Build up the concept of the Taylor series
Get further into power series using the fascinating Bessel's equation.
Look at the advanced way of viewing sin and cos through their power series.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Get some practice using big and small numbers in chemistry.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Use vectors and matrices to explore the symmetries of crystals.
Which line graph, equations and physical processes go together?
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 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?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Was it possible that this dangerous driving penalty was issued in error?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Can you make matrices which will fix one lucky vector and crush another to zero?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Which of these infinitely deep vessels will eventually full up?
Why MUST these statistical statements probably be at least a little bit wrong?
Explore the properties of matrix transformations with these 10 stimulating questions.
Which pdfs match the curves?
Explore the shape of a square after it is transformed by the action of a matrix.
Invent scenarios which would give rise to these probability density functions.
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.
Formulate and investigate a simple mathematical model for the design of a table mat.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
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?
Where should runners start the 200m race so that they have all run the same distance by the finish?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Who will be the first investor to pay off their debt?
When you change the units, do the numbers get bigger or smaller?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Which units would you choose best to fit these situations?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Can you work out what this procedure is doing?
Go on a vector walk and determine which points on the walk are closest to the origin.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
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.
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?