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.

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

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

What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?

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?

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

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

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

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.

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

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 physical contexts.

Which units would you choose best to fit these situations?

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?

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

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

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?

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

Build up the concept of the Taylor series

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

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

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

Which line graph, equations and physical processes go together?

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

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

Get some practice using big and small numbers in chemistry.

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

Which dilutions can you make using only 10ml pipettes?

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

Use vectors and matrices to explore the symmetries of crystals.

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

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

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

Can you work out which processes are represented by the graphs?

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?

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. . . .

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.

Make an accurate diagram of the solar system and explore the concept of a grand conjunction.

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

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

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?