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

Which line graph, equations and physical processes go together?

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

How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?

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?

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

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

Simple models which help us to investigate how epidemics grow and die out.

How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.

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

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.

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

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

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

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

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?

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.

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?

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

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.

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

Work out the numerical values for these physical quantities.

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

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

Use vectors and matrices to explore the symmetries of crystals.

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

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

Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .

Which dilutions can you make using only 10ml pipettes?

Can Jo make a gym bag for her trainers from the piece of fabric she has?

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

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?

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

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

Get some practice using big and small numbers in chemistry.

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

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

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?

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

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

How would you go about estimating populations of dolphins?

Which units would you choose best to fit these situations?