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.
Get further into power series using the fascinating Bessel's equation.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
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.
Which pdfs match the curves?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Get some practice using big and small numbers in chemistry.
Invent scenarios which would give rise to these probability density functions.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Why MUST these statistical statements probably be at least a little bit wrong?
How much energy has gone into warming the planet?
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?
Build up the concept of the Taylor series
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
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?
Work out the numerical values for these physical quantities.
Can you find the volumes of the mathematical vessels?
Was it possible that this dangerous driving penalty was issued in error?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Explore the shape of a square after it is transformed by the action of a matrix.
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 matrix transformations with these 10 stimulating questions.
Go on a vector walk and determine which points on the walk are closest to the origin.
Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Can you make matrices which will fix one lucky vector and crush another to zero?
Use vectors and matrices to explore the symmetries of crystals.
When you change the units, do the numbers get bigger or smaller?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
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.
Which units would you choose best to fit these situations?
Who will be the first investor to pay off their debt?
How would you go about estimating populations of dolphins?
Match the descriptions of physical processes to these differential equations.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
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?
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 charts of these functions to the charts of their integrals.
Are these estimates of physical quantities accurate?
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.