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.

Various solids are lowered into a beaker of water. How does the water level rise in each case?

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

Can you draw the height-time chart as this complicated vessel fills with water?

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?

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

Use vectors and matrices to explore the symmetries of crystals.

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

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

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

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?

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 properties of matrix transformations with these 10 stimulating questions.

Formulate and investigate a simple mathematical model for the design of a table mat.

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

Get some practice using big and small numbers in chemistry.

In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?

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

Can Jo make a gym bag for her trainers from the piece of fabric she has?

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

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

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

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

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

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

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

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

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.

Match the descriptions of physical processes to these differential equations.

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

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

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

In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?

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

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