First of all, pick the number of times a week that you would like
to eat chocolate. Multiply this number by 2...
Given the graph of a supply network and the maximum capacity for
flow in each section find the maximum flow across the network.
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!
Invent scenarios which would give rise to these probability density functions.
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.
At what positions and speeds can the bomb be dropped to destroy the
First in our series of problems on population dynamics for advanced students.
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
Second in our series of problems on population dynamics for advanced students.
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?
How do these modelling assumption affect the solutions?
Why MUST these statistical statements probably be at least a little
See how differential equations might be used to make a realistic
model of a system containing predators and their prey.
This is the section of stemNRICH devoted to the advanced applied
mathematics underlying the study of the sciences at higher levels
Explore the transformations and comment on what you find.
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
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.
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. . . .
Look at the calculus behind the simple act of a car going over a
This is about a fiendishly difficult jigsaw and how to solve it
using a computer program.
A player has probability 0.4 of winning a single game. What is his
probability of winning a 'best of 15 games' tournament?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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?
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.
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.
An account of how mathematics is used in computer games including
geometry, vectors, transformations, 3D graphics, graph theory and
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. . . .
Fourth in our series of problems on population dynamics for advanced students.
Third in our series of problems on population dynamics for advanced students.
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.
The third installment in our series on the shape of astronomical systems, this article explores galaxies and the universe beyond our solar system.
Fifth in our series of problems on population dynamics for advanced students.
Sixth in our series of problems on population dynamics for advanced students.
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?
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. . . .
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. . . .
Simple models which help us to investigate how epidemics grow and die out.
How many eggs should a bird lay to maximise the number of chicks
that will hatch? An introduction to optimisation.
See how the motion of the simple pendulum is not-so-simple after
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
How do scores on dice and factors of polynomials relate to each
Bricks are 20cm long and 10cm high. How high could an arch be built
without mortar on a flat horizontal surface, to overhang by 1
metre? How big an overhang is it possible to make like this?
The second in a series of articles on visualising and modelling shapes in the history of astronomy.
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
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
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?