Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Can you work out what this procedure is doing?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Get further into power series using the fascinating Bessel's equation.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Look at the advanced way of viewing sin and cos through their power series.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
How much energy has gone into warming the planet?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Get some practice using big and small numbers in chemistry.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Which dilutions can you make using only 10ml pipettes?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Which line graph, equations and physical processes go together?
Build up the concept of the Taylor series
Work out the numerical values for these physical quantities.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Can you make matrices which will fix one lucky vector and crush another to zero?
Use vectors and matrices to explore the symmetries of crystals.
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?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
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.
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Where should runners start the 200m race so that they have all run the same distance by the finish?
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.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Invent scenarios which would give rise to these probability density functions.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Can you sketch these difficult curves, which have uses in mathematical modelling?
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 how matrices can fix vectors and vector directions.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Which pdfs match the curves?
Are these estimates of physical quantities accurate?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
When you change the units, do the numbers get bigger or smaller?
Which units would you choose best to fit these situations?
How would you go about estimating populations of dolphins?
Who will be the first investor to pay off their debt?