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.
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.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Explore the properties of matrix transformations with these 10 stimulating questions.
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?
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.
Which line graph, equations and physical processes go together?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
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.
Go on a vector walk and determine which points on the walk are closest to the origin.
Can you match these equations to these graphs?
How would you go about estimating populations of dolphins?
How efficiently can you pack together disks?
Look at the advanced way of viewing sin and cos through their power series.
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.
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.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
When you change the units, do the numbers get bigger or smaller?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
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.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Are these estimates of physical quantities accurate?
Explore the properties of perspective drawing.
Explore the shape of a square after it is transformed by the action of a matrix.
Explore how matrices can fix vectors and vector directions.
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?