Can you work out what this procedure is doing?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Get further into power series using the fascinating Bessel's equation.
Which line graph, equations and physical processes go together?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
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?
Work out the numerical values for these physical quantities.
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Get some practice using big and small numbers in chemistry.
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
Where should runners start the 200m race so that they have all run the same distance by the finish?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Look at the advanced way of viewing sin and cos through their power series.
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.
How much energy has gone into warming the planet?
This problem explores the biology behind Rudolph's glowing red nose.
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Build up the concept of the Taylor series
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Have you ever wondered what it would be like to race against Usain Bolt?
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.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.
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. . . .
Why MUST these statistical statements probably be at least a little
Use trigonometry to determine whether solar eclipses on earth can be perfect.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Analyse these beautiful biological images and attempt to rank them in size order.
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?
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
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 draw the height-time chart as this complicated vessel fills
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
Does weight confer an advantage to shot putters?
Imagine different shaped vessels being filled. Can you work out
what the graphs of the water level should look like?
Which units would you choose best to fit these situations?
How efficiently can you pack together disks?
Which dilutions can you make using only 10ml pipettes?
Explore the properties of perspective drawing.
When you change the units, do the numbers get bigger or smaller?
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Are these estimates of physical quantities accurate?