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

Which curve is which, and how would you plan a route to pass between them?

Several graphs of the sort occurring commonly in biology are given. How many processes can you map to each graph?

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

Can you hit the target functions using a set of input functions and a little calculus and algebra?

Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.

See how differential equations might be used to make a realistic model of a system containing predators and their prey.

Here are several equations from real life. Can you work out which measurements are possible from each equation?

Analyse these beautiful biological images and attempt to rank them in size order.

How would you go about estimating populations of dolphins?

The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?

Explore the Lorentz force law for charges moving in different ways.

Starting with two basic vector steps, which destinations can you reach on a vector walk?

Can you arrange a set of charged particles so that none of them start to move when released from rest?

Maths is everywhere in the world! Take a look at these images. What mathematics can you see?

Work out the numerical values for these physical quantities.

Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?

Explore the lattice and vector structure of this crystal.

Explore how can changing the axes for a plot of an equation can lead to different shaped graphs emerging

Go on a vector walk and determine which points on the walk are closest to the origin.

In an extension to the Stonehenge problem, consider the mechanical possibilities for an arrangement of frictional rollers.

Look at the calculus behind the simple act of a car going over a step.

Explore the shape of a square after it is transformed by the action of a matrix.

Which line graph, equations and physical processes go together?

From the atomic masses recorded in a mass spectrometry analysis can you deduce the possible form of these compounds?

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

Have you ever wondered what it would be like to race against Usain Bolt?

Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.

Explore the properties of matrix transformations with these 10 stimulating questions.

Explore the rates of growth of the sorts of simple polynomials often used in mathematical modelling.

When you change the units, do the numbers get bigger or smaller?

Are these statistical statements sometimes, always or never true? Or it is impossible to say?

How many generations would link an evolutionist to a very distant ancestor?

Which units would you choose best to fit these situations?

Get into the exponential distribution through an exploration of its pdf.

Work with numbers big and small to estimate and calulate various quantities in biological contexts.

Explore displacement/time and velocity/time graphs with this mouse motion sensor.

Match the descriptions of physical processes to these differential equations.

Use your skill and judgement to match the sets of random data.

What will happen when you switch on these circular circuits?

How efficiently can various flat shapes be fitted together?

Problems which make you think about the kinetic ideas underlying the ideal gas laws.

Gravity on the Moon is about 1/6th that on the Earth. A pole-vaulter 2 metres tall can clear a 5 metres pole on the Earth. How high a pole could he clear on the Moon?

Where will the spaceman go when he falls through these strange planetary systems?