Look at the advanced way of viewing sin and cos through their power series.
Get further into power series using the fascinating Bessel's equation.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Match the descriptions of physical processes to these differential equations.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Build up the concept of the Taylor series
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
How much energy has gone into warming the planet?
Which line graph, equations and physical processes go together?
Was it possible that this dangerous driving penalty was issued in error?
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.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Get some practice using big and small numbers in chemistry.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Work out the numerical values for these physical quantities.
Which units would you choose best to fit these situations?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Explore the relationship between resistance and temperature
Invent scenarios which would give rise to these probability density functions.
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?
When you change the units, do the numbers get bigger or smaller?
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?
Why MUST these statistical statements probably be at least a little bit wrong?
Go on a vector walk and determine which points on the walk are closest to the origin.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Are these estimates of physical quantities accurate?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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 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...
Can you work out what this procedure is doing?
Formulate and investigate a simple mathematical model for the design of a table mat.
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.
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?
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?
Analyse these beautiful biological images and attempt to rank them in size order.
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?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Match the charts of these functions to the charts of their integrals.
How would you design the tiering of seats in a stadium so that all spectators have a good view?
A problem about genetics and the transmission of disease.
How efficiently can you pack together disks?
Can you match these equations to these graphs?