Shopping basket
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
Summing geometric progressions
Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?
Mega quadratic equations
Trapezium four
The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?
Curve fitter
This problem challenges you to find cubic equations which satisfy different conditions.
Back fitter
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?
Fill me up too
In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?
Sitting pretty
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?
Why 24?
Iff
Always perfect
Squirty
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.
Difference Sudoku
Use the differences to find the solution to this Sudoku.
Partly circles
What is the same and what is different about these circle questions? What connections can you make?
2-digit square
Angle trisection
It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.