Get further into power series using the fascinating Bessel's equation.
Was it possible that this dangerous driving penalty was issued in error?
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?
Look at the advanced way of viewing sin and cos through their power series.
Which line graph, equations and physical processes go together?
Work out the numerical values for these physical quantities.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
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.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
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?
Build up the concept of the Taylor series
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
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 the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.
Match the charts of these functions to the charts of their integrals.
Can you work out what this procedure is doing?
How do you choose your planting levels to minimise the total loss at harvest time?
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?
Invent scenarios which would give rise to these probability density functions.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Use vectors and matrices to explore the symmetries of crystals.
Explore the shape of a square after it is transformed by the action of a matrix.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Which pdfs match the curves?
Why MUST these statistical statements probably be at least a little bit wrong?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Use your skill and judgement to match the sets of random data.
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
Estimate areas using random grids
When you change the units, do the numbers get bigger or smaller?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Which units would you choose best to fit these situations?
Explore how matrices can fix vectors and vector directions.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Which dilutions can you make using only 10ml pipettes?
Go on a vector walk and determine which points on the walk are closest to the origin.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Explore the properties of matrix transformations with these 10 stimulating questions.
Where should runners start the 200m race so that they have all run the same distance by the finish?
Explore the properties of perspective drawing.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .
Can you make matrices which will fix one lucky vector and crush another to zero?