Stationary Points and Optimisation | AQA L2 Further 8365 | 40 Worked Examples

40 fully worked stationary-points and optimisation questions for AQA Level 2 Certificate in Further Mathematics (8365), pitched exactly at the untiered 8365 standard (above GCSE Higher, bridging to AS). Covers the calculus of spec section 4: the gradient function dy/dx, the power rule for kx^n with integer n including ‘simplify first’ cases (expanding a product, or rewriting a fraction such as 9/x as 9x^-1 before differentiating), locating stationary points by solving dy/dx=0, classifying their nature by both the second derivative d2y/dx2 and the sign of the gradient either side (with a genuine second-derivative-test-fails point of inflection example), increasing and decreasing functions, finding unknown coefficients from a stationary-point condition, and full optimisation problems (maximum rectangle area, an open box from a square of card, a farmer’s three-sided enclosure, minimum surface area and minimum sum of squares), each using a constraint to reduce to one variable before differentiating. Progressive difficulty runs Easy through Standard to Challenging. 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) folded in on the real mark-earning lines, so students see exactly where the marks come from. Diagrams are drawn inline for the optimisation setups and curve sketches. A key-facts box states the power rule, the stationary-point method, both nature tests and the optimisation routine (none of which are given in the 8365 exam). Ideal for classwork, homework, revision and 1-1 tuition.