Explaining, convincing and proving

This group tasks allows you to search for arithmetic progressions in the prime numbers. How many of the challenges will you discover for yourself?

How do these modelling assumption affect the solutions?

In this short challenge, can you use angle properties in a circle to figure out some trig identities?

Can you prove our inequality holds for all values of x and y between 0 and 1?

What can you deduce about the gradients of curves linking (0,0), (8,8) and (4,6)?

Get started with calculus by exploring the connections between the sign of a curve and the sign of its gradient.

Can you solve this inequalities challenge?

How did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

The twelve edge totals of a standard six-sided die are distributed symmetrically. Will the same symmetry emerge with a dodecahedral die?

Prove that k.k! = (k+1)! - k! and sum the series 1.1! + 2.2! + 3.3! +...+n.n!