This problem explores the biology behind Rudolph's glowing red nose.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Get further into power series using the fascinating Bessel's equation.
Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?
How would you go about estimating populations of dolphins?
Which units would you choose best to fit these situations?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
How much energy has gone into warming the planet?
When you change the units, do the numbers get bigger or smaller?
Are these estimates of physical quantities accurate?
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
Look at the advanced way of viewing sin and cos through their power series.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Get some practice using big and small numbers in chemistry.
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?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Analyse these beautiful biological images and attempt to rank them in size order.
Which dilutions can you make using only 10ml pipettes?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Build up the concept of the Taylor series
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Work out the numerical values for these physical quantities.
Use vectors and matrices to explore the symmetries of crystals.
Which line graph, equations and physical processes go together?
Which pdfs match the curves?
Which of these infinitely deep vessels will eventually full up?
Can you find the volumes of the mathematical vessels?
Can you draw the height-time chart as this complicated vessel fills with water?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Was it possible that this dangerous driving penalty was issued in error?
Explore the properties of matrix transformations with these 10 stimulating questions.
Can you match the charts of these functions to the charts of their integrals?
Who will be the first investor to pay off their debt?
Explore the relationship between resistance and temperature
Can you work out which processes are represented by the graphs?
Match the descriptions of physical processes to these differential equations.
A problem about genetics and the transmission of disease.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Can you match these equations to these graphs?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Invent scenarios which would give rise to these probability density functions.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Use trigonometry to determine whether solar eclipses on earth can be perfect.