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

Which line graph, equations and physical processes go together?

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

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

How would you go about estimating populations of dolphins?

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

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 properties of matrix transformations with these 10 stimulating questions.

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

Which of these infinitely deep vessels will eventually full up?

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

Use your skill and judgement to match the sets of random data.

How do you choose your planting levels to minimise the total loss at harvest time?

Explore the relationship between resistance and temperature

Use vectors and matrices to explore the symmetries of crystals.

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

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

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

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

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

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

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

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?

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.

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

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

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

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

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?

Which dilutions can you make using only 10ml pipettes?

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

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.

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

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

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

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.

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