Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Can you work out what this procedure is doing?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Get further into power series using the fascinating Bessel's equation.
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.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
How much energy has gone into warming the planet?
Look at the advanced way of viewing sin and cos through their power series.
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.
Get some practice using big and small numbers in chemistry.
Explore the relationship between resistance and temperature
Formulate and investigate a simple mathematical model for the design of a table mat.
Build up the concept of the Taylor series
Which dilutions can you make using only 10ml pipettes?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Why MUST these statistical statements probably be at least a little bit wrong?
Which line graph, equations and physical processes go together?
Where should runners start the 200m race so that they have all run the same distance by the finish?
Use vectors and matrices to explore the symmetries of crystals.
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?
Can you make matrices which will fix one lucky vector and crush another to zero?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
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.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Invent scenarios which would give rise to these probability density functions.
Have you ever wondered what it would be like to race against Usain Bolt?
Which pdfs match the curves?
Who will be the first investor to pay off their debt?
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 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?
Which units would you choose best to fit these situations?
When you change the units, do the numbers get bigger or smaller?
Can you match the charts of these functions to the charts of their integrals?