Match the charts of these functions to the charts of their integrals.
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
Can you construct a cubic equation with a certain distance between
its turning points?
Can you sketch these difficult curves, which have uses in
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?
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 suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Was it possible that this dangerous driving penalty was issued in
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?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Can you find the volumes of the mathematical vessels?
Get some practice using big and small numbers in chemistry.
Estimate areas using random grids
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Which line graph, equations and physical processes go together?
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
How much energy has gone into warming the planet?
Match the descriptions of physical processes to these differential
Build up the concept of the Taylor series
Look at the advanced way of viewing sin and cos through their power series.
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
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.
Go on a vector walk and determine which points on the walk are
closest to the origin.
How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Explore the properties of matrix transformations with these 10 stimulating questions.
Can you make matrices which will fix one lucky vector and crush another to zero?
Simple models which help us to investigate how epidemics grow and die out.
Use vectors and matrices to explore the symmetries of crystals.
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.
Who will be the first investor to pay off their debt?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
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.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Explore the relationship between resistance and temperature
Can you work out what this procedure is doing?
Can you work out which processes are represented by the graphs?
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?
A problem about genetics and the transmission of disease.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Explore how matrices can fix vectors and vector directions.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Analyse these beautiful biological images and attempt to rank them in size order.