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.

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.

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

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

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

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

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

How would you go about estimating populations of dolphins?

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

Work out the numerical values for these physical quantities.

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

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

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

Use vectors and matrices to explore the symmetries of crystals.

Get some practice using big and small numbers in chemistry.

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

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

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

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

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

Which units would you choose best to fit these situations?

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?

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

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

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

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

Match the descriptions of physical processes to these differential equations.

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

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

Build up the concept of the Taylor series

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.

Use trigonometry to determine whether solar eclipses on earth can be perfect.

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

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

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

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

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

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

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