Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
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?
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 work out what this procedure is doing?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
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 dilutions can you make using only 10ml pipettes?
Get further into power series using the fascinating Bessel's equation.
Which line graph, equations and physical processes go together?
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.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Look at the advanced way of viewing sin and cos through their power series.
Work out the numerical values for these physical quantities.
Get some practice using big and small numbers in chemistry.
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Build up the concept of the Taylor series
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Use vectors and matrices to explore the symmetries of crystals.
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?
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.
10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?
Formulate and investigate a simple mathematical model for the design of a table mat.
Which pdfs match the curves?
Have you ever wondered what it would be like to race against Usain Bolt?
Why MUST these statistical statements probably be at least a little bit wrong?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Can you make matrices which will fix one lucky vector and crush another to zero?
Analyse these beautiful biological images and attempt to rank them in size order.
Explore how matrices can fix vectors and vector directions.
Invent scenarios which would give rise to these probability density functions.
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.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
This problem explores the biology behind Rudolph's glowing red nose.
Explore the shape of a square after it is transformed by the action of a matrix.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Go on a vector walk and determine which points on the walk are closest to the origin.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Explore the properties of matrix transformations with these 10 stimulating questions.
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 choose your planting levels to minimise the total loss at harvest time?
Match the descriptions of physical processes to these differential equations.
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?
Where should runners start the 200m race so that they have all run the same distance by the finish?