Which of these infinitely deep vessels will eventually full up?
Can you find the volumes of the mathematical vessels?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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.
Invent scenarios which would give rise to these probability density functions.
Are these estimates of physical quantities accurate?
Why MUST these statistical statements probably be at least a little
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Can you sketch these difficult curves, which have uses in
Various solids are lowered into a beaker of water. How does the
water level rise in each case?
Match the charts of these functions to the charts of their integrals.
Analyse these beautiful biological images and attempt to rank them in size order.
Imagine different shaped vessels being filled. Can you work out
what the graphs of the water level should look like?
Practice your skills of measurement and estimation using this interactive measurement tool based around fascinating images from biology.
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?
Can you draw the height-time chart as this complicated vessel fills
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Is it really greener to go on the bus, or to buy local?
Which pdfs match the curves?
How do you choose your planting levels to minimise the total loss
at harvest time?
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Which line graph, equations and physical processes go together?
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?
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.
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...
A problem about genetics and the transmission of disease.
Can you work out which processes are represented by the graphs?
Formulate and investigate a simple mathematical model for the design of a table mat.
Explore the properties of perspective drawing.
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?
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.
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?
Can you construct a cubic equation with a certain distance between
its turning points?
Explore the properties of matrix transformations with these 10 stimulating questions.
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.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
How much energy has gone into warming the planet?
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Use your skill and judgement to match the sets of random data.
Which countries have the most naturally athletic populations?
Look at the advanced way of viewing sin and cos through their power series.
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
Who will be the first investor to pay off their debt?
Estimate areas using random grids