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 mathematical modelling?
Match the charts of these functions to the charts of their integrals.
Why MUST these statistical statements probably be at least a little bit wrong?
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.
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 construct a cubic equation with a certain distance between its turning points?
Which line graph, equations and physical processes go together?
Was it possible that this dangerous driving penalty was issued in error?
Which units would you choose best to fit these situations?
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. . . .
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.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Build up the concept of the Taylor series
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?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Explore how matrices can fix vectors and vector directions.
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.
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?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Can Jo make a gym bag for her trainers from the piece of fabric she has?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Go on a vector walk and determine which points on the walk are closest to the origin.
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.
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...
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
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?
Analyse these beautiful biological images and attempt to rank them in size order.