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?

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

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

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

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

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

Match the descriptions of physical processes to these differential equations.

Build up the concept of the Taylor series

Which line graph, equations and physical processes go together?

Use vectors and matrices to explore the symmetries of crystals.

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.

Which of these infinitely deep vessels will eventually full up?

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

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

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

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

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

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

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

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?

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

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

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.

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.

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?

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

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

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

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

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.

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

Which dilutions can you make using only 10ml pipettes?

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

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

Go on a vector walk and determine which points on the walk are closest to the origin.

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

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

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

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