Which line graph, equations and physical processes go together?
Work out the numerical values for these physical quantities.
Get further into power series using the fascinating Bessel's equation.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Look at the advanced way of viewing sin and cos through their power series.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Where should runners start the 200m race so that they have all run the same distance by the finish?
Get some practice using big and small numbers in chemistry.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
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.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Analyse these beautiful biological images and attempt to rank them in size order.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
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?
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
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?
Go on a vector walk and determine which points on the walk are
closest to the origin.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Why MUST these statistical statements probably be at least a little
Was it possible that this dangerous driving penalty was issued in
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
How efficiently can you pack together disks?
Invent scenarios which would give rise to these probability density functions.
Which units would you choose best to fit these situations?
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
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?
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
Formulate and investigate a simple mathematical model for the design of a table mat.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
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.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Is it really greener to go on the bus, or to buy local?
Explore the relationship between resistance and temperature
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 of the scalar and vector cross products and see how the two are related.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
How would you go about estimating populations of dolphins?
Are these estimates of physical quantities accurate?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Which dilutions can you make using only 10ml pipettes?