A player has probability 0.4 of winning a single game. What is his probability of winning a 'best of 15 games' tournament?

You have two bags, four red balls and four white balls. You must put all the balls in the bags although you are allowed to have one bag empty. How should you distribute the balls between the two. . . .

To win on a scratch card you have to uncover three numbers that add up to more than fifteen. What is the probability of winning a prize?

In four years 2001 to 2004 Arsenal have been drawn against Chelsea in the FA cup and have beaten Chelsea every time. What was the probability of this? Lots of fractions in the calculations!

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

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

Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.

This article explains the concepts involved in scientific mathematical computing. It will be very useful and interesting to anyone interested in computer programming or mathematics.

Your school has been left a million pounds in the will of an ex- pupil. What model of investment and spending would you use in order to ensure the best return on the money?

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

Edward Wallace based his A Level Statistics Project on The Mean Game. Each picks 2 numbers. The winner is the player who picks a number closest to the mean of all the numbers picked.

Can you make sense of information about trees in order to maximise the profits of a forestry company?

In this article for teachers, Alan Parr looks at ways that mathematics teaching and learning can start from the useful and interesting things can we do with the subject, including. . . .

See how the motion of the simple pendulum is not-so-simple after all.

Work in groups to try to create the best approximations to these physical quantities.

A car is travelling along a dual carriageway at constant speed. Every 3 minutes a bus passes going in the opposite direction, while every 6 minutes a bus passes the car travelling in the same. . . .

engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering

PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics

bioNRICH is the area of the stemNRICH site devoted to the mathematics underlying the study of the biological sciences, designed to help develop the mathematics required to get the most from your. . . .

chemNRICH is the area of the stemNRICH site devoted to the mathematics underlying the study of chemistry, designed to help develop the mathematics required to get the most from your study. . . .

Look at the calculus behind the simple act of a car going over a step.

This is the section of stemNRICH devoted to the advanced applied mathematics underlying the study of the sciences at higher levels

PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics

This problem opens a major sequence of activities on the mathematics of population dynamics for advanced students.

How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.

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

An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.

First in our series of problems on population dynamics for advanced students.

Second in our series of problems on population dynamics for advanced students.

Third in our series of problems on population dynamics for advanced students.

Fourth in our series of problems on population dynamics for advanced students.

Fifth in our series of problems on population dynamics for advanced students.

Sixth in our series of problems on population dynamics for advanced students.

An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.

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

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.

See how differential equations might be used to make a realistic model of a system containing predators and their prey.

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.

An article demonstrating mathematically how various physical modelling assumptions affect the solution to the seemingly simple problem of the projectile.

An account of how mathematics is used in computer games including geometry, vectors, transformations, 3D graphics, graph theory and simulations.

This article for students introduces the idea of naming knots using numbers. You'll need some paper and something to write with handy!

A brief video explaining the idea of a mathematical knot.

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.

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?

Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.

At Holborn underground station there is a very long escalator. Two people are in a hurry and so climb the escalator as it is moving upwards, thus adding their speed to that of the moving steps. . . .

The builders have dug a hole in the ground to be filled with concrete for the foundations of our garage. How many cubic metres of ready-mix concrete should the builders order to fill this hole to. . . .

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?