Which line graph, equations and physical processes go together?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Which pdfs match the curves?
Why MUST these statistical statements probably be at least a little bit wrong?
Get further into power series using the fascinating Bessel's equation.
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?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
How would you go about estimating populations of dolphins?
Use vectors and matrices to explore the symmetries of crystals.
Invent scenarios which would give rise to these probability density functions.
Get some practice using big and small numbers in chemistry.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Explore the properties of matrix transformations with these 10 stimulating questions.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Who will be the first investor to pay off their debt?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Work out the numerical values for these physical quantities.
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
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?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
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?
Build up the concept of the Taylor series
How do you choose your planting levels to minimise the total loss at harvest time?
Can you find the volumes of the mathematical vessels?
Can you make matrices which will fix one lucky vector and crush another to zero?
Explore the meaning of the scalar and vector cross products and see how the two are related.
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?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you work out which processes are represented by the graphs?
Explore the shape of a square after it is transformed by the action of a matrix.
Was it possible that this dangerous driving penalty was issued in error?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
When you change the units, do the numbers get bigger or smaller?
Look at the advanced way of viewing sin and cos through their power series.
Which units would you choose best to fit these situations?
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?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Are these estimates of physical quantities accurate?
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.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Match the descriptions of physical processes to these differential equations.
Go on a vector walk and determine which points on the walk are closest to the origin.