Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
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.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
How much energy has gone into warming the planet?
Work out the numerical values for these physical quantities.
Look at the advanced way of viewing sin and cos through their power series.
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?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Which line graph, equations and physical processes go together?
Get further into power series using the fascinating Bessel's equation.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
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?
When you change the units, do the numbers get bigger or smaller?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Build up the concept of the Taylor series
Which dilutions can you make using only 10ml pipettes?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
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?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Explore the relationship between resistance and temperature
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?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Invent scenarios which would give rise to these probability density functions.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
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.
Is it really greener to go on the bus, or to buy local?
Where should runners start the 200m race so that they have all run the same distance by the finish?
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.
Explore the meaning of the scalar and vector cross products and see how the two are related.
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?
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.
Go on a vector walk and determine which points on the walk are closest to the origin.
Can you work out what this procedure is doing?
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 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?
Which pdfs match the curves?