Match the descriptions of physical processes to these differential
Get further into power series using the fascinating Bessel's equation.
Look at the advanced way of viewing sin and cos through their power series.
Match the charts of these functions to the charts of their integrals.
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
Was it possible that this dangerous driving penalty was issued in
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Why MUST these statistical statements probably be at least a little
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Get some practice using big and small numbers in chemistry.
Invent scenarios which would give rise to these probability density functions.
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?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
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.
Build up the concept of the Taylor series
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?
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?
How would you go about estimating populations of dolphins?
Explore the relationship between resistance and temperature
Here are several equations from real life. Can you work out which measurements are possible from each equation?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
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.
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Are these estimates of physical quantities accurate?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Go on a vector walk and determine which points on the walk are
closest to the origin.
Various solids are lowered into a beaker of water. How does the
water level rise in each case?
Can you work out what this procedure is doing?
When you change the units, do the numbers get bigger or smaller?
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
Which units would you choose best to fit these situations?
Analyse these beautiful biological images and attempt to rank them in size order.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
This problem explores the biology behind Rudolph's glowing red nose.
Explore the shape of a square after it is transformed by the action
of a matrix.
Can you sketch these difficult curves, which have uses in
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Explore the properties of matrix transformations with these 10 stimulating questions.
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
Explore how matrices can fix vectors and vector directions.
Can you work out which processes are represented by the graphs?
How would you design the tiering of seats in a stadium so that all spectators have a good view?
Simple models which help us to investigate how epidemics grow and die out.