Why MUST these statistical statements probably be at least a little bit wrong?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Get further into power series using the fascinating Bessel's equation.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Who will be the first investor to pay off their debt?
Which line graph, equations and physical processes go together?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Invent scenarios which would give rise to these probability density functions.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Explore the shape of a square after it is transformed by the action of a matrix.
Explore the properties of matrix transformations with these 10 stimulating questions.
Can you sketch these difficult curves, which have uses in mathematical modelling?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
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?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
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 make matrices which will fix one lucky vector and crush another to zero?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Which pdfs match the curves?
Can you construct a cubic equation with a certain distance between its turning points?
Which of these infinitely deep vessels will eventually full up?
How do you choose your planting levels to minimise the total loss at harvest time?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Go on a vector walk and determine which points on the walk are closest to the origin.
In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?
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.
Which dilutions can you make using only 10ml pipettes?
Explore the properties of perspective drawing.
Formulate and investigate a simple mathematical model for the design of a table mat.
Get some practice using big and small numbers in chemistry.
This problem explores the biology behind Rudolph's glowing red nose.
Explore the relationship between resistance and temperature
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.
Can you find the volumes of the mathematical vessels?
Use vectors and matrices to explore the symmetries of crystals.
Can you match these equations to these graphs?
How would you go about estimating populations of dolphins?
Are these estimates of physical quantities accurate?
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Which units would you choose best to fit these situations?
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?
When you change the units, do the numbers get bigger or smaller?
Look at the advanced way of viewing sin and cos through their power series.