How efficiently can you pack together disks?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Invent scenarios which would give rise to these probability density functions.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Which line graph, equations and physical processes go together?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Why MUST these statistical statements probably be at least a little bit wrong?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
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.
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. . . .
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?
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?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Get further into power series using the fascinating Bessel's equation.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Which of these infinitely deep vessels will eventually full up?
Was it possible that this dangerous driving penalty was issued in error?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Simple models which help us to investigate how epidemics grow and die out.
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.
Which dilutions can you make using only 10ml pipettes?
Can Jo make a gym bag for her trainers from the piece of fabric she has?
Formulate and investigate a simple mathematical model for the design of a table mat.
Get some practice using big and small numbers in chemistry.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Go on a vector walk and determine which points on the walk are closest to the origin.
How would you go about estimating populations of dolphins?
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.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
How much energy has gone into warming the planet?
Match the descriptions of physical processes to these differential equations.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
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.
Explore the relationship between resistance and temperature
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Look at the advanced way of viewing sin and cos through their power series.
Analyse these beautiful biological images and attempt to rank them in size order.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
When you change the units, do the numbers get bigger or smaller?
Are these estimates of physical quantities accurate?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
This problem explores the biology behind Rudolph's glowing red nose.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Which units would you choose best to fit these situations?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Build up the concept of the Taylor series
How would you design the tiering of seats in a stadium so that all spectators have a good view?