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Broad Topics > Applications > Maths Supporting SET

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?

David and Goliath

Age 14 to 18 Challenge Level:

Does weight confer an advantage to shot putters?

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?

Mystery Procedure

Age 14 to 16 Challenge Level:

Can you work out what this procedure is doing?

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?

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?

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?

Elastic Maths

Age 14 to 18

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.

Carbon Footprints

Age 14 to 16 Challenge Level:

Is it really greener to go on the bus, or to buy local?

Investigating the Dilution Series

Age 14 to 16 Challenge Level:

Which dilutions can you make using only 10ml pipettes?

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?

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?

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.

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.

Witch's Hat

Age 11 to 16 Challenge Level:

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

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.

Perfect Eclipse

Age 14 to 16 Challenge Level:

Use trigonometry to determine whether solar eclipses on earth can be perfect.

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?

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.

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.

Big and Small Numbers in Chemistry

Age 14 to 16 Challenge Level:

Get some practice using big and small numbers in chemistry.

What Do Functions Do for Tiny X?

Age 16 to 18 Challenge Level:

Looking at small values of functions. Motivating the existence of the Taylor expansion.

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?

Bessel's Equation

Age 16 to 18 Challenge Level:

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

Pdf Matcher

Age 16 to 18 Challenge Level:

Which pdfs match the curves?

Gym Bag

Age 11 to 16 Challenge Level:

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

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

Biology Measurement Challenge

Age 14 to 16 Challenge Level:

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

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?

Building Approximations for Sin(x)

Age 16 to 18 Challenge Level:

Build up the concept of the Taylor series

Taking Trigonometry Series-ly

Age 16 to 18 Challenge Level:

Look at the advanced way of viewing sin and cos through their power series.

Reaction Rates

Age 16 to 18 Challenge Level:

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

Bigger or Smaller?

Age 14 to 16 Challenge Level:

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

Stats Statements

Age 16 to 18 Challenge Level:

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

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.

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.

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?

Efficient Packing

Age 14 to 16 Challenge Level:

How efficiently can you pack together disks?

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?

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...

Differential Equation Matcher

Age 16 to 18 Challenge Level:

Match the descriptions of physical processes to these differential equations.

Production Equation

Age 16 to 18 Challenge Level:

Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?

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.