Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Get some practice using big and small numbers in chemistry.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
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?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Formulate and investigate a simple mathematical model for the design of a table mat.
When you change the units, do the numbers get bigger or smaller?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
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?
Which units would you choose best to fit these situations?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Which line graph, equations and physical processes go together?
Why MUST these statistical statements probably be at least a little bit wrong?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Which dilutions can you make using only 10ml pipettes?
Explore the relationship between resistance and temperature
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.
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?
Invent scenarios which would give rise to these probability density functions.
Build up the concept of the Taylor series
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Is it really greener to go on the bus, or to buy local?
Was it possible that this dangerous driving penalty was issued in error?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Look at the advanced way of viewing sin and cos through their power series.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Go on a vector walk and determine which points on the walk are closest to the origin.
Explore how matrices can fix vectors and vector directions.
Can you make matrices which will fix one lucky vector and crush another to zero?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Use vectors and matrices to explore the symmetries of crystals.
Explore the shape of a square after it is transformed by the action of a matrix.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Explore the properties of matrix transformations with these 10 stimulating questions.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Which pdfs match the curves?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
This problem explores the biology behind Rudolph's glowing red nose.