Was it possible that this dangerous driving penalty was issued in error?
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.
Where should runners start the 200m race so that they have all run the same distance by the finish?
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.
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
Here are several equations from real life. Can you work out which measurements are possible from each equation?
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?
Why MUST these statistical statements probably be at least a little bit wrong?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
How efficiently can you pack together disks?
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?
Match the descriptions of physical processes to these differential equations.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Which units would you choose best to fit these situations?
How would you go about estimating populations of dolphins?
Go on a vector walk and determine which points on the walk are closest to the origin.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Invent scenarios which would give rise to these probability density functions.
Can you work out what this procedure is doing?
Analyse these beautiful biological images and attempt to rank them in size order.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
When you change the units, do the numbers get bigger or smaller?
Are these estimates of physical quantities accurate?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Use trigonometry to determine whether solar eclipses on earth can be perfect.
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.
Explore the meaning of the scalar and vector cross products and see how the two are related.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.
Is it really greener to go on the bus, or to buy local?
Explore the relationship between resistance and temperature
Can you draw the height-time chart as this complicated vessel fills with water?
Use simple trigonometry to calculate the distance along the flight path from London to Sydney.
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.