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

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

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

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

Build up the concept of the Taylor series

Explore the relationship between resistance and temperature

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

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

Work out the numerical values for these physical quantities.

Estimate these curious quantities sufficiently accurately that you can rank them in order of size

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

Use vectors and matrices to explore the symmetries of crystals.

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

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

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

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

Which line graph, equations and physical processes go together?

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

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

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

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. . . .

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.

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

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

Get some practice using big and small numbers in chemistry.

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

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

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.

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

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

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

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

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.

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.

Which units would you choose best to fit these situations?

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

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

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?

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

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

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

In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?