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

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

Which line graph, equations and physical processes go together?

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

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

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

How would you go about estimating populations of dolphins?

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

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

Use vectors and matrices to explore the symmetries of crystals.

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

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?

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

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

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

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

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

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

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

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

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

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

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

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

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.

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

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

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?

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

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

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

Match the descriptions of physical processes to these differential equations.

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

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.

Build up the concept of the Taylor series

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

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.

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

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.

Investigate circuits and record your findings in this simple introduction to truth tables and logic.