Can you work out what this procedure is doing?
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.
Does weight confer an advantage to shot putters?
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
Which line graph, equations and physical processes go together?
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.
Invent scenarios which would give rise to these probability density functions.
Why MUST these statistical statements probably be at least a little
Which countries have the most naturally athletic populations?
How would you go about estimating populations of dolphins?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Have you ever wondered what it would be like to race against Usain Bolt?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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 Jo make a gym bag for her trainers from the piece of fabric she has?
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?
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?
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?
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Was it possible that this dangerous driving penalty was issued in
Get further into power series using the fascinating Bessel's equation.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Which dilutions can you make using only 10ml pipettes?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Go on a vector walk and determine which points on the walk are
closest to the origin.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Simple models which help us to investigate how epidemics grow and die out.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Formulate and investigate a simple mathematical model for the design of a table mat.
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Which units would you choose best to fit these situations?
When you change the units, do the numbers get bigger or smaller?
Build up the concept of the Taylor series
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Match the descriptions of physical processes to these differential
Are these estimates of physical quantities accurate?
In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?
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.
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?
Look at the advanced way of viewing sin and cos through their power series.
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
Analyse these beautiful biological images and attempt to rank them in size order.