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Resources tagged with Mathematical modelling similar to Weekly Challenge 42: What's My Equation?:

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

The Wrong Stats

Stage: 5 Challenge Level:

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

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.

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.

Dam Busters 1

Stage: 5 Challenge Level:

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

Pdf Stories

Stage: 5 Challenge Level:

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

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.

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?

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.

Ramping it Up

Stage: 5 Challenge Level:

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

The Not-so-simple Pendulum 1

Stage: 5 Challenge Level:

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

Spot the Card

Stage: 4 Challenge Level:

It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?

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. . . .

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?

Population Dynamics

Stage: 5 Challenge Level:

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

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!

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.

Engnrich

Stage: 5 Challenge Level:

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

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. . . .

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

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

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.

Physnrich

Stage: 4 and 5 Challenge Level:

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

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.

Stringing it Out

Stage: 4 Challenge Level:

Explore the transformations and comment on what you find.

Bird-brained

Stage: 5 Challenge Level:

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

Population Dynamics - Part 4

Stage: 5 Challenge Level:

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

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. . . .

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?

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. . . .

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?

Designing Table Mats

Stage: 3 and 4 Challenge Level:

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

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?

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!

What's a Knot?

Stage: 2, 3 and 4 Challenge Level:

A brief video explaining the idea of a mathematical knot.

Population Dynamics - Part 2

Stage: 5 Challenge Level:

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

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.

Impuzzable

Stage: 5

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

Population Dynamics - Part 5

Stage: 5 Challenge Level:

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

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. . . .

Population Dynamics - Part 3

Stage: 5 Challenge Level:

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

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 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.

Population Ecology Using Probability

Stage: 5 Challenge Level:

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

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.

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?

Population Dynamics - Part 6

Stage: 5 Challenge Level:

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

Witch's Hat

Stage: 3 and 4 Challenge Level:

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