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

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

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

Which countries have the most naturally athletic populations?

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

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.

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

Use vectors and matrices to explore the symmetries of crystals.

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?

Which line graph, equations and physical processes go together?

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

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

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

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

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

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?

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?

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

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

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.

Get some practice using big and small numbers in chemistry.

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.

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

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

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

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

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

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.

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.

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.