From the STEP Support Programme from The University of Cambridge, I do like these A-level notes; currently available are notes on Algebra, Coordinate Geometry and Introduction to Calculus.
Also available are notes on the parts of the STEP specification not included in the prescribed DfE content for A-level Maths and Further Maths.
The Algebra notes, for example, include the following topics: manipulation, surds, quadratic equations, inequalities, polynomials, rational functions, logarithms, and binomial expansions.
The notes link to many excellent problems from Underground Maths and Nrich, for inequalities we have from Underground Maths Inequalities for some occasions, a brilliant way to practice inequalities. and When are these quadratic inequalities true together?
When are these quadratic inequalities true together is one of the Review questions I have often mentioned from Underground Maths.
On the Underground Maths site you can find resource suggestions clearly mapped to the subject content for the A Level specification. This is an Excel spreadsheet; for each content statement, Underground Maths has suggested up to three rich resources and up to three Review questions. Each suggestion is hyperlinked to take you directly to the resource on the Underground Mathematics site. Resources that are particularly good at supporting the overarching theme of Mathematical modelling have been highlighted.
These, of course, are suggestions. There are so many outstanding resources on Underground Maths.
An ongoing project, I do find the Review Questions can be excellent for either introducing ideas or for review and have created a spreadsheet of my own for just the Review Questions which lists the questions by title rather than by number. Excel File: Underground Maths Mapping Review Questions August 19 or the same file in pdf format: Underground Maths Mapping Review Questions August 19
To look at another extract from the Cambridge Algebra notes, on Logarithms, we see the suggestions Power Match from Nrich for investigating logs base 10, and from Underground Maths
- Logarithm Lineup
- Changing Bases
- How far did the earth move?
- …and a little history, 1950s Calculators,
On logs, I have to mention the brilliant Underground Maths resource – To log or not to log? I have used this resource many times and it has always resulted in some great discussions and highlighted some misconceptions.
This has worked really well every time I have used it. The activity requires students to think about the methods which could be used to solve the various equations. I have always found that in addition to working on indices and logarithms, this task has exposed some misconceptions, with students trying to invent some new and invalid laws of logarithms!
This problem is classified as a Problem Requiring Decisions.
Students are often used to problems being posed in such a way that they have all the information that they require in order to start, and no more. Problems (especially from the real world) are very often not like this, and so resources of this type will give students the opportunity to develop the skills needed to deal with this. Some problems might not contain enough information, so students may need to decide on classifications, make assumptions or approximations, or do some research in order to move forward. Some problems might contain too much data, so that part of the challenge is to identify the useful information.
Here’s what my students said:
See also: