Was it possible that this dangerous driving penalty was issued in error?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
How much energy has gone into warming the planet?
Get further into power series using the fascinating Bessel's equation.
Use vectors and matrices to explore the symmetries of crystals.
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.
How would you go about estimating populations of dolphins?
Explore the properties of matrix transformations with these 10 stimulating questions.
Go on a vector walk and determine which points on the walk are closest to the origin.
Which pdfs match the curves?
Can you match the charts of these functions to the charts of their integrals?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Can you find the volumes of the mathematical vessels?
Can you make matrices which will fix one lucky vector and crush another to zero?
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?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Invent scenarios which would give rise to these probability density functions.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Who will be the first investor to pay off their debt?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Match the descriptions of physical processes to these differential equations.
This problem explores the biology behind Rudolph's glowing red nose.
Analyse these beautiful biological images and attempt to rank them in size order.
Are these estimates of physical quantities accurate?
Explore the properties of perspective drawing.
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?
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?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Explore the relationship between resistance and temperature
Which line graph, equations and physical processes go together?
Why MUST these statistical statements probably be at least a little bit wrong?
Build up the concept of the Taylor series
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?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Can you match these equations to these graphs?
Look at the advanced way of viewing sin and cos through their power series.
Can you work out which processes are represented by the graphs?
Formulate and investigate a simple mathematical model for the design of a table mat.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Can you work out what this procedure is doing?
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...