Ratio and proportion

problem

Extreme Dissociation

Age

16 to 18

Challenge level

1 out of 3

In this question we push the pH formula to its theoretical limits.
problem

Another Triangle in a Triangle

Age

16 to 18

Challenge level

2 out of 3

Can you work out the fraction of the original triangle that is covered by the green triangle?
problem

Five Circuits, Seven Spins

Age

16 to 18

Challenge level

2 out of 3

A circular plate rolls inside a rectangular tray making five circuits and rotating about its centre seven times. Find the dimensions of the tray.
problem

Striking Gold

Age

16 to 18

Challenge level

2 out of 3

Investigate some of the issues raised by Geiger and Marsden's famous scattering experiment in which they fired alpha particles at a sheet of gold.
problem

Golden Ratio

Age

16 to 18

Challenge level

3 out of 3

Solve an equation involving the Golden Ratio phi where the unknown occurs as a power of phi.
problem

Rarity

Age

16 to 18

Challenge level

3 out of 3

Show that it is rare for a ratio of ratios to be rational.