What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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?
Which line graph, equations and physical processes go together?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Why MUST these statistical statements probably be at least a little
Can you draw the height-time chart as this complicated vessel fills
Work out the numerical values for these physical quantities.
Can you match these equations to these graphs?
Get further into power series using the fascinating Bessel's equation.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
Imagine different shaped vessels being filled. Can you work out
what the graphs of the water level should look like?
Where should runners start the 200m race so that they have all run the same distance by the finish?
Get some practice using big and small numbers in chemistry.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Go on a vector walk and determine which points on the walk are
closest to the origin.
Invent scenarios which would give rise to these probability density functions.
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
How much energy has gone into warming the planet?
Look at the advanced way of viewing sin and cos through their power series.
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Explore the relationship between resistance and temperature
Match the descriptions of physical processes to these differential
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
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?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Can you work out which processes are represented by the graphs?
Formulate and investigate a simple mathematical model for the design of a table mat.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
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 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 sketch these difficult curves, which have uses in
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Explore the meaning of the scalar and vector cross products and see
how the two are related.
Various solids are lowered into a beaker of water. How does the
water level rise in each case?
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?
Analyse these beautiful biological images and attempt to rank them in size order.
Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .
How efficiently can you pack together disks?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
How would you go about estimating populations of dolphins?
Which units would you choose best to fit these situations?