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

Explore the relationship between resistance and temperature

Can you work out which processes are represented by the graphs?

Can you draw the height-time chart as this complicated vessel fills with water?

Build up the concept of the Taylor series

What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?

Which line graph, equations and physical processes go together?

Look at the advanced way of viewing sin and cos through their power series.

Get further into power series using the fascinating Bessel's equation.

Can you match the charts of these functions to the charts of their integrals?

Was it possible that this dangerous driving penalty was issued in error?

This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.

Invent scenarios which would give rise to these probability density functions.

Which of these infinitely deep vessels will eventually full up?

Why MUST these statistical statements probably be at least a little bit wrong?

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

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

Work out the numerical values for these physical quantities.

Estimate these curious quantities sufficiently accurately that you can rank them in order of size

Use vectors and matrices to explore the symmetries of crystals.

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

Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.

See how enormously large quantities can cancel out to give a good approximation to the factorial function.

Use trigonometry to determine whether solar eclipses on earth can be perfect.

How would you go about estimating populations of dolphins?

Make an accurate diagram of the solar system and explore the concept of a grand conjunction.

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

Looking at small values of functions. Motivating the existence of the Taylor expansion.

The probability that a passenger books a flight and does not turn up is 0.05. For an aeroplane with 400 seats how many tickets can be sold so that only 1% of flights are over-booked?

Use simple trigonometry to calculate the distance along the flight path from London to Sydney.

Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.

How would you design the tiering of seats in a stadium so that all spectators have a good view?

By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.

Explore the meaning of the scalar and vector cross products and see how the two are related.

Get some practice using big and small numbers in chemistry.

Work with numbers big and small to estimate and calculate various quantities in physical contexts.

Where should runners start the 200m race so that they have all run the same distance by the finish?

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

Investigate circuits and record your findings in this simple introduction to truth tables and logic.

To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...

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

In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?

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