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.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Can you sketch these difficult curves, which have uses in mathematical modelling?
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. . . .
Invent scenarios which would give rise to these probability density functions.
Match the charts of these functions to the charts of their integrals.
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 is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
How efficiently can you pack together disks?
Can you match these equations to these graphs?
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?
Can you find the volumes of the mathematical vessels?
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?
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?
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.
Can you construct a cubic equation with a certain distance between its turning points?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Why MUST these statistical statements probably be at least a little bit wrong?
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Explore the meaning of the scalar and vector cross products and see how the two are related.
Can you make matrices which will fix one lucky vector and crush another to zero?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Use vectors and matrices to explore the symmetries of crystals.
Go on a vector walk and determine which points on the walk are closest to the origin.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
How would you design the tiering of seats in a stadium so that all spectators have a good view?
Simple models which help us to investigate how epidemics grow and die out.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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.
Which dilutions can you make using only 10ml pipettes?
Can Jo make a gym bag for her trainers from the piece of fabric she has?
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.
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you work out which processes are represented by the graphs?
Explore how matrices can fix vectors and vector directions.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Explore the shape of a square after it is transformed by the action of a matrix.
Which line graph, equations and physical processes go together?
A problem about genetics and the transmission of disease.
Get some practice using big and small numbers in chemistry.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Explore the properties of matrix transformations with these 10 stimulating questions.
How much energy has gone into warming the planet?