What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
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.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Can you match the charts of these functions to the charts of their integrals?
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
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?
Which line graph, equations and physical processes go together?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
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?
Invent scenarios which would give rise to these probability density functions.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Get further into power series using the fascinating Bessel's equation.
Was it possible that this dangerous driving penalty was issued in error?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
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.
How much energy has gone into warming the planet?
When you change the units, do the numbers get bigger or smaller?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Work out the numerical values for these physical quantities.
Build up the concept of the Taylor series
Explore the relationship between resistance and temperature
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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?
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.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Which dilutions can you make using only 10ml pipettes?
Get some practice using big and small numbers in chemistry.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Look at the advanced way of viewing sin and cos through their power series.
Estimate areas using random grids
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.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
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.
Which pdfs match the curves?
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.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Explore how matrices can fix vectors and vector directions.
Can you make matrices which will fix one lucky vector and crush another to zero?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...