Being curious

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?

If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?

Your school has been left a million pounds in the will of an ex-pupil. What model of investment and spending would you use in order to ensure the best return on the money?

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

Charlie has moved between countries and the average income of both has increased. How can this be so?

Various solids are lowered into a beaker of water. How does the water level rise in each case?

Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?

Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?

I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?