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?
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.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
How efficiently can you pack together disks?
Why MUST these statistical statements probably be at least a little
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. . . .
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.
How do you choose your planting levels to minimise the total loss
at harvest time?
Formulate and investigate a simple mathematical model for the design of a table mat.
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
Can you construct a cubic equation with a certain distance between
its turning points?
Is it really greener to go on the bus, or to buy local?
Which line graph, equations and physical processes go together?
Can you sketch these difficult curves, which have uses in
Estimate areas using random grids
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.
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.
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
This problem explores the biology behind Rudolph's glowing red nose.
Simple models which help us to investigate how epidemics grow and die out.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Can Jo make a gym bag for her trainers from the piece of fabric she has?
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.
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.
Imagine different shaped vessels being filled. Can you work out
what the graphs of the water level should look like?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
Explore the properties of perspective drawing.
Can you make matrices which will fix one lucky vector and crush another to zero?
Explore the shape of a square after it is transformed by the action
of a matrix.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Which dilutions can you make using only 10ml pipettes?
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Use vectors and matrices to explore the symmetries of crystals.
Get some practice using big and small numbers in chemistry.
Can you work out which processes are represented by the graphs?
Can you work out what this procedure is doing?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
How would you design the tiering of seats in a stadium so that all spectators have a good view?
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?