How do scores on dice and factors of polynomials relate to each other?

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.

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

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

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

Can you find the lap times of the two cyclists travelling at constant speeds?

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.

First 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.

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.

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

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

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

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

How do these modelling assumption affect the solutions?

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. . . .

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.

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

Chris is enjoying a swim but needs to get back for lunch. If she can swim at 3 m/s and run at 7m/sec, how far along the bank should she land in order to get back as quickly as possible?

Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever. . . .

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

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!

Given the graph of a supply network and the maximum capacity for flow in each section find the maximum flow across the network.

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?

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?

First of all, pick the number of times a week that you would like to eat chocolate. Multiply this number by 2...

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.

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

This is about a fiendishly difficult jigsaw and how to solve it using a computer program.

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

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. . . .

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

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

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

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

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

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

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

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

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. . . .

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

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

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?

It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?

A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance. . . .