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.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Work out the numerical values for these physical quantities.
Get some practice using big and small numbers in chemistry.
How much energy has gone into warming the planet?
Get further into power series using the fascinating Bessel's equation.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
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?
Explore the relationship between resistance and temperature
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Which dilutions can you make using only 10ml pipettes?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
When you change the units, do the numbers get bigger or smaller?
Which line graph, equations and physical processes go together?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Look at the advanced way of viewing sin and cos through their power series.
Build up the concept of the Taylor series
Invent scenarios which would give rise to these probability density functions.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Was it possible that this dangerous driving penalty was issued in error?
Use vectors and matrices to explore the symmetries of crystals.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Why MUST these statistical statements probably be at least a little bit wrong?
Which pdfs match the curves?
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?
How would you go about estimating populations of dolphins?
Can you make matrices which will fix one lucky vector and crush another to zero?
Who will be the first investor to pay off their debt?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Explore the properties of matrix transformations with these 10 stimulating questions.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Formulate and investigate a simple mathematical model for the design of a table mat.
Explore how matrices can fix vectors and vector directions.
Match the descriptions of physical processes to these differential equations.
Explore the shape of a square after it is transformed by the action of a matrix.
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.
This problem explores the biology behind Rudolph's glowing red nose.
Can you work out what this procedure is doing?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Is it really greener to go on the bus, or to buy local?