A problem about genetics and the transmission of disease.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
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?
Simple models which help us to investigate how epidemics grow and die out.
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.
How do you choose your planting levels to minimise the total loss
at harvest time?
Why MUST these statistical statements probably be at least a little
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Can Jo make a gym bag for her trainers from the piece of fabric she has?
How efficiently can you pack together disks?
Which line graph, equations and physical processes go together?
Invent scenarios which would give rise to these probability density functions.
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. . . .
Formulate and investigate a simple mathematical model for the design of a table mat.
Estimate areas using random grids
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.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
How much energy has gone into warming the planet?
Use your skill and judgement to match the sets of random data.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
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.
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.
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Build up the concept of the Taylor series
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
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.
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
Can you make matrices which will fix one lucky vector and crush another to zero?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Who will be the first investor to pay off their debt?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Can you sketch these difficult curves, which have uses in
Explore the shape of a square after it is transformed by the action
of a matrix.
Explore the properties of matrix transformations with these 10 stimulating questions.
Go on a vector walk and determine which points on the walk are
closest to the origin.
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?
Explore the relationship between resistance and temperature
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
Which dilutions can you make using only 10ml pipettes?
Imagine different shaped vessels being filled. Can you work out
what the graphs of the water level should look like?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Explore the properties of perspective drawing.
This problem explores the biology behind Rudolph's glowing red nose.
Analyse these beautiful biological images and attempt to rank them in size order.