Match the charts of these functions to the charts of their integrals.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
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?
Get further into power series using the fascinating Bessel's equation.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
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?
Why MUST these statistical statements probably be at least a little
Invent scenarios which would give rise to these probability density functions.
Can you sketch these difficult curves, which have uses in
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Match the descriptions of physical processes to these differential
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
How much energy has gone into warming the planet?
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?
Explore the relationship between resistance and temperature
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Which of these infinitely deep vessels will eventually full up?
Various solids are lowered into a beaker of water. How does the
water level rise in each case?
Which line graph, equations and physical processes go together?
Can you find the volumes of the mathematical vessels?
Build up the concept of the Taylor series
Was it possible that this dangerous driving penalty was issued in
Can you draw the height-time chart as this complicated vessel fills
Work out the numerical values for these physical quantities.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Can you work out which processes are represented by the graphs?
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
Imagine different shaped vessels being filled. Can you work out
what the graphs of the water level should look like?
Can you work out what this procedure is doing?
Get some practice using big and small numbers in chemistry.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Estimate areas using random grids
Can you match these equations to these graphs?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Who will be the first investor to pay off their debt?
A problem about genetics and the transmission of disease.
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
This problem explores the biology behind Rudolph's glowing red
Explore the shape of a square after it is transformed by the action
of a matrix.
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?
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
Explore how matrices can fix vectors and vector directions.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?