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
Match the descriptions of physical processes to these differential equations.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
When you change the units, do the numbers get bigger or smaller?
Are these estimates of physical quantities accurate?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Work out the numerical values for these physical quantities.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Which line graph, equations and physical processes go together?
How would you go about estimating populations of dolphins?
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?
Which units would you choose best to fit these situations?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
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.
Get some practice using big and small numbers in chemistry.
Get further into power series using the fascinating Bessel's equation.
How much energy has gone into warming the planet?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Analyse these beautiful biological images and attempt to rank them in size order.
Was it possible that this dangerous driving penalty was issued in error?
Which dilutions can you make using only 10ml pipettes?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Have you ever wondered what it would be like to race against Usain Bolt?
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?
Can you find the volumes of the mathematical vessels?
Can you make matrices which will fix one lucky vector and crush another to zero?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Explore how matrices can fix vectors and vector directions.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Invent scenarios which would give rise to these probability density functions.
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.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Which of these infinitely deep vessels will eventually full up?
Why MUST these statistical statements probably be at least a little bit wrong?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
This problem explores the biology behind Rudolph's glowing red nose.
Look at the advanced way of viewing sin and cos through their power series.
Can you match the charts of these functions to the charts of their integrals?
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
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Explore the shape of a square after it is transformed by the action of a matrix.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Can you construct a cubic equation with a certain distance between its turning points?
The design technology curriculum requires students to be able to represent 3-dimensional objects on paper. This article introduces some of the mathematical ideas which underlie such methods.