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

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

Explore the relationship between resistance and temperature

Can you match the charts of these functions to the charts of their integrals?

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

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

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.

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

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

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

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

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

Which line graph, equations and physical processes go together?

Work out the numerical values for these physical quantities.

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

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

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

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

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

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

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

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?

Build up the concept of the Taylor series

Get some practice using big and small numbers in chemistry.

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

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

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.

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

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

Which dilutions can you make using only 10ml pipettes?

Investigate circuits and record your findings in this simple introduction to truth tables and logic.

Is it really greener to go on the bus, or to buy local?

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

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

Can you make matrices which will fix one lucky vector and crush another to zero?

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

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

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

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

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

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.

In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?