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.
Why MUST these statistical statements probably be at least a little bit wrong?
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?
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?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
How would you go about estimating populations of dolphins?
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.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Get further into power series using the fascinating Bessel's equation.
Are these estimates of physical quantities accurate?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Get some practice using big and small numbers in chemistry.
Was it possible that this dangerous driving penalty was issued in error?
Match the charts of these functions to the charts of their integrals.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Build up the concept of the Taylor series
Look at the advanced way of viewing sin and cos through their power series.
Match the descriptions of physical processes to these differential equations.
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.
Can you construct a cubic equation with a certain distance between its turning points?
Can you work out what this procedure is doing?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Work out the numerical values for these physical quantities.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Go on a vector walk and determine which points on the walk are closest to the origin.
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.
Analyse these beautiful biological images and attempt to rank them in size order.
Explore the relationship between resistance and temperature
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...
Formulate and investigate a simple mathematical model for the design of a table mat.
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 units would you choose best to fit these situations?
How efficiently can you pack together disks?
When you change the units, do the numbers get bigger or smaller?
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?
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. . . .
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
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 behind the algebra and geometry of matrices with these 10 individual problems.