Was it possible that this dangerous driving penalty was issued in
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.
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.
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.
Match the descriptions of physical processes to these differential
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
How would you go about estimating populations of dolphins?
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
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.
Analyse these beautiful biological images and attempt to rank them in size order.
Why MUST these statistical statements probably be at least a little
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?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
How efficiently can you pack together disks?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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?
Go on a vector walk and determine which points on the walk are
closest to the origin.
Explore the relationship between resistance and temperature
Can you work out what this procedure is doing?
Which units would you choose best to fit these situations?
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?
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.
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.
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.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Is it really greener to go on the bus, or to buy local?
Formulate and investigate a simple mathematical model for the design of a table mat.
Match the charts of these functions to the charts of their integrals.
Are these estimates of physical quantities accurate?
Shows that Pythagoras for Spherical Triangles reduces to
Pythagoras's Theorem in the plane when the triangles are small
relative to the radius of the sphere.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Imagine different shaped vessels being filled. Can you work out
what the graphs of the water level should look like?