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?
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.
How would you go about estimating populations of dolphins?
Look at the advanced way of viewing sin and cos through their power series.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
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.
Can you find the volumes of the mathematical vessels?
Work out the numerical values for these physical quantities.
Get some practice using big and small numbers in chemistry.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Which dilutions can you make using only 10ml pipettes?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Explore the shape of a square after it is transformed by the action of a matrix.
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.
Which line graph, equations and physical processes go together?
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.
Match the descriptions of physical processes to these differential equations.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Build up the concept of the Taylor series
Explore the relationship between resistance and temperature
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Go on a vector walk and determine which points on the walk are closest to the origin.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Can you make matrices which will fix one lucky vector and crush another to zero?
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?
Why MUST these statistical statements probably be at least a little bit wrong?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Explore the properties of matrix transformations with these 10 stimulating questions.
Estimate areas using random grids
Starting with two basic vector steps, which destinations can you reach on a vector walk?
A problem about genetics and the transmission of disease.
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?
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.
Formulate and investigate a simple mathematical model for the design of a table mat.
This problem explores the biology behind Rudolph's glowing red nose.
Invent scenarios which would give rise to these probability density functions.
Which pdfs match the curves?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
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.
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?
When you change the units, do the numbers get bigger or smaller?
Match the charts of these functions to the charts of their integrals.