An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Go on a vector walk and determine which points on the walk are closest to the origin.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
How would you go about estimating populations of dolphins?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Get further into power series using the fascinating Bessel's equation.
Was it possible that this dangerous driving penalty was issued in error?
Can you work out which processes are represented by the graphs?
Can you find the volumes of the mathematical vessels?
Get some practice using big and small numbers in chemistry.
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
How efficiently can you pack together disks?
Which line graph, equations and physical processes go together?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
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?
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.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Can you match these equations to these graphs?
Which units would you choose best to fit these situations?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
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.
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.
Where should runners start the 200m race so that they have all run the same distance by the finish?
Use simple trigonometry to calculate the distance along the flight path from London to Sydney.
Build up the concept of the Taylor series
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.
Match the descriptions of physical processes to these differential equations.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
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
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
When you change the units, do the numbers get bigger or smaller?
Who will be the first investor to pay off their debt?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Are these estimates of physical quantities accurate?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Explore the properties of matrix transformations with these 10 stimulating questions.
The design technology curriculum requires students to be able to represent 3-dimensional objects on paper. This article introduces some of the mathematical ideas which underlie such methods.
Explore how matrices can fix vectors and vector directions.
Explore the properties of perspective drawing.