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

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

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?

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

Which line graph, equations and physical processes go together?

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.

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

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

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

Explore the relationship between resistance and temperature

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?

Get further into power series using the fascinating Bessel's equation.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Build up the concept of the Taylor series

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

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

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

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

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

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

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

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

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

Get some practice using big and small numbers in chemistry.

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

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

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