Over the summer holidays I like my prospective Year 12 Further Mathematicians to look at some maths over the holiday (I do emphasise the importance of having a proper holiday too!). For the last couple of years I have given them these 3 questions (which I have found from various places over the years) to look at:
I admit that these questions are not reflective of further mathematics questions and I say this to the students. In addition, I emphasise that I am not expecting full solutions, that they are hard questions and that they shouldn’t be worried if they get stuck. I explain that I am interested in seeing how they think mathematically and them building up the resilience to spend longer struggling through a problem and trying multiple approaches. For many of them this will be the first time they have come up against a problem that requires a bit more thought than “just do it”.
If you want, you can download the questions here – let me know what you think.