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

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?

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?

Which line graph, equations and physical processes go together?

Build up the concept of the Taylor series

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 out the numerical values for these physical quantities.

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?

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

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

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

Use vectors and matrices to explore the symmetries of crystals.

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

Which of these infinitely deep vessels will eventually full up?

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

How do you choose your planting levels to minimise the total loss at harvest time?

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

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

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

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

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

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

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.

Get some practice using big and small numbers in chemistry.

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

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

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

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

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

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.

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

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

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

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.

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

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

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

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