What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Can you match the charts of these functions to the charts of their integrals?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Which pdfs match the curves?
Get further into power series using the fascinating Bessel's equation.
Why MUST these statistical statements probably be at least a little bit wrong?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Use vectors and matrices to explore the symmetries of crystals.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Work out the numerical values for these physical quantities.
How much energy has gone into warming the planet?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Explore the properties of matrix transformations with these 10 stimulating questions.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Invent scenarios which would give rise to these probability density functions.
Formulate and investigate a simple mathematical model for the design of a table mat.
Get some practice using big and small numbers in chemistry.
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?
Where should runners start the 200m race so that they have all run the same distance by the finish?
Build up the concept of the Taylor series
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
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.
Can you work out what this procedure is doing?
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 how matrices can fix vectors and vector directions.
Can you work out which processes are represented by the graphs?
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
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?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Is it really greener to go on the bus, or to buy local?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Go on a vector walk and determine which points on the walk are closest to the origin.
Explore the shape of a square after it is transformed by the action of a matrix.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Can you make matrices which will fix one lucky vector and crush another to zero?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Can you construct a cubic equation with a certain distance between its turning points?
Which line graph, equations and physical processes go together?
Various solids are lowered into a beaker of water. How does the water level rise in each case?
Explore the relationship between resistance and temperature
This problem explores the biology behind Rudolph's glowing red nose.