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

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

Which line graph, equations and physical processes go together?

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

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

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

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

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

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

How do you choose your planting levels to minimise the total loss at harvest time?

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

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?

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

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?

Use vectors and matrices to explore the symmetries of crystals.

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

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

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

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

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

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

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

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

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

Build up the concept of the Taylor series

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

Match the descriptions of physical processes to these differential equations.

Which units would you choose best to fit these situations?

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

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

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?

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

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

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

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.

How would you design the tiering of seats in a stadium so that all spectators have a good view?

Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?

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

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