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

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

Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.

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

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

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

See how enormously large quantities can cancel out to give a good approximation to the factorial function.

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

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

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

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

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. . . .

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

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?

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?

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.

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

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

Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.

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

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

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.

Use simple trigonometry to calculate the distance along the flight path from London to Sydney.

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?

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.

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.

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?

Analyse these beautiful biological images and attempt to rank them in size order.

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.

Which dilutions can you make using only 10ml pipettes?

Explore the relationship between resistance and temperature

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

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

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

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