Get further into power series using the fascinating Bessel's equation.
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.
Which line graph, equations and physical processes go together?
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 physical contexts.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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.
How much energy has gone into warming the planet?
When you change the units, do the numbers get bigger or smaller?
Get some practice using big and small numbers in chemistry.
Was it possible that this dangerous driving penalty was issued in error?
Why MUST these statistical statements probably be at least a little bit wrong?
Invent scenarios which would give rise to these probability density functions.
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?
Work out the numerical values for these physical quantities.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Which units would you choose best to fit these situations?
Build up the concept of the Taylor series
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?
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?
Formulate and investigate a simple mathematical model for the design of a table mat.
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.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Explore how matrices can fix vectors and vector directions.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Can you make matrices which will fix one lucky vector and crush another to zero?
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 trigonometry to determine whether solar eclipses on earth can be perfect.
Explore the shape of a square after it is transformed by the action of a matrix.
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?
Use vectors and matrices to explore the symmetries of crystals.
How do you choose your planting levels to minimise the total loss at harvest time?
Go on a vector walk and determine which points on the walk are closest to the origin.
Which pdfs match the curves?
Which of these infinitely deep vessels will eventually full up?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Explore the relationship between resistance and temperature
This problem explores the biology behind Rudolph's glowing red nose.
Analyse these beautiful biological images and attempt to rank them in size order.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
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?
Explore the properties of perspective drawing.
Match the descriptions of physical processes to these differential equations.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.