Are these statistical statements sometimes, always or never true? Or it is impossible to say?
A problem about genetics and the transmission of disease.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Estimate areas using random grids
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.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Get further into power series using the fascinating Bessel's equation.
Which line graph, equations and physical processes go together?
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?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Work out the numerical values for these physical quantities.
Which units would you choose best to fit these situations?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Simple models which help us to investigate how epidemics grow and die out.
Which dilutions can you make using only 10ml pipettes?
Get some practice using big and small numbers in chemistry.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
When you change the units, do the numbers get bigger or smaller?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
How much energy has gone into warming the planet?
Look at the advanced way of viewing sin and cos through their power series.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Explore the relationship between resistance and temperature
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?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Build up the concept of the Taylor series
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
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.
Can you sketch these difficult curves, which have uses in mathematical modelling?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Explore how matrices can fix vectors and vector directions.
Explore the shape of a square after it is transformed by the action of a matrix.
Explore the properties of matrix transformations with these 10 stimulating questions.
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.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Go on a vector walk and determine which points on the walk are closest to the origin.
Invent scenarios which would give rise to these probability density functions.
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?
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Explore the properties of perspective drawing.
Where should runners start the 200m race so that they have all run the same distance by the finish?