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?
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.
Invent scenarios which would give rise to these probability density functions.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Which line graph, equations and physical processes go together?
Get further into power series using the fascinating Bessel's equation.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
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?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Can you sketch these difficult curves, which have uses in mathematical modelling?
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.
Simple models which help us to investigate how epidemics grow and die out.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
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?
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
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.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Which pdfs match the curves?
Build up the concept of the Taylor series
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?
Use vectors and matrices to explore the symmetries of crystals.
10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?
Which dilutions can you make using only 10ml pipettes?
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Explore the meaning of the scalar and vector cross products and see how the two are related.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Go on a vector walk and determine which points on the walk are closest to the origin.
Formulate and investigate a simple mathematical model for the design of a table mat.
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?
Analyse these beautiful biological images and attempt to rank them in size order.
This problem explores the biology behind Rudolph's glowing red nose.
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. . . .
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
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.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
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.
Explore the properties of perspective drawing.
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.
Who will be the first investor to pay off their debt?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Can you match these equations to these graphs?
How would you go about estimating populations of dolphins?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.