Was it possible that this dangerous driving penalty was issued in error?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Which line graph, equations and physical processes go together?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Invent scenarios which would give rise to these probability density functions.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Work out the numerical values for these physical quantities.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
How much energy has gone into warming the planet?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Get some practice using big and small numbers in chemistry.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Which units would you choose best to fit these situations?
When you change the units, do the numbers get bigger or smaller?
Why MUST these statistical statements probably be at least a little bit wrong?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Get further into power series using the fascinating Bessel's equation.
This problem explores the biology behind Rudolph's glowing red nose.
Analyse these beautiful biological images and attempt to rank them in size order.
Use vectors and matrices to explore the symmetries of crystals.
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?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Can you work out which processes are represented by the graphs?
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?
Build up the concept of the Taylor series
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you find the volumes of the mathematical vessels?
Look at the advanced way of viewing sin and cos through their power series.
Which pdfs match the curves?
Match the descriptions of physical processes to these differential equations.
Who will be the first investor to pay off their debt?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
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.
Are these estimates of physical quantities accurate?
How would you go about estimating populations of dolphins?
Can you match these equations to these graphs?
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?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Can you work out what this procedure is doing?
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Explore the relationship between resistance and temperature
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Explore how matrices can fix vectors and vector directions.