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?
Get further into power series using the fascinating Bessel's equation.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Look at the advanced way of viewing sin and cos through their power series.
Can you construct a cubic equation with a certain distance between its turning points?
Which line graph, equations and physical processes go together?
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.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
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.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Can you find the volumes of the mathematical vessels?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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.
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.
Match the charts of these functions to the charts of their integrals.
Was it possible that this dangerous driving penalty was issued in error?
Invent scenarios which would give rise to these probability density functions.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Go on a vector walk and determine which points on the walk are closest to the origin.
Explore the relationship between resistance and temperature
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Analyse these beautiful biological images and attempt to rank them in size order.
How would you go about estimating populations of dolphins?
Work out the numerical values for these physical quantities.
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.
Why MUST these statistical statements probably be at least a little bit wrong?
Can you work out what this procedure is doing?
Are these estimates of physical quantities accurate?
Match the descriptions of physical processes to these differential equations.
Can you match these equations to these graphs?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
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?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
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?
Can you work out which processes are represented by the graphs?
Where should runners start the 200m race so that they have all run the same distance by the finish?
How would you design the tiering of seats in a stadium so that all spectators have a good view?
Which dilutions can you make using only 10ml pipettes?
Explore the properties of matrix transformations with these 10 stimulating questions.
Explore the properties of perspective drawing.