Was it possible that this dangerous driving penalty was issued in error?
Get further into power series using the fascinating Bessel's equation.
How much energy has gone into warming the planet?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Invent scenarios which would give rise to these probability density functions.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
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 biological contexts.
Can you find the volumes of the mathematical vessels?
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?
Match the charts of these functions to the charts of their integrals.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Why MUST these statistical statements probably be at least a little bit wrong?
Which of these infinitely deep vessels will eventually full up?
Use vectors and matrices to explore the symmetries of crystals.
How do you choose your planting levels to minimise the total loss at harvest time?
Can you construct a cubic equation with a certain distance between its turning points?
Work out the numerical values for these physical quantities.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Explore how matrices can fix vectors and vector directions.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Get some practice using big and small numbers in chemistry.
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 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.
Can you make matrices which will fix one lucky vector and crush another to zero?
Explore the meaning of the scalar and vector cross products and see how the two are related.
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.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Which pdfs match the curves?
Are these estimates of physical quantities accurate?
Build up the concept of the Taylor series
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?
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.
Look at the advanced way of viewing sin and cos through their power 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?
Analyse these beautiful biological images and attempt to rank them in size order.
How would you go about estimating populations of dolphins?
Explore the relationship between resistance and temperature
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Can you work out what this procedure is doing?
A problem about genetics and the transmission of disease.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?