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.
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.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Which line graph, equations and physical processes go together?
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Why MUST these statistical statements probably be at least a little
Go on a vector walk and determine which points on the walk are
closest to the origin.
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
Invent scenarios which would give rise to these probability density functions.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Explore how matrices can fix vectors and vector directions.
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?
Get further into power series using the fascinating Bessel's equation.
Was it possible that this dangerous driving penalty was issued in
How would you go about estimating populations of dolphins?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Formulate and investigate a simple mathematical model for the design of a table mat.
Get some practice using big and small numbers in chemistry.
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Explore the properties of matrix transformations with these 10 stimulating questions.
How efficiently can you pack together disks?
Explore the shape of a square after it is transformed by the action
of a matrix.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
How much energy has gone into warming the planet?
Build up the concept of the Taylor series
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.
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Look at the advanced way of viewing sin and cos through their power series.
Use simple trigonometry to calculate the distance along the flight
path from London to Sydney.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Explore the relationship between resistance and temperature
Analyse these beautiful biological images and attempt to rank them in size order.
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
Match the descriptions of physical processes to these differential
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Are these estimates of physical quantities accurate?
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.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
This problem explores the biology behind Rudolph's glowing red nose.
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.
A problem about genetics and the transmission of disease.
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.
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
Can you find the volumes of the mathematical vessels?