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.
Invent scenarios which would give rise to these probability density functions.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
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?
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?
Work out the numerical values for these physical quantities.
Use vectors and matrices to explore the symmetries of crystals.
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?
How do you choose your planting levels to minimise the total loss at harvest time?
Match the charts of these functions to the charts of their integrals.
Can you find the volumes of the mathematical vessels?
Which of these infinitely deep vessels will eventually full up?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Get further into power series using the fascinating Bessel's equation.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Get some practice using big and small numbers in chemistry.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
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 properties of perspective drawing.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Explore how matrices can fix vectors and vector directions.
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.
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.
Can you make matrices which will fix one lucky vector and crush another to zero?
Which line graph, equations and physical processes go together?
Look at the advanced way of viewing sin and cos through their power series.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Are these estimates of physical quantities accurate?
Who will be the first investor to pay off their debt?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Match the descriptions of physical processes to these differential equations.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
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?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Estimate areas using random grids
Can you work out what this procedure is doing?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Here are several equations from real life. Can you work out which measurements are possible from each equation?