Which line graph, equations and physical processes go together?
Get further into power series using the fascinating Bessel's equation.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
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.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Why MUST these statistical statements probably be at least a little bit wrong?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
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 suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Match the charts of these functions to the charts of their integrals.
Was it possible that this dangerous driving penalty was issued in error?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Work out the numerical values for these physical quantities.
Invent scenarios which would give rise to these probability density functions.
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
Look at the advanced way of viewing sin and cos through their power series.
Can you construct a cubic equation with a certain distance between its turning points?
Can you make matrices which will fix one lucky vector and crush another to zero?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Which of these infinitely deep vessels will eventually full up?
Can you find the volumes of the mathematical vessels?
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.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Which pdfs match the curves?
Explore the relationship between resistance and temperature
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.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
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?
Who will be the first investor to pay off their debt?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Are these estimates of physical quantities accurate?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
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.
Explore the properties of perspective drawing.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Match the descriptions of physical processes to these differential equations.
When you change the units, do the numbers get bigger or smaller?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Formulate and investigate a simple mathematical model for the design of a table mat.
How would you go about estimating populations of dolphins?
Go on a vector walk and determine which points on the walk are closest to the origin.