Which line graph, equations and physical processes go together?
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?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Get further into power series using the fascinating Bessel's equation.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Which pdfs match the curves?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Get some practice using big and small numbers in chemistry.
Invent scenarios which would give rise to these probability density functions.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Why MUST these statistical statements probably be at least a little bit wrong?
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?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Can you make matrices which will fix one lucky vector and crush another to zero?
Work out the numerical values for these physical quantities.
Analyse these beautiful biological images and attempt to rank them in size order.
Can you find the volumes of the mathematical vessels?
Which of these infinitely deep vessels will eventually full up?
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?
Formulate and investigate a simple mathematical model for the design of a table mat.
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?
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.
Can you work out which processes are represented by the graphs?
Explore the shape of a square after it is transformed by the action of a matrix.
Go on a vector walk and determine which points on the walk are closest to the origin.
Explore the properties of matrix transformations with these 10 stimulating questions.
Was it possible that this dangerous driving penalty was issued in error?
Use vectors and matrices to explore the symmetries of crystals.
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
Who will be the first investor to pay off their debt?
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
How would you go about estimating populations of dolphins?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Which units would you choose best to fit these situations?
When you change the units, do the numbers get bigger or smaller?
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?
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.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.