Look at the advanced way of viewing sin and cos through their power series.
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Get further into power series using the fascinating Bessel's equation.
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.
Build up the concept of the Taylor series
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Was it possible that this dangerous driving penalty was issued in
Match the charts of these functions to the charts of their integrals.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Match the descriptions of physical processes to these differential
Invent scenarios which would give rise to these probability density functions.
Get some practice using big and small numbers in chemistry.
Why MUST these statistical statements probably be at least a little
Which line graph, equations and physical processes go together?
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?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Can you sketch these difficult curves, which have uses in
Go on a vector walk and determine which points on the walk are
closest to the origin.
Explore the relationship between resistance and temperature
Can you construct a cubic equation with a certain distance between
its turning points?
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 out the numerical values for these physical quantities.
Which units would you choose best to fit these situations?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
Are these estimates of physical quantities accurate?
When you change the units, do the numbers get bigger or smaller?
In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?
Explore the properties of perspective drawing.
Which dilutions can you make using only 10ml pipettes?
Formulate and investigate a simple mathematical model for the design of a table mat.
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?
Which of these infinitely deep vessels will eventually full up?
Explore the meaning of the scalar and vector cross products and see how the two are related.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Can you work out what this procedure is doing?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
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?
Analyse these beautiful biological images and attempt to rank them in size order.
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
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.