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

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

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

Which dilutions can you make using only 10ml pipettes?

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.

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

Which line graph, equations and physical processes go together?

Work out the numerical values for these physical quantities.

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

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 calculate various quantities in physical contexts.

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?

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

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

Get some practice using big and small numbers in chemistry.

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

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

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

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

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

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.

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

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

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

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

Build up the concept of the Taylor series

Match the descriptions of physical processes to these differential equations.

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

Explore the relationship between resistance and temperature

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?

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.

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

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

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.

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

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

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

In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.

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

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.

Where should runners start the 200m race so that they have all run the same distance by the finish?

Can Jo make a gym bag for her trainers from the piece of fabric she has?