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?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Invent scenarios which would give rise to these probability density functions.
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.
Which line graph, equations and physical processes go together?
Get further into power series using the fascinating Bessel's equation.
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 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.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
How much energy has gone into warming the planet?
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.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Build up the concept of the Taylor series
Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.
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?
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
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.
Get some practice using big and small numbers in chemistry.
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 properties of perspective drawing.
This problem explores the biology behind Rudolph's glowing red nose.
Explore how matrices can fix vectors and vector directions.
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.
Can you find the volumes of the mathematical vessels?
Use vectors and matrices to explore the symmetries of crystals.
Look at the advanced way of viewing sin and cos through their power series.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Are these estimates of physical quantities accurate?
When you change the units, do the numbers get bigger or smaller?
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?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
How would you go about estimating populations of dolphins?
Can you match these equations to these graphs?