Which line graph, equations and physical processes go together?
Get further into power series using the fascinating Bessel's equation.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Look at the advanced way of viewing sin and cos through their power series.
Work out the numerical values for these physical quantities.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
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.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Build up the concept of the Taylor series
Was it possible that this dangerous driving penalty was issued in error?
Why MUST these statistical statements probably be at least a little bit wrong?
Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Which units would you choose best to fit these situations?
Can you make matrices which will fix one lucky vector and crush another to zero?
Explore the properties of matrix transformations with these 10 stimulating questions.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Explore the relationship between resistance and temperature
Invent scenarios which would give rise to these probability density functions.
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?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Who will be the first investor to pay off their debt?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
When you change the units, do the numbers get bigger or smaller?
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?
Formulate and investigate a simple mathematical model for the design of a table mat.
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?
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.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Explore how matrices can fix vectors and vector directions.
Which pdfs match the curves?
Match the descriptions of physical processes to these differential equations.
Can you work out what this procedure is doing?
Go on a vector walk and determine which points on the walk are closest to the origin.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Explore the shape of a square after it is transformed by the action of a matrix.
This problem explores the biology behind Rudolph's glowing red nose.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
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.