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Resources tagged with Mathematical modelling similar to Vector Walk:

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

The Use of Mathematics in Computer Games

Stage: 5

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

Over-booking

Stage: 5 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?

Population Dynamics

Stage: 5 Challenge Level:

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

Ramping it Up

Stage: 5 Challenge Level:

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

Dam Busters 1

Stage: 5 Challenge Level:

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

Stringing it Out

Stage: 4 Challenge Level:

Explore the transformations and comment on what you find.

Model Solutions

Stage: 5 Challenge Level:

How do these modelling assumption affect the solutions?

The Wrong Stats

Stage: 5 Challenge Level:

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

Branching Processes and Extinction

Stage: 5 Challenge Level:

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

Pdf Stories

Stage: 5 Challenge Level:

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

Population Dynamics Collection

Stage: 5 Challenge Level:

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

Population Dynamics - Part 6

Stage: 5 Challenge Level:

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

Physnrich

Stage: 4 and 5 Challenge Level:

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

Population Dynamics - Part 5

Stage: 5 Challenge Level:

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

Population Ecology Using Probability

Stage: 5 Challenge Level:

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

Predator - Prey Systems

Stage: 5 Challenge Level:

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

Designing Table Mats

Stage: 3 and 4 Challenge Level:

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

Guessing the Graph

Stage: 4 Challenge Level:

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

Engnrich

Stage: 5 Challenge Level:

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

Stage: 5 Challenge Level:

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

Big and Small Numbers in Physics - Group Task

Stage: 5 Challenge Level:

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

Population Dynamics - Part 4

Stage: 5 Challenge Level:

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

Population Dynamics - Part 3

Stage: 5 Challenge Level:

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

Population Dynamics - Part 2

Stage: 5 Challenge Level:

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

In Constantly Passing

Stage: 4 Challenge Level:

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. . . .

Twenty20

Stage: 2, 3 and 4 Challenge Level:

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

The Not-so-simple Pendulum 1

Stage: 5 Challenge Level:

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

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. . . .

Stemnrich - the Physical World

Stage: 3 and 4 Challenge Level:

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

Population Dynamics - Part 1

Stage: 5 Challenge Level:

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

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.

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.

Maximum Flow

Stage: 5 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.

Concrete Calculation

Stage: 4 Challenge Level:

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. . . .

Time to Evolve 2

Stage: 5 Challenge Level:

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

Fixing the Odds

Stage: 4 Challenge Level:

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. . . .

FA Cup

Stage: 5 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!

Impuzzable

Stage: 5

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

Scratch Cards

Stage: 4 Challenge Level:

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 prize?

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.

Drawing Doodles and Naming Knots

Stage: 2, 3, 4 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!

Escalator

Stage: 4 Challenge Level:

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. . . .

What's a Knot?

Stage: 2, 3 and 4 Challenge Level:

A brief video explaining the idea of a mathematical knot.

Logic, Truth Tables and Switching Circuits

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 record your findings in truth tables.

Stonehenge

Stage: 5 Challenge Level:

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

Investigating Epidemics

Stage: 3 and 4 Challenge Level:

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

The Legacy

Stage: 4 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?

Ball Bearings

Stage: 5 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.

Overarch 2

Stage: 5 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?