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Broad Topics > Applications > Maths Supporting SET

Pdf Stories

Stage: 5 Challenge Level:

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

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.

The Wrong Stats

Stage: 5 Challenge Level:

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

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?

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?

Scale Invariance

Stage: 5 Challenge Level:

By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.

Whose Line Graph Is it Anyway?

Stage: 5 Challenge Level:

Which line graph, equations and physical processes go together?

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?

Counting Dolphins

Stage: 4 Challenge Level:

How would you go about estimating populations of dolphins?

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. . . .

Efficient Packing

Stage: 4 Challenge Level:

How efficiently can you pack together disks?

Big and Small Numbers in the Physical World

Stage: 4 Challenge Level:

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

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?

Bessel's Equation

Stage: 5 Challenge Level:

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

Stats Statements

Stage: 5 Challenge Level:

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

Stirling Work

Stage: 5 Challenge Level:

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

Big and Small Numbers in Chemistry

Stage: 4 Challenge Level:

Get some practice using big and small numbers in chemistry.

Dangerous Driver?

Stage: 5 Challenge Level:

Was it possible that this dangerous driving penalty was issued in error?

Integration Matcher

Stage: 5 Challenge Level:

Match the charts of these functions to the charts of their integrals.

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.

Global Warming

Stage: 4 Challenge Level:

How much energy has gone into warming the planet?

Taking Trigonometry Series-ly

Stage: 5 Challenge Level:

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

Differential Equation Matcher

Stage: 5 Challenge Level:

Match the descriptions of physical processes to these differential equations.

Building Approximations for Sin(x)

Stage: 5 Challenge Level:

Build up the concept of the Taylor series

Big and Small Numbers in the Living World

Stage: 3 and 4 Challenge Level:

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

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.

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?

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.

Designing Table Mats

Stage: 3 and 4 Challenge Level:

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

Weekly Challenge 48: Quorum-sensing

Stage: 4 Short Challenge Level:

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

Mystery Procedure

Stage: 4 Challenge Level:

Can you work out what this procedure is doing?

Operating Machines

Stage: 5 Challenge Level:

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

Approximately Certain

Stage: 4 and 5 Challenge Level:

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

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.

Biology Measurement Challenge

Stage: 4 Challenge Level:

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

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...

Electric Kettle

Stage: 4 Challenge Level:

Explore the relationship between resistance and temperature

Construct the Solar System

Stage: 4 and 5 Challenge Level:

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

Big and Small Numbers in Physics

Stage: 4 Challenge Level:

Work out the numerical values for these physical quantities.

Curve Fitter 2

Stage: 5 Challenge Level:

Can you construct a cubic equation with a certain distance between its turning points?

Bigger or Smaller?

Stage: 4 Challenge Level:

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

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.

Reaction Rates

Stage: 5 Challenge Level:

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

Stage: 4 Challenge Level:

Which units would you choose best to fit these situations?

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.

A Question of Scale

Stage: 4 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?

Investigating Epidemics

Stage: 3 and 4 Challenge Level:

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

Big and Small Numbers in Biology

Stage: 4 Challenge Level:

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

More or Less?

Stage: 4 Challenge Level:

Are these estimates of physical quantities accurate?