Which line graph, equations and physical processes go together?

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

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

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

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

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

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

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

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

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

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

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

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

Match the descriptions of physical processes to these differential equations.

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

Build up the concept of the Taylor series

Use vectors and matrices to explore the symmetries of crystals.

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

Get some practice using big and small numbers in chemistry.

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

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

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

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

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

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

Work out the numerical values for these physical quantities.

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?

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

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

In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.

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.

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

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

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?

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

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

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

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

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

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

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

Explore the relationship between resistance and temperature

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