See how enormously large quantities can cancel out to give a good approximation to the factorial function.
How much energy has gone into warming the planet?
Look at the advanced way of viewing sin and cos through their power series.
Get further into power series using the fascinating Bessel's equation.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Match the descriptions of physical processes to these differential equations.
When you change the units, do the numbers get bigger or smaller?
Are these estimates of physical quantities accurate?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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?
Which units would you choose best to fit these situations?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Build up the concept of the Taylor series
Get some practice using big and small numbers in chemistry.
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Was it possible that this dangerous driving penalty was issued in error?
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?
Analyse these beautiful biological images and attempt to rank them in size order.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Invent scenarios which would give rise to these probability density functions.
Can you make matrices which will fix one lucky vector and crush another to zero?
Explore how matrices can fix vectors and vector directions.
Explore the shape of a square after it is transformed by the action of a matrix.
Why MUST these statistical statements probably be at least a little bit wrong?
Explore the properties of matrix transformations with these 10 stimulating questions.
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?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Can you match the charts of these functions to the charts of their integrals?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Formulate and investigate a simple mathematical model for the design of a table mat.
Explore the relationship between resistance and temperature
This problem explores the biology behind Rudolph's glowing red nose.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Which dilutions can you make using only 10ml pipettes?
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
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?
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?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Explore the meaning of the scalar and vector cross products and see how the two are related.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.