Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Here are several equations from real life. Can you work out which measurements are possible from each equation?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Get further into power series using the fascinating Bessel's equation.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
How efficiently can you pack together disks?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Which line graph, equations and physical processes go together?
Work out the numerical values for these physical quantities.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Which dilutions can you make using only 10ml pipettes?
Get some practice using big and small numbers in chemistry.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Look at the advanced way of viewing sin and cos through their power series.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
How much energy has gone into warming the planet?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Explore the relationship between resistance and temperature
Build up the concept of the Taylor series
Explore the properties of matrix transformations with these 10 stimulating questions.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Go on a vector walk and determine which points on the walk are closest to the origin.
Can you make matrices which will fix one lucky vector and crush another to zero?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Use vectors and matrices to explore the symmetries of crystals.
Why MUST these statistical statements probably be at least a little bit wrong?
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?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Explore the shape of a square after it is transformed by the action of a matrix.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?
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?
Explore the properties of perspective drawing.
Where should runners start the 200m race so that they have all run the same distance by the finish?
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
This problem explores the biology behind Rudolph's glowing red nose.
Which pdfs match the curves?
Invent scenarios which would give rise to these probability density functions.
Analyse these beautiful biological images and attempt to rank them in size order.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Explore how matrices can fix vectors and vector directions.
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.
Which units would you choose best to fit these situations?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.