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

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

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

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

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

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?

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?

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

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

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

Work out the numerical values for these physical quantities.

Which line graph, equations and physical processes go together?

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

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

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

Have you ever wondered what it would be like to race against Usain Bolt?

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.

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.

Get some practice using big and small numbers in chemistry.

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

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

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

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

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

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.

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

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

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?

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

Match the descriptions of physical processes to these differential equations.

In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?

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

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

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

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