Year 11+ Working systematically

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

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?

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

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.

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.

A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?