Can you sketch these difficult curves, which have uses in
10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Are these estimates of physical quantities accurate?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Look at the advanced way of viewing sin and cos through their power series.
Can you match these equations to these graphs?
Can you construct a cubic equation with a certain distance between
its turning points?
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
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.
Get further into power series using the fascinating Bessel's equation.
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.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Match the charts of these functions to the charts of their integrals.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Explore the relationship between resistance and temperature
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?
Was it possible that this dangerous driving penalty was issued in
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Analyse these beautiful biological images and attempt to rank them in size order.
Can you work out what this procedure is doing?
Work out the numerical values for these physical quantities.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Can you work out which processes are represented by the graphs?
Why MUST these statistical statements probably be at least a little
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.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
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.
When you change the units, do the numbers get bigger or smaller?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Where should runners start the 200m race so that they have all run the same distance by the finish?
Match the descriptions of physical processes to these differential
Invent scenarios which would give rise to these probability density functions.
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
Which units would you choose best to fit these situations?
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?
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?
Get some practice using big and small numbers in chemistry.