Here are several equations from real life. Can you work out which measurements are possible from each equation?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Which pdfs match the curves?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Why MUST these statistical statements probably be at least a little bit wrong?
Which line graph, equations and physical processes go together?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
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?
Invent scenarios which would give rise to these probability density functions.
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.
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 some practice using big and small numbers in chemistry.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
How much energy has gone into warming the planet?
Which dilutions can you make using only 10ml pipettes?
Formulate and investigate a simple mathematical model for the design of a table mat.
Was it possible that this dangerous driving penalty was issued in error?
Get further into power series using the fascinating Bessel's equation.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Are these estimates of physical quantities accurate?
Analyse these beautiful biological images and attempt to rank them in size order.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Build up the concept of the Taylor series
Explore the meaning of the scalar and vector cross products and see how the two are related.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Use vectors and matrices to explore the symmetries of crystals.
Which units would you choose best to fit these situations?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Can you make matrices which will fix one lucky vector and crush another to zero?
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?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Explore the properties of matrix transformations with these 10 stimulating questions.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
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.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
This problem explores the biology behind Rudolph's glowing red nose.
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?
Work out the numerical values for these physical quantities.
Is it really greener to go on the bus, or to buy local?
Match the descriptions of physical processes to these differential equations.
Look at the advanced way of viewing sin and cos through their power series.
When you change the units, do the numbers get bigger or smaller?