Year 11+ Being resilient

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?

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?

Use the differences to find the solution to this Sudoku.

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?