Was it possible that this dangerous driving penalty was issued in error?
Which line graph, equations and physical processes go together?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Why MUST these statistical statements probably be at least a little bit wrong?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
How much energy has gone into warming the planet?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Get further into power series using the fascinating Bessel's equation.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Invent scenarios which would give rise to these probability density functions.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Match the descriptions of physical processes to these differential equations.
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?
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
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.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Can you make matrices which will fix one lucky vector and crush another to zero?
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.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Explore how matrices can fix vectors and vector directions.
Build up the concept of the Taylor series
Which units would you choose best to fit these situations?
Work out the numerical values for these physical quantities.
Get some practice using big and small numbers in chemistry.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Look at the advanced way of viewing sin and cos through their power series.
When you change the units, do the numbers get bigger or smaller?
Are these estimates of physical quantities accurate?
Who will be the first investor to pay off their debt?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Use vectors and matrices to explore the symmetries of crystals.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you sketch these difficult curves, which have uses in mathematical modelling?
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 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.
Have you ever wondered what it would be like to race against Usain Bolt?
How would you go about estimating populations of dolphins?