Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
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.
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?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Which line graph, equations and physical processes go together?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
Invent scenarios which would give rise to these probability density functions.
Why MUST these statistical statements probably be at least a little
How would you go about estimating populations of dolphins?
How efficiently can you pack together disks?
Are these estimates of physical quantities accurate?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Get further into power series using the fascinating Bessel's equation.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Go on a vector walk and determine which points on the walk are
closest to the origin.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Was it possible that this dangerous driving penalty was issued in
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Match the descriptions of physical processes to these differential
Analyse these beautiful biological images and attempt to rank them in size order.
Build up the concept of the Taylor series
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Explore the relationship between resistance and temperature
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.
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.
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.
A problem about genetics and the transmission of disease.
This problem explores the biology behind Rudolph's glowing red
Explore the properties of perspective drawing.
Explore the shape of a square after it is transformed by the action
of a matrix.
Can Jo make a gym bag for her trainers from the piece of fabric she has?
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
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
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.
Explore the properties of matrix transformations with these 10 stimulating questions.
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
Can you work out what this procedure is doing?
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?
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.
Looking at small values of functions. Motivating the existence of
the Taylor expansion.