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Resources tagged with Maths Supporting SET similar to The Dodecahedron Explained:

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Broad Topics > Applications > Maths Supporting SET

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Spherical Triangles on Very Big Spheres

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.

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Flight Path

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Use simple trigonometry to calculate the distance along the flight path from London to Sydney.

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Cross with the Scalar Product

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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A Question of Scale

Stage: 4 Short Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Perspective Drawing

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Explore the properties of perspective drawing.

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Stirling Work

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Constantly Changing

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Big and Small Numbers in Physics

Stage: 4 Challenge Level: Challenge Level:1

Work out the numerical values for these physical quantities.

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Approximately Certain

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Operating Machines

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Speed-time Problems at the Olympics

Stage: 4 Challenge Level: Challenge Level:1

Have you ever wondered what it would be like to race against Usain Bolt?

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Nutrition and Cycling

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

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Real-life Equations

Stage: 5 Challenge Level: Challenge Level:1

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

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Bessel's Equation

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Brimful 2

Stage: 5 Challenge Level: Challenge Level:1

Which of these infinitely deep vessels will eventually full up?

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Whose Line Graph Is it Anyway?

Stage: 5 Challenge Level: Challenge Level:1

Which line graph, equations and physical processes go together?

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Robot Camera

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Guessing the Graph

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Designing Table Mats

Stage: 3 and 4 Challenge Level: Challenge Level:1

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

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What Do Functions Do for Tiny X?

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Investigating the Dilution Series

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Which dilutions can you make using only 10ml pipettes?

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Track Design

Stage: 4 Challenge Level: Challenge Level:1

Where should runners start the 200m race so that they have all run the same distance by the finish?

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Alternative Record Book

Stage: 4 and 5 Challenge Level: Challenge Level:1

In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.

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Big and Small Numbers in Chemistry

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Get some practice using big and small numbers in chemistry.

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Scientific Measurement

Stage: 4 Challenge Level: Challenge Level:1

Practice your skills of measurement and estimation using this interactive measurement tool based around fascinating images from biology.

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Population Dynamics Collection

Stage: 5 Challenge Level: Challenge Level:1

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

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Construct the Solar System

Stage: 4 and 5 Challenge Level: Challenge Level:1

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

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Epidemic Modelling

Stage: 4 and 5 Challenge Level: Challenge Level:1

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.

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Polygon Walk

Stage: 5 Challenge Level: Challenge Level:1

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

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Global Warming

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

How much energy has gone into warming the planet?

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Stats Statements

Stage: 5 Challenge Level: Challenge Level:1

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

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Building Approximations for Sin(x)

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Build up the concept of the Taylor series

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Bigger or Smaller?

Stage: 4 Challenge Level: Challenge Level:1

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

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Taking Trigonometry Series-ly

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Scale Invariance

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Big and Small Numbers in the Living World

Stage: 3 and 4 Challenge Level: Challenge Level:1

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

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Reaction Rates

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Big and Small Numbers in the Physical World

Stage: 4 Challenge Level: Challenge Level:1

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

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Choose Your Units

Stage: 4 Challenge Level: Challenge Level:1

Which units would you choose best to fit these situations?

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Air Routes

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Over-booking

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Mystery Procedure

Stage: 4 Challenge Level: Challenge Level:1

Can you work out what this procedure is doing?

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Genetics

Stage: 4 Challenge Level: Challenge Level:1

A problem about genetics and the transmission of disease.

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Differential Equation Matcher

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Match the descriptions of physical processes to these differential equations.

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Nine Eigen

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Explore how matrices can fix vectors and vector directions.

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Pdf Stories

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Odd One Out

Stage: 5 Short Challenge Level: Challenge Level:1

In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?

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How Do You React?

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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What's That Graph?

Stage: 4 Challenge Level: Challenge Level:1

Can you work out which processes are represented by the graphs?

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Production Equation

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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