Match the charts of these functions to the charts of their integrals.
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 sketch these difficult curves, which have uses in
Why MUST these statistical statements probably be at least a little
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
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?
Match the descriptions of physical processes to these differential
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.
Can you find the volumes of the mathematical vessels?
Simple models which help us to investigate how epidemics grow and die out.
Can you construct a cubic equation with a certain distance between
its turning points?
Was it possible that this dangerous driving penalty was issued in
Get further into power series using the fascinating Bessel's equation.
How would you go about estimating populations of dolphins?
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?
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. . . .
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
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?
Get some practice using big and small numbers in chemistry.
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Estimate areas using random grids
Build up the concept of the Taylor series
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Look at the advanced way of viewing sin and cos through their power series.
When you change the units, do the numbers get bigger or smaller?
Are these estimates of physical quantities accurate?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Which units would you choose best to fit these situations?
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.
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 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?
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
A problem about genetics and the transmission of disease.
Can you work out which processes are represented by the graphs?
Investigate circuits and record your findings in this simple introduction to truth tables and logic.