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Resources tagged with Mathematical modelling similar to Production Equation:

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

Dam Busters 1

Stage: 5 Challenge Level:

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

The Wrong Stats

Stage: 5 Challenge Level:

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

Model Solutions

Stage: 5 Challenge Level:

How do these modelling assumption affect the solutions?

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.

Pdf Stories

Stage: 5 Challenge Level:

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

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?

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

Ramping it Up

Stage: 5 Challenge Level:

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

Physnrich

Stage: 4 and 5 Challenge Level:

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

Engnrich

Stage: 5 Challenge Level:

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

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.

Population Dynamics - Part 4

Stage: 5 Challenge Level:

Fourth 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.

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. . . .

Population Dynamics - Part 6

Stage: 5 Challenge Level:

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

Population Dynamics - Part 5

Stage: 5 Challenge Level:

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

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.

The Not-so-simple Pendulum 1

Stage: 5 Challenge Level:

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

Population Dynamics - Part 3

Stage: 5 Challenge Level:

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

Population Dynamics

Stage: 5 Challenge Level:

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

Branching Processes and Extinction

Stage: 5 Challenge Level:

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

Population Dynamics - Part 1

Stage: 5 Challenge Level:

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

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.

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?

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

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!

Population Dynamics - Part 2

Stage: 5 Challenge Level:

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

Where to Land

Stage: 4 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?

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.

Snooker

Stage: 5 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?

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. . . .

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?

Designing Table Mats

Stage: 3 and 4 Challenge Level:

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

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.

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. . . .

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!

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?

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.

What's a Knot?

Stage: 2, 3 and 4 Challenge Level:

A brief video explaining the idea of a mathematical knot.

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.

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?

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. . . .

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.

Cushion Ball

Stage: 5 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?

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.

Chocolate 2010

Stage: 4 Challenge Level:

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

Bionrich

Stage: 4 and 5 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. . . .