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

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

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

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

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

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

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

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

Which line graph, equations and physical processes go together?

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

Build up the concept of the Taylor series

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?

Can you draw the height-time chart as this complicated vessel fills with water?

How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?

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

Explore the properties of matrix transformations with these 10 stimulating questions.

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

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

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

Work out the numerical values for these physical quantities.

Various solids are lowered into a beaker of water. How does the water level rise in each case?

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

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

Use vectors and matrices to explore the symmetries of crystals.

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

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

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

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

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

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.

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

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

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.

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

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

Explore the shape of a square after it is transformed by the action of a matrix.

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

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

Simple models which help us to investigate how epidemics grow and die out.

How would you design the tiering of seats in a stadium so that all spectators have a good view?

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