Year 11+ Being resilient

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.

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

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

A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?

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 sums of the squares of three related numbers is also a perfect square - can you explain why?

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

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

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

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.

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.

Use the differences to find the solution to this Sudoku.

What is the same and what is different about these circle questions? What connections can you make?

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

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

Quadratic graphs are very familiar, but what patterns can you explore with cubics?

Find the sum of this series of surds.

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

This problem challenges you to find cubic equations which satisfy different conditions.

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

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

Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.