Get further into power series using the fascinating Bessel's equation.
Which line graph, equations and physical processes go together?
How efficiently can you pack together disks?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Look at the advanced way of viewing sin and cos through their power series.
Work out the numerical values for these physical quantities.
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.
Where should runners start the 200m race so that they have all run the same distance by the finish?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
How much energy has gone into warming the planet?
Build up the concept of the Taylor series
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Why MUST these statistical statements probably be at least a little bit wrong?
Can you work out what this procedure is doing?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Here are several equations from real life. Can you work out which measurements are possible from each 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?
Was it possible that this dangerous driving penalty was issued in error?
Invent scenarios which would give rise to these probability density functions.
Analyse these beautiful biological images and attempt to rank them in size order.
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 the relationship between resistance and temperature
Which units would you choose best to fit these situations?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
When you change the units, do the numbers get bigger or smaller?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Go on a vector walk and determine which points on the walk are closest to the origin.
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?
If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Can you make matrices which will fix one lucky vector and crush another to zero?
This problem explores the biology behind Rudolph's glowing red nose.
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?
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Which dilutions can you make using only 10ml pipettes?
Explore the properties of perspective drawing.
Formulate and investigate a simple mathematical model for the design of a table mat.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Explore the shape of a square after it is transformed by the action of a matrix.