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.

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

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

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

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.

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

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

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

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

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.

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.

Build up the concept of the Taylor 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?

Can you make matrices which will fix one lucky vector and crush another to zero?

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

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

This problem explores the biology behind Rudolph's glowing red nose.

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

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

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

Work out the numerical values for these physical quantities.

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

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

Use vectors and matrices to explore the symmetries of crystals.

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

Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.

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

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?

Formulate and investigate a simple mathematical model for the design of a table mat.

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

Explore the relationship between resistance and temperature

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

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

In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.

Which line graph, equations and physical processes go together?

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

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

Get some practice using big and small numbers in chemistry.

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