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

Use vectors and matrices to explore the symmetries of crystals.

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

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?

Which of these infinitely deep vessels will eventually full up?

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

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

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

Build up the concept of the Taylor series

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

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

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

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

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

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

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?

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

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?

Which units would you choose best to fit these situations?

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

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

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

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

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

Match the descriptions of physical processes to these differential equations.

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

Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.

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

Work out the numerical values for these physical quantities.

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

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

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

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

Get some practice using big and small numbers in chemistry.

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

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

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

How would you go about estimating populations of dolphins?