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

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.

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

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

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

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.

Which line graph, equations and physical processes go together?

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 calculate various quantities in biological contexts.

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

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

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

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

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.

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

Explore the relationship between resistance and temperature

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

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

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

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

Use vectors and matrices to explore the symmetries of crystals.

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

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

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

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?

Match the descriptions of physical processes to these differential equations.

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

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

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.

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?

Get some practice using big and small numbers in chemistry.

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?

Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.

Which dilutions can you make using only 10ml pipettes?

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

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