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Broad Topics > Applications > Maths Supporting SET

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.

Mystery Procedure

Stage: 4 Challenge Level:

Can you work out what this procedure is doing?

Nutrition and Cycling

Stage: 3 and 4 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?

Epidemic Modelling

Stage: 4 and 5 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.

Speed-time Problems at the Olympics

Stage: 4 Challenge Level:

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

David and Goliath

Stage: 4 and 5 Challenge Level:

Does weight confer an advantage to shot putters?

Gym Bag

Stage: 3 and 4 Challenge Level:

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

Who's the Best?

Stage: 3 and 4 Challenge Level:

Which countries have the most naturally athletic populations?

Stats Statements

Stage: 5 Challenge Level:

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

The Wrong Stats

Stage: 5 Challenge Level:

Why MUST these statistical statements probably be at least a little bit wrong?

Population Dynamics Collection

Stage: 5 Challenge Level:

This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.

Robot Camera

Stage: 4 Challenge Level:

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

Time to Evolve 2

Stage: 5 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 Stories

Stage: 5 Challenge Level:

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

Real-life Equations

Stage: 5 Challenge Level:

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

Guessing the Graph

Stage: 4 Challenge Level:

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

Efficient Packing

Stage: 4 Challenge Level:

How efficiently can you pack together disks?

Designing Table Mats

Stage: 3 and 4 Challenge Level:

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

Over-booking

Stage: 5 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?

Investigating Epidemics

Stage: 3 and 4 Challenge Level:

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

Air Routes

Stage: 5 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.

Far Horizon

Stage: 4 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?

Perspective Drawing

Stage: 3 and 4 Challenge Level:

Explore the properties of perspective drawing.

Ball Bearings

Stage: 5 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.

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. . . .

Truth Tables and Electronic Circuits

Stage: 3, 4 and 5

Investigate circuits and record your findings in this simple introduction to truth tables and logic.

Odd One Out

Stage: 5 Short Challenge Level:

In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?

Whose Line Graph Is it Anyway?

Stage: 5 Challenge Level:

Which line graph, equations and physical processes go together?

Production Equation

Stage: 5 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?

Stage: 4 and 5 Challenge Level:

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

Back Fitter

Stage: 4 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?

Scientific Curves

Stage: 5 Challenge Level:

Can you sketch these difficult curves, which have uses in mathematical modelling?

Polygon Walk

Stage: 5 Challenge Level:

Go on a vector walk and determine which points on the walk are closest to the origin.

Cross with the Scalar Product

Stage: 5 Challenge Level:

Explore the meaning of the scalar and vector cross products and see how the two are related.

Constantly Changing

Stage: 4 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.

Fix Me or Crush Me

Stage: 5 Challenge Level:

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

Stirling Work

Stage: 5 Challenge Level:

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

Vector Walk

Stage: 4 and 5 Challenge Level:

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

Crystal Symmetry

Stage: 5 Challenge Level:

Use vectors and matrices to explore the symmetries of crystals.

How Do You React?

Stage: 4 Challenge Level:

To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...

Fill Me up Too

Stage: 4 Challenge Level:

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?

What's That Graph?

Stage: 4 Challenge Level:

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

Witch's Hat

Stage: 3 and 4 Challenge Level:

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

Investigating the Dilution Series

Stage: 4 Challenge Level:

Which dilutions can you make using only 10ml pipettes?

Maths Filler

Stage: 4 Challenge Level:

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

Alternative Record Book

Stage: 4 and 5 Challenge Level:

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

Big and Small Numbers in Chemistry

Stage: 4 Challenge Level:

Get some practice using big and small numbers in chemistry.

Matrix Meaning

Stage: 5 Challenge Level:

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

Square Pair

Stage: 5 Challenge Level:

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

Nine Eigen

Stage: 5 Challenge Level:

Explore how matrices can fix vectors and vector directions.