Invent scenarios which would give rise to these probability density functions.
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?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Get further into power series using the fascinating Bessel's equation.
Which line graph, equations and physical processes go together?
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.
Was it possible that this dangerous driving penalty was issued in error?
How much energy has gone into warming the planet?
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?
Explore the meaning of the scalar and vector cross products and see how the two are related.
How would you go about estimating populations of dolphins?
Use vectors and matrices to explore the symmetries of crystals.
Get some practice using big and small numbers in chemistry.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Match the charts of these functions to the charts of their integrals.
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.
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?
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.
Can you find the volumes of the mathematical vessels?
Which pdfs match the curves?
Explore the shape of a square after it is transformed by the action of a matrix.
Can you make matrices which will fix one lucky vector and crush another to zero?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
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.
Look at the advanced way of viewing sin and cos through their power series.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
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.
Match the descriptions of physical processes to these differential equations.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Who will be the first investor to pay off their debt?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
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?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Are these estimates of physical quantities accurate?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
This problem explores the biology behind Rudolph's glowing red nose.
Analyse these beautiful biological images and attempt to rank them in size order.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
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. . . .
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Simple models which help us to investigate how epidemics grow and die out.