Year 11+ Being curious

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

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?

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

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?

It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.

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

Using a ruler, pencil and compasses only, it is possible to construct a square inside any triangle so that all four vertices touch the sides of the triangle.

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?

What do you get when you raise a quadratic to the power of a quadratic?

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

Find the sum of this series of surds.

There are many different methods to solve this geometrical problem - how many can you find?

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