Build up the concept of the Taylor series
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.
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.
Get some practice using big and small numbers in chemistry.
Get further into power series using the fascinating Bessel's equation.
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 error?
Are these estimates of physical quantities accurate?
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.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Work out the numerical values for these physical quantities.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Go on a vector walk and determine which points on the walk are closest to the origin.
Invent scenarios which would give rise to these probability density functions.
How would you go about estimating populations of dolphins?
Analyse these beautiful biological images and attempt to rank them in size order.
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?
Explore the relationship between resistance and temperature
Which units would you choose best to fit these situations?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Why MUST these statistical statements probably be at least a little bit wrong?
Match the descriptions of physical processes to these differential equations.
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?
Explore the meaning of the scalar and vector cross products and see how the two are related.
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?
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
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.
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you work out what this procedure is doing?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Explore the properties of perspective drawing.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Which dilutions can you make using only 10ml pipettes?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
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.
Match the charts of these functions to the charts of their integrals.
How efficiently can you pack together disks?
A problem about genetics and the transmission of disease.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?