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Broad Topics > Applications > Maths Supporting SET

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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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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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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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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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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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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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Efficient Packing

Stage: 4 Challenge Level: Challenge Level:1

How efficiently can you pack together disks?

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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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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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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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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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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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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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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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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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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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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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Electric Kettle

Stage: 4 Challenge Level: Challenge Level:1

Explore the relationship between resistance and temperature

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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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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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Counting Dolphins

Stage: 4 Challenge Level: Challenge Level:1

How would you go about estimating populations of dolphins?

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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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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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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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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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Ball Bearings

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

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.

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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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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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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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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 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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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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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. . . .

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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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The Monte Carlo Method

Stage: 5 Challenge Level: Challenge Level:1

Estimate areas using random grids

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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.

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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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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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Gym Bag

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

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

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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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Choose Your Units

Stage: 4 Challenge Level: Challenge Level:1

Which units would you choose best to fit these situations?

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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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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.

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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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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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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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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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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.