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

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

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?

Match the descriptions of physical processes to these differential equations.

Which of these infinitely deep vessels will eventually full up?

Which line graph, equations and physical processes go together?

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

Use vectors and matrices to explore the symmetries of crystals.

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

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

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.

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

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

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

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?

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

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

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

Work out the numerical values for these physical quantities.

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

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?

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

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

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

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

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.

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

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

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

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.

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.

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?

Build up the concept of the Taylor series

Which dilutions can you make using only 10ml pipettes?

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

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

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

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