Match the descriptions of physical processes to these differential
Was it possible that this dangerous driving penalty was issued in
Get further into power series using the fascinating Bessel's equation.
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.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
How would you go about estimating populations of dolphins?
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
Are these estimates of physical quantities accurate?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Why MUST these statistical statements probably be at least a little
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 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.
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
How much energy has gone into warming the planet?
Analyse these beautiful biological images and attempt to rank them in size order.
Build up the concept of the Taylor series
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.
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
Work with numbers big and small to estimate and calculate various quantities in biological 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?
Explore the relationship between resistance and temperature
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Can you make matrices which will fix one lucky vector and crush another to zero?
Who will be the first investor to pay off their debt?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
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?
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Use vectors and matrices to explore the symmetries of crystals.
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
This problem explores the biology behind Rudolph's glowing red nose.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
A problem about genetics and the transmission of disease.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Can you work out what this procedure is doing?
Explore how matrices can fix vectors and vector directions.
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
Can you work out which processes are represented by the graphs?
Formulate and investigate a simple mathematical model for the design of a table mat.
Explore the properties of matrix transformations with these 10 stimulating questions.
Explore the shape of a square after it is transformed by the action
of a matrix.