Explore the properties of perspective drawing.
Use simple trigonometry to calculate the distance along the flight
path from London to Sydney.
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.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Is it really greener to go on the bus, or to buy local?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Which line graph, equations and physical processes go together?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
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?
Get further into power series using the fascinating Bessel's equation.
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Go on a vector walk and determine which points on the walk are
closest to the origin.
Get some practice using big and small numbers in chemistry.
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?
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
Where should runners start the 200m race so that they have all run the same distance by the finish?
Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.
Which dilutions can you make using only 10ml pipettes?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
How efficiently can you pack together disks?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Explore the meaning of the scalar and vector cross products and see how the two are related.
How much energy has gone into warming the planet?
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.
When you change the units, do the numbers get bigger or smaller?
Build up the concept of the Taylor series
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
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.
Explore the relationship between resistance and temperature
Which units would you choose best to fit these situations?
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 biological contexts.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
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?
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
Invent scenarios which would give rise to these probability density functions.
Explore how matrices can fix vectors and vector directions.
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
Match the descriptions of physical processes to these differential
Can you work out what this procedure is doing?
A problem about genetics and the transmission of disease.
In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...