Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
This shape comprises four semi-circles. What is the relationship
between the area of the shaded region and the area of the circle on
AB as diameter?
An irregular tetrahedron has two opposite sides the same length a
and the line joining their midpoints is perpendicular to these two
edges and is of length b. What is the volume of the tetrahedron?
If the radius of the tubing used to make this stand is r cm, what is the volume of tubing used?
What is the longest stick that can be carried horizontally along a
narrow corridor and around a right-angled bend?
Explore the hyperbolic functions sinh and cosh using what you know about the exponential function.
Solve the equation sin z = 2 for complex z. You only need the
formula you are given for sin z in terms of the exponential
function, and to solve a quadratic equation and use the logarithmic
The diagram really says it all. You need to know the distance between 2 points is the modulus but that's just Pythagoras Theorem.
Go to last month's problems to see more solutions.
Imagine two identical cylindrical pipes meeting at right angles and think about the shape of the space which belongs to both pipes. Early Chinese mathematicians call this shape the mouhefanggai.