Starting with two basic vector steps, which destinations can you reach on a vector walk?
Can you make matrices which will fix one lucky vector and crush another to zero?
Explore the meaning of the scalar and vector cross products and see how the two are related.
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 how matrices can fix vectors and vector directions.
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.
Which of these infinitely deep vessels will eventually full up?
Explore the properties of matrix transformations with these 10 stimulating questions.
Can Jo make a gym bag for her trainers from the piece of fabric she has?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Where should runners start the 200m race so that they have all run the same distance by the finish?
Explore the shape of a square after it is transformed by the action
of a matrix.
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.
Go on a vector walk and determine which points on the walk are
closest to the origin.
Use simple trigonometry to calculate the distance along the flight
path from London to Sydney.
How efficiently can you pack together disks?
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Invent scenarios which would give rise to these probability density functions.
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Is it really greener to go on the bus, or to buy local?
Use vectors and matrices to explore the symmetries of crystals.
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
A problem about genetics and the transmission of disease.
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?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Get some practice using big and small numbers in chemistry.
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.
Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .
How would you design the tiering of seats in a stadium so that all spectators have a good view?
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Which dilutions can you make using only 10ml pipettes?
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
Explore the properties of perspective drawing.
Imagine different shaped vessels being filled. Can you work out
what the graphs of the water level should look like?
Simple models which help us to investigate how epidemics grow and die out.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Work out the numerical values for these physical quantities.
Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
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.
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?
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you work out which processes are represented by the graphs?