Which line graph, equations and physical processes go together?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
When you change the units, do the numbers get bigger or smaller?
Get some practice using big and small numbers in chemistry.
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.
Get further into power series using the fascinating Bessel's equation.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
How much energy has gone into warming the planet?
Work out the numerical values for these physical quantities.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
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
Look at the advanced way of viewing sin and cos through their power series.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
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?
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?
Build up the concept of the Taylor series
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Formulate and investigate a simple mathematical model for the design of a table mat.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
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?
Why MUST these statistical statements probably be at least a little bit wrong?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Explore the relationship between resistance and temperature
Analyse these beautiful biological images and attempt to rank them in size order.
Invent scenarios which would give rise to these probability density functions.
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 how matrices can fix vectors and vector directions.
Which dilutions can you make using only 10ml pipettes?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Match the descriptions of physical processes to these differential equations.
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.
Is it really greener to go on the bus, or to buy local?
Explore the properties of matrix transformations with these 10 stimulating questions.
Use vectors and matrices to explore the symmetries of crystals.
Can you work out what this procedure is doing?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Can you make matrices which will fix one lucky vector and crush another to zero?
Go on a vector walk and determine which points on the walk are closest to the origin.
Which pdfs match the curves?
Can you match the charts of these functions to the charts of their integrals?
How do you choose your planting levels to minimise the total loss at harvest time?
This problem explores the biology behind Rudolph's glowing red nose.