Match the charts of these functions to the charts of their integrals.
Can you construct a cubic equation with a certain distance between
its turning points?
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
Match the descriptions of physical processes to these differential
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?
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 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
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Can you find the volumes of the mathematical vessels?
Get further into power series using the fascinating Bessel's equation.
Get some practice using big and small numbers in chemistry.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
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.
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?
How much energy has gone into warming the planet?
Estimate areas using random grids
Look at the advanced way of viewing sin and cos through their power series.
Build up the concept of the Taylor series
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
Explore the shape of a square after it is transformed by the action
of a matrix.
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?
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.
Explore the properties of matrix transformations with these 10 stimulating questions.
Go on a vector walk and determine which points on the walk are
closest to the origin.
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.
Use vectors and matrices to explore the symmetries of crystals.
Are these estimates of physical quantities accurate?
Can you make matrices which will fix one lucky vector and crush another to zero?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Analyse these beautiful biological images and attempt to rank them in size order.
A problem about genetics and the transmission of disease.
Can you work out which processes are represented by the graphs?
Can you work out what this procedure is doing?
Formulate and investigate a simple mathematical model for the design of a table mat.
Explore the relationship between resistance and temperature
Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .
This problem explores the biology behind Rudolph's glowing red nose.
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.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...