A Colab notebook on continued fractions, with nice applications to Pell's Equation and to finding certain Pythagorean triples. Could be worked through independently by pupils, but perhaps better as a collaborative, teacher-led exercise.
A nice set of problems about circles with tangents at whole numbered coordinates that pass through the origin.
A set of problems involving integrals, some coordinate geometry and the odd cubic equation... One instruction for each question: find the exact value of the green area.
Volumes of revolution
A worksheet on volumes of revolution.
Reversing the chain and product rules
A guided worksheet and a follow up exercise for reversing the chain and product rules without explicitly mentioning substitution or integration by parts. I've used these in the past for getting pupils familiar with the underlying ideas (rather than learning a technique by rote). Also useful for developing fluency in the chain and product rules themselves. Some follow up questions towards the end of the first sheet, with linked video solutions.
See also this Desmos graph to show how graph transformations can be used as a way of understanding integration by substitution.
A set of problems involving improper integrals. Only one instruction for each question (find the green area) but plenty to think about!
Compound angle formulae
A set of problems that can be solved using compound angle formula. I hope these are a bit different from the routine examples in text books.
A complex iteration
An introduction to the idea of integrating factors to solve differential equations, starting with the idea of finding a product with that differentiates to a given two-term expression.