Get some practice using big and small numbers in chemistry.
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.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Work out the numerical values for these physical quantities.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
When you change the units, do the numbers get bigger or smaller?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Which units would you choose best to fit these situations?
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?
Why MUST these statistical statements probably be at least a little bit wrong?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Which line graph, equations and physical processes go together?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
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?
Who will be the first investor to pay off their debt?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Formulate and investigate a simple mathematical model for the design of a table mat.
Get further into power series using the fascinating Bessel's equation.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Which dilutions can you make using only 10ml pipettes?
Build up the concept of the Taylor series
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?
Invent scenarios which would give rise to these probability density functions.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Explore the relationship between resistance and temperature
Is it really greener to go on the bus, or to buy local?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Was it possible that this dangerous driving penalty was issued in error?
Which pdfs match the curves?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
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?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Go on a vector walk and determine which points on the walk are closest to the origin.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Explore the properties of matrix transformations with these 10 stimulating questions.
Explore the shape of a square after it is transformed by the action of a matrix.
Can you match the charts of these functions to the charts of their integrals?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Explore the properties of perspective drawing.
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?
Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.
Where should runners start the 200m race so that they have all run the same distance by the finish?