Challenge Level

What is the remainder if you divide a square number by $8$?

Challenge Level

Can you show that $n^5-n^3$ is always divisible by $24$?

Challenge Level

Can you find the smallest integer which has exactly 426 proper factors?

Challenge Level

Which numbers can you write as a difference of two squares? In how many ways can you write $pq$ as a difference of two squares if $p$ and $q$ are prime?

Challenge Level

Which is larger cos(sin x) or sin(cos x) ? Does this depend on x ?

Challenge Level

Draw graphs of the sine and modulus functions and explain the humps.

Challenge Level

Can you find a way to prove the trig identities using a diagram?

Challenge Level

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

Challenge Level

If I tell you two sides of a right-angled triangle, you can easily work out the third. But what if the angle between the two sides is not a right angle?