Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Mathematical Modelling - Advanced

### physNRICH

### bioNRICH

### chemNRICH

### What's That Graph?

### Elastic Maths

### The Use of Mathematics in Computer Games

### Big and Small Numbers in Physics - Group Task

### engNRICH

### An Introduction to Computer Programming and Mathematics

### Maximum Flow

### Advanced Scientific Mathematics

### Cushion Ball

### Population Dynamics Collection

### The Wrong Stats

### Stonehenge

### Snooker

### 10 Olympic Starters

### Dangerous Driver?

### The Mean Game

### Bird-brained

### Modelling Assumptions in Mechanics

### Ball Bearings

### Ramping it Up

### pdf Stories

### Population Dynamics - Part 6

### Population Dynamics - Part 1

### Population Dynamics - Part 5

### The Not-so-simple Pendulum 1

### Population Dynamics - Part 3

### Population Dynamics - Part 2

### Population Dynamics

### Spinners

### Population Dynamics - Part 4

### Branching Processes and Extinction

### Impuzzable

### Overarch 2

### FA Cup

### Population Ecology Using Probability

### Time to Evolve 2

### Predator - Prey Systems

### Over-booking

Or search by topic

Age 14 to 18

Challenge Level

PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics

Age 14 to 18

Challenge Level

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 study of biology at A-level and university.

Age 14 to 18

Challenge Level

chemNRICH is the area of the stemNRICH site devoted to the mathematics underlying the study of chemistry, designed to help develop the mathematics required to get the most from your study of chemistry at A-level and university.

Age 14 to 18

Challenge Level

Can you work out which processes are represented by the graphs?

Age 14 to 18

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.

Age 16 to 18

An account of how mathematics is used in computer games including geometry, vectors, transformations, 3D graphics, graph theory and simulations.

Age 16 to 18

Challenge Level

Work in groups to try to create the best approximations to these physical quantities.

Age 16 to 18

Challenge Level

engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering

Age 16 to 18

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.

Age 16 to 18

Challenge Level

Given the graph of a supply network and the maximum capacity for flow in each section find the maximum flow across the network.

Age 16 to 18

Challenge Level

This is the section of stemNRICH devoted to the advanced applied mathematics underlying the study of the sciences at higher levels

Age 16 to 18

Challenge Level

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?

Age 16 to 18

Challenge Level

This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.

Age 16 to 18

Challenge Level

Why MUST these statistical statements probably be at least a little bit wrong?

Age 16 to 18

Challenge Level

Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.

Age 16 to 18

Challenge Level

A player has probability 0.4 of winning a single game. What is his probability of winning a 'best of 15 games' tournament?

Age 16 to 18

Challenge Level

10 intriguing starters related to the mechanics of sport.

Age 16 to 18

Challenge Level

Was it possible that this dangerous driving penalty was issued in error?

Age 16 to 18

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.

Age 16 to 18

Challenge Level

How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.

Age 16 to 18

An article demonstrating mathematically how various physical modelling assumptions affect the solution to the seemingly simple problem of the projectile.

Age 16 to 18

Challenge Level

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.

Age 16 to 18

Challenge Level

Look at the calculus behind the simple act of a car going over a step.

Age 16 to 18

Challenge Level

Invent scenarios which would give rise to these probability density functions.

Age 16 to 18

Challenge Level

Sixth in our series of problems on population dynamics for advanced students.

Age 16 to 18

Challenge Level

First in our series of problems on population dynamics for advanced students.

Age 16 to 18

Challenge Level

Fifth in our series of problems on population dynamics for advanced students.

Age 16 to 18

Challenge Level

See how the motion of the simple pendulum is not-so-simple after all.

Age 16 to 18

Challenge Level

Third in our series of problems on population dynamics for advanced students.

Age 16 to 18

Challenge Level

Second in our series of problems on population dynamics for advanced students.

Age 16 to 18

Challenge Level

This problem opens a major sequence of activities on the mathematics of population dynamics for advanced students.

Age 16 to 18

Challenge Level

How do scores on dice and factors of polynomials relate to each other?

Age 16 to 18

Challenge Level

Fourth in our series of problems on population dynamics for advanced students.

Age 16 to 18

Challenge Level

An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.

Age 16 to 18

This is about a fiendishly difficult jigsaw and how to solve it using a computer program.

Age 16 to 18

Challenge Level

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?

Age 16 to 18

Challenge Level

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!

Age 16 to 18

Challenge Level

An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.

Age 16 to 18

Challenge Level

How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?

Age 16 to 18

Challenge Level

See how differential equations might be used to make a realistic model of a system containing predators and their prey.

Age 16 to 18

Challenge Level

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?