Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Which line graph, equations and physical processes go together?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
How would you go about estimating populations of dolphins?
When you change the units, do the numbers get bigger or smaller?
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?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Which units would you choose best to fit these situations?
Can you work out which processes are represented by the graphs?
Can you match these equations to these graphs?
Work out the numerical values for these physical quantities.
Get further into power series using the fascinating Bessel's equation.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Was it possible that this dangerous driving penalty was issued in error?
Get some practice using big and small numbers in chemistry.
Can you find the volumes of the mathematical vessels?
Are these estimates of physical quantities accurate?
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.
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.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Match the descriptions of physical processes to these differential equations.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Invent scenarios which would give rise to these probability density functions.
This problem explores the biology behind Rudolph's glowing red nose.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Which dilutions can you make using only 10ml pipettes?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Which pdfs match the curves?
Use vectors and matrices to explore the symmetries of crystals.
Explore how matrices can fix vectors and vector directions.
Can you sketch these difficult curves, which have uses in mathematical modelling?
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?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Why MUST these statistical statements probably be at least a little bit wrong?
Explore the properties of matrix transformations with these 10 stimulating questions.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Explore the relationship between resistance and temperature
Build up the concept of the Taylor series
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Which of these infinitely deep vessels will eventually full up?
Who will be the first investor to pay off their debt?
Look at the advanced way of viewing sin and cos through their power series.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.