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.
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.
Go on a vector walk and determine which points on the walk are
closest to the origin.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Explore the relationship between resistance and temperature
Match the descriptions of physical processes to these differential
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Match the charts of these functions to the charts of their integrals.
Was it possible that this dangerous driving penalty was issued in
Why MUST these statistical statements probably be at least a little
Work out the numerical values for these physical quantities.
Invent scenarios which would give rise to these probability density functions.
Can you work out what this procedure is doing?
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Can you work out which processes are represented by the graphs?
Where should runners start the 200m race so that they have all run the same distance by the finish?
Get some practice using big and small numbers in chemistry.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
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.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Analyse these beautiful biological images and attempt to rank them in size order.
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?
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
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.
Are these estimates of physical quantities accurate?
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
How would you go about estimating populations of dolphins?
In this short problem, try to find the location of the roots of
some unusual functions by finding where they change sign.
A problem about genetics and the transmission of disease.
Explore the properties of perspective drawing.
When you change the units, do the numbers get bigger or smaller?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Explore the properties of matrix transformations with these 10 stimulating questions.