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

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.

Which line graph, equations and physical processes go together?

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

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

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

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.

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

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

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.

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

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

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

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

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

Match the descriptions of physical processes to these differential equations.

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

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

Which of these infinitely deep vessels will eventually full up?

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

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

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

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.

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

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

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

Get some practice using big and small numbers in chemistry.

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

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

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

Which units would you choose best to fit these situations?

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

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

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

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

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

Starting with two basic vector steps, which destinations can you reach on a vector walk?

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.