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

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

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.

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

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

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

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?

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

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

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

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

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.

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

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

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

How do these modelling assumption affect the solutions?

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

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. . . .

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

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.

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?

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.

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

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.

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?

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

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.

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 third installment in our series on the shape of astronomical systems, this article explores galaxies and the universe beyond our solar system.

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.

At what positions and speeds can the bomb be dropped to destroy the dam?

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?

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

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!

Two buses leave at the same time from two towns Shipton and Veston on the same long road, travelling towards each other. At each mile along the road are milestones. The buses' speeds are constant. . . .

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