How efficiently can you pack together disks?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Where should runners start the 200m race so that they have all run the same distance by the finish?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
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.
Have you ever wondered what it would be like to race against Usain Bolt?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Was it possible that this dangerous driving penalty was issued in error?
Can you find the volumes of the mathematical vessels?
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.
Various solids are lowered into a beaker of water. How does the water level rise in each case?
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Which line graph, equations and physical processes go together?
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?
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Get further into power series using the fascinating Bessel's equation.
Is it really greener to go on the bus, or to buy local?
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?
Can you make matrices which will fix one lucky vector and crush another to zero?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Explore how matrices can fix vectors and vector directions.
Go on a vector walk and determine which points on the walk are closest to the origin.
Explore the properties of matrix transformations with these 10 stimulating questions.
Formulate and investigate a simple mathematical model for the design of a table mat.
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?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
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.
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.
Explore the properties of perspective drawing.
Use simple trigonometry to calculate the distance along the flight path from London to Sydney.
Build up the concept of the Taylor series
Which dilutions can you make using only 10ml pipettes?
Match the descriptions of physical processes to these differential equations.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
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.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
How would you go about estimating populations of dolphins?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?