Some more problems for A-level/high-school mathematics (including some for teachers)
After a long period without posting problems, I'm back. Here, you will find a list of problems to stretch students doing A-level mathematics. I intend to grow this list gradually by adding to this post a new PDF document for each problem that I set.
Some might say that my problems are too difficult but they are not. On the other hand, they reflect the exceptionally high standard of A-level mathematics at St. Dunstan's College in the period 1969-1971, when it had quite possibly the best school mathematics department in the country. I'd be curious to know how difficult your students think they are ... although I may end up privately laughing at reports of unenterprising solvers.
If you are sitting comfortably, then I'll begin:
1. SinCosIntegrals.pdf: This asks students to use a simple graphical argument to justify the proposition that two simple definite Fourier integrals evaluate to zero.
2. TweedleCoffee.pdf: This problem pays a brief and whimsical visit to Wonderland to work out how much Tweedledum and Tweedledee pay for coffee.
3. PrimeProp.pdf: This problem deals with a property of odd primes and is actually a lot easier than it may at first look.