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

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

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 line graph, equations and physical processes go together?

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

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.

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

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

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

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

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

Match the charts of these functions to the charts of their integrals.

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

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

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

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

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

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

Get some practice using big and small numbers in chemistry.

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

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?

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

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.

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

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.

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

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

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

Use your skill and judgement to match the sets of random data.

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

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

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.

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

Explore the relationship between resistance and temperature

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

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