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Resources tagged with Mathematical modelling similar to Aim High:

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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

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

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Epidemic Modelling

Stage: 4 and 5 Challenge Level: Challenge Level:1

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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Time to Evolve 2

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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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Investigating Epidemics

Stage: 3 and 4 Challenge Level: Challenge Level:1

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

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Over-booking

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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 Mean Game

Stage: 5

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.

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Population Dynamics Collection

Stage: 5 Challenge Level: Challenge Level:1

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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Dam Busters 1

Stage: 5 Challenge Level: Challenge Level:1

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

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The Wrong Stats

Stage: 5 Challenge Level: Challenge Level:1

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

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Model Solutions

Stage: 5 Challenge Level: Challenge Level:1

How do these modelling assumption affect the solutions?

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Pdf Stories

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Designing Table Mats

Stage: 3 and 4 Challenge Level: Challenge Level:1

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

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Elastic Maths

Stage: 4 and 5

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.

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An Introduction to Computer Programming and Mathematics

Stage: 5

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

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Advanced Scientific Mathematics

Stage: 5 Challenge Level: Challenge Level:1

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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In Constantly Passing

Stage: 4 Challenge Level: Challenge Level:1

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. . . .

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Stringing it Out

Stage: 4 Challenge Level: Challenge Level:1

Explore the transformations and comment on what you find.

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Predator - Prey Systems

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Modelling Assumptions in Mechanics

Stage: 5

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

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Physnrich

Stage: 4 and 5 Challenge Level: Challenge Level:1

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

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Population Dynamics - Part 2

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Stemnrich - the Physical World

Stage: 3 and 4 Challenge Level: Challenge Level:1

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

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Twenty20

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

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

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Population Dynamics

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Branching Processes and Extinction

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Rocking Chairs, Railway Games and Rayboxes

Stage: 1, 2, 3, 4 and 5

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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The Not-so-simple Pendulum 1

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Bionrich

Stage: 4 and 5 Challenge Level: Challenge Level:1

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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Population Dynamics - Part 4

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Engnrich

Stage: 5 Challenge Level: Challenge Level:1

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

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Big and Small Numbers in Physics - Group Task

Stage: 5 Challenge Level: Challenge Level:1

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

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Population Dynamics - Part 3

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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FA Cup

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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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Concrete Calculation

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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. . . .

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Escalator

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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. . . .

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Shaping the Universe III - to Infinity and Beyond

Stage: 3 and 4

The third installment in our series on the shape of astronomical systems, this article explores galaxies and the universe beyond our solar system.

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Guessing the Graph

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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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Chocolate 2010

Stage: 4 Challenge Level: Challenge Level:1

First of all, pick the number of times a week that you would like to eat chocolate. Multiply this number by 2...

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Snooker

Stage: 5 Challenge Level: Challenge Level:1

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

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Cushion Ball

Stage: 5 Challenge Level: Challenge Level:1

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?

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Witch's Hat

Stage: 3 and 4 Challenge Level: Challenge Level:1

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

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Drawing Doodles and Naming Knots

Stage: 2, 3 and 5

This article for students introduces the idea of naming knots using numbers. You'll need some paper and something to write with handy!

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What's a Knot?

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

A brief video explaining the idea of a mathematical knot.

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Ball Bearings

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Where to Land

Stage: 4 Challenge Level: Challenge Level:1

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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Logic, Truth Tables and Switching Circuits Challenge

Stage: 3, 4 and 5

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. . . .

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Maximum Flow

Stage: 5 Challenge Level: Challenge Level:1

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

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Population Dynamics - Part 1

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Population Dynamics - Part 6

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Circuit Training

Stage: 4 Challenge Level: Challenge Level:1

Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever. . . .