Was it possible that this dangerous driving penalty was issued in error?
Invent scenarios which would give rise to these probability density functions.
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.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Can you find the volumes of the mathematical vessels?
How much energy has gone into warming the planet?
Which of these infinitely deep vessels will eventually full up?
Match the charts of these functions to the charts of their integrals.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
How would you go about estimating populations of dolphins?
Get further into power series using the fascinating Bessel's equation.
Why MUST these statistical statements probably be at least a little bit wrong?
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?
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 shape of a square after it is transformed by the action of a matrix.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Can you make matrices which will fix one lucky vector and crush another to zero?
Are these estimates of physical quantities accurate?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Use vectors and matrices to explore the symmetries of crystals.
Which pdfs match the curves?
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.
Who will be the first investor to pay off their debt?
Analyse these beautiful biological images and attempt to rank them in size order.
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.
Work out the numerical values for these physical quantities.
Match the descriptions of physical processes to these differential equations.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Get some practice using big and small numbers in chemistry.
Which line graph, equations and physical processes go together?
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?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
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.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Build up the concept of the Taylor series
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
How do you choose your planting levels to minimise the total loss at harvest time?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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 construct a cubic equation with a certain distance between its turning points?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Explore the relationship between resistance and temperature
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Look at the advanced way of viewing sin and cos through their power series.