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.
Was it possible that this dangerous driving penalty was issued in
How would you go about estimating populations of dolphins?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Are these estimates of physical quantities accurate?
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
Can you find the volumes of the mathematical vessels?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
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?
Analyse these beautiful biological images and attempt to rank them in size order.
Explore the relationship between resistance and temperature
Build up the concept of the Taylor series
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?
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.
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?
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Can you sketch these difficult curves, which have uses in
Explore the properties of matrix transformations with these 10 stimulating questions.
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
Explore how matrices can fix vectors and vector directions.
Explore the shape of a square after it is transformed by the action
of a matrix.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Explore the properties of perspective drawing.
Who will be the first investor to pay off their debt?
Which dilutions can you make using only 10ml pipettes?
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?
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
Can you work out what this procedure is doing?
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.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
This problem explores the biology behind Rudolph's glowing red nose.