Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Get some practice using big and small numbers in chemistry.
Get further into power series using the fascinating Bessel's equation.
Look at the advanced way of viewing sin and cos through their power series.
Was it possible that this dangerous driving penalty was issued in
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Work out the numerical values for these physical quantities.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Which line graph, equations and physical processes go together?
How much energy has gone into warming the planet?
Build up the concept of the Taylor series
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
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.
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?
Why MUST these statistical statements probably be at least a little
How would you go about estimating populations of dolphins?
Invent scenarios which would give rise to these probability density functions.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Explore the properties of perspective drawing.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Explore the relationship between resistance and temperature
Which units would you choose best to fit these situations?
Go on a vector walk and determine which points on the walk are
closest to the origin.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
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 possibilities for reaction rates versus concentrations
with this non-linear differential equation
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
When you change the units, do the numbers get bigger or smaller?
Match the descriptions of physical processes to these differential
Which dilutions can you make using only 10ml pipettes?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Analyse these beautiful biological images and attempt to rank them in size order.
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
Can you work out what this procedure is doing?
Formulate and investigate a simple mathematical model for the design of a table mat.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Are these estimates of physical quantities accurate?
Use simple trigonometry to calculate the distance along the flight
path from London to Sydney.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Match the charts of these functions to the charts of their integrals.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
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.
In this short problem, try to find the location of the roots of
some unusual functions by finding where they change sign.
Use your skill and judgement to match the sets of random data.