Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Can you work out what this procedure is doing?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
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?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
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.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
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.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Work out the numerical values for these physical quantities.
How much energy has gone into warming the planet?
Which dilutions can you make using only 10ml pipettes?
Which line graph, equations and physical processes go together?
Explore the relationship between resistance and temperature
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Get some practice using big and small numbers in chemistry.
Build up the concept of the Taylor series
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Use vectors and matrices to explore the symmetries of crystals.
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?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Have you ever wondered what it would be like to race against Usain Bolt?
Explore the shape of a square after it is transformed by the action of a matrix.
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.
Invent scenarios which would give rise to these probability density functions.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Formulate and investigate a simple mathematical model for the design of a table mat.
Explore the properties of perspective drawing.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Explore how matrices can fix vectors and vector directions.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Go on a vector walk and determine which points on the walk are closest to the origin.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Explore the properties of matrix transformations with these 10 stimulating questions.
How do you choose your planting levels to minimise the total loss at harvest time?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Which pdfs match the curves?
Who will be the first investor to pay off their debt?
Are these estimates of physical quantities accurate?
When you change the units, do the numbers get bigger or smaller?
Which units would you choose best to fit these situations?
Estimate areas using random grids
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.