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?

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

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

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

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

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

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

Use vectors and matrices to explore the symmetries of crystals.

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?

Which line graph, equations and physical processes go together?

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

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

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

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

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

Which of these infinitely deep vessels will eventually full up?

Match the charts of these functions to the charts of their integrals.

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

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

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?

Get some practice using big and small numbers in chemistry.

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

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

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

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.

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

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?

Which units would you choose best to fit these situations?

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

Build up the concept of the Taylor series

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

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

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

How would you go about estimating populations of dolphins?

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

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.

How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?

Explore the relationship between resistance and temperature

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