What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
Match the charts of these functions to the charts of their integrals.
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.
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 perspective drawing.
Which dilutions can you make using only 10ml pipettes?
Which line graph, equations and physical processes go together?
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
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?
Which units would you choose best to fit these situations?
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?
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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.
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.
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.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Formulate and investigate a simple mathematical model for the design of a table mat.
How much energy has gone into warming the planet?
Estimate areas using random grids
Match the descriptions of physical processes to these differential
Look at the advanced way of viewing sin and cos through their power series.
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
Build up the concept of the Taylor series
When you change the units, do the numbers get bigger or smaller?
A problem about genetics and the transmission of disease.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
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?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
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.
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.
Explore how matrices can fix vectors and vector directions.
Invent scenarios which would give rise to these probability density functions.
Can you work out which processes are represented by the graphs?
This problem explores the biology behind Rudolph's glowing red nose.
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.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Explore the relationship between resistance and temperature