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

Which of these infinitely deep vessels will eventually full up?

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

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

Which line graph, equations and physical processes go together?

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

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

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?

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

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

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

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

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

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

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

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

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

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.

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

Use vectors and matrices to explore the symmetries of crystals.

Match the descriptions of physical processes to these differential equations.

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

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

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?

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

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

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?

Work out the numerical values for these physical quantities.

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?

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

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

How would you go about estimating populations of dolphins?

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

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

Explore the relationship between resistance and temperature

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

Which dilutions can you make using only 10ml pipettes?

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

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