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

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

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?

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

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

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

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

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

Which line graph, equations and physical processes go together?

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

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

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

Build up the concept of the Taylor series

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

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

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

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.

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

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

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

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

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

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

Work out the numerical values for these physical quantities.

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

Can you work out which processes are represented by the graphs?

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.

Explore the relationship between resistance and temperature

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?

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

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?

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

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

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

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

Get some practice using big and small numbers in chemistry.

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

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?

How would you go about estimating populations of dolphins?

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

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

Which dilutions can you make using only 10ml pipettes?