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?
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.
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?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Which line graph, equations and physical processes go together?
Can you sketch these difficult curves, which have uses in mathematical modelling?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
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.
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
How do you choose your planting levels to minimise the total loss at harvest time?
Which pdfs match the curves?
Work out the numerical values for these physical quantities.
Get some practice using big and small numbers in chemistry.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Can you find the volumes of the mathematical vessels?
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.
Was it possible that this dangerous driving penalty was issued in error?
Use vectors and matrices to explore the symmetries of crystals.
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?
Go on a vector walk and determine which points on the walk are closest to the origin.
Explore the properties of matrix transformations with these 10 stimulating questions.
Explore the shape of a square after it is transformed by the action of a matrix.
This problem explores the biology behind Rudolph's glowing red nose.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Can you make matrices which will fix one lucky vector and crush another to zero?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Which of these infinitely deep vessels will eventually full up?
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Are these estimates of physical quantities accurate?
Look at the advanced way of viewing sin and cos through their power series.
Build up the concept of the Taylor series
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Who will be the first investor to pay off their debt?
Explore the properties of perspective drawing.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
How would you go about estimating populations of dolphins?
Match the descriptions of physical processes to these differential equations.
Can you work out what this procedure is doing?
Analyse these beautiful biological images and attempt to rank them in size order.
Explore how matrices can fix vectors and vector directions.
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