Get some practice using big and small numbers in chemistry.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Look at the advanced way of viewing sin and cos through their power series.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
How much energy has gone into warming the planet?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Which line graph, equations and physical processes go together?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Get further into power series using the fascinating Bessel's equation.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Work out the numerical values for these physical quantities.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
When you change the units, do the numbers get bigger or smaller?
Which units would you choose best to fit these situations?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
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.
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?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Why MUST these statistical statements probably be at least a little bit wrong?
Was it possible that this dangerous driving penalty was issued in error?
Build up the concept of the Taylor series
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?
Can you make matrices which will fix one lucky vector and crush another to zero?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Use vectors and matrices to explore the symmetries of crystals.
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?
Explore the properties of matrix transformations with these 10 stimulating questions.
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you work out what this procedure is doing?
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?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Which dilutions can you make using only 10ml pipettes?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Explore how matrices can fix vectors and vector directions.
Go on a vector walk and determine which points on the walk are closest to the origin.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
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.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Which pdfs match the curves?
Match the charts of these functions to the charts of their integrals.
Analyse these beautiful biological images and attempt to rank them in size order.
Match the descriptions of physical processes to these differential equations.
How would you go about estimating populations of dolphins?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?