Which line graph, equations and physical processes go together?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
How much energy has gone into warming the planet?
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.
Why MUST these statistical statements probably be at least a little bit wrong?
Work out the numerical values for these physical quantities.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Invent scenarios which would give rise to these probability density functions.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
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 suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Get further into power series using the fascinating Bessel's equation.
Build up the concept of the Taylor series
Get some practice using big and small numbers in chemistry.
Use vectors and matrices to explore the symmetries of crystals.
Can you construct a cubic equation with a certain distance between its turning points?
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?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Which pdfs match the curves?
Which of these infinitely deep vessels will eventually full up?
How do you choose your planting levels to minimise the total loss at harvest time?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Can you work out which processes are represented by the graphs?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Formulate and investigate a simple mathematical model for the design of a table mat.
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?
Explore the properties of perspective drawing.
Explore the shape of a square after it is transformed by the action of a matrix.
Explore the properties of matrix transformations with these 10 stimulating questions.
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 find the volumes of the mathematical vessels?
Go on a vector walk and determine which points on the walk are closest to the origin.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
This problem explores the biology behind Rudolph's glowing red nose.
Who will be the first investor to pay off their debt?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Are these estimates of physical quantities accurate?
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
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.
Match the descriptions of physical processes to these differential equations.
Which units would you choose best to fit these situations?