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

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

Match the charts of these functions to the charts of their integrals.

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?

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

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

Practice your skills of measurement and estimation using this interactive measurement tool based around fascinating images from biology.

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

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 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?

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

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

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

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.

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

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. . . .

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.

This problem explores the biology behind Rudolph's glowing red nose.

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

Match the descriptions of physical processes to these differential equations.

Which dilutions can you make using only 10ml pipettes?

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

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.

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

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.

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

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

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

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.

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

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

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

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

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

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

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

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

Get some practice using big and small numbers in chemistry.

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.

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

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