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Broad Topics > Applications > Maths Supporting SET

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David and Goliath

Age 14 to 18 Challenge Level:

Does weight confer an advantage to shot putters?

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The Monte Carlo Method

Age 16 to 18 Challenge Level:

Estimate areas using random grids

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Speed-time Problems at the Olympics

Age 14 to 16 Challenge Level:

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

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Epidemic Modelling

Age 14 to 18 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.

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Stats Statements

Age 16 to 18 Challenge Level:

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

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Data Matching

Age 14 to 18 Challenge Level:

Use your skill and judgement to match the sets of random data.

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Nutrition and Cycling

Age 14 to 16 Challenge Level:

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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Stadium Sightline

Age 14 to 18 Challenge Level:

How would you design the tiering of seats in a stadium so that all spectators have a good view?

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Mystery Procedure

Age 14 to 16 Challenge Level:

Can you work out what this procedure is doing?

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Operating Machines

Age 16 to 18 Challenge Level:

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

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Time to Evolve 2

Age 16 to 18 Challenge Level:

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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Integration Matcher

Age 16 to 18 Challenge Level:

Can you match the charts of these functions to the charts of their integrals?

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Track Design

Age 14 to 16 Challenge Level:

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

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Brimful

Age 16 to 18 Challenge Level:

Can you find the volumes of the mathematical vessels?

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Brimful 2

Age 16 to 18 Challenge Level:

Which of these infinitely deep vessels will eventually full up?

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Aim High

Age 16 to 18 Challenge Level:

How do you choose your planting levels to minimise the total loss at harvest time?

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Big and Small Numbers in the Living World

Age 11 to 16 Challenge Level:

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

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Investigating Epidemics

Age 11 to 16 Challenge Level:

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

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Back Fitter

Age 14 to 16 Challenge Level:

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

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Pdf Stories

Age 16 to 18 Challenge Level:

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

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Crystal Symmetry

Age 16 to 18 Challenge Level:

Use vectors and matrices to explore the symmetries of crystals.

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Alternative Record Book

Age 14 to 18 Challenge Level:

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

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Counting Dolphins

Age 14 to 16 Challenge Level:

How would you go about estimating populations of dolphins?

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Fix Me or Crush Me

Age 16 to 18 Challenge Level:

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

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Transformations for 10

Age 16 to 18 Challenge Level:

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

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Square Pair

Age 16 to 18 Challenge Level:

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

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Matrix Meaning

Age 16 to 18 Challenge Level:

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

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Nine Eigen

Age 16 to 18 Challenge Level:

Explore how matrices can fix vectors and vector directions.

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Robot Camera

Age 14 to 16 Challenge Level:

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

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Vector Walk

Age 14 to 18 Challenge Level:

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

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Pdf Matcher

Age 16 to 18 Challenge Level:

Which pdfs match the curves?

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Odd One Out

Age 16 to 18 Short Challenge Level:

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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Quorum-sensing

Age 16 to 18 Short Challenge Level:

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

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Debt Race

Age 16 to 18 Challenge Level:

Who will be the first investor to pay off their debt?

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Scale Invariance

Age 16 to 18 Challenge Level:

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 Biology

Age 14 to 16 Challenge Level:

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

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Root Hunter

Age 16 to 18 Challenge Level:

In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.

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More or Less?

Age 14 to 16 Challenge Level:

Are these estimates of physical quantities accurate?

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Far Horizon

Age 14 to 16 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?

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Big and Small Numbers in Chemistry

Age 14 to 16 Challenge Level:

Get some practice using big and small numbers in chemistry.

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Air Routes

Age 16 to 18 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.

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What's That Graph?

Age 14 to 16 Challenge Level:

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

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Construct the Solar System

Age 14 to 18 Challenge Level:

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

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How Do You React?

Age 14 to 16 Challenge Level:

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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Genetics

Age 14 to 16 Challenge Level:

A problem about genetics and the transmission of disease.

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Population Dynamics Collection

Age 16 to 18 Challenge Level:

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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Over-booking

Age 16 to 18 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?

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Flight Path

Age 16 to 18 Challenge Level:

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

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Ball Bearings

Age 16 to 18 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.

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Equation Matcher

Age 16 to 18 Challenge Level:

Can you match these equations to these graphs?