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Resources tagged with Maths Supporting SET similar to Air Routes:

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Broad Topics > Applications > Maths Supporting SET

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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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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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Vector Walk

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

Starting with two basic vector steps, which destinations can you reach on a vector walk?

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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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The Wrong Stats

Stage: 5 Challenge Level: Challenge Level:1

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

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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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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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Fix Me or Crush Me

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

Can you make matrices which will fix one lucky vector and crush another to zero?

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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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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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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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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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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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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?

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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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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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Time to Evolve 2

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

How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?

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Electric Kettle

Stage: 4 Challenge Level: Challenge Level:1

Explore the relationship between resistance and temperature

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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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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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Counting Dolphins

Stage: 4 Challenge Level: Challenge Level:1

How would you go about estimating populations of dolphins?

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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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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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Brimful 2

Stage: 5 Challenge Level: Challenge Level:1

Which of these infinitely deep vessels will eventually full up?

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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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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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Biology Measurement Challenge

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

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

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Dangerous Driver?

Stage: 5 Challenge Level: Challenge Level:1

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

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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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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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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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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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Square Pair

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

Explore the shape of a square after it is transformed by the action of a matrix.

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Transformations for 10

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

Explore the properties of matrix transformations with these 10 stimulating questions.

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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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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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Far Horizon

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

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

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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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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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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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More or Less?

Stage: 4 Challenge Level: Challenge Level:1

Are these estimates of physical quantities accurate?

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Big and Small Numbers in Biology

Stage: 4 Challenge Level: Challenge Level:1

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

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Efficient Packing

Stage: 4 Challenge Level: Challenge Level:1

How efficiently can you pack together disks?

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Matrix Meaning

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

Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.

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Weekly Challenge 48: Quorum-sensing

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

This problem explores the biology behind Rudolph's glowing red nose.

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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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Genetics

Stage: 4 Challenge Level: Challenge Level:1

A problem about genetics and the transmission of disease.

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Investigating Epidemics

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

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

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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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Truth Tables and Electronic Circuits

Stage: 2, 3 and 4

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