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

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

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

Can you match the charts of these functions to the charts of their integrals?

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

Match the descriptions of physical processes to these differential equations.

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

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

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

Which line graph, equations and physical processes go together?

How would you go about estimating populations of dolphins?

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?

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

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

Use vectors and matrices to explore the symmetries of crystals.

Which of these infinitely deep vessels will eventually full up?

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

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

Can you construct a cubic equation with a certain distance between its turning points?

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

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

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

Get some practice using big and small numbers in chemistry.

Explore the relationship between resistance and temperature

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

Which dilutions can you make using only 10ml pipettes?

Investigate circuits and record your findings in this simple introduction to truth tables and logic.

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

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

Build up the concept of the Taylor series

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

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

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

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.

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

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

Which units would you choose best to fit these situations?

Work out the numerical values for these physical quantities.

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

Have you ever wondered what it would be like to race against Usain Bolt?