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#### Resources tagged with Maths Supporting SET similar to Population Dynamics - Part 4:

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Broad Topics > Applications > Maths Supporting SET

### 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.

### Whose Line Graph Is it Anyway?

##### Stage: 5 Challenge Level:

Which line graph, equations and physical processes go together?

### 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?

### 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?

### The Wrong Stats

##### Stage: 5 Challenge Level:

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

### Real-life Equations

##### Stage: 5 Challenge Level:

Here are several equations from real life. Can you work out which measurements are possible from each equation?

### 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?

### A Question of Scale

##### Stage: 4 Challenge Level:

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

##### Stage: 4 Challenge Level:

Which units would you choose best to fit these situations?

### Stats Statements

##### Stage: 5 Challenge Level:

Are these statistical statements sometimes, always or never true? Or it is impossible to say?

### Big and Small Numbers in the Physical World

##### Stage: 4 Challenge Level:

Work with numbers big and small to estimate and calculate various quantities in physical contexts.

### Bessel's Equation

##### Stage: 5 Challenge Level:

Get further into power series using the fascinating Bessel's equation.

### Approximately Certain

##### Stage: 4 and 5 Challenge Level:

Estimate these curious quantities sufficiently accurately that you can rank them in order of size

### Big and Small Numbers in Chemistry

##### Stage: 4 Challenge Level:

Get some practice using big and small numbers in chemistry.

### 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. . . .

### Stirling Work

##### Stage: 5 Challenge Level:

See how enormously large quantities can cancel out to give a good approximation to the factorial function.

### Constantly Changing

##### Stage: 4 Challenge Level:

Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.

### Bigger or Smaller?

##### Stage: 4 Challenge Level:

When you change the units, do the numbers get bigger or smaller?

### Dangerous Driver?

##### Stage: 5 Challenge Level:

Was it possible that this dangerous driving penalty was issued in error?

### Global Warming

##### Stage: 4 Challenge Level:

How much energy has gone into warming the planet?

### Scale Invariance

##### Stage: 5 Challenge Level:

By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.

### Building Approximations for Sin(x)

##### Stage: 5 Challenge Level:

Build up the concept of the Taylor series

### 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.

### Differential Equation Matcher

##### Stage: 5 Challenge Level:

Match the descriptions of physical processes to these differential equations.

### Taking Trigonometry Series-ly

##### Stage: 5 Challenge Level:

Look at the advanced way of viewing sin and cos through their power series.

### Big and Small Numbers in the Living World

##### Stage: 3 and 4 Challenge Level:

Work with numbers big and small to estimate and calculate various quantities in biological contexts.

### Reaction Rates

##### Stage: 5 Challenge Level:

Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation

### Investigating the Dilution Series

##### Stage: 4 Challenge Level:

Which dilutions can you make using only 10ml pipettes?

### Polygon Walk

##### Stage: 5 Challenge Level:

Go on a vector walk and determine which points on the walk are closest to the origin.

### Big and Small Numbers in Physics

##### Stage: 4 Challenge Level:

Work out the numerical values for these physical quantities.

### Operating Machines

##### Stage: 5 Challenge Level:

What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?

### Truth Tables and Electronic Circuits

##### Stage: 3, 4 and 5

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

### Epidemic Modelling

##### Stage: 4 and 5 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.

### 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.

### What Do Functions Do for Tiny X?

##### Stage: 5 Challenge Level:

Looking at small values of functions. Motivating the existence of the Taylor expansion.

### Investigating Epidemics

##### Stage: 3 and 4 Challenge Level:

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

### Designing Table Mats

##### Stage: 3 and 4 Challenge Level:

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

### Construct the Solar System

##### Stage: 4 and 5 Challenge Level:

Make an accurate diagram of the solar system and explore the concept of a grand conjunction.

### Air Routes

##### Stage: 5 Challenge Level:

Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.

### Efficient Packing

##### Stage: 4 Challenge Level:

How efficiently can you pack together disks?

### Production Equation

##### Stage: 5 Challenge Level:

Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?

### Integration Matcher

##### Stage: 5 Challenge Level:

Match the charts of these functions to the charts of their integrals.

### Far Horizon

##### Stage: 4 Challenge Level:

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

### Electric Kettle

##### Stage: 4 Challenge Level:

Explore the relationship between resistance and temperature

### Cross with the Scalar Product

##### Stage: 5 Challenge Level:

Explore the meaning of the scalar and vector cross products and see how the two are related.

### Scientific Curves

##### Stage: 5 Challenge Level:

Can you sketch these difficult curves, which have uses in mathematical modelling?

### How Do You React?

##### Stage: 4 Challenge Level:

To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...

### Robot Camera

##### Stage: 4 Challenge Level:

Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?

### Counting Dolphins

##### Stage: 4 Challenge Level:

How would you go about estimating populations of dolphins?