Can you sketch these difficult curves, which have uses in mathematical modelling?
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?
Are these estimates of physical quantities accurate?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Look at the advanced way of viewing sin and cos through their power series.
Get further into power series using the fascinating Bessel's equation.
Which line graph, equations and physical processes go together?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
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.
Can you construct a cubic equation with a certain distance between its turning points?
How much energy has gone into warming the planet?
Build up the concept of the Taylor series
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Explore the relationship between resistance and temperature
Use trigonometry to determine whether solar eclipses on earth can be perfect.
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.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Match the charts of these functions to the charts of their integrals.
Was it possible that this dangerous driving penalty was issued in error?
Why MUST these statistical statements probably be at least a little bit wrong?
Invent scenarios which would give rise to these probability density functions.
Work out the numerical values for these physical quantities.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Can you work out which processes are represented by the graphs?
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?
Where should runners start the 200m race so that they have all run the same distance by the finish?
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?
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.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Get some practice using big and small numbers in chemistry.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Analyse these beautiful biological images and attempt to rank them in size order.
Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.
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?
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
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
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 match these equations to these graphs?
Match the descriptions of physical processes to these differential equations.
How would you go about estimating populations of dolphins?
When you change the units, do the numbers get bigger or smaller?
A problem about genetics and the transmission of disease.
Use simple trigonometry to calculate the distance along the flight path from London to Sydney.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Explore the shape of a square after it is transformed by the action of a matrix.