Get some practice using big and small numbers in chemistry.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
How much energy has gone into warming the planet?
Get further into power series using the fascinating Bessel's equation.
Which line graph, equations and physical processes go together?
Look at the advanced way of viewing sin and cos through their power series.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Work out the numerical values for these physical quantities.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
How would you go about estimating populations of dolphins?
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?
Explore the relationship between resistance and temperature
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Invent scenarios which would give rise to these probability density functions.
Was it possible that this dangerous driving penalty was issued in error?
Explore the shape of a square after it is transformed by the action of a matrix.
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?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Why MUST these statistical statements probably be at least a little bit wrong?
When you change the units, do the numbers get bigger or smaller?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
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?
Build up the concept of the Taylor series
Match the descriptions of physical processes to these differential equations.
This problem explores the biology behind Rudolph's glowing red nose.
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.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Go on a vector walk and determine which points on the walk are closest to the origin.
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?
Which dilutions can you make using only 10ml pipettes?
Explore the properties of perspective drawing.
Formulate and investigate a simple mathematical model for the design of a table mat.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Which pdfs match the curves?
Explore the properties of matrix transformations with these 10 stimulating questions.
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.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Can you make matrices which will fix one lucky vector and crush another to zero?
Can you find the volumes of the mathematical vessels?
Match the charts of these functions to the charts of their integrals.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.