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.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
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 Jo make a gym bag for her trainers from the piece of fabric she has?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Invent scenarios which would give rise to these probability density functions.
How would you go about estimating populations of dolphins?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Why MUST these statistical statements probably be at least a little bit wrong?
Use vectors and matrices to explore the symmetries of crystals.
Explore the properties of matrix transformations with these 10 stimulating questions.
Formulate and investigate a simple mathematical model for the design of a table mat.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
How efficiently can you pack together disks?
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.
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 visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Which pdfs match the curves?
Who will be the first investor to pay off their debt?
Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.
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.
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?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Can you make matrices which will fix one lucky vector and crush another to zero?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Go on a vector walk and determine which points on the walk are closest to the origin.
Match the descriptions of physical processes to these differential equations.
Explore the shape of a square after it is transformed by the action of a matrix.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Explore how matrices can fix vectors and vector directions.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Can you work out which processes are represented by the graphs?
A problem about genetics and the transmission of disease.
Build up the concept of the Taylor series
Is it really greener to go on the bus, or to buy local?
Use simple trigonometry to calculate the distance along the flight path from London to Sydney.
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?
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
How would you design the tiering of seats in a stadium so that all spectators have a good view?
Analyse these beautiful biological images and attempt to rank them in size order.
This problem explores the biology behind Rudolph's glowing red nose.
Which dilutions can you make using only 10ml pipettes?
Explore the properties of perspective drawing.
Where should runners start the 200m race so that they have all run the same distance by the finish?
Explore the relationship between resistance and temperature