Why MUST these statistical statements probably be at least a little
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.
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?
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
Which line graph, equations and physical processes go together?
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
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.
Was it possible that this dangerous driving penalty was issued in
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Look at the advanced way of viewing sin and cos through their power series.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Get some practice using big and small numbers in chemistry.
Match the charts of these functions to the charts of their integrals.
How much energy has gone into warming the planet?
Match the descriptions of physical processes to these differential
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?
Build up the concept of the Taylor series
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Can you work out what this procedure is doing?
Explore the relationship between resistance and temperature
Can you construct a cubic equation with a certain distance between
its turning points?
Which of these infinitely deep vessels will eventually full up?
Formulate and investigate a simple mathematical model for the design of a table mat.
Work out the numerical values for these physical quantities.
Can you sketch these difficult curves, which have uses in
Go on a vector walk and determine which points on the walk are
closest to the origin.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Analyse these beautiful biological images and attempt to rank them in size order.
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.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
Simple models which help us to investigate how epidemics grow and die out.
Which countries have the most naturally athletic populations?
Which units would you choose best to fit these situations?
When you change the units, do the numbers get bigger or smaller?
Are these estimates of physical quantities accurate?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
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.
How efficiently can you pack together disks?
Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?
How would you go about estimating populations of dolphins?
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. . . .
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.