Get further into power series using the fascinating Bessel's equation.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Look at the advanced way of viewing sin and cos through their power series.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Build up the concept of the Taylor series
How much energy has gone into warming the planet?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Get some practice using big and small numbers in chemistry.
Analyse these beautiful biological images and attempt to rank them in size order.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Are these estimates of physical quantities accurate?
Match the descriptions of physical processes to these differential equations.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
When you change the units, do the numbers get bigger or smaller?
Which pdfs match the curves?
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?
Invent scenarios which would give rise to these probability density functions.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Was it possible that this dangerous driving penalty was issued in error?
Which line graph, equations and physical processes go together?
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Explore the properties of matrix transformations with these 10 stimulating questions.
Why MUST these statistical statements probably be at least a little bit wrong?
Various solids are lowered into a beaker of water. How does the water level rise in each case?
Explore how matrices can fix vectors and vector directions.
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?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Use vectors and matrices to explore the symmetries of crystals.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Formulate and investigate a simple mathematical model for the design of a table mat.
Explore the relationship between resistance and temperature
This problem explores the biology behind Rudolph's glowing red nose.
Where should runners start the 200m race so that they have all run the same distance by the finish?
Which dilutions can you make using only 10ml pipettes?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
How would you go about estimating populations of dolphins?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Who will be the first investor to pay off their debt?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Can you make matrices which will fix one lucky vector and crush another to zero?
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Explore the shape of a square after it is transformed by the action of a matrix.