Invent scenarios which would give rise to these probability density functions.
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?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Why MUST these statistical statements probably be at least a little
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Which line graph, equations and physical processes go together?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
How much energy has gone into warming the planet?
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
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.
How efficiently can you pack together disks?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
How would you go about estimating populations of dolphins?
Was it possible that this dangerous driving penalty was issued in
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.
Match the charts of these functions to the charts of their integrals.
Get further into power series using the fascinating Bessel's equation.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Get some practice using big and small numbers in chemistry.
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
Match the descriptions of physical processes to these differential
Look at the advanced way of viewing sin and cos through their power series.
Build up the concept of the Taylor series
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.
Analyse these beautiful biological images and attempt to rank them in size order.
This problem explores the biology behind Rudolph's glowing red nose.
Imagine different shaped vessels being filled. Can you work out
what the graphs of the water level should look like?
Work out the numerical values for these physical quantities.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
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. . . .
Can you construct a cubic equation with a certain distance between
its turning points?
Explore the relationship between resistance and temperature
Can you work out what this procedure is doing?
Formulate and investigate a simple mathematical model for the design of a table mat.
Go on a vector walk and determine which points on the walk are
closest to the origin.
Simple models which help us to investigate how epidemics grow and die out.
Can you sketch these difficult curves, which have uses in
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
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?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
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?