Which line graph, equations and physical processes go together?
Get further into power series using the fascinating Bessel's equation.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
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.
Why MUST these statistical statements probably be at least a little bit wrong?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Work out the numerical values for these physical quantities.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Look at the advanced way of viewing sin and cos through their power series.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Build up the concept of the Taylor series
Get some practice using big and small numbers in chemistry.
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?
Was it possible that this dangerous driving penalty was issued in error?
Invent scenarios which would give rise to these probability density functions.
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 of these infinitely deep vessels will eventually full up?
Which pdfs match the curves?
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.
Can you construct a cubic equation with a certain distance between its turning points?
How do you choose your planting levels to minimise the total loss at harvest time?
Can you make matrices which will fix one lucky vector and crush another to zero?
Explore the properties of matrix transformations with these 10 stimulating questions.
Explore the shape of a square after it is transformed by the action of a matrix.
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?
Formulate and investigate a simple mathematical model for the design of a table mat.
Go on a vector walk and determine which points on the walk are closest to the origin.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Explore the relationship between resistance and temperature
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Can you work out which processes are represented by the graphs?
Use vectors and matrices to explore the symmetries of crystals.
Can you find the volumes of the mathematical vessels?
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?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
When you change the units, do the numbers get bigger or smaller?
Explore the properties of perspective drawing.
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.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Match the descriptions of physical processes to these differential equations.
Which units would you choose best to fit these situations?