Which line graph, equations and physical processes go together?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Match the descriptions of physical processes to these differential equations.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Was it possible that this dangerous driving penalty was issued in error?
Get further into power series using the fascinating Bessel's equation.
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.
How much energy has gone into warming the planet?
Can you find the volumes of the mathematical vessels?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Can you match the charts of these functions to the charts of their integrals?
Invent scenarios which would give rise to these probability density functions.
Why MUST these statistical statements probably be at least a little bit wrong?
Which pdfs match the curves?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
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?
Work out the numerical values for these physical quantities.
Explore how matrices can fix vectors and vector directions.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
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 properties of matrix transformations with these 10 stimulating questions.
Can you work out what this procedure is doing?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
How would you go about estimating populations of dolphins?
Who will be the first investor to pay off their debt?
Explore the relationship between resistance and temperature
This problem explores the biology behind Rudolph's glowing red nose.
Analyse these beautiful biological images and attempt to rank them in size order.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Build up the concept of the Taylor series
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Go on a vector walk and determine which points on the walk are closest to the origin.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Look at the advanced way of viewing sin and cos through their power series.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
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.
Which units would you choose best to fit these situations?
When you change the units, do the numbers get bigger or smaller?
Are these estimates of physical quantities accurate?
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?
The design technology curriculum requires students to be able to represent 3-dimensional objects on paper. This article introduces some of the mathematical ideas which underlie such methods.