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

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

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

How would you go about estimating populations of dolphins?

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

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

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

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

Which line graph, equations and physical processes go together?

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

Explore the relationship between resistance and temperature

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

Can you draw the height-time chart as this complicated vessel fills with water?

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

Work out the numerical values for these physical quantities.

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

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

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

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

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

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

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.

How do you choose your planting levels to minimise the total loss at harvest time?

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.

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

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

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

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?

Match the descriptions of physical processes to these differential equations.

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

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.

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

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

Use vectors and matrices to explore the symmetries of crystals.

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

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?

Build up the concept of the Taylor series

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?