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

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

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

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

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

Which line graph, equations and physical processes go together?

Use vectors and matrices to explore the symmetries of crystals.

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

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

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

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

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?

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

How would you go about estimating populations of dolphins?

Which of these infinitely deep vessels will eventually full up?

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

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

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

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

Which dilutions can you make using only 10ml pipettes?

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.

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

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

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

Get some practice using big and small numbers in chemistry.

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

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

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

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

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

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

Build up the concept of the Taylor series

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

Explore the relationship between resistance and temperature

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

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

Match the descriptions of physical processes to these differential equations.

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

Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?

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.

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.