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?
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
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. . . .
How do these modelling assumption affect the solutions?
Explore the transformations and comment on what you find.
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!
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?
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 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. . . .
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
Invent scenarios which would give rise to these probability density functions.
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.
Fourth in our series of problems on population dynamics for advanced students.
Third in our series of problems on population dynamics for advanced students.
This problem opens a major sequence of activities on the mathematics of population dynamics for advanced students.
First in our series of problems on population dynamics for advanced students.
Second in our series of problems on population dynamics for advanced students.
Given the graph of a supply network and the maximum capacity for
flow in each section find the maximum flow across the network.
How do scores on dice and factors of polynomials relate to each
At what positions and speeds can the bomb be dropped to destroy the
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. . . .
This is about a fiendishly difficult jigsaw and how to solve it
using a computer program.
An account of how mathematics is used in computer games including
geometry, vectors, transformations, 3D graphics, graph theory and
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.
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. . . .
This article for students introduces the idea of naming knots using numbers. You'll need some paper and something to write with handy!
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?
A brief video explaining the idea of a mathematical knot.
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. . . .
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.
A player has probability 0.4 of winning a single game. What is his
probability of winning a 'best of 15 games' tournament?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
You have two bags, four red balls and four white balls. You must
put all the balls in the bags although you are allowed to have one
bag empty. How should you distribute the balls between the two. . . .
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
Look at the calculus behind the simple act of a car going over a
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...
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. . . .
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. . . .
Simple models which help us to investigate how epidemics grow and die out.
The second in a series of articles on visualising and modelling shapes in the history of astronomy.
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.