Here's this week's collection. Answers & extensions can be found here. Why not discuss the problems on Twitter using #SundayAfternoonMaths. This Tuesday is Maths Jam, although I won't be there as it is also parents' evening at my school.
Arccos + Arcsin
What is the value of arccos(x) + arcsin(x)?
What is the value of i to the power of i?
If xxxxxx... [x to the power of (x to the power of (x to the power of (x to the power of (...)))) with an infinite number of xs] is equal to two, what is the value of x?
4 and 5 digit numbers
Adam chooses a 5-digit positive integer and deletes one of its digits to form a 4-digit integer. The sum of this 4-digit integer and the original 5-digit integer is 52713. What is the sum of the digits of the original 5-digit integer?