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?
Get further into power series using the fascinating Bessel's equation.
Look at the advanced way of viewing sin and cos through their power series.
Which line graph, equations and physical processes go together?
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.
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Can you construct a cubic equation with a certain distance between
its turning points?
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.
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...
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Get some practice using big and small numbers in chemistry.
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.
Match the charts of these functions to the charts of their integrals.
Was it possible that this dangerous driving penalty was issued in
Invent scenarios which would give rise to these probability density functions.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
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
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.
How would you go about estimating populations of dolphins?
Work out the numerical values for these physical quantities.
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
Why MUST these statistical statements probably be at least a little
Can you work out what this procedure is doing?
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.
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
Can you match these equations to these graphs?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
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?
Can you work out which processes are represented by the graphs?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Match the descriptions of physical processes to these differential
Where should runners start the 200m race so that they have all run the same distance by the finish?
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?
Explore the properties of matrix transformations with these 10 stimulating questions.
Imagine different shaped vessels being filled. Can you work out
what the graphs of the water level should look like?
Explore the properties of perspective drawing.
Explore how matrices can fix vectors and vector directions.