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?

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

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

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

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

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

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.

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

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.

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

Which line graph, equations and physical processes go together?

Which of these infinitely deep vessels will eventually full up?

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

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

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

Work out the numerical values for these physical quantities.

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

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

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

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.

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

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

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

Build up the concept of the Taylor series

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.

Explore the relationship between resistance and temperature

Get some practice using big and small numbers in chemistry.

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

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

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

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?

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

Which dilutions can you make using only 10ml pipettes?

When you change the units, do the numbers get bigger or smaller?

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

Which units would you choose best to fit these situations?

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?