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Broad Topics > Applications > Maths Supporting SET

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?

David and Goliath

Age 14 to 18 Challenge Level:

Does weight confer an advantage to shot putters?

Stats Statements

Age 16 to 18 Challenge Level:

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

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.

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?

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?

Bessel's Equation

Age 16 to 18 Challenge Level:

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

Aim High

Age 16 to 18 Challenge Level:

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

Global Warming

Age 14 to 16 Challenge Level:

How much energy has gone into warming the planet?

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.

Whose Line Graph Is it Anyway?

Age 16 to 18 Challenge Level:

Which line graph, equations and physical processes go together?

Big and Small Numbers in Physics

Age 14 to 16 Challenge Level:

Work out the numerical values for these physical quantities.

Approximately Certain

Age 14 to 18 Challenge Level:

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

Crystal Symmetry

Age 16 to 18 Challenge Level:

Use vectors and matrices to explore the symmetries of crystals.

Stirling Work

Age 16 to 18 Challenge Level:

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

Constantly Changing

Age 14 to 16 Challenge Level:

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

A Question of Scale

Age 14 to 16 Challenge Level:

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?

Transformations for 10

Age 16 to 18 Challenge Level:

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

Square Pair

Age 16 to 18 Challenge Level:

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

Pdf Stories

Age 16 to 18 Challenge Level:

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

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.

Big and Small Numbers in Chemistry

Age 14 to 16 Challenge Level:

Get some practice using big and small numbers in chemistry.

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.

Designing Table Mats

Age 11 to 16 Challenge Level:

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

Guessing the Graph

Age 14 to 16 Challenge Level:

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

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?

Investigating the Dilution Series

Age 14 to 16 Challenge Level:

Which dilutions can you make using only 10ml pipettes?

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?

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?

Pdf Matcher

Age 16 to 18 Challenge Level:

Which pdfs match the curves?

Counting Dolphins

Age 14 to 16 Challenge Level:

How would you go about estimating populations of dolphins?

Big and Small Numbers in the Physical World

Age 14 to 16 Challenge Level:

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

Debt Race

Age 16 to 18 Challenge Level:

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

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?

More or Less?

Age 14 to 16 Challenge Level:

Are these estimates of physical quantities accurate?

Bigger or Smaller?

Age 14 to 16 Challenge Level:

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

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.

Biology Measurement Challenge

Age 14 to 16 Challenge Level:

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

Age 14 to 16 Challenge Level:

Which units would you choose best to fit these situations?

Electric Kettle

Age 14 to 16 Challenge Level:

Explore the relationship between resistance and temperature

Real-life Equations

Age 16 to 18 Challenge Level:

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

Reaction Rates

Age 16 to 18 Challenge Level:

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

Genetics

Age 14 to 16 Challenge Level:

A problem about genetics and the transmission of disease.

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.

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.

Building Approximations for Sin(x)

Age 16 to 18 Challenge Level:

Build up the concept of the Taylor series

Spherical Triangles on Very Big Spheres

Age 16 to 18 Challenge Level:

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.

Nine Eigen

Age 16 to 18 Challenge Level:

Explore how matrices can fix vectors and vector directions.

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?

Mystery Procedure

Age 14 to 16 Challenge Level:

Can you work out what this procedure is doing?