problem
Summing geometric progressions
Age
14 to 18
Challenge level
Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?
problem
Parabolic patterns
Age
14 to 18
Challenge level
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.
problem
Expenses
Age
14 to 16
Challenge level
What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?
problem
Why 24?
Age
14 to 16
Challenge level
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.
problem
Areas of parallelograms
Age
14 to 16
Challenge level
Can you find the area of a parallelogram defined by two vectors?
problem
Trapezium four
Age
14 to 16
Challenge level
The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?
problem
Tangled trig graphs
Age
16 to 18
Challenge level
Can you work out the equations of the trig graphs I used to make my pattern?