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.
Use simple trigonometry to calculate the distance along the flight
path from London to Sydney.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Explore the properties of perspective drawing.
Is it really greener to go on the bus, or to buy local?
Which line graph, equations and physical processes go together?
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?
Which of these infinitely deep vessels will eventually full up?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
How efficiently can you pack together disks?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Get further into power series using the fascinating Bessel's equation.
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.
Go on a vector walk and determine which points on the walk are
closest to the origin.
Formulate and investigate a simple mathematical model for the design of a table mat.
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
Where should runners start the 200m race so that they have all run the same distance by the finish?
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
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.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
How much energy has gone into warming the planet?
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
Look at the advanced way of viewing sin and cos through their power series.
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Match the descriptions of physical processes to these differential
Build up the concept of the Taylor series
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 relationship between resistance and temperature
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
This problem explores the biology behind Rudolph's glowing red nose.
Explore how matrices can fix vectors and vector directions.
Imagine different shaped vessels being filled. Can you work out
what the graphs of the water level should look like?
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
Explore the shape of a square after it is transformed by the action
of a matrix.
Can you sketch these difficult curves, which have uses in
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Explore the properties of matrix transformations with these 10 stimulating questions.
Invent scenarios which would give rise to these probability density functions.
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 suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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?
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?