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

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

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

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

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

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

How would you go about estimating populations of dolphins?

Which line graph, equations and physical processes go together?

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

Use vectors and matrices to explore the symmetries of crystals.

Get some practice using big and small numbers in chemistry.

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

Which dilutions can you make using only 10ml pipettes?

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

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

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

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

Work out the numerical values for these physical quantities.

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.

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

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

Build up the concept of the Taylor series

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

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

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

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.

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

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

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

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

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.

Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.

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

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?

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.

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

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

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

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

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.

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

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