Which line graph, equations and physical processes go together?
How much energy has gone into warming the planet?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Was it possible that this dangerous driving penalty was issued in error?
Get further into power series using the fascinating Bessel's equation.
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.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
When you change the units, do the numbers get bigger or smaller?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Build up the concept of the Taylor series
Get some practice using big and small numbers in chemistry.
Why MUST these statistical statements probably be at least a little bit wrong?
Explore the relationship between resistance and temperature
Analyse these beautiful biological images and attempt to rank them in size order.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Formulate and investigate a simple mathematical model for the design of a table mat.
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?
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?
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?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Look at the advanced way of viewing sin and cos through their power series.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
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?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Use vectors and matrices to explore the symmetries of crystals.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Explore how matrices can fix vectors and vector directions.
Explore the properties of matrix transformations with these 10 stimulating questions.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Can you make matrices which will fix one lucky vector and crush another to zero?
Explore the shape of a square after it is transformed by the action of a matrix.
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.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Which pdfs match the curves?
Which dilutions can you make using only 10ml pipettes?
Explore the properties of perspective drawing.
Can you match the charts of these functions to the charts of their integrals?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
How do you choose your planting levels to minimise the total loss at harvest time?
Who will be the first investor to pay off their debt?