Get some practice using big and small numbers in chemistry.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Look at the advanced way of viewing sin and cos through their power series.
How much energy has gone into warming the planet?
Get further into power series using the fascinating Bessel's equation.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
When you change the units, do the numbers get bigger or smaller?
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 line graph, equations and physical processes go together?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Build up the concept of the Taylor series
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Which units would you choose best to fit these situations?
Invent scenarios which would give rise to these probability density functions.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Was it possible that this dangerous driving penalty was issued in error?
Which dilutions can you make using only 10ml pipettes?
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.
Which pdfs match the curves?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
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?
Match the descriptions of physical processes to these differential equations.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Explore the relationship between resistance and temperature
Explore the meaning of the scalar and vector cross products and see how the two are related.
Go on a vector walk and determine which points on the walk are closest to the origin.
Explore the properties of matrix transformations with these 10 stimulating questions.
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.
Is it really greener to go on the bus, or to buy local?
Explore the shape of a square after it is transformed by the action of a matrix.
Can you make matrices which will fix one lucky vector and crush another to zero?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Analyse these beautiful biological images and attempt to rank them in size order.
This problem explores the biology behind Rudolph's glowing red nose.
Can you work out what this procedure is doing?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Explore how matrices can fix vectors and vector directions.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.