What you need to know
Check yourself against these “I can” statements.
- I can write a quadratic in the form (x + a)² + b
- I can write a quadratic in the form a(x + b)² + c
- I can solve a quadratic equation by completing the square
Practise this topic
6 resourcesComplete the Square
a = 1 with even and odd b, then a > 1 and a < 0. Five difficulty levels, timed, click to reveal.
⬢ BlockbustersComplete the Square Blockbusters
Blockbusters with the questions from the Complete the Square worksheet: choose its levels for the ordinary hexagons and for the harder ★ ones. Show the answer and the worked solution, or play against the computer with multiple…
🔤 Fill the GapsFill the Gaps: Maths Vocabulary
A sentence explaining one of the unit’s key words, with gaps. Pick the right word for each gap from the words scattered round it: the right ones and plenty of wrong ones. A deck for every unit.
🔗 MatchingGraph Sketching: Matching
Twelve equations: match each to its graph, which shows only where it meets the axes. Easy: quadratics in factorised form. Normal: quadratics to factorise, each also matched to its turning point, with look-alike graphs and turning…
🧩 ConnectionsQuadratics
Match quadratics to their factorised form, solutions, x-axis crossings and y-intercept. Sign-swapped families from Standard; a > 1, completed square and turning points on Hard.
🧮 ToolVisual Proofs
Animated visual proofs of Pythagoras’ theorem, of the sums of integers, odd numbers, squares and cubes, and of key results in algebra, geometric series, trigonometry and inequalities. They play like Shape Formulas: drag the bar…
These are the pages for Completing the square in the GCSE + AQA Further Maths scheme of work, following Pearson Edexcel GCSE (9–1) Higher (1MA1), plus AQA Level 2 Further Mathematics (8365). Open this topic in Mr Wells Maths to see it alongside the rest of the course.