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

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

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

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

Match the descriptions of physical processes to these differential equations.

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.

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?

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.

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?

How would you go about estimating populations of dolphins?

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

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

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

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

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.

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

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

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. . . .

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.

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?

Get some practice using big and small numbers in chemistry.

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?

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

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

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

Build up the concept of the Taylor series

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

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 calculate various quantities in physical contexts.

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

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

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.

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

Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.

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

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

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

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

Explore the relationship between resistance and temperature

Which dilutions can you make using only 10ml pipettes?