How do scores on dice and factors of polynomials relate to each
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Fourth in our series of problems on population dynamics for advanced students.
Fifth 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.
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.
Third in our series of problems on population dynamics for advanced students.
Second 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.
PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics
Invent scenarios which would give rise to these probability density functions.
See how differential equations might be used to make a realistic
model of a system containing predators and their prey.
First in our series of problems on population dynamics for advanced students.
Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and record your findings in truth tables.
Sixth in our series of problems on population dynamics for advanced students.
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 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?
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.
How do these modelling assumption affect the solutions?
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. . . .
Explore the transformations and comment on what you find.
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.
Why MUST these statistical statements probably be at least a little
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 problem opens a major sequence of activities on the mathematics of population dynamics for advanced students.
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. . . .
Look at the calculus behind the simple act of a car going over a
This is the section of stemNRICH devoted to the advanced applied
mathematics underlying the study of the sciences at higher levels
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?
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?
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
An account of how mathematics is used in computer games including
geometry, vectors, transformations, 3D graphics, graph theory and
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 third installment in our series on the shape of astronomical systems, this article explores galaxies and the universe beyond our solar system.
First of all, pick the number of times a week that you would like
to eat chocolate. Multiply this number by 2...
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 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. . . .
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. . . .
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!
Given the graph of a supply network and the maximum capacity for
flow in each section find the maximum flow across the network.
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. . . .
How many eggs should a bird lay to maximise the number of chicks
that will hatch? An introduction to optimisation.
Formulate and investigate a simple mathematical model for the design of a table mat.
Simple models which help us to investigate how epidemics grow and die out.