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

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

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

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

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

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

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

Match the charts of these functions to the charts of their integrals.

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

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

Match the descriptions of physical processes to these differential equations.

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

Build up the concept of the Taylor series

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

Explore the relationship between resistance and temperature

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?

Can you construct a cubic equation with a certain distance between its turning points?

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?

Get some practice using big and small numbers in chemistry.

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

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

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.

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

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

Work out the numerical values for these physical quantities.

How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?

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

Which line graph, equations and physical processes go together?

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

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

How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.

Which units would you choose best to fit these situations?

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

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?

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.

Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .

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

Simple models which help us to investigate how epidemics grow and die out.

Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?

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

Can Jo make a gym bag for her trainers from the piece of fabric she has?

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

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

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