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

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

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

Can you sketch these difficult curves, which have uses in mathematical modelling?

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

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

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

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

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

Which line graph, equations and physical processes go together?

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

Get some practice using big and small numbers in chemistry.

Explore the relationship between resistance and temperature

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

Match the descriptions of physical processes to these differential equations.

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

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

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

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

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

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

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

Work out the numerical values for these physical quantities.

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

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

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

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

Use vectors and matrices to explore the symmetries of crystals.

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?

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

Which units would you choose best to fit these situations?

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?

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.

In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.

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

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

Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation

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

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

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?

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?