Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Get further into power series using the fascinating Bessel's equation.
Look at the advanced way of viewing sin and cos through their power series.
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?
How would you go about estimating populations of dolphins?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Who will be the first investor to pay off their debt?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Which line graph, equations and physical processes go together?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Which dilutions can you make using only 10ml pipettes?
Get some practice using big and small numbers in chemistry.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Use vectors and matrices to explore the symmetries of crystals.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Which pdfs match the curves?
How much energy has gone into warming the planet?
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.
Match the descriptions of physical processes to these differential equations.
Build up the concept of the Taylor series
How do you choose your planting levels to minimise the total loss at harvest time?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Explore the shape of a square after it is transformed by the action of a matrix.
Which of these infinitely deep vessels will eventually full up?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Explore the properties of matrix transformations with these 10 stimulating questions.
Can you find the volumes of the mathematical vessels?
Explore the relationship between resistance and temperature
Why MUST these statistical statements probably be at least a little bit wrong?
Invent scenarios which would give rise to these probability density functions.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Work out the numerical values for these physical quantities.
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?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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?
Was it possible that this dangerous driving penalty was issued in error?
Formulate and investigate a simple mathematical model for the design of a table mat.
Explore the properties of perspective drawing.
Which units would you choose best to fit these situations?
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?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
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?
Can you make matrices which will fix one lucky vector and crush another to zero?
Match the charts of these functions to the charts of their integrals.