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

Are these statistical statements sometimes, always or never true? Or it is impossible to say?

How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?

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

The probability that a passenger books a flight and does not turn up is 0.05. For an aeroplane with 400 seats how many tickets can be sold so that only 1% of flights are over-booked?

Use vectors and matrices to explore the symmetries of crystals.

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

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

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

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

Simple models which help us to investigate how epidemics grow and die out.

What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?

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

Which line graph, equations and physical processes go together?

Which of these infinitely deep vessels will eventually full up?

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

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

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

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

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?

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.

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

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

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.

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

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

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

Make an accurate diagram of the solar system and explore the concept of a grand conjunction.

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

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

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

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.

Build up the concept of the Taylor series

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.

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

Match the descriptions of physical processes to these differential equations.

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

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

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