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.

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

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.

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?

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.

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?

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

Which line graph, equations and physical processes go together?

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

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

Use vectors and matrices to explore the symmetries of crystals.

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

Work out the numerical values for these physical quantities.

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

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

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

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

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

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

Which units would you choose best to fit these situations?

Analyse these beautiful biological images and attempt to rank them in size order.

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

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.

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.

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

Can you match the charts of these functions to the charts of their integrals?

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

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?

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

Explore the relationship between resistance and temperature

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

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

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.

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

Looking at small values of functions. Motivating the existence of the Taylor expansion.