Here are several equations from real life. Can you work out which measurements are possible from each equation?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Why MUST these statistical statements probably be at least a little bit wrong?
Who will be the first investor to pay off their debt?
Invent scenarios which would give rise to these probability density functions.
Explore the properties of matrix transformations with these 10 stimulating questions.
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?
Use vectors and matrices to explore the symmetries of crystals.
Get further into power series using the fascinating Bessel's equation.
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Which pdfs match the curves?
Which line graph, equations and physical processes go together?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Which dilutions can you make using only 10ml pipettes?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Get some practice using big and small numbers in chemistry.
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?
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.
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?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Build up the concept of the Taylor series
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Go on a vector walk and determine which points on the walk are closest to the origin.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
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?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Explore the shape of a square after it is transformed by the action of a matrix.
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.
Work out the numerical values for these physical quantities.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Explore how matrices can fix vectors and vector directions.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Analyse these beautiful biological images and attempt to rank them in size order.
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?
Explore the relationship between resistance and temperature
Match the descriptions of physical processes to these differential equations.
Is it really greener to go on the bus, or to buy local?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Was it possible that this dangerous driving penalty was issued in error?
When you change the units, do the numbers get bigger or smaller?