Completing the Square | OCR Level 3 FSMQ Additional Maths (6993) | 40 Worked Examples

Forty fully worked examples on completing the square for OCR Level 3 FSMQ: Additional Mathematics (6993), the qualification that bridges GCSE Higher into AS and A-Level and carries up to 10 UCAS points. Every solution is broken down one line at a time with a plain-English note beside each step and OCR mark-scheme codes (M1, A1, B1) folded in on the real mark-earning lines, so students see exactly where the marks fall. Progressive difficulty runs from monic and non-monic quadratics (write in the form (x+p)^2+q and a(x+p)^2+q), through minimum and maximum values, coordinates of the turning point, solving quadratics in exact surd form and proving an expression is always positive, up to circle centre-and-radius, quadratic modelling, range, tangency and full detailed-reasoning (DR) proofs in two variables. Written to match authentic 6993 question style and the memorise-versus-given formula split (the quadratic formula is NOT on the 6993 sheet, so completing the square is a core exam skill). Ideal as a topic pack for classroom, homework or independent revision. Answers grade A to E.