Two cyclists, practising on a track, pass each other at the starting line and go at constant speeds... Can you find lap times that are such that the cyclists will meet exactly half way round the. . . .
Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .
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?
At what positions and speeds can the bomb be dropped to destroy the
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
How do these modelling assumption affect the solutions?
Why MUST these statistical statements probably be at least a little
Formulate and investigate a simple mathematical model for the design of a table mat.
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.
Invent scenarios which would give rise to these probability density functions.
This is the section of stemNRICH devoted to the advanced applied
mathematics underlying the study of the sciences at higher levels
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.
An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.
See how differential equations might be used to make a realistic
model of a system containing predators and their prey.
Look at the calculus behind the simple act of a car going over a
An article demonstrating mathematically how various physical
modelling assumptions affect the solution to the seemingly simple
problem of the projectile.
Explore the transformations and comment on what you find.
Fourth in our series of problems on population dynamics for advanced students.
Third in our series of problems on population dynamics for advanced students.
Second in our series of problems on population dynamics for advanced students.
First in our series of problems on population dynamics for advanced students.
See how the motion of the simple pendulum is not-so-simple after
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. . . .
PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics
Sixth in our series of problems on population dynamics for advanced students.
Work in groups to try to create the best approximations to these
Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.
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. . . .
engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering
This problem opens a major sequence of activities on the mathematics of population dynamics for advanced students.
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
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. . . .
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
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.
Simple models which help us to investigate how epidemics grow and die out.
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.
A player has probability 0.4 of winning a single game. What is his
probability of winning a 'best of 15 games' tournament?
This article for students introduces the idea of naming knots using numbers. You'll need some paper and something to write with handy!
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
A brief video explaining the idea of a mathematical knot.
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.
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.