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Broad Topics > Applications > Maths Supporting SET

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Who's the Best?

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

Which countries have the most naturally athletic populations?

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Mixing Lemonade

Stage: 3 Challenge Level: Challenge Level:1

Can you work out which drink has the stronger flavour?

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Back Fitter

Stage: 4 Challenge Level: Challenge Level:1

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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Immersion

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

Various solids are lowered into a beaker of water. How does the water level rise in each case?

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Aim High

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

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

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Maths Filler

Stage: 4 Challenge Level: Challenge Level:1

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

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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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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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A Question of Scale

Stage: 4 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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Equation Matcher

Stage: 5 Challenge Level: Challenge Level:1

Can you match these equations to these graphs?

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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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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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The Monte Carlo Method

Stage: 5 Challenge Level: Challenge Level:1

Estimate areas using random grids

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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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Root Hunter

Stage: 5 Challenge Level: Challenge Level:1

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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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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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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Temperature

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Water freezes at 0°Celsius (32°Fahrenheit) and boils at 100°C (212°Fahrenheit). Is there a temperature at which Celsius and Fahrenheit readings are the same?

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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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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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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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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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Toad in the Hole

Stage: 3 Challenge Level: Challenge Level:1

Is it cheaper to cook a meal from scratch or to buy a ready meal? What difference does the number of people you're cooking for make?

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Isometric Drawing

Stage: 3 Challenge Level: Challenge Level:1

Explore the properties of isometric drawings.

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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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Witch's Hat

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

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

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Make Your Own Pencil Case

Stage: 3 Challenge Level: Challenge Level:1

What shape would fit your pens and pencils best? How can you make it?

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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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Olympic Measures

Stage: 3 Challenge Level: Challenge Level:1

These Olympic quantities have been jumbled up! Can you put them back together again?

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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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Pinhole Camera

Stage: 3 Challenge Level: Challenge Level:1

Make your own pinhole camera for safe observation of the sun, and find out how it works.

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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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Food Chains

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

When a habitat changes, what happens to the food chain?

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Triathlon and Fitness

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

The triathlon is a physically gruelling challenge. Can you work out which athlete burnt the most calories?

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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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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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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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Place Your Orders

Stage: 3 Challenge Level: Challenge Level:1

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

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Fill Me up Too

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

In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?

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Olympic Records

Stage: 3 Challenge Level: Challenge Level:1

Can you deduce which Olympic athletics events are represented by the graphs?

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Stadium Sightline

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

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

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Chocolate Cake

Stage: 3 Challenge Level: Challenge Level:1

If I don't have the size of cake tin specified in my recipe, will the size I do have be OK?

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Electric Kettle

Stage: 4 Challenge Level: Challenge Level:1

Explore the relationship between resistance and temperature

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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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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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Genetics

Stage: 4 Challenge Level: Challenge Level:1

A problem about genetics and the transmission of disease.

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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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Fill Me Up

Stage: 3 Challenge Level: Challenge Level:1

Can you sketch graphs to show how the height of water changes in different containers as they are filled?

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Does This Sound about Right?

Stage: 3 Challenge Level: Challenge Level:1

Examine these estimates. Do they sound about right?


The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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NRICH is part of the family of activities in the Millennium Mathematics Project.