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?
Can you sketch these difficult curves, which have uses in
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Why MUST these statistical statements probably be at least a little
Invent scenarios which would give rise to these probability density functions.
Can you construct a cubic equation with a certain distance between
its turning points?
Which units would you choose best to fit these situations?
Which line graph, equations and physical processes go together?
Was it possible that this dangerous driving penalty was issued in
Here are several equations from real life. Can you work out which measurements are possible from each equation?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
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?
Get further into power series using the fascinating Bessel's equation.
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?
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.
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.
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
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.
Work out the numerical values for these physical quantities.
How much energy has gone into warming the planet?
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.
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.
Match the descriptions of physical processes to these differential
Build up the concept of the Taylor series
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
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.
When you change the units, do the numbers get bigger or smaller?
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.
Imagine different shaped vessels being filled. Can you work out
what the graphs of the water level should look like?
A problem about genetics and the transmission of disease.
Explore the properties of perspective drawing.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Explore the shape of a square after it is transformed by the action
of a matrix.
Explore the properties of matrix transformations with these 10 stimulating questions.
Can Jo make a gym bag for her trainers from the piece of fabric she has?
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
Explore how matrices can fix vectors and vector directions.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Analyse these beautiful biological images and attempt to rank them in size order.