Conjecturing and generalising

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

Generalise the sum of a GP by using derivatives to make the coefficients into powers of the natural numbers.

When if ever do you get the right answer if you add two fractions by adding the numerators and adding the denominators?

Your data is a set of positive numbers. What is the maximum value that the standard deviation can take?

Generalise this inequality involving integrals.

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”

What is the last-but-one digit of 99! ?

Make some loops out of regular hexagons. What rules can you discover?

Multiply a sequence of n terms together. Can you work out when this product is equal to an integer?