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

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?

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

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

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

Which line graph, equations and physical processes go together?

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

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

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

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

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

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

Explore the relationship between resistance and temperature

Which dilutions can you make using only 10ml pipettes?

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

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.

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

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

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

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

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

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

Use vectors and matrices to explore the symmetries of crystals.

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.

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

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

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

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

Get some practice using big and small numbers in chemistry.

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

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

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?

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

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

Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.

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

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.

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

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

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

Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .