Formulate and investigate a simple mathematical model for the design of a table mat.
Invent scenarios which would give rise to these probability density functions.
Why MUST these statistical statements probably be at least a little
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?
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
How do these modelling assumption affect the solutions?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
This is the section of stemNRICH devoted to the advanced applied
mathematics underlying the study of the sciences at higher levels
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.
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.
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
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.
Sixth in our series of problems on population dynamics for advanced students.
An article demonstrating mathematically how various physical
modelling assumptions affect the solution to the seemingly simple
problem of the projectile.
See how differential equations might be used to make a realistic
model of a system containing predators and their prey.
Explore the transformations and comment on what you find.
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.
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
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.
Third in our series of problems on population dynamics for advanced students.
Second in our series of problems on population dynamics for advanced students.
Fifth in our series of problems on population dynamics for advanced students.
engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering
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?
Work in groups to try to create the best approximations to these
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. . . .
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. . . .
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. . . .
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. . . .
Simple models which help us to investigate how epidemics grow and die out.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
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.
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.
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?
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?
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?
Given the graph of a supply network and the maximum capacity for
flow in each section find the maximum flow across the network.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.