Get some practice using big and small numbers in chemistry.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Which line graph, equations and physical processes go together?
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Which pdfs match the curves?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
How much energy has gone into warming the planet?
Which units would you choose best to fit these situations?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
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?
Why MUST these statistical statements probably be at least a little bit wrong?
Who will be the first investor to pay off their debt?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Explore the properties of matrix transformations with these 10 stimulating questions.
Build up the concept of the Taylor series
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?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Get further into power series using the fascinating Bessel's 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?
Explore the shape of a square after it is transformed by the action of a matrix.
Explore how matrices can fix vectors and vector directions.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
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.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Look at the advanced way of viewing sin and cos through their power series.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Analyse these beautiful biological images and attempt to rank them in size order.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Are these estimates of physical quantities accurate?
How would you go about estimating populations of dolphins?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Go on a vector walk and determine which points on the walk are closest to the origin.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Match the descriptions of physical processes to these differential equations.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
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.
Can you work out what this procedure is doing?
This problem explores the biology behind Rudolph's glowing red nose.