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
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
Which line graph, equations and physical processes go together?
Was it possible that this dangerous driving penalty was issued in
Which units would you choose best to fit these situations?
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?
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.
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.
Simple models which help us to investigate how epidemics grow and die out.
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. . . .
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.
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.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Get some practice using big and small numbers in chemistry.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
How much energy has gone into warming the planet?
Look at the advanced way of viewing sin and cos through their power series.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Estimate areas using random grids
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
When you change the units, do the numbers get bigger or smaller?
Match the descriptions of physical processes to these differential
Build up the concept of the Taylor series
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.
A problem about genetics and the transmission of disease.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
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.
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.
Go on a vector walk and determine which points on the walk are
closest to the origin.
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.
Explore the shape of a square after it is transformed by the action
of a matrix.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Explore how matrices can fix vectors and vector directions.
Can you work out what this procedure is doing?
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Explore the relationship between resistance and temperature
Which dilutions can you make using only 10ml pipettes?
Imagine different shaped vessels being filled. Can you work out
what the graphs of the water level should look like?