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.
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?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Was it possible that this dangerous driving penalty was issued in error?
Which line graph, equations and physical processes go together?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Use vectors and matrices to explore the symmetries of crystals.
How much energy has gone into warming the planet?
Can you find the volumes of the mathematical vessels?
Match the charts of these functions to the charts of their integrals.
Get further into power series using the fascinating Bessel's equation.
Which of these infinitely deep vessels will eventually full up?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Get some practice using big and small numbers in chemistry.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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.
Explore how matrices can fix vectors and vector directions.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
How would you go about estimating populations of dolphins?
Can you make matrices which will fix one lucky vector and crush another to zero?
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.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Which pdfs match the curves?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Are these estimates of physical quantities accurate?
When you change the units, do the numbers get bigger or smaller?
Look at the advanced way of viewing sin and cos through their power series.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Analyse these beautiful biological images and attempt to rank them in size order.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
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?
Which units would you choose best to fit these situations?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
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?
Explore the properties of perspective drawing.
Explore the relationship between resistance and temperature
Match the descriptions of physical processes to these differential equations.
Formulate and investigate a simple mathematical model for the design of a table mat.