Match the descriptions of physical processes to these differential
Look at the advanced way of viewing sin and cos through their power series.
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
Get further into power series using the fascinating Bessel's equation.
How would you go about estimating populations of dolphins?
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?
Are these estimates of physical quantities accurate?
Was it possible that this dangerous driving penalty was issued in
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
Invent scenarios which would give rise to these probability density functions.
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.
Go on a vector walk and determine which points on the walk are
closest to the origin.
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Which line graph, equations and physical processes go together?
Work out the numerical values for these physical quantities.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
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.
Build up the concept of the Taylor series
Analyse these beautiful biological images and attempt to rank them in size order.
Explore the relationship between resistance and temperature
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
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?
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Explore the properties of matrix transformations with these 10 stimulating questions.
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
Explore the shape of a square after it is transformed by the action
of a matrix.
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
Explore how matrices can fix vectors and vector directions.
Can you sketch these difficult curves, which have uses in
Explore the meaning of the scalar and vector cross products and see how the two are related.
Use your skill and judgement to match the sets of random data.
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?
Can you make matrices which will fix one lucky vector and crush another to zero?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
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?
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
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.
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?
Can you work out what this procedure is doing?
Estimate areas using random grids
This problem explores the biology behind Rudolph's glowing red nose.