
  • Check by substituting solutions back into the original equation.

Common mistakes

  • Forgetting there are often two solutions.
  • Sign errors in the quadratic formula (especially −b ± √…).
  • Factorising incorrectly (wrong pair of factors).
  • Losing solutions when taking square roots (missing ±).

Quick notes

  • If you get stuck, try a simpler version of the problem first or plug in easy numbers to test your method.
  • For multi-step questions, label each step and keep intermediate results.
  • For exam questions, always aim to make your work “mark-scheme readable”.

Self-assessment

  • Can I define it? Write a one-sentence definition of Constructing and solving quadratic equations (or the key term in the question).
  • Can I do it? Do 3 questions: one easy, one standard, one harder. Don’t look at notes until you’ve tried.
  • Can I explain it? In 2–3 sentences, explain why the method works (or what would go wrong with a common mistake).
  • Can I check it? State one quick check (estimate, units, sign, reasonableness).

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Notes