Year 11 Extension Being curious

If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.

What is the largest number which, when divided into these five numbers in turn, leaves the same remainder each time?

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

Can you work out the probability of winning the Mathsland National Lottery?

A 2-digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

The illustration shows the graphs of fifteen functions. Two of them have equations $y=x^2$ and $y=-(x-4)^2$. Find the equations of all the other graphs.

Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?

Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?