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Rich Tasks. Real world. Mathematical modelling. Maths Supporting SET. biology. Calculus generally. engineering. physics. chemistry. Logarithmic functions.

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Broad Topics > Applications > Maths Supporting SET

### 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.

### 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?

### The Wrong Stats

##### Stage: 5 Challenge Level:

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

### Whose Line Graph Is it Anyway?

##### Stage: 5 Challenge Level:

Which line graph, equations and physical processes go together?

### 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?

### 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?

### Global Warming

##### Stage: 4 Challenge Level:

How much energy has gone into warming the planet?

### Stats Statements

##### Stage: 5 Challenge Level:

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

### Bigger or Smaller?

##### Stage: 4 Challenge Level:

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

### 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.

### 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.

### 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.

##### Stage: 4 Challenge Level:

Which units would you choose best to fit these situations?

### Big and Small Numbers in Chemistry

##### Stage: 4 Challenge Level:

Get some practice using big and small numbers in chemistry.

### 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?

### Bessel's Equation

##### Stage: 5 Challenge Level:

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

### A Question of Scale

##### Stage: 4 Short 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?

### Reaction Rates

##### Stage: 5 Challenge Level:

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

### 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.

### Approximately Certain

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

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

### Building Approximations for Sin(x)

##### Stage: 5 Challenge Level:

Build up the concept of the Taylor series

### Taking Trigonometry Series-ly

##### Stage: 5 Challenge Level:

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

### Stirling Work

##### Stage: 5 Challenge Level:

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

### 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.

### 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.

### 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.

### Big and Small Numbers in Physics

##### Stage: 4 Challenge Level:

Work out the numerical values for these physical quantities.

### Integration Matcher

##### Stage: 5 Challenge Level:

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

### Dangerous Driver?

##### Stage: 5 Challenge Level:

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

### Polygon Walk

##### Stage: 5 Challenge Level:

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

### Designing Table Mats

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

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

### Investigating the Dilution Series

##### Stage: 4 Challenge Level:

Which dilutions can you make using only 10ml pipettes?

### Differential Equation Matcher

##### Stage: 5 Challenge Level:

Match the descriptions of physical processes to these differential equations.

### 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.

### 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?

### 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.

### Gym Bag

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

Can Jo make a gym bag for her trainers from the piece of fabric she has?

### 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.

### 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.

### Perspective Drawing

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

Explore the properties of perspective drawing.

### Robot Camera

##### Stage: 4 Challenge Level:

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

### Mystery Procedure

##### Stage: 4 Challenge Level:

Can you work out what this procedure is doing?

### 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...

### Biology Measurement Challenge

##### Stage: 4 Challenge Level:

Analyse these beautiful biological images and attempt to rank them in size order.

### 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. . . .

### 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.

### Electric Kettle

##### Stage: 4 Challenge Level:

Explore the relationship between resistance and temperature

### Scientific Curves

##### Stage: 5 Challenge Level:

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