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?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Invent scenarios which would give rise to these probability density functions.
Can you sketch these difficult curves, which have uses in
Why MUST these statistical statements probably be at least a little
Match the descriptions of physical processes to these differential
Can you construct a cubic equation with a certain distance between
its turning points?
Look at the advanced way of viewing sin and cos through their power series.
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?
Get further into power series using the fascinating Bessel's equation.
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?
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?
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?
Was it possible that this dangerous driving penalty was issued in
Can you draw the height-time chart as this complicated vessel fills
Which of these infinitely deep vessels will eventually full up?
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Can you work out what this procedure is doing?
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?
Get some practice using big and small numbers in chemistry.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
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?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Can you match these equations to these graphs?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Work out the numerical values for these physical quantities.
How much energy has gone into warming the planet?
Build up the concept of the Taylor series
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Estimate areas using random grids
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Use simple trigonometry to calculate the distance along the flight
path from London to Sydney.
Shows that Pythagoras for Spherical Triangles reduces to
Pythagoras's Theorem in the plane when the triangles are small
relative to the radius of the sphere.
A problem about genetics and the transmission of disease.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Explore the properties of matrix transformations with these 10 stimulating questions.
How would you go about estimating populations of dolphins?
Explore the shape of a square after it is transformed by the action
of a matrix.
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
Explore how matrices can fix vectors and vector directions.
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.
If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.