Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
How would you go about estimating populations of dolphins?
Get further into power series using the fascinating Bessel's equation.
Which line graph, equations and physical processes go together?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
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.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
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.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Get some practice using big and small numbers in chemistry.
Invent scenarios which would give rise to these probability density functions.
Go on a vector walk and determine which points on the walk are
closest to the origin.
Which dilutions can you make using only 10ml pipettes?
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
How much energy has gone into warming the planet?
Build up the concept of the Taylor series
Explore the relationship between resistance and temperature
Match the descriptions of physical processes to these differential
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Look at the advanced way of viewing sin and cos through their power series.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Explore the meaning of the scalar and vector cross products and see how the two are related.
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?
Where should runners start the 200m race so that they have all run the same distance by the finish?
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
Why MUST these statistical statements probably be at least a little
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.
Explore the properties of perspective drawing.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
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?
This problem explores the biology behind Rudolph's glowing red nose.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Which of these infinitely deep vessels will eventually full up?
Analyse these beautiful biological images and attempt to rank them in size order.
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
Are these estimates of physical quantities accurate?
Was it possible that this dangerous driving penalty was issued in
Which units would you choose best to fit these situations?
How efficiently can you pack together disks?
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?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
When you change the units, do the numbers get bigger or smaller?
Use your skill and judgement to match the sets of random data.