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Broad Topics > Using, Applying and Reasoning about Mathematics > Mathematical modelling

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Time to Evolve 2

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?

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The Not-so-simple Pendulum 1

Age 16 to 18 Challenge Level:

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

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The Legacy

Age 14 to 16 Challenge Level:

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?

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Dam Busters 1

Age 16 to 18 Challenge Level:

At what positions and speeds can the bomb be dropped to destroy the dam?

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Over-booking

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?

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Epidemic Modelling

Age 14 to 18 Challenge Level:

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.

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Spinners

Age 16 to 18 Challenge Level:

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

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Where to Land

Age 14 to 16 Challenge Level:

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?

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FA Cup

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!

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Buses

Age 11 to 14 Challenge Level:

A bus route has a total duration of 40 minutes. Every 10 minutes, two buses set out, one from each end. How many buses will one bus meet on its way from one end to the other end?

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Rule of Three

Age 11 to 14 Challenge Level:

If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?

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Straw Scaffold

Age 11 to 14 Challenge Level:

Build a scaffold out of drinking-straws to support a cup of water

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Witch's Hat

Age 11 to 16 Challenge Level:

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

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Investigating Epidemics

Age 11 to 16 Challenge Level:

Simple models which help us to investigate how epidemics grow and die out.

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Designing Table Mats

Age 11 to 16 Challenge Level:

Formulate and investigate a simple mathematical model for the design of a table mat.

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Troublesome Triangles

Age 7 to 14 Challenge Level:

Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple. . . .

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Observing the Sun and the Moon

Age 7 to 14 Challenge Level:

How does the time of dawn and dusk vary? What about the Moon, how does that change from night to night? Is the Sun always the same? Gather data to help you explore these questions.

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Population Dynamics Collection

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.

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Population Dynamics - Part 1

Age 16 to 18 Challenge Level:

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

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More Realistic Electric Kettle

Age 14 to 18 Challenge Level:

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Food Web

Age 11 to 14 Challenge Level:

Is this eco-system sustainable?

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Triathlon and Fitness

Age 11 to 14 Challenge Level:

The triathlon is a physically gruelling challenge. Can you work out which athlete burnt the most calories?

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Pdf Stories

Age 16 to 18 Challenge Level:

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

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Twenty20

Age 7 to 16 Challenge Level:

Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.

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Bird-brained

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.

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Population Ecology Using Probability

Age 16 to 18 Challenge Level:

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

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Population Dynamics - Part 5

Age 16 to 18 Challenge Level:

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

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Population Dynamics - Part 6

Age 16 to 18 Challenge Level:

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

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Stemnrich - the Physical World

Age 11 to 16 Challenge Level:

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

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Branching Processes and Extinction

Age 16 to 18 Challenge Level:

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

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Population Dynamics - Part 4

Age 16 to 18 Challenge Level:

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

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Population Dynamics

Age 16 to 18 Challenge Level:

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

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Population Dynamics - Part 2

Age 16 to 18 Challenge Level:

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

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Rocking Chairs, Railway Games and Rayboxes

Age 5 to 18

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. . . .

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Population Dynamics - Part 3

Age 16 to 18 Challenge Level:

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

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Guessing the Graph

Age 14 to 16 Challenge Level:

Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?

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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.

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Ramping it Up

Age 16 to 18 Challenge Level:

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

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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.

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Model Solutions

Age 16 to 18 Challenge Level:

How do these modelling assumption affect the solutions?

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Poiseuille's Equation

Look at the flow of fluids down circular pipes.

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Predator - Prey Systems

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.

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The Wrong Stats

Age 16 to 18 Challenge Level:

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

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Advanced Scientific Mathematics

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

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Engnrich

Age 16 to 18 Challenge Level:

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

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Physnrich

Age 14 to 18 Challenge Level:

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

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Chemnrich

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. . . .

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Bionrich

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. . . .

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Truth Tables and Electronic Circuits

Age 11 to 18

Investigate circuits and record your findings in this simple introduction to truth tables and logic.

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Logic, Truth Tables and Switching Circuits Challenge

Age 11 to 18

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. . . .