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.

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

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

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

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 physical contexts.

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.

Match the descriptions of physical processes to these differential equations.

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

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

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

Explore the relationship between resistance and temperature

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

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

How would you go about estimating populations of dolphins?

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

Use vectors and matrices to explore the symmetries of crystals.

Which line graph, equations and physical processes go together?

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

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

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

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

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

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

Build up the concept of the Taylor series

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

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.

Which dilutions can you make using only 10ml pipettes?

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

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?

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

Get some practice using big and small numbers in chemistry.

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

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

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

In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?

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

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

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

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