Here are several equations from real life. Can you work out which measurements are possible from each equation?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Why MUST these statistical statements probably be at least a little
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
Which line graph, equations and physical processes go together?
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?
How much energy has gone into warming the planet?
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.
Get further into power series using the fascinating Bessel's equation.
Formulate and investigate a simple mathematical model for the design of a table mat.
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Go on a vector walk and determine which points on the walk are
closest to the origin.
Explore the relationship between resistance and temperature
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Can you match these equations to these graphs?
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
Build up the concept of the Taylor series
Look at the advanced way of viewing sin and cos through their power series.
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 suggest a curve to fit some experimental data? Can you work out where the data might have come from?
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Which of these infinitely deep vessels will eventually full up?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Various solids are lowered into a beaker of water. How does the
water level rise in each case?
Work out the numerical values for these physical quantities.
Analyse these beautiful biological images and attempt to rank them in size order.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
Which dilutions can you make using only 10ml pipettes?
Imagine different shaped vessels being filled. Can you work out
what the graphs of the water level should look like?
Explore the properties of perspective drawing.
How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.
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?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Can you construct a cubic equation with a certain distance between
its turning points?
Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.
Can you work out which processes are represented by the graphs?
Can you sketch these difficult curves, which have uses in
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
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?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Are these estimates of physical quantities accurate?
Which units would you choose best to fit these situations?