Completing the Square | AQA L2 Further 8365 | 40 Worked Examples

40 fully worked completing-the-square questions for AQA Level 2 Certificate in Further Mathematics (8365), pitched exactly at the untiered 8365 standard (above GCSE Higher, bridging to AS). Progressive difficulty runs from Easy through Standard to Challenging: writing monic quadratics in the form (x+b)^2+c, the general a(x+b)^2+c form with a leading coefficient factored out, fractional completions from odd x-coefficients, reading the turning point and minimum or maximum value straight off the completed square, solving quadratics by completing the square with surd and (p+/-root q)/r answers, sketching parabolas via vertex and intercepts, and ‘prove the expression is positive for all x’ arguments, including parameterised proofs in k. Every solution is broken down to one atomic step per line with a plain-English note on each line and AQA mark-scheme codes (M1, A1, B1, M1dep) folded in on the real mark-earning lines, so students see exactly where the marks come from. Includes a key-facts box with the monic and general formulae, the vertex and least-value rule, and the AQA target form a(x+b)^2+c, plus a Paper 1 reminder to leave surds exact. Ideal for classwork, homework, revision and 1-1 tuition.