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

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

Which line graph, equations and physical processes go together?

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

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

Work out the numerical values for these physical quantities.

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.

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

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

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

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

Get some practice using big and small numbers in chemistry.

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

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

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

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.

Build up the concept of the Taylor series

Explore the relationship between resistance and temperature

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

Use simple trigonometry to calculate the distance along the flight path from London to Sydney.

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

Use trigonometry to determine whether solar eclipses on earth can be perfect.

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

In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?

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

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

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.

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.

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

Which dilutions can you make using only 10ml pipettes?

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

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

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

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

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

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

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

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.

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

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