Creating and manipulating expressions and formulae

Think of any whole number. Each time you perform a sequence of operations on it, what do you notice about the divisors of your answer?

How does the perimeter change when we fold this isosceles triangle in half?

The nth term of a sequence is given by the formula n^3 + 11n. Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. Prove that all terms of the sequence are divisible by 6.

I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same...

First of all, pick the number of times a week that you would like to eat chocolate. Multiply this number by 2...

Can you find a rule which relates triangular numbers to square numbers?

Look at the times that Harry, Christine and Betty take to pack boxes when working in pairs, to find how fast Christine can pack boxes by herself.

Prove that the product of the sum of n positive numbers with the sum of their reciprocals is not less than n^2.

Can you use the diagram to prove the AM-GM inequality?

Choose any four consecutive even numbers. Multiply the two middle numbers together. Multiply the first and last numbers. Now subtract your second answer from the first. Try it with your own numbers. Why is the answer always 8?