Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Get further into power series using the fascinating Bessel's equation.
Look at the advanced way of viewing sin and cos through their power series.
Get some practice using big and small numbers in chemistry.
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
Who will be the first investor to pay off their debt?
Work out the numerical values for these physical quantities.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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.
Which line graph, equations and physical processes go together?
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Build up the concept of the Taylor series
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Why MUST these statistical statements probably be at least a little bit wrong?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Which units would you choose best to fit these situations?
Explore the relationship between resistance and temperature
Invent scenarios which would give rise to these probability density functions.
Was it possible that this dangerous driving penalty was issued in error?
Explore the shape of a square after it is transformed by the action of a matrix.
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?
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?
Explore the properties of matrix transformations with these 10 stimulating questions.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Match the descriptions of physical processes to these differential equations.
When you change the units, do the numbers get bigger or smaller?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Go on a vector walk and determine which points on the walk are closest to the origin.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Use vectors and matrices to explore the symmetries of crystals.
This problem explores the biology behind Rudolph's glowing red nose.
Can you make matrices which will fix one lucky vector and crush another to zero?
Explore how matrices can fix vectors and vector directions.
Formulate and investigate a simple mathematical model for the design of a table mat.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
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?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Which dilutions can you make using only 10ml pipettes?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Explore the properties of perspective drawing.
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?
How efficiently can you pack together disks?
Are these estimates of physical quantities accurate?