Work out the numerical values for these physical quantities.
Which line graph, equations and physical processes go together?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
How much energy has gone into warming the planet?
Was it possible that this dangerous driving penalty was issued in error?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
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?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Which units would you choose best to fit these situations?
Explore the relationship between resistance and temperature
Why MUST these statistical statements probably be at least a little bit wrong?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Invent scenarios which would give rise to these probability density functions.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
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?
When you change the units, do the numbers get bigger or smaller?
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.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Build up the concept of the Taylor series
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Explore the properties of perspective drawing.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Go on a vector walk and determine which points on the walk are closest to the origin.
Are these estimates of physical quantities accurate?
Formulate and investigate a simple mathematical model for the design of a table mat.
Match the descriptions of physical processes to these differential equations.
How would you go about estimating populations of dolphins?
Which dilutions can you make using only 10ml pipettes?
How efficiently can you pack together disks?
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.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
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.
Analyse these beautiful biological images and attempt to rank them in size order.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Explore the meaning of the scalar and vector cross products and see how the two are related.
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.
Is it really greener to go on the bus, or to buy local?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
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. . . .
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.