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Number and algebra

  • The Number System and Place Value
  • Calculations and Numerical Methods
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Geometry and measure

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Probability and statistics

  • Handling, Processing and Representing Data
  • Probability

Working mathematically

  • Thinking mathematically
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Advanced mathematics

  • Decision Mathematics and Combinatorics
  • Advanced Probability and Statistics
  • Mechanics
  • Calculus

For younger learners

  • Early Years Foundation Stage

Mathematical Modelling - Advanced

physNRICH

Age 14 to 18
Challenge Level Yellow star

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

bioNRICH

Age 14 to 18
Challenge Level Yellow star

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.

chemNRICH

Age 14 to 18
Challenge Level Yellow star

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.

What's That Graph?

Age 14 to 18
Challenge Level Yellow starYellow star

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

Elastic Maths

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.

The Use of Mathematics in Computer Games

Age 16 to 18

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

Big and Small Numbers in Physics - Group Task

Age 16 to 18
Challenge Level Yellow star

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

engNRICH

Age 16 to 18
Challenge Level Yellow star

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

An Introduction to Computer Programming and Mathematics

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.

Maximum Flow

Age 16 to 18
Challenge Level Yellow star

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

Advanced Scientific Mathematics

Age 16 to 18
Challenge Level Yellow star

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

Cushion Ball

Age 16 to 18
Challenge Level Yellow star

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?

Population Dynamics Collection

Age 16 to 18
Challenge Level Yellow star

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

The Wrong Stats

Age 16 to 18
Challenge Level Yellow star

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

Stonehenge

Age 16 to 18
Challenge Level Yellow star

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

Snooker

Age 16 to 18
Challenge Level Yellow star

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

10 Olympic Starters

Age 16 to 18
Challenge Level Yellow star

10 intriguing starters related to the mechanics of sport.

Dangerous Driver?

Age 16 to 18
Challenge Level Yellow star

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

Model Solutions

Age 16 to 18
Challenge Level Yellow star

How do these modelling assumption affect the solutions?

The Mean Game

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.

Bird-brained

Age 16 to 18
Challenge Level Yellow star

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

Modelling Assumptions in Mechanics

Age 16 to 18

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

Ball Bearings

Age 16 to 18
Challenge Level Yellow starYellow star

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.

Ramping it Up

Age 16 to 18
Challenge Level Yellow starYellow star

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

pdf Stories

Age 16 to 18
Challenge Level Yellow starYellow star

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

Population Dynamics - Part 6

Age 16 to 18
Challenge Level Yellow starYellow star

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

Population Dynamics - Part 1

Age 16 to 18
Challenge Level Yellow starYellow star

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

Population Dynamics - Part 5

Age 16 to 18
Challenge Level Yellow starYellow star

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

The Not-so-simple Pendulum 1

Age 16 to 18
Challenge Level Yellow starYellow star

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

Population Dynamics - Part 3

Age 16 to 18
Challenge Level Yellow starYellow star

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

Population Dynamics - Part 2

Age 16 to 18
Challenge Level Yellow starYellow star

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

Population Dynamics

Age 16 to 18
Challenge Level Yellow starYellow star

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

Spinners

Age 16 to 18
Challenge Level Yellow starYellow star

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

Population Dynamics - Part 4

Age 16 to 18
Challenge Level Yellow starYellow star

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

Branching Processes and Extinction

Age 16 to 18
Challenge Level Yellow starYellow starYellow star

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

Impuzzable

Age 16 to 18

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

Overarch 2

Age 16 to 18
Challenge Level Yellow starYellow starYellow star

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?

FA Cup

Age 16 to 18
Challenge Level Yellow starYellow starYellow star

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!

Population Ecology Using Probability

Age 16 to 18
Challenge Level Yellow starYellow starYellow star

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

Time to Evolve 2

Age 16 to 18
Challenge Level Yellow starYellow starYellow star

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

Predator - Prey Systems

Age 16 to 18
Challenge Level Yellow starYellow starYellow star

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

Over-booking

Age 16 to 18
Challenge Level Yellow starYellow starYellow star

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?

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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