Estimate areas using random grids
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
How do you choose your planting levels to minimise the total loss at harvest time?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Explore how matrices can fix vectors and vector directions.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Explore the shape of a square after it is transformed by the action of a matrix.
Explore the properties of matrix transformations with these 10 stimulating questions.
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.
Can you match the charts of these functions to the charts of their integrals?
Are these estimates of physical quantities accurate?
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?
Can you find the volumes of the mathematical vessels?
Can you construct a cubic equation with a certain distance between its turning points?
Which of these infinitely deep vessels will eventually full up?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Why MUST these statistical statements probably be at least a little bit wrong?
Use vectors and matrices to explore the symmetries of crystals.
Invent scenarios which would give rise to these probability density functions.
Which pdfs match the curves?
This problem explores the biology behind Rudolph's glowing red nose.
Analyse these beautiful biological images and attempt to rank them in size order.
Use your skill and judgement to match the sets of random data.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
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?
Who will be the first investor to pay off their debt?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Explore the properties of perspective drawing.
Is it really greener to go on the bus, or to buy local?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
How would you design the tiering of seats in a stadium so that all spectators have a good view?
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Can you work out which processes are represented by the graphs?
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?
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you work out what this procedure is doing?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Get some practice using big and small numbers in chemistry.
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.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
A problem about genetics and the transmission of disease.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
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?