Can you match the charts of these functions to the charts of their integrals?

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

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

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

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

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

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.

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

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.

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

Which line graph, equations and physical processes go together?

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

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

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?

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

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.

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

Which of these infinitely deep vessels will eventually full up?

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

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

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?

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

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

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

Get some practice using big and small numbers in chemistry.

Work out the numerical values for these physical quantities.

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?

Use vectors and matrices to explore the symmetries of crystals.

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

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

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

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

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

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

Was it possible that this dangerous driving penalty was issued in error?

Match the descriptions of physical processes to these differential equations.

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

Which units would you choose best to fit these situations?

When you change the units, do the numbers get bigger or smaller?

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.

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.