Use simple trigonometry to calculate the distance along the flight
path from London to Sydney.
Find the distance of the shortest air route at an altitude of 6000
metres between London and Cape Town given the latitudes and
longitudes. A simple application of scalar products of vectors.
Shows that Pythagoras for Spherical Triangles reduces to
Pythagoras's Theorem in the plane when the triangles are small
relative to the radius of the sphere.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
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?
Where should runners start the 200m race so that they have all run the same distance by the finish?
Which line graph, equations and physical processes go together?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
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.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Have you ever wondered what it would be like to race against Usain Bolt?
How would you go about estimating populations of dolphins?
Get further into power series using the fascinating Bessel's equation.
Was it possible that this dangerous driving penalty was issued in
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Why MUST these statistical statements probably be at least a little
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Can you work out what this procedure is doing?
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
Which dilutions can you make using only 10ml pipettes?
Explore the properties of perspective drawing.
Get some practice using big and small numbers in chemistry.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
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?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Go on a vector walk and determine which points on the walk are
closest to the origin.
How much energy has gone into warming the planet?
Look at the advanced way of viewing sin and cos through their power series.
Match the descriptions of physical processes to these differential
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
When you change the units, do the numbers get bigger or smaller?
Are these estimates of physical quantities accurate?
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
Build up the concept of the Taylor series
Explore the relationship between resistance and temperature
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
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?
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?
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Which units would you choose best to fit these situations?
Practice your skills of measurement and estimation using this interactive measurement tool based around fascinating images from biology.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
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.