Match the charts of these functions to the charts of their integrals.
Can you sketch these difficult curves, which have uses in
Invent scenarios which would give rise to these probability density functions.
Match the descriptions of physical processes to these differential
Why MUST these statistical statements probably be at least a little
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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?
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.
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.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Which of these infinitely deep vessels will eventually full up?
Can you construct a cubic equation with a certain distance between
its turning points?
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?
Which line graph, equations and physical processes go together?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Get further into power series using the fascinating Bessel's equation.
Was it possible that this dangerous driving penalty was issued 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?
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?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Simple models which help us to investigate how epidemics grow and die out.
Get some practice using big and small numbers in chemistry.
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Which units would you choose best to fit these situations?
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?
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
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.
Build up the concept of the Taylor series
When you change the units, do the numbers get bigger or smaller?
Estimate areas using random grids
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
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.
A problem about genetics and the transmission of disease.
Explore the properties of perspective drawing.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Explore how matrices can fix vectors and vector directions.
Go on a vector walk and determine which points on the walk are
closest to the origin.
Can Jo make a gym bag for her trainers from the piece of fabric she has?
Explore the properties of matrix transformations with these 10 stimulating questions.
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.
Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
How would you design the tiering of seats in a stadium so that all spectators have a good view?
Explore the relationship between resistance and temperature