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.
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.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
How much energy has gone into warming the planet?
Get further into power series using the fascinating Bessel's equation.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
How do you choose your planting levels to minimise the total loss at harvest time?
Which line graph, equations and physical processes go together?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Explore the properties of matrix transformations with these 10 stimulating questions.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Build up the concept of the Taylor series
Was it possible that this dangerous driving penalty was issued in error?
Formulate and investigate a simple mathematical model for the design of a table mat.
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 out the numerical values for these physical quantities.
Use vectors and matrices to explore the symmetries of crystals.
Which pdfs match the curves?
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?
Can you construct a cubic equation with a certain distance between its turning points?
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.
Explore the shape of a square after it is transformed by the action of a matrix.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Explore how matrices can fix vectors and vector directions.
Get some practice using big and small numbers in chemistry.
Can you work out what this procedure is doing?
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?
Simple models which help us to investigate how epidemics grow and die out.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Which of these infinitely deep vessels will eventually full up?
Can you find the volumes of the mathematical vessels?
Are these estimates of physical quantities accurate?
Explore the relationship between resistance and temperature
This problem explores the biology behind Rudolph's glowing red nose.
Analyse these beautiful biological images and attempt to rank them in size order.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
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.
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 equations.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Explore the properties of perspective drawing.