Jonny Griffiths investigative activities for the pure A Level Mathematics classroom are well known (details are below). He has now published Further Risps, forty rich tasks for the pure Further Mathematics classroom.
I thoroughly enjoyed Jonny’s excellent session for London Maths, ATM and MA London Branch in May 2019, where teachers enjoyed working on these activities.
The pdf not only provides the forty problems but also full teachers notes for each. The notes for each task begin with the topic or topics covered, identify the type of task, for example, introductory and state any preliminary knowledge required. This is a valuable resource for teaching Further Mathematics.
Investigating the first Risp on Matrices at the session this certainly would help students with fluency in finding the determinant of a matrix. Rich tasks like this can provide students with a greater understanding than just a traditional exercise and will hopefully stick for longer! The tasks very much remind me of Colin Foster’s wonderful Mathematical Etudes.
For the A Level collection (all free, you can optionally purchase an e book version for £1) use RISPS (Rich Starting Points), these open-ended investigative activities are for the A Level Pure Mathematics classroom. Note the helpful index by topic, choose a personal favourite of mine, Risp 21 Advanced Arithmagons for example and you will see not only the task but also teachers notes.
Arithmagons provide a wonderful activity for making students of all ages think; I always tell my students that good mathematicians can go backwards!
(For a whole collection of Arithmagons activities see this post).
Also from Jonny Griffiths his companion sites on Statistics and Carom-Maths -activities to bridge the gap between A Level and University. You can find a resource collection from Jonny Griffiths on TES Resources.
Making Statistics Vital has some tasks which are excellent for the A Level specification, look at this task on World Wide Statistics for example which includes the task with answers and a spreadsheet with data for 191 countries.
…and on the subject of bargains – note the free/cheap Maths books available!