Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Does weight confer an advantage to shot putters?
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.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Have you ever wondered what it would be like to race against Usain Bolt?
Get further into power series using the fascinating Bessel's equation.
How do you choose your planting levels to minimise the total loss at harvest time?
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Which line graph, equations and physical processes go together?
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Use vectors and matrices to explore the symmetries of crystals.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
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 properties of matrix transformations with these 10 stimulating questions.
Explore the shape of a square after it is transformed by the action of a matrix.
Invent scenarios which would give rise to these probability density functions.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Get some practice using big and small numbers in chemistry.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
How would you design the tiering of seats in a stadium so that all spectators have a good view?
Which dilutions can you make using only 10ml pipettes?
Where should runners start the 200m race so that they have all run the same distance by the finish?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Which pdfs match the curves?
How would you go about estimating populations of dolphins?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Who will be the first investor to pay off their debt?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Are these estimates of physical quantities accurate?
When you change the units, do the numbers get bigger or smaller?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Analyse these beautiful biological images and attempt to rank them in size order.
Which units would you choose best to fit these situations?
Explore the relationship between resistance and temperature
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
A problem about genetics and the transmission of disease.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
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.
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.
Explore how matrices can fix vectors and vector directions.
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?
Can you work out what this procedure is doing?