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?
Invent scenarios which would give rise to these probability density functions.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Can you construct a cubic equation with a certain distance between
its turning points?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Can you sketch these difficult curves, which have uses in
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
Explore the relationship between resistance and temperature
Look at the advanced way of viewing sin and cos through their power series.
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?
Which line graph, equations and physical processes go together?
Various solids are lowered into a beaker of water. How does the
water level rise in each case?
Can you find the volumes of the mathematical vessels?
Can you match these equations to these graphs?
Was it possible that this dangerous driving penalty was issued in
Can you draw the height-time chart as this complicated vessel fills
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.
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?
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Build up the concept of the Taylor series
Estimate areas using random grids
Match the descriptions of physical processes to these differential
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
A problem about genetics and the transmission of disease.
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.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Explore the shape of a square after it is transformed by the action
of a matrix.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
Explore how matrices can fix vectors and vector directions.
Explore the properties of matrix transformations with these 10 stimulating questions.
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.
How would you design the tiering of seats in a stadium so that all spectators have a good view?
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?