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

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

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

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

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

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

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

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

Which line graph, equations and physical processes go together?

Use vectors and matrices to explore the symmetries of crystals.

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

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

Which of these infinitely deep vessels will eventually full up?

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.

Match the descriptions of physical processes to these differential equations.

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 dilutions can you make using only 10ml pipettes?

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.

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

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

Work out the numerical values for these physical quantities.

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

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?

Get some practice using big and small numbers in chemistry.

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.

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

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

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

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

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

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

Are these statistical statements sometimes, always or never true? Or it is impossible to say?

Build up the concept of the Taylor series

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.

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

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

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