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

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

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

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

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

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

Match the descriptions of physical processes to these differential equations.

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

Which dilutions can you make using only 10ml pipettes?

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

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

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

Get some practice using big and small numbers in chemistry.

Which line graph, equations and physical processes go together?

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

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

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

Build up the concept of the Taylor series

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

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

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

Use vectors and matrices to explore the symmetries of crystals.

Work out the numerical values for these physical quantities.

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?

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

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

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

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.

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?

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?

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

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

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

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

Which of these infinitely deep vessels will eventually full up?

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

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

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

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

How would you go about estimating populations of dolphins?

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

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

Which units would you choose best to fit these situations?

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