How do you choose your planting levels to minimise the total loss
at harvest time?
Use your skill and judgement to match the sets of random data.
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?
In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?
A problem about genetics and the transmission of disease.
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 is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Simple models which help us to investigate how epidemics grow and die out.
Estimate areas using random grids
Can you make matrices which will fix one lucky vector and crush another to zero?
Use vectors and matrices to explore the symmetries of crystals.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
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?
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Which pdfs match the curves?
Can you construct a cubic equation with a certain distance between
its turning points?
Can you find the volumes of the mathematical vessels?
Which of these infinitely deep vessels will eventually full up?
Various solids are lowered into a beaker of water. How does the
water level rise in each case?
Why MUST these statistical statements probably be at least a little
Explore the meaning of the scalar and vector cross products and see how the two are related.
Which line graph, equations and physical processes go together?
Explore the properties of matrix transformations with these 10 stimulating questions.
Get some practice using big and small numbers in chemistry.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Can you work out which processes are represented by the graphs?
Formulate and investigate a simple mathematical model for the design of a table mat.
Explore the properties of perspective drawing.
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?
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.
Can you draw the height-time chart as this complicated vessel fills
Go on a vector walk and determine which points on the walk are
closest to the origin.
Explore the shape of a square after it is transformed by the action
of a matrix.
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Explore how matrices can fix vectors and vector directions.
Can you sketch these difficult curves, which have uses in
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.
In this short problem, try to find the location of the roots of
some unusual functions by finding where they change sign.
Who will be the first investor to pay off their debt?
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?
Are these estimates of physical quantities accurate?
Match the descriptions of physical processes to these differential
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
This problem explores the biology behind Rudolph's glowing red nose.