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?
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?
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.
Which line graph, equations and physical processes go together?
How much energy has gone into warming the planet?
How would you go about estimating populations of dolphins?
Go on a vector walk and determine which points on the walk are closest to the origin.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
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.
Get some practice using big and small numbers in chemistry.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Get further into power series using the fascinating Bessel's equation.
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.
Use vectors and matrices to explore the symmetries of crystals.
Which pdfs match the curves?
Can you find the volumes of the mathematical vessels?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Was it possible that this dangerous driving penalty was issued in error?
Can you make matrices which will fix one lucky vector and crush another to zero?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
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. . . .
Build up the concept of the Taylor series
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?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Are these estimates of physical quantities accurate?
Who will be the first investor to pay off their debt?
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?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
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.
Explore the properties of perspective drawing.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Can you work out what this procedure is doing?
Simple models which help us to investigate how epidemics grow and die out.
Explore the relationship between resistance and temperature
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.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Work out the numerical values for these physical quantities.
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?