Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Get further into power series using the fascinating Bessel's equation.
Was it possible that this dangerous driving penalty was issued in error?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Which line graph, equations and physical processes go together?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
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.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in 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.
Build up the concept of the Taylor series
How do you choose your planting levels to minimise the total loss at harvest time?
Use vectors and matrices to explore the symmetries of crystals.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Why MUST these statistical statements probably be at least a little bit wrong?
Analyse these beautiful biological images and attempt to rank them in size order.
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?
Which pdfs match the curves?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
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.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
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?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Can you sketch these difficult curves, which have uses in mathematical modelling?
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Which of these infinitely deep vessels will eventually full up?
Explore the relationship between resistance and temperature
Can you find the volumes of the mathematical vessels?
How would you go about estimating populations of dolphins?
Match the descriptions of physical processes to these differential equations.
Are these estimates of physical quantities accurate?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Which units would you choose best to fit these situations?
When you change the units, do the numbers get bigger or smaller?