Ratio and proportion

P is the midpoint of an edge of a cube and Q divides another edge in the ratio 1 to 4. Find the ratio of the volumes of the two pieces of the cube cut by a plane through PQ and a vertex.

Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever meet at the start again? If so, after how many circuits?

Why is the modern piano tuned using an equal tempered scale and what has this got to do with logarithms?

When a mixture of gases burn, will the volume change?

Ever wondered what it would be like to vaporise a diamond? Find out inside...

A brief introduction to PCR and restriction mapping, with relevant calculations...

If the sides of the triangle in the diagram are 3, 4 and 5, what is the area of the shaded square?

A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance up the wall which the ladder can reach?

What does the empirical formula of this mixture of iron oxides tell you about its consituents?

Do each of these scenarios allow you fully to deduce the required facts about the reactants?