Match the descriptions of physical processes to these differential
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.
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
How would you go about estimating populations of dolphins?
Was it possible that this dangerous driving penalty was issued in
Here are several equations from real life. Can you work out which measurements are possible from each equation?
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?
Why MUST these statistical statements probably be at least a little
Work out the numerical values for these physical quantities.
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.
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.
Which line graph, equations and physical processes go together?
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.
Analyse these beautiful biological images and attempt to rank them in size order.
Build up the concept of the Taylor 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
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?
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 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.
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.
Use vectors and matrices to explore the symmetries of crystals.
Who will be the first investor to pay off their debt?
Can you make matrices which will fix one lucky vector and crush another to zero?
Explore how matrices can fix vectors and vector directions.
Can you sketch these difficult curves, which have uses in
A problem about genetics and the transmission of disease.
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Which dilutions can you make using only 10ml pipettes?
Imagine different shaped vessels being filled. Can you work out
what the graphs of the water level should look like?
Explore the properties of perspective drawing.
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?
Formulate and investigate a simple mathematical model for the design of a table mat.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
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?