Year 11+ Conjecturing and generalising

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.

Can you find the area of a parallelogram defined by two vectors?

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?

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.

Starting with two basic vector steps, which destinations can you reach on a vector walk?

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

Can you work out the equations of the trig graphs I used to make my pattern?