Look at the calculus behind the simple act of a car going over a
First of all, pick the number of times a week that you would like
to eat chocolate. Multiply this number by 2...
How many eggs should a bird lay to maximise the number of chicks
that will hatch? An introduction to optimisation.
This is the section of stemNRICH devoted to the advanced applied
mathematics underlying the study of the sciences at higher levels
See how differential equations might be used to make a realistic
model of a system containing predators and their prey.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
An advanced mathematical exploration supporting our series of articles on 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. . . .
Why MUST these statistical statements probably be at least a little
How do these modelling assumption affect the solutions?
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. . . .
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
Second in our series of problems on population dynamics for advanced students.
Third in our series of problems on population dynamics for advanced students.
Fourth in our series of problems on population dynamics for advanced students.
Fifth in our series of problems on population dynamics for advanced students.
First in our series of problems on population dynamics for advanced students.
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!
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.
This problem opens a major sequence of activities on the mathematics of population dynamics for advanced students.
Sixth in our series of problems on population dynamics for advanced students.
How do scores on dice and factors of polynomials relate to each
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.
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?
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.
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?
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. . . .
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.
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. . . .
At what positions and speeds can the bomb be dropped to destroy the
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. . . .
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
The third installment in our series on the shape of astronomical systems, this article explores galaxies and the universe beyond our solar system.
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.
Given the graph of a supply network and the maximum capacity for
flow in each section find the maximum flow across the network.
A brief video explaining the idea of a mathematical knot.
This article for students introduces the idea of naming knots using numbers. You'll need some paper and something to write with handy!
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?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Explain why, when moving heavy objects on rollers, the object moves
twice as fast as the rollers. Try a similar experiment yourself.
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.