Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
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.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
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?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Work out the numerical values for these physical quantities.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
When you change the units, do the numbers get bigger or smaller?
Was it possible that this dangerous driving penalty was issued in error?
Get further into power series using the fascinating Bessel's equation.
Why MUST these statistical statements probably be at least a little bit wrong?
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?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Which dilutions can you make using only 10ml pipettes?
Which line graph, equations and physical processes go together?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Which units would you choose best to fit these situations?
Explore the relationship between resistance and temperature
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
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?
Formulate and investigate a simple mathematical model for the design of a table mat.
Build up the concept of the Taylor series
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.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Explore the properties of matrix transformations with these 10 stimulating questions.
Is it really greener to go on the bus, or to buy local?
Analyse these beautiful biological images and attempt to rank them in size order.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Look at the advanced way of viewing sin and cos through their power series.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
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.
Go on a vector walk and determine which points on the walk are closest to the origin.
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?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Explore how matrices can fix vectors and vector directions.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
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?
Use vectors and matrices to explore the symmetries of crystals.
Simple models which help us to investigate how epidemics grow and die out.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?