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?

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

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.

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?

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.

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

Work out the numerical values for these physical quantities.

Which line graph, equations and physical processes go together?

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

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

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.

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.

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

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.

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. . . .

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.

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

Which dilutions can you make using only 10ml pipettes?

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

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

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?

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

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

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.

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?

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

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

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

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

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?

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