Get some practice using big and small numbers in chemistry.

Which line graph, equations and physical processes go together?

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?

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

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

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

Work out the numerical values for these physical quantities.

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

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

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

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

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

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

Use vectors and matrices to explore the symmetries of crystals.

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?

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

Build up the concept of the Taylor series

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.

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

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

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?

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

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

Explore the relationship between resistance and temperature

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

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.

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

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

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

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

Which dilutions can you make using only 10ml pipettes?

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.

How would you go about estimating populations of dolphins?

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

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

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

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

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

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