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?

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

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

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

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.

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

How would you go about estimating populations of dolphins?

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

Use vectors and matrices to explore the symmetries of crystals.

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

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

Work out the numerical values for these physical quantities.

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

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

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

Looking at small values of functions. Motivating the existence of the Taylor expansion.

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

Get some practice using big and small numbers in chemistry.

Build up the concept of the Taylor series

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

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

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

Which of these infinitely deep vessels will eventually full up?

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

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

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.

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

Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.

Which line graph, equations and physical processes go together?

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?

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

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

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?

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.

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

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