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

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

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

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

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

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?

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

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

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

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

Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?

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

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

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

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

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

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

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

Go on a vector walk and determine which points on the walk are closest to the origin.

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

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

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

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

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.

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

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

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?

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

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?

The design technology curriculum requires students to be able to represent 3-dimensional objects on paper. This article introduces some of the mathematical ideas which underlie such methods.

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

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

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.

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.

Use vectors and matrices to explore the symmetries of crystals.

Get some practice using big and small numbers in chemistry.

Is it really greener to go on the bus, or to buy local?

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